Compute the derivative of the following functions.

(You may use any method from class, and you do not need to simplify your answer.)

(a) g(t)=t^2e^t/t^5-π
(b) f(x)=(1+x)^4(1+x^2)^3
(c) h(x)= secx/xe^x
(d) Find f′′(x), if f(x) = e^x sin(2x)
(e) g(x) = √(3x+√x)
(f) f(x)=2x^3+3x^2/3−e^x+2

Answers

Answer 1

(a) The derivative of g(t) is (t^3e^t(t^5 - π) - 2t^2e^t(t^4))/(t^5 - π)^2.

(b) The derivative of f(x) is 4(1+x)^3(1+x^2)^3 + 3(1+x)^4(1+x^2)^2(2x).

(c) The derivative of h(x) is (sec(x)tan(x)xe^x - sec(x)e^x)/x^2.

(d) The second derivative of f(x) is f′′(x) = e^x(4cos(2x) - 8sin(2x) - 4cos(2x) + 8sin(2x)) = -8e^xsin(2x).

(e) The derivative of g(x) is (3/2sqrt(3x+sqrt(x)) + 1/2sqrt(x))/sqrt(3x+sqrt(x)).

(f) The derivative of f(x) is (6x^2 + 6x - e^x)/(3 - e^x)^2.

(a) To find the derivative of g(t), we can apply the quotient rule and the product rule.

(b) The derivative of f(x) can be obtained using the chain rule and the power rule.

(c) The derivative of h(x) can be found using the quotient rule and the chain rule.

(d) To find the second derivative of f(x), we differentiate f(x) twice using the product rule and the chain rule.

(e) The derivative of g(x) can be computed using the chain rule and the power rule.

(f) The derivative of f(x) is computed by applying the power rule and the quotient rule.

In each case, the derivative is calculated using the appropriate rules of differentiation. The final results are presented without further simplification.

Learn more about quotient rule here: brainly.com/question/30278964

#SPJ11


Related Questions

In a breadth-first traversal of a graph, what type of collection is used in the generic algorithm? queue Ostack set Oheap

Answers

In a breadth-first traversal of a graph, a queue is typically used as the collection in the generic algorithm.

Breadth-first traversal is an algorithm used to visit all the vertices of a graph in a breadth-first manner, exploring all the neighbors of a vertex before moving on to the next level of vertices. To implement this algorithm, a queue data structure is commonly used. A queue follows the First-In-First-Out (FIFO) principle, meaning that the element that has been in the queue for the longest time is the first one to be removed. In the context of a breadth-first traversal, the queue is used to hold the vertices that have been discovered but not yet explored. As the traversal progresses, vertices are added to the queue and then processed in the order they were added, ensuring that vertices at the same level are explored before moving to the next level. The queue data structure provides the necessary functionality for adding elements to the back and removing elements from the front efficiently, making it suitable for the breadth-first traversal algorithm.

Learn more about Breadth-first traversal here:

https://brainly.com/question/31953449

#SPJ11

Find the measure​ (in degrees, not equal to the given​ measure) of the least positive angle that is coterminal with A.
A=343

Answers

The smallest positive angle that is equivalent to A=343 degrees is 703 degrees.

To find the measure of the least positive angle that is coterminal with A, we need to determine the equivalent angle within one full revolution (360 degrees) of A.

A is given as 343 degrees. To find the coterminal angle within one revolution, we can subtract or add multiples of 360 degrees until we obtain a positive angle.

Let's subtract 360 degrees from A:

343 - 360 = -17

The result is a negative angle, so we need to add 360 degrees instead:

343 + 360 = 703

Now, we have a positive angle of 703 degrees, which is coterminal with 343 degrees.

The measure of the least positive angle that is coterminal with A is 703 degrees.

For more question on angle visit:

https://brainly.com/question/30693441

#SPJ8

Find limx→−[infinity] x^5 -15x^3 + 1 /100 -21x^2 – 9x^3

Answers

The limit as x approaches negative infinity of the given expression, (x^5 - 15x^3 + 1) / (100 - 21x^2 - 9x^3), is negative infinity.

To find the limit as x approaches negative infinity, we need to evaluate the expression for extremely large negative values of x. Let's examine the terms in the numerator and denominator separately.

In the numerator, as x approaches negative infinity, the dominant term is x^5. Since x is negative, x^5 will also be negative, and its magnitude will increase without bound as x becomes more negative. The other terms, -15x^3 and 1, become insignificant compared to x^5 as x approaches negative infinity.

In the denominator, as x approaches negative infinity, the dominant term is -9x^3. Similar to the numerator, as x becomes more negative, the magnitude of -9x^3 increases without bound. The other terms, 100 and -21x^2, become insignificant compared to -9x^3.

When we divide the numerator by the denominator, we have a dominant negative term in the numerator and a dominant negative term in the denominator. Thus, the expression tends towards negative infinity as x approaches negative infinity.

Learn more about denominator here:

https://brainly.com/question/32621096

#SPJ11

Suppose that y=f(x) is a differentiable function of x. Then,
d/dx (ytany) = _______
NOTE: If your answer contains the derivative of y with respect to x, type dy/dx or y′(x). Typing y′ alone will not be accepted as correct.

Answers

The derivative of the product of two functions is the sum of their products with the derivative of the other function.

So, according to the product rule of differentiation,

d/dx (ytany)

= y(d/dx (tany)) + (dy/dx) (tany)

Since y=f(x),

we have

dy/dx = f'(x)and,

tany = y/xsec^2t

= 1/cos^2t => sec^2t = 1 + tan^2t

We know that tan⁡t=y/x Differentiating both sides with respect to x, we get

dy/dx (tan⁡t) = (1/x) dy/dx (y) - (y/x^2)

We get,

dy/dx (tan⁡t)

= (1/x) dy/dx (y) - (y/x^2)dy/dx (tany)

= sec^2t(dy/dx (tan⁡t)) => dy/dx (tany)

= sec^2t((1/x) dy/dx (y) - (y/x^2))

Now,

d/dx (ytany)

= y'd/dx (tany) + dy/dx (tany) => d/dx (ytany)

= y'tany + y(sec^2t)

Hence, d/dx (ytany) = y'tany + y(sec^2t).

To know more about derivative visit:

https://brainly.com/question/25324584

#SPJ11

For a unity feedback system with feedforward transfer function as
G(s)= 2+2x+10
the root locus is sketched as follows.
-plane
ba
0
R
-4
find the values of a, b, and c on the real axis and d on the imaginary axis (Note: For negative values, the sign is already inserted, you just need to insert the value).
a
b-
CF
d=

Answers

The final answer is: a = -6, b+ = √3/2, c = -3, and d = ∞

Given the unity feedback system with feedforward transfer function as G(s)= 2+2s+10 and the root locus is sketched in the -plane as below:

For this system, let's find the values of a, b, c, and d on the real axis and the imaginary axis using the root locus sketch.

The general equation of a straight line in the complex plane can be expressed as:

{}=+ ,

where

: real-axis intercept.

: slope.

For the given root locus plot, the  value is 0.382.

The angle of the asymptotes is given as:

θ=×360°±180°

where n is the number of open-loop poles minus the number of open-loop zeros.

Here,

n=2-1

=1.θ

=360°±180°

=±180°

For the locus to intersect the real-axis at =, we have to determine the value of .

This can be determined using the angle condition:

Angle condition:∑=2−1×180°

where  is the angle of departure (→∞) or the angle of arrival (→) of the th branch of the root locus.

For the given root locus plot, we have three branches.

Therefore, we will have three angles:

1

=π−π/3

=2π/32

=π+π/3

=4π/33

=−π

In the figure, there are 2 open-loop poles at =−1, and =−5, and no open-loop zeros.

Therefore, the number of branches in the root locus is 2 for this system.

The root locus plot has two branches that terminate on the real-axis at =1 and =2, respectively.

The angle condition gives:

=2−1×180°

=(2×1−1)×180°

=180°.1+2+3

=2π/3+4π/3−π

=2π/3

Then, we have,

=180°−2π/3=60°

Slope (b) of the line joining =−5 and =1 is given by:

=()=tan(60°)=√3x=-(1+2)/2

where 1 and 2 are the  values of the two points in the real axis where the root locus intersects the real axis.

=−()=(−5+1)=(−5+1)√3/2

For the line joining =−1 and =2:

Slope (b) of the line joining =−5 and =1 is given by:

=()

=tan(−60°)

=−√3

=−()

=(−1+2)/2

=−(−1+2)√3/2

The transfer function of the given system is:

G(s)=2+2s+10=12/s+5+s

Let's write the transfer function using pole-zero form:

G(s)=12(1+s/6.67)/(1+s/5)/(1+s/1.5)

Now, we can use the breakaway and break-in points of the real-axis segments of the root locus to solve for the real-axis intercepts 1 and 2.

We have:

Breakaway point:

=−(/2)=−(√3/4)

Break-in point:

=−5

Let's compute the value of d (on the imaginary-axis) using the angle asymptotes.

Due to the two poles of the transfer function, the angle asymptotes intersect at:

θa

=180°/(n−z)

=180°/(2−0)

=90°

Therefore, we have,

=±tan(90°−60°)

=±∞

Finally, the values of a, b, c, and d are:

a=-5.99 (The value of a is approximately equal to -6)

+=+√3/2

c=-3.01 (The value of c is approximately equal to -3)

=∞The sign of b is positive as it intersects =1 on the right-hand side of the origin.

Therefore, the final answer is:

a=-6b+=√3/2c=-3d=∞

a = -6, b+ = √3/2, c = -3, and d = ∞

Learn more about imaginary axis from this link:

https://brainly.com/question/23947644

#SPJ11

Suppose f(x)=x^2. If we are at the point x=1 and Δx=dx=0.1, what is Δy ? What is dy?
dy=f′(1)⋅dx=f′(1)⋅0.1
Δy = ____
dy = ____

Answers

calculate Δy and dy, we need to find the derivative of f(x) = x^2 and substitute the given values.

The derivative of f(x) = x^2 is given by f'(x) = 2x.

Given that x = 1 and Δx = dx = 0.1, we can calculate dy and Δy as follows:

dy = f'(1) ⋅ dx

= 2(1) ⋅ 0.1

= 0.2

Δy represents the change in the y-value when x changes by Δx. Since f(x) = x^2 is a quadratic function, the change in y will not be constant for different values of x. In this case, Δy can be calculated as the difference in y-values at the points x = 1 and x = 1 + Δx.

Δy = f(1 + Δx) - f(1)

= (1 + Δx)^2 - 1^2

= (1 + 0.1)^2 - 1^2

= 1.21 - 1

= 0.21

Therefore, Δy = 0.21 and dy = 0.2

To learn more about quadratic  equation

brainly.com/question/30098550

#SPJ11

\

A concert promoter sells fekets ard has a marginal-peofit function given beiow, ahere P′(k) is in dolars per ticket. This means that the rate of chargo of total proft with respect bo the number of tickets sold, x, is P′(x). Find the tolal profit from the sale of the first 200 tekets, disregarding any fixed cosis. P′(x)=3x−1148 The total proft is 5 (Peand in the nearest oeet as needed).

Answers

The total profit from the sale of the first 200 tickets is $60,395. The nearest dollar is $60,395.

The given marginal-profit function for the concert promoter is P′(x)=3x−1148, where P′(k) is in dollars per ticket and x is the number of tickets sold.

We need to find the total profit from the sale of the first 200 tickets, disregarding any fixed costs.

Now, let us integrate the given marginal-profit function P′(x) to find the total profit function P(x):P′(x) = 3x − 1148 ... given function Integrating both sides with respect to x, we get:

P(x) = ∫ P′(x) dx= ∫ (3x − 1148) dx

= (3/2) x² − 1148x + C, where C is the constant of integration.

To find the constant C, we need to use the given information that the total profit is 5 when x = 200:P(200)

= 5=> (3/2) (200²) - 1148 (200) + C

= 5=> 60000 - 229600 + C

= 5=> C = 229995

Therefore, the total profit function is:P(x) = (3/2) x² − 1148x + 229995

Now, we need to find the total profit from the sale of the first 200 tickets: P(200) = (3/2) (200²) − 1148(200) + 229995

= 60,000 - 229,600 + 229,995

= $60,395Therefore, the total profit from the sale of the first 200 tickets is $60,395.

The nearest dollar is $60,395.

To know more about profit visit:

https://brainly.com/question/32864864

#SPJ11

The graph of f(x,y)=1/x​+1/y​+42xy has One saddle point only. One local maximum point and one local minimum point. One local maximum point only. One local maximum point and one saddle point. One local minimum point and one saddle point. One local minimum point only.

Answers

Therefore, the graph of the function f(x, y) = 1/x + 1/y + 42xy has one local minimum point only.

The graph of the function f(x, y) = 1/x + 1/y + 42xy can have different types of critical points. To determine the nature of the critical points, we need to find the partial derivatives and analyze their values.

Let's start by finding the partial derivatives:

[tex]∂f/∂x = -1/x^2 + 42y\\∂f/∂y = -1/y^2 + 42x[/tex]

To find the critical points, we set both partial derivatives equal to zero:

[tex]-1/x^2 + 42y = 0\\-1/y^2 + 42x = 0[/tex]

From these equations, we can solve for x and y:

[tex]42y = 1/x^2 (equation 1)\\42x = 1/y^2 (equation 2)[/tex]

Solving equation 1 for y, we get:

[tex]y = 1/(42x^2)[/tex]

Substituting this into equation 2, we have:

[tex]42x = 1/(1/(42x^2))^2\\42x = 1/(1/(1764x^4))\\42x = 1764x^4\\42 = 1764x^3\\x^3 = 42/1764\\x^3 = 1/42\\[/tex]

x = 1/∛42

Substituting this value of x back into equation 1, we get:

42y = 1/(1/∛42)²

42y = (∛42)²

42y = 42

y = 1

Therefore, we have found one critical point at (1/∛42, 1).

To determine the nature of this critical point, we need to analyze the second-order partial derivatives:

[tex]∂^2f/∂x^2 = 2/x^3\\∂^2f/∂y^2 = 2/y^3\\∂^2f/∂x∂y = 0[/tex]

Evaluating the second-order partial derivatives at the critical point (1/∛42, 1), we have:

∂²f/∂x² = 2/(1/∛42)³

= 2/(1/∛42³)

= 2*(∛42³)

= 2*(42)

= 84

[tex]∂^2f/∂y^2 = 2/1^3 \\= 2[/tex]

[tex]D = (∂^2f/∂x^2)(∂^2f/∂y^2) - (∂^2f/∂x∂y)^2 \\= 842 - 0 \\= 168 > 0[/tex]

Since the discriminant is positive and [tex]∂^2f/∂x^2 = 84 > 0[/tex], we conclude that the critical point (1/∛42, 1) is a local minimum point.

To know more about function,

https://brainly.com/question/32927162

#SPJ11

Let z(x,y)=xy where x=rcos(2θ) & y=rsin(−θ).
Calculate ∂z/∂r & ∂z/∂θ by first finding ∂x/∂r , ∂y/∂r , ∂x/ /∂θ &∂y/∂θ and using the chain rule.

Answers

Using chain rule, the partial derivatives are found to be ∂z/∂r = -2r^2sin(θ)cos(θ) and ∂z/∂θ = -2r^2sin²(θ) - r^2cos(θ).

The partial derivative of z with respect to r (∂z/∂r) is equal to cos(2θ)sin(-θ) + sin(2θ)cos(-θ) = -sin(θ)cos(θ) - sin(θ)cos(θ) = -2sin(θ)cos(θ). The partial derivative of z with respect to θ (∂z/∂θ) is equal to -r(sin(2θ)cos(-θ) - cos(2θ)sin(-θ)) = -r(cos(θ)cos(θ) - sin(θ)sin(θ)) = -r(cos²(θ) + sin²(θ)) = -r.

To find the partial derivatives, we first compute the partial derivatives of x and y with respect to r and θ. We have ∂x/∂r = cos(2θ) and ∂y/∂r = sin(-θ). The partial derivatives of x and y with respect to θ are ∂x/∂θ = -2rsin(2θ) and ∂y/∂θ = -rcos(-θ).

Now, using the chain rule, we can find the partial derivatives of z with respect to r and θ. Applying the chain rule, ∂z/∂r = ∂z/∂x * ∂x/∂r + ∂z/∂y * ∂y/∂r = xy' + yx' = x*sin(-θ) + y*cos(2θ) = -r^2sin(θ)cos(θ) - r^2sin(θ)cos(θ) = -2r^2sin(θ)cos(θ). Similarly, ∂z/∂θ = ∂z/∂x * ∂x/∂θ + ∂z/∂y * ∂y/∂θ = xy" + yx" = x*(-2rsin(2θ)) + y*(-rcos(-θ)) = -2r^2sin²(θ) - r^2cos(θ).

In conclusion, ∂z/∂r = -2r^2sin(θ)cos(θ) and ∂z/∂θ = -2r^2sin²(θ) - r^2cos(θ). These are the partial derivatives of z with respect to r and θ, respectively.

Learn more about partial derivatives here:

https://brainly.com/question/28750217

#SPJ11

If f(x)=(x²+2x+7)², then
(a) f′(x)=
(b) f′(5)=

Answers

The derivative of f(x) is given by the equation (x2 + 2x + 7).² equals f'(x) = 2(x² + 2x + 7)(2x + 2).

The power rule and the chain rule are two methods that can be utilised to determine the derivative of the function f(x). According to the power rule, the derivative of a function with the form g(x) = (h(x))n can be calculated as follows: g'(x) = n(h(x))(n-1) * h'(x). If the function has the form g(x) = (h(x))n. In this particular instance, h(x) equals x2 plus 2x plus 7, and n equals 2.

First, we apply the power rule to the inner function h(x), which gives us the following expression for h'(x): h'(x) = 2(x2 + 2x + 7)(2-1) * (2x + 2).

The last step is to multiply this derivative by the derivative of the exponent, which is 2, resulting in the following equation: f'(x) = 2(x2 + 2x + 7)(2-1) * (2x + 2).

Further simplification yields the following formula: f'(x) = 2(x2 + 2x + 7)(2x + 2).

In order to calculate f'(5), we need to change f'(x) to read as follows: f'(5) = 2(52 + 2(5) + 7)(2(5) + 2).

The numerical value of f'(5) can be determined by evaluating the equation in question.

Learn more about derivative here:

https://brainly.com/question/29144258

#SPJ11

Find the absolute extrema of the given function on the indicated closed and bounded set R. (Order your answers from smallest to largest x, then from smallest to largest y.)
f(x, y) = x³-3xy-y³ on R= {(x, y): -2 ≤ x ≤ 2,-2 sy s 2}

Answers

The smallest value of f(x, y) occurs at the point (-2, -2) and is equal to -16. The largest value of f(x, y) occurs at the point (2, 2) and is equal to 16.

 

To find the absolute extrema, we need to evaluate the function at the critical points, which are the endpoints of the given set R and the points where the partial derivatives of f(x, y) are zero.  

The critical points of f(x, y) are (-2, -2), (-2, 2), (2, -2), and (2, 2). By evaluating the function at these points, we find that f(-2, -2) = -16, f(-2, 2) = -16, f(2, -2) = 16, and f(2, 2) = 16.

Therefore, the absolute minimum value of f(x, y) on R is -16, which occurs at the point (-2, -2), and the absolute maximum value of f(x, y) on R is 16, which occurs at the point (2, 2). These points represent the smallest and largest values of the function within the given closed and bounded set.

Learn more about partial derivatives here:

https://brainly.com/question/29652032

#SPJ11

Determine the equation of the circle with center (–2,–2) containing the point (–7,–14)

Answers

Answer:

r2=(x−2)2+(y−4)2.

Step-by-step explanation:

Recall that the method of implicit differentiation consists of differentiating both side We begin by differentiating both sides of the given equation x²−12xy+y²=12. constant rule for differentiation.
d/dx(x²−12xy+y²) = d/dx (12)

Answers

The method of implicit differentiation involves differentiating both sides of an equation. Applying this method to the equation x²−12xy+y²=12, the derivative of the left side is determined using the constant rule for differentiation, while the derivative of the right side is zero.

To apply implicit differentiation to the equation x²−12xy+y²=12, we differentiate both sides with respect to x. Taking the derivative of the left side, we use the constant rule for differentiation. For the term x², the derivative is 2x. For the term -12xy, we treat y as a function of x and apply the product rule, yielding -12y - 12xy'. Finally, for the term y², we apply the chain rule and get 2yy'. The derivative of the right side, 12, with respect to x is zero since it is a constant.

Combining all the derivatives, we have 2x - 12y - 12xy' + 2yy' = 0. This equation can be rearranged to isolate the derivative of y, denoted as y'. Factoring out y' from the terms involving it, we get y'(2x - 12x) = 12y - 2x. Simplifying further, we obtain y' = (12y - 2x)/(2x - 12y).

Therefore, the derivative of y with respect to x, or y', is given by (12y - 2x)/(2x - 12y). This represents the rate of change of y with respect to x based on the original equation x²−12xy+y²=12.

Learn more about implicit differentiation here:

https://brainly.com/question/14027997

#SPJ11

Find the relative maximum value of ​f(x,y)​=x^2-10y^2 subject to
the constraint x-y=18

Answers

The relative maximum value of f(x,y) = x² - 10y² subject to the constraint x - y = 18 is 360.

Given the function

f(x,y) = x² - 10y²

and

the constraint x - y = 18,

we have to find the relative maximum value.

Therefore, we need to use the method of Lagrange Multipliers to solve the problem.

Let us define the Lagrangian function:

L(x, y, λ) = x² - 10y² + λ(x - y - 18)

Taking the partial derivative of L(x, y, λ) with respect to x and setting it equal to zero, we get,

∂L/∂x = 2x + λ = 0   ..... (1)

Taking the partial derivative of L(x, y, λ) with respect to y and setting it equal to zero, we get,

∂L/∂y = -20y - λ = 0   ..... (2)

Taking the partial derivative of L(x, y, λ) with respect to λ and setting it equal to zero, we get,

∂L/∂λ = x - y - 18 = 0  ..... (3)

Solving the equations (1) and (2) for x and y, we get

,x = - λ/2  ..... (4)

y = - λ/20  ..... (5)

Substituting equations (4) and (5) in equation (3), we get,

- λ/2 - (- λ/20) - 18 = 0

⇒ 9λ = 360

⇒ λ = 40

Substituting the value of λ in equations (4) and (5), we get,

x = - λ/2 = -20  ..... (6)

y = - λ/20 = -2  ..... (7)

Therefore, the relative maximum value of f(x,y) = x² - 10y² subject to the constraint x - y = 18 is:

f(-20, -2)

= (-20)² - 10(-2)²

= 400 - 40

= 360

Know more about the relative maximum value

https://brainly.com/question/29502088

#SPJ11


Verify that the divergence theorem is true for the vector field F on the region E. Give the flux.
F(x,y,z) = 4xi+xyj+2xzk, E is the cube bounded by the planes x=0, x=2, y=0, y=2, z=0, and z=2

Answers

The divergence theorem holds for the vector field F on the given region E. The flux of F across the surface of the cube is 12.

The divergence theorem states that the flux of a vector field across a closed surface is equal to the volume integral of the divergence of that field over the region enclosed by the surface. In this case, the region E is a cube bounded by the planes x=0, x=2, y=0, y=2, z=0, and z=2. The vector field F(x,y,z) = 4xi + xyj + 2xzk is defined in three dimensions.

To calculate the flux, we need to find the divergence of F and integrate it over the volume of the cube. The divergence of F is given by div(F) = ∇·F = ∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z.

Calculating the partial derivatives, we have:

∂Fx/∂x = 4

∂Fy/∂y = x

∂Fz/∂z = 2x

Therefore, div(F) = 4 + x + 2x = 3x + 4.

Integrating the divergence over the volume of the cube, we have:

∫∫∫ div(F) dV = ∫∫∫ (3x + 4) dV = ∫[0,2]∫[0,2]∫[0,2] (3x + 4) dxdydz.

Evaluating this triple integral, we get:

∫[0,2] (3x + 4) dx = [[tex]3/2x^2[/tex] + 4x] from 0 to 2 = (3/2 * [tex]2^2[/tex]+ 4*2) - (3/2 *[tex]0^2[/tex] + 4*0) = 12.

Therefore, the flux of F across the surface of the cube is 12.

LEARN MORE ABOUT divergence theorem here: brainly.com/question/28155645

#SPJ11

18) VISUALIZATION Is there an angle measure that is so small that any triangle with that angle measure will be an obtuse triangle? Explain.

Answers

No, there is no angle measure that is so small that any triangle with that angle measure will be an obtuse triangle.

In a triangle, the sum of the three interior angles is always 180 degrees. For any triangle to be classified as an obtuse triangle, it must have one angle greater than 90 degrees. Since the sum of all three angles is fixed at 180 degrees, it is not possible for all three angles to be less than or equal to 90 degrees.

Even if one angle is extremely small, the sum of the other two angles will compensate to ensure that the sum remains 180 degrees. Therefore, regardless of the size of one angle, it is always possible to construct a non-obtuse triangle by adjusting the sizes of the other two angles.

Learn more about Obtuse triangle here :

brainly.com/question/15168230

#SPJ11

as a general rule, the larger the degrees of freedom for a chi-square test

Answers

As a general rule, the larger the degrees of freedom for a chi-square test, the more reliable and accurate the test results become.

In statistical hypothesis testing using the chi-square distribution, degrees of freedom (df) play a crucial role. The degrees of freedom represent the number of independent pieces of information available for estimation or inference in a statistical analysis.

For a chi-square test, the degrees of freedom are calculated based on the number of categories or cells involved in the analysis. As the degrees of freedom increase, it allows for more variability in the data and provides a better approximation of the chi-square distribution.

Having a larger degrees of freedom value provides a more accurate estimation of the expected frequencies under the null hypothesis. This, in turn, leads to a more reliable assessment of the goodness-of-fit or independence in the data being tested.

Therefore, in general, larger degrees of freedom provide greater statistical power and precision in chi-square tests, allowing for more confident conclusions to be drawn from the analysis.

to learn more about chi-square test click here:

brainly.com/question/30760432

#SPJ11

Evaluate ∫C/(A)^B dt where A=4−t2,B=3/2, and C=t2. Show all your steps clearly.

Answers

By applying the power rule and integrating term by term, the antiderivative of the function with respect to t is : 4(ln|2/(√(4 - t^2)) + t/√(4 - t^2)| - t) + C.

To evaluate the integral ∫C/(A)^B dt, where A = 4 - t^2, B = 3/2, and C = t^2, we can substitute the given values into the integral and then simplify the expression.

Given A = 4 - t^2, B = 3/2, and C = t^2, we substitute these values into the integral: ∫C/(A)^B dt = ∫(t^2)/(4 - t^2)^(3/2) dt.

To simplify the expression, we can factor out t^2 in the numerator: ∫(t^2)/(4 - t^2)^(3/2) dt = ∫(t^2)/(2^2 - t^2)^(3/2) dt.

Next, we can use a trigonometric substitution to further simplify the integral. Let t = 2sinθ, which implies dt = 2cosθ dθ. Substituting these values, we have:

∫(t^2)/(2^2 - t^2)^(3/2) dt = ∫(4sin^2θ)/(4 - (2sinθ)^2)^(3/2) (2cosθ dθ).

Simplifying the expression inside the integral, we have:

∫(4sin^2θ)/(4 - 4sin^2θ)^(3/2) (2cosθ dθ) = ∫(4sin^2θ)/(4cos^2θ)^(3/2) (2cosθ dθ).

Further simplifying, we get:

∫(4sin^2θ)/(4cos^2θ)^(3/2) (2cosθ dθ) = ∫(4sin^2θ)/(4cos^3θ) (2cosθ dθ).

Canceling out common factors, we have:

∫(4sin^2θ)/(4cos^3θ) (2cosθ dθ) = 4 ∫sin^2θ/cosθ dθ.

Using the identity sin^2θ = 1 - cos^2θ, we can rewrite the integral as:

4 ∫(1 - cos^2θ)/cosθ dθ = 4 ∫(secθ - cosθ) dθ.

Integrating term by term, we have:

4 ∫(secθ - cosθ) dθ = 4(ln|secθ + tanθ| - sinθ) + C.

Finally, substituting back θ = arcsin(t/2), we obtain:

4(ln|sec(arcsin(t/2)) + tan(arcsin(t/2))| - sin(arcsin(t/2))) + C.

Simplifying further, we have the final result:

4(ln|2/(√(4 - t^2)) + t/√(4 - t^2)| - t) + C.

Learn more about integral here:

https://brainly.com/question/31109342

#SPJ11

y= x+1 on the interval [0,3] with n=6

Answers

The given function is y = x + 1 on the interval [0, 3] with n = 6.

Using the trapezoidal rule with n = 6, the approximate value of the integral is __________.

To approximate the integral of the function y = x + 1 over the interval [0, 3] using the trapezoidal rule, we divide the interval into n subintervals of equal width. Here, n = 6, so we have 6 subintervals of width Δx = (3 - 0)/6 = 0.5.

Using the trapezoidal rule, the integral approximation is given by the formula:

∫(a to b) f(x) dx ≈ Δx/2 * [f(a) + 2(f(a + Δx) + f(a + 2Δx) + ... + f(a + (n-1)Δx)) + f(b)]

Plugging in the values, we have:

∫(0 to 3) (x + 1) dx ≈ 0.5/2 * [f(0) + 2(f(0.5) + f(1.0) + f(1.5) + f(2.0) + f(2.5)) + f(3)]

Simplifying further, we evaluate the function at each point:

∫(0 to 3) (x + 1) dx ≈ 0.5/2 * [1 + 2(1.5 + 2.0 + 2.5 + 3.0 + 3.5) + 4]

Adding the values inside the brackets and multiplying by 0.5/2, we obtain the approximate value of the integral.

The final answer will depend on the calculations, but it can be determined using the provided formula.

Learn more about trapezoidal rule:

brainly.com/question/30886083

#SPJ11

Water is leaking out of an inverted conical tank at a rate of 6000.0 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 8.0 meters and the diameter at the top is 6.5 meters. If the water level is rising at a rate of 27.0 centimeters per minute when the height of the water is 4.0 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute. _____

Note: Let " R " be the unknown rate at which water is being pumped in. Then you know that if V is volume of water, dV/dt = R − 6000.0. Use geometry (similar triangles?) to find the relationship between the height of the water and the volume of the water at any given time. Recall that the volume of a cone with base radius r and height h is given by 1/3πr^2h.

Answers

We have R = dV/dt + 6000.0 = (169π/128)h^2(dh/dt) + 6000.0. Substituting h = 4.0, we can calculate the value of R in cubic centimeters per minute.

By considering similar triangles, we can establish a proportional relationship between the height and radius of the water in the tank. Let's denote the radius of the water as r and the height as h. Given that the diameter at the top of the tank is 6.5 meters, the radius can be expressed as a linear function of the height: r = (6.5/8)h.

The volume of the water in the tank can be calculated using the volume formula for a cone: V = (1/3)πr^2h. Substituting the expression for r, we have V = (1/3)π[(6.5/8)h]^2h = (169π/384)h^3.

To determine the rate at which the volume of water is changing with respect to time (dV/dt), we can differentiate the volume equation with respect to time (t). Differentiating both sides yields dV/dt = (169π/128)h^2(dh/dt).

Given that the water level is rising at a rate of 27.0 centimeters per minute when the height is 4.0 meters, we can substitute these values into the equation: 27 = (169π/128)(4)^2(dh/dt). Solving for dh/dt, we find dh/dt = (27 * 128)/(169π * 16) = 2/π cm/min.

Finally, we can use the relation dV/dt = R - 6000.0, where R represents the rate at which water is being pumped into the tank. Substituting the known value for dV/dt and solving for R, we have R = dV/dt + 6000.0 = (169π/128)h^2(dh/dt) + 6000.0. Substituting h = 4.0, we can calculate the value of R in cubic centimeters per minute.

For more information on rate visit: brainly.com/question/31396315

#SPJ11

Determine whether or not the vector field is conservative. If it is conservative, find a function f such that F=∇f. F(x,y,z)=yzexzi+exzj+xyexzk.

Answers

Therefore, there is no function f such that F = ∇f.

To determine if the vector field [tex]F(x, y, z) = yze^xzi + e^xzj + xyexzk[/tex] is conservative, we can check if the curl of F is zero.

The curl of F is given by ∇ × F, where ∇ is the del operator.

[tex]∇ × F = (d/dy)(xye^xz) - (d/dz)(exz) i + (d/dz)(yzexz) - (d/dx)(exz) j + (d/dx)(e^xz) - (d/dy)(xye^xz) k[/tex]

Evaluating the partial derivatives, we get:

[tex]∇ × F = (xe^xz + 0) i + (0 - 0) j + (0 - xe^xz) k\\∇ × F = xe^xz i - xe^xz k\\[/tex]

Since the curl of F is not zero, the vector field F is not conservative.

To know more about function,

https://brainly.com/question/14172308

#SPJ11

one girl has 9 cents less than another girl . they have 29cents between them how much does each girl have​

Answers

The amount of cent each girl has is 9 and 20

Using the parameters given:

girl, a = 9girl, b = 9 + a

Total = 9 + 9 + a = 29

We can solve for a thus :

18 + a = 29

a = 29 - 18

a = 11

Therefore, each girl has 9cent and 20 cents .

Learn more on word problems:https://brainly.com/question/25693822

#SPJ1

During a winter storm, nearly a foot of snowfall covered parts of central Indiana. While some areas received as little as 5 % inches, Indiana Online recorded the most, 17 % inches at the Pyramids.

Answers

It is common to observe variations in snowfall measurements across different areas during a winter storm.

During a winter storm in central Indiana, significant snowfall was recorded. The snowfall varied across different areas, with some receiving less snow than others. In this case, the snowfall at Indiana Online, specifically at the Pyramids location, was the highest, measuring 17 inches.

The phrase "nearly a foot of snowfall" indicates that the snow accumulation was close to 12 inches. However, it does not provide an exact measurement. It gives us an idea that the snowfall was substantial.

On the other hand, the mention of "5 % inches" indicates that some areas received less snow than the average. It specifies a measurement of 5.5 inches, which is less than a foot but still significant.

It is important to note that these measurements may vary across different locations within central Indiana. Snowfall amounts can be influenced by factors such as elevation, temperature, and local weather patterns. Therefore, it is common to observe variations in snowfall measurements across different areas during a winter storm.

for such more question on variations

https://brainly.com/question/25215474

#SPJ8

Rapunzel was trapped in the top of a cone-shaped tower. Her evil
stepmother was
painting the top of the tower to camouflage it. The top of the
tower was 20 feet tall and
the 15 feet across at the base

Answers

The slant height of the cone-shaped tower is approximately 21.36 feet.

We are given that Rapunzel was trapped at the top of a cone-shaped tower. We know that her evil stepmother was painting the top of the tower to camouflage it. We also know that the top of the tower was 20 feet tall and 15 feet across at the base.

To find the slant height of the cone-shaped tower, we will apply the Pythagorean theorem as shown in the following diagram: Pythagorean-theorem-150 The slant height can be found using the Pythagorean Theorem, which states that the square of the hypotenuse (in this case, the slant height) of a right triangle is equal to the sum of the squares of the other two sides (in this case, the height and the radius of the base).

Hence, we have:

[tex]\[{{\text{Slant height}}^{2}}={{\text{Height}}^{2}}+{{\text{Radius}}^{2}}\]\[{{\text{Slant height}}^{2}}={{20}^{2}}+{{7.5}^{2}}\]\[{{\text{Slant height}}^{2}}=400+56.25\]\[{{\text{Slant height}}^{2}}=456.25\]\[{{\text{Slant height}}}=\sqrt{456.25}\]\[{{\text{Slant height}}}=21.36 \ \text{feet}\][/tex]

Learn more about cone-shaped

https://brainly.com/question/808471

#SPJ11

Using the method of undetermined coefficients, solve the differential equation d2y​/dx2−9y=x+e2x

Answers

A differential equation is an equation that relates a function and its derivatives, describing how the function changes over time or space.the general solution of the given differential equation is[tex]= C_1 e^{3x} + C_2 e^{-3x} + \dfrac{9}{2} x - \dfrac{2}{9} + C e^{2x}[/tex]

Given differential equation is[tex]\dfrac{d^2 y}{dx^2} - 9 y &= x + e^{2x} \\[/tex] Here, the auxiliary equation is m² - 9 = 0 which gives m = ±3 From the characteristic roots, the complementary solution will be given by [tex]y_c = C_1 e^{3x} + C_2[/tex] e^(-3x)

Now we must use the method of uncertain coefficients to find the solution of a differential equation. For the particular solution, assume y_p = Ax + B + Ce^(2x)

Substituting this in the differential equation, we get:

[tex]\dfrac{d^2 y_p}{dx^2} - 9 y_p &= x + e^{2x} \\\\A e^{2x} + 4C e^{2x} - 9(Ax + B + Ce^{2x}) &= x + e^{2x}[/tex]

On compare the coefficient, we get:

A - 9C = 0 => A

9C4C - 9B = 0

=> B = 4C/9

Therefore, the particular solution is:

[tex]y_p = \dfrac{9}{2} x - \dfrac{2}{9} + C e^{2x}[/tex]

Hence, the general solution of the given differential equation is:

[tex]y &= y_c + y_p \\\\&= C_1 e^{3x} + C_2 e^{-3x} + \dfrac{9}{2} x - \dfrac{2}{9} + C e^{2x}[/tex]

To know more about  differential equation this:

https://brainly.com/question/32645495

#SPJ11

Maria went on a vacation for 8 weeks last summer how many days long was maria's vacation?

Answers

Answer:

Maria's vacation was 56 days long

Step-by-step explanation:

Maria went on a vacation for 8 weeks.

We have to find how many days long her vacation was,

Now,

there are 7 days in 1 week.

so, in 8 weeks we will have,

1 week = 7 days

8 weeks = (8)(7) days

8 weeks = 56 days

Hence, she went on vacation for 56 days.

Describe the given region in polar coordinates. ≤θ≤≤r≤ (Type an exact answer, using π as needed.)

Answers

≤θ≤π/4, ≤r≤4The given region in polar coordinates is an area that is defined by the limits of θ and r as given above.

Here, θ is an angle made by the line segment with the positive x-axis and r is the distance of the point from the origin. In this case, the angle θ can be measured from the positive x-axis and r is the radius of the circle centered at the origin that bounds the region.

Therefore, the region is a sector of the circle of radius 4 centered at the origin which includes all points with angles between 0 and π/4 radians and with distances from the origin between 0 and 4.

The polar coordinates system is an alternative coordinate system that is used to describe points in a plane.

In this system, the position of a point is given by its distance from the origin and the angle it makes with a fixed line, usually the positive x-axis.

To know more about radius visit:

https://brainly.com/question/13449316

#SPJ11

A mechanical system having input fa(t) and output y=x₂ is governed by the following differential equations: mx₁ + ₁x₁ + (K₁ + K₂)X₁ - K₂X₂=fa(t) (1) (2) b₂x₂ + (K₂ + K3)x₂ - K₂X1 = 0 Please answer the below questions. Show all work. Please take a picture or scan your work and upload it as a single file. d Question 1. Determine the input-output equation for the output y=x2 using the operator p = dt Question 2. Use Equations (1) and (2) to construct a block diagram for the dynamic system described by the above equations.

Answers

Question 1The input-output equation for the output y = x2 can be determined by taking Laplace Transform of the given differential equations: mx₁ + ₁x₁ + (K₁ + K₂)X₁ - K₂X₂ = fa(t)                            

(1) b₂x₂ + (K₂ + K3)x₂ - K₂X1 = 0                                                      

.(2) Taking Laplace Transform on both sides, we have;LHS of (1)

=> [mx₁ + ₁x₁ + (K₁ + K₂)X₁ - K₂X₂]

⇔ mX₁p + X₁

⇔ [m + p]X₁and RHS of (1)

=> [fa(t)]

⇔ F(p)Similarly,LHS of (2)

=> [b₂x₂ + (K₂ + K3)x₂ - K₂X1]

⇔ b₂X₂p + X₂

⇔ [b₂p + K₂]X₂RHS of (2)

=> [0] ⇔ 0

Hence, we have;[m + p]X₁ + (K₁ + K₂)X₁ - K₂X₂

= F(p)    

(3)[b₂p + K₂]X₂ = [m + p]X₁      

(4)Now, Solving (4) for X₂, we have;

X₂ = [m + p]X₁/[b₂p + K₂]     .(

5)Multiplying (5) by p gives;

pX₂ = [m + p]pX₁/[b₂p + K₂]    

(6)Substituting (6) into (3), we have;

[m + p]X₁ + (K₁ + K₂)X₁ - [m + p]pX₁/[b₂p + K₂] =

F(p)Now, Solving for X₁, we have; X₁

= F(p)[b₂p + K₂]/[D], where D

= m + p + K₁[b₂p + K₂] - (m + p)²

Hence, the Input-output equation for the output y

=x2 is given by;Y(p) = X₂(p) = [m + p]X₁(p)/[b₂p + K₂]    

(7)Substituting X₁(p), we have;Y(p)

= [F(p)[m + p][b₂p + K₂]]/[D],

where D

= m + p + K₁[b₂p + K₂] - (m + p)²

The block diagram for the dynamic system described by the above equations can be constructed using the equations as follows;[tex] \begin{cases} mx_{1} + \dot{x}_{1} + (K_{1}+K_{2})x_{1} - K_{2}x_{2}

= f_{a}(t) \\  b_{2}x_{2} + (K_{2}+K_{3})x_{2} - K_{2}x_{1}

= 0 \end{cases}[/tex]

Taking Laplace Transform of both equations gives:

[tex] \begin{cases} (ms + s^{2} + K_{1}+K_{2})X_{1} - K_{2}X_{2}

= F_{a}(s) \\  b_{2}X_{2} + (K_{2}+K_{3})X_{2} - K_{2}X_{1}

= 0 \end{cases}[/tex]

Rearranging and Solving (2) for X2, we have;X2(s)

= [ms + s² + K1 + K2]/[K2 + b2s + K3] X1(s)        ..............

(8)Substituting (8) into (1), we have;X1(s)

= [1/(ms + s² + K1 + K2)] F(p)[b2s + K2]/[K2 + b2s + K3].

To know more about equation visit :

https://brainly.com/question/29657983

#SPJ11

Old MathJax webview
For system shown, knowing that \( \operatorname{Vin}(t) \) given by the followix. find and sketch \( i(t) \) if \( z(t)=\operatorname{sgn}(t) \)
sem shown, knowing that \( \operatorname{Vin}(t) \) gi

Answers

The current i(t) is shown below. The current is a square wave with a period of 2. The current is equal to 0 when z(t) is negative, and it is equal to V/R when z(t) is positive.

The current i(t) can be found using the following equation:

i(t) = V/R * z(t)

where V is the input voltage, R is the resistance, and z(t) is the signum function. The signum function is a function that returns 0 when its argument is negative, and it returns 1 when its argument is positive.

In this case, the input voltage is Vin(t), and the resistance is R. The signum function of z(t) is shown below:

z(t) =

   0 when z(t) < 0

   1 when z(t) >= 0

The current i(t) is shown below:

i(t) =

   0 when z(t) < 0

   V/R when z(t) >= 0

The current is a square wave with a period of 2. The current is equal to 0 when z(t) is negative, and it is equal to V/R when z(t) is positive.

To learn more about function click here : brainly.com/question/30721594

#SPJ11

Question 9 Consider the following Fourier transfos pairs: W x(t) = 2 sinc (t) + X(w) = 2 mrect() find the Fourier Transforms X(w) in each of the following cases: v(t) = 2x(4t-2) 3 Marks v(t) = 2 rect() 3 Marks 3 r v(t) = cos(2)x(t) v(t) = 2e²i sinc (t) ml For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).

Answers

Main Answer:

The Fourier Transform X(w) for the given cases is as follows:

1. v(t) = 2x(4t-2): X(w) = 1/2 rect(w/4) * e^(-jw/2)

2. v(t) = 2 rect(t): X(w) = 1/2 sinc(w/2)

3. v(t) = cos(2)x(t): X(w) = 1/2 [mrect(w - 2) + mrect(w + 2)]

4. v(t) = 2e^(2i) sinc(t): X(w) = 1/2 [mrect(w + 2) + mrect(w - 2)]

In the given question, we are provided with a set of Fourier Transform pairs. The task is to find the Fourier Transform X(w) for different cases of v(t). Let's analyze each case:

1. For v(t) = 2x(4t-2):

  By applying the time-scaling property of the Fourier Transform, we can express v(t) as 2x(t/4) * e^(-j(2/4)w).

  The Fourier Transform of x(t) = sinc(t) is given as X(w) = rect(w) * e^(-jw/2).

  Using the time-scaling property, the Fourier Transform X(w) for v(t) is obtained as 1/2 rect(w/4) * e^(-jw/2).

2. For v(t) = 2 rect(t):

  The rectangular pulse function rect(t) has a Fourier Transform of sinc(w).

  By scaling the amplitude by a factor of 2, the Fourier Transform X(w) for v(t) is obtained as 1/2 sinc(w/2).

3. For v(t) = cos(2)x(t):

  The Fourier Transform of cos(at) is given by 1/2 [mrect(w - a) + mrect(w + a)] multiplied by the Fourier Transform X(w) of x(t).

  Here, a = 2, and X(w) is sinc(w).

  Therefore, the Fourier Transform X(w) for v(t) is 1/2 [mrect(w - 2) + mrect(w + 2)].

4. For v(t) = 2e^(2i) sinc(t):

  By applying the complex modulation property, we can express v(t) as e^(2i) * 2x(t), where x(t) = sinc(t).

  The Fourier Transform X(w) of x(t) = sinc(t) is given as rect(w).

  Applying the complex modulation property, the Fourier Transform X(w) for v(t) is obtained as 1/2 [mrect(w + 2) + mrect(w - 2)].

Learn more about: Fourier Transform

brainly.com/question/1542972

#SPJ11

Other Questions
anki can solicit new products from internal research, customers, or competitors products. in which stage of the new product development process does this occur? Multiple Choice concept testing product launch product development market testing idea generation What makes up the structure of a shaft of a hair?Dead epidermal cellsLiving epidermal cellsDead dermal cellsLiving dermal cellsLiving fibroblasts Complete the following problems, applying the properties oftangent lines.If \( \overline{P Q} \) and \( \overline{P R} \) are tangent to \( \odot E \), find the value of \( x \). See Example \( 5 . \) 39 \( 40 . \) the delicate, ______ ribbons in the girl's hair seemed to glow. a medical order for life-sustaining treatment (molst) would most likely apply to a patient: With which Old Testament character is Saint Catherine's Monastery at Mt. Sinai associated?a. Solomonb. Abrahamc. Davidd. Moses notadvancExercise 2: Writing programs using if OR if/else if 1. Write a program that reads two numbers a and b. Print the maximum value of the two numbers. 2. Write a program that reads two values a and \( b \ A certain processor uses separate instruction and data caches with hit ratios 98% and 92% respectively. The access time from the processor to either cache is 1 clock cycle, and the block transfer time between the caches and main memory is 78 clock cycles. Among blocks replaced in the data cache, 20% is the percentage of dirty blocks (Dirty means that the cache copy is different from the memory copy). Assuming a write-back policy, what is the AMAT for the instructions in this system? Round to 2 decimal places. Answer: 8 2 24 Q Po P Learning Objective: To effectively write and call overloaded methods. Instructions: Type the solution in asurite-h02.pdf. Problem: True or False? It is legal to write a method in a class which overloads another method declared in the same class. Explain. 3.15 Learning Objective: To effectively write and call overridden methods. Problem: True or False? It is legal to write a method in a superclass which overrides a method declared in a sub- class. Explain. Problem 6-2A (Algo) Calculate ending inventory, cost of goods sold, sales revenue, and gross profit for four inventory methods (LO6-3, 6-4, 6-5) Ariana Bicycle Shop has the following transactions related to its top-selling Mongoose mountain bike for the month of March. Ariana Bicycle Shop uses a periodic inventory system. If Ariana Bicycle Shop chooses to report inventory using LIFO instead of FIFO, record the LIFO adjustment. (If no entry is required for a transaction/event, select "No Journal Entry Required" in the first account field.) Journal entry worksheet Note: Enter debits before credits 10. Color Doppler ultrasound devices are often used to assess the health of the fetal heart during pregnancy. During a fetal ultrasound exam, a transducer placed against the expectant mother abdomen transmits ultrasound waves with a frequency of 3.500 MHz and receives the Doppler shifted echo from the fetal heart. If the echo received from the fetal heart by the transducer has a frequency of 3.498 MHz and 3.503 MHz from the left and right ventricles, respectively, what is the speed (in cm/s) of the blood flow in these two chambers of the fetal heart? The blood in the left ventricle flows away from the transducer while the blood in the right ventricle flows toward the transducer. Use v = 1,500 m/s for the speed of sound in tissue. left ventricle cm/s right ventricle cm/s Can someone PLEASE check if I am doing this correctly?a. Prepare a purchases budget for the first quarter of the year in units, in total, and in dollars. The person tasked with the responsibility of carrying out a will's directions and disposing of the deceased's property is known as:a. The heir.b. An attorney.c. The executor.d. A relative. Write a program that couts the number of words contained within a file. The name of the file will be passed on the command line A word is considered to be 1 or more consecutive non-whitespace characters A character is considered whitespace if isspace would return true if passed that character as an arguement The files used for grading are contained in problem1-tests. Example: In test2.txt, there are two words: Hello and world!. Your program should print "There are 2 word(s).\n" Requirements: No global variables may be used Your main function may only declare variables and call other functions YOU MAY NOT ALLOCATE ANY FIXED AMOUNT OF SPACE IN THIS PROBLEM - Doing so will result in 0 credit - Fixed amount of space would mean doing something like only allocating at most space for 100 lines or allocating 1000 characters per line. Your code needs to be able to work with files that have any number of lines with any number of characters per line. - It doesn't matter whether you dynamically allocate this space or statically allocate the space. You will still lose credit. For example, all of these are forbidden char line calloc (100, sizeof (char)). char line [100]; char lines calloc (500, sizeof (char*)); char lines [500] You must submit four files for this assignment: - main.c: only contains the main function and the #includes - a source file that contains the definitions of all the functions (besides main) - a header file that contains the declarations of all the functions defined in the above source file - a makefile . Must be named Makefile or makefile . You must write it on your own using the method we talked about in class. You are NOT allowed to use cmake for this assignment. The executable must be named main. out The high resistivity of dry skin, about 2 x 105 m, combined with the 1.5 mm thickness of the skin on your palm can limit the flow of current deeper into tissues of the body. Suppose a worker accidentally places his palm against an electrified panel. The palm of an adult is approximately a 9 cm x 9 cm square. Part A What is the approximate resistance of the worker's palm? Express your answer with the appropriate units. A ? -3 R= 2.10 Submit Previous Answers Request Answer X Incorrect; Try Again; One attempt remaining Provide Feedback 5- (10) Select and briefly describe the 3 most important of key business issues for The B2B company (or any other company). A client is diagnosed with intermittent explosive disorder (IED). What drugs are likely to be prescribed for the client? Select all that apply.a) Typical antipsychoticsb) Mood-stabilizing agentsc) Stimulantsd) Antidepressantse) Barbiturates -4t (20 pts) Q4) A voltage signal is described by x(t)= eu(t) It is applied to the input of an ideal low-pass filter. The gain of the filter is unity, the bandwidth is 8 rad/sec and the resistance levels are 60 Ohm. Calculate: 1- the energy of the Input signal. 2- the energy of the output signal. during the depolarization repolarization cycle a cell can be stimulated during What is identified as the key issue to consider when deciding on policy ownership in the event of a claim? Select one: Othe tax liability on the policy proceeds is kept to nil Osufficient insurance is bought for the risk involved Othe policy proceeds are made payable to the relevant and appropriate person or party Oeach policy should be purchased by the life insured to make the process of a claim less complex