Kinematics Formulae velocity help

The surface area of the rectangular pyramid is approximately 387.6 square yards.

To find the surface area of a rectangular pyramid, we need to find the area of the base and the area of the four triangular faces.

The area of the base is:

Area of base = length x width

Area of base = 14 yards x 14 yards

Area of base = 196 square yards

To find the area of the four triangular faces, we need to first find the height of each triangle using the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the sum of the squares of the legs (the two shorter sides) is equal to the square of the hypotenuse (the longest side).

In this case, the hypotenuse is the slant height of the pyramid, which is 12 yards. The legs are half the length and width of the base, which are both 7 yards.

So we have:

h² + 7² = 12²

h² + 49 = 144

h² = 95

h = √95

Now we can find the area of each triangular face using the formula:

Area of triangle = 1/2 x base x height

The base of each triangle is 14 yards, and the height is √95 yards. So we have:

Area of triangle = 1/2 x 14 yards x √95 yards

Area of triangle = 7√95 square yards

There are four triangular faces, so the total area of the four triangular faces is:

Total area of triangular faces = 4 x 7√95 square yards

Total area of triangular faces = 28√95 square yards

Finally, we can find the total surface area by adding the area of the base and the area of the four triangular faces:

Total surface area = Area of base + Total area of triangular faces

Total surface area = 196 square yards + 28√95 square yards

Total surface area ≈ 387.6 square yards (rounded to one decimal place)

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The capacity of the bottle is 16 ounces

From the question, we have the following parameters that can be used in our computation:

A water bottle is 3/4 full.

When half of the water is drained, we have

Remainder = 1/2 * 3/4x

Evaluate

Remainder = 3/8x

Where x is the capacity of the bottle

We understand that 6 ounces of water remain in the bottle.

This means that

3/8x = 6

So, we have

x = 8 * 6/3

Evaluate

x = 16

Hence. the capacity of the bottle is 16 ounces

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Answer: D. Parallelogram

Step-by-step explanation: Step 1. Input all the points on a graph, there's not really much to it, sorry if I didn't help but the answer is D

After considering the given data we conclude that the x-coordinate of the inflection points for the function are x = - 2 and x = 2, which is option A.

To evaluate the x-coordinate of the inflection points for the function f(x) = ln(x² + 4) we need to evaluate the second derivative of the function and find for x when the second derivative equals zero.
The first derivative of f(x) is:
f' * (x) = (2x)/(x² + 4)
The second derivative of f(x) is:
f"(x) = 2(x² + 4)-4x² /(x²+4)² = 8 - 2x²/(x²+4)²
To evaluate the inflection points, we need to find the equation f'' (x) = 0 for x:
8 - 2x²/(x²+4)² = 0
After applying simplification this equation, we get:
8 - 2x² = 0
Evaluating for x, we get:
x = +/- √4) = +/- 2
Therefore, the x-coordinate of the inflection points for the function f(x) = ln(x² + 4)
x = - 2 and x = 2 .
The answer is A. x = - 2 and x = 2.
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Answer:

9 - 5 (x + 4) = 12 (x + 1)

-5x - 11 = 12x + 12

-5x - 11 + 11 = 12x + 12 + 11

-5x = 12x + 23

-5x - 12x = 12x + 23 - 12x

x = -23/17

Answer:

x=−23/17

Step-by-step explanation:

Distribute: 9-5(x+4) = 12(x+1)

= 9+−5x+−20=12x+12

Combine like term 9&-220:

−5x+−11=12x+12

Subtract 12x:

−5x−11−12x=12x+12−12x

=−17x−11=12

Add 11:

−17x−11+11=12+11

=−17x=23

Divide by -17:

−17x/-17=23/-17

x=−23/17

.

The equation that relates the cost of a bouquet to the number of balloons in the bouquet is: Y = 5.75x

The bouquet with 6 balloons, and the cost per balloon is:

34.50 / 6 = 5.75

We can repeat this process for each bouquet to get:

6 balloons: cost per balloon = 5.75

9 balloons: cost per balloon = 3.83

12 balloons: cost per balloon = 3.04

we can write an equation of the form: Y = kx

where Y is the cost of a bouquet,

x is the number of balloons in the bouquet, and

k is a constant that represents the cost per balloon.

To solve for k, we can use any one of the bouquets to get:

34.50 = k(6)

Solving for k, we get:

k = 5.75

Therefore, the equation that relates the cost of a bouquet to the number of balloons in the bouquet is:

Y = 5.75x

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Complete question:

Brenda sells balloon bouquets. She charges the same price for each

balloon in a bouquet. The costs for several bouquets are shown in the

table. Write an equation that relates the cost of a bouquet to the number

of balloons in the bouquet.

Number of balloons,

(x= # of balloons)

6

9

12

(Y=cost)

3

4.50

6

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{0}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{0}-\stackrel{y1}{(-3)}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{4}}} \implies \cfrac{0 +3}{-2} \implies \cfrac{ 3 }{ -2 } \implies - \cfrac{3}{2}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{- \cfrac{3}{2}}(x-\stackrel{x_1}{4}) \implies y +3 = - \cfrac{3}{2} ( x -4) \\\\\\ y+3=- \cfrac{3}{2}x+6\implies {\Large \begin{array}{llll} y=- \cfrac{3}{2}x+3 \end{array}}[/tex]

Answer:

y = -1.5x + 3

Step-by-step explanation:

gradient = (-3 - 0) / (4 - 2) = -3/2 = -1.5.

equation on line through two points is given by

y - y1 = m (x - x1)

where y1 and x1 are the coordinates of the point and m is the gradient.

we can choose either point to use in the equation.

y - 0 = -1.5 (x - 2) = -1.5x + 3

y = -1.5x + 3

Denis was  told  to write the first non-objective statement by the arising trend of Neotraditionism.            

As he explains in his composition" The description of Neotraditionism,"" The  thing of Neotraditionism is to make  commodity new that isn't a  dupe, nor a simple extension, nor a parody of the old"( Denis, 1911). He believed that this movement  needed a new language of art, one that wasn't tied to emblematic  forms.

Kandinsky's  appearance atnon-objective  oil was  told  by his spiritual beliefs and his desire to express the inner nature of  effects. As he writes in Concerning the Spiritual in Art," The artist must have  commodity to say, for mastery over form isn't his  thing but rather the adapting of form to its inner meaning"( Kandinsky, 1977,p. 10). He believed that art should be a spiritual expression and that the inner world of the artist should be  restated into visual language.  

Kandinsky wrote  considerably about color in Concerning the Spiritual in Art. He believed that color had its own language and could convey  feelings and ideas. As he writes," Color is a means of  plying direct influence upon the soul. Color is the keyboard. The eye is the hammer. The soul is the piano, with its  numerous strings"( Kandinsky, 1977,p. 43). He believed that colors could be arranged in a way that would produce a symphony of  feelings in the bystander.

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Answer:

It is 3y^3.

Step-by-step explanation:

We can simplify the expression as follows:

-15(y^2)^4/(-5y^3y^2)

= -15y^8/(-5y^5)

= 3y^3

So, the simplified expression is 3y^3.

Answer:

Step-by-step explanation:

The equivalent value of the fraction is A = 533 / 99

Given data ,

To find equivalent fractions for the repeating decimal 5.38383838..., we can use the concept of converting a repeating decimal to a fraction.

Let's denote the repeating decimal as x: x = 5.38383838...

Step 1:

Multiply x by a power of 10 to eliminate the repeating part.

100x = 538.38383838...

Step 2:

Subtract x from the product obtained in Step 1 to eliminate the repeating part.

100x - x = 538.38383838... - 5.38383838...

99x = 533

Step 3:

Solve for x by dividing both sides by 99.

x = 533 / 99

Hence , the fraction is A = 533 / 99

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The total cost of the snow thrower on the installment plan is $1,641.60.

To find the total cost of the snow thrower on the installment plan, we will first calculate the down payment and then add the total monthly payments. Here's the step-by-step explanation:
1. Calculate the down payment:
Down payment = 20% of the original price
Down payment = 0.20 * $1,248
Down payment = $249.60
2. Calculate the total of the 12 monthly payments:
Total monthly payments = 12 * $116
Total monthly payments = $1,392
3. Calculate the total cost on the installment plan:
Total cost = Down payment + Total monthly payments
Total cost = $249.60 + $1,392
Total cost = $1,641.60
So, the total cost of the snow thrower on the installment plan is $1,641.60.

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The chances that, at least, one of the dinosaur toys in Franklin's set is a T.rex is 57%.

We can use the complement rule to find the probability that none of the dinosaur toys in Franklin's set is a T. rex, and then subtract this from 1 to get the probability that at least one of the toys is a T. rex.

The probability that a given toy is not a T. rex is 90%, or 0.9.

Since there are 8 toys in the set, the probability that none of them are T. rex is:

0.9 x 0.9 x 0.9 x 0.9 x 0.9 x 0.9 x 0.9 x 0.9 = 0.43

So the probability that at least one of the toys is a T. rex is:

1 - 0.43 = 0.57, or 57%

In other words, it is 57% likely that at least one of the dinosaur toys in Franklin's set is a T. rex.

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A. The initial size of the culture is 222.11

B. The doubling period is approximately 13.53 minutes.

C. The population after 100 minutes is 5807.76

D . The population will reach 13000 after approximately 44.59 minutes.

Use the formula for exponential growth:

N = N0 × eʳᵗ

where N is the population size at time t, N0 is the initial population size, r is the growth rate, and t is the time elapsed.

Using the given data:

At t=10, N=500

500 = N0 × eʳ×¹⁰

At t=30, N=1500

1500 = N0 × eʳ׳⁰

To solve for N0 and r, we can divide the second equation by the first:

¹⁵⁰⁰/₅₀₀ = eʳ׳⁰ / eʳ×¹⁰

3 = eʳ× ²⁰

Taking the natural logarithm of both sides:

ln(3) = r × 20

r = ln³/₂₀

r ≈ 0.0513 (rounded to 4 decimal places)

Now we can use N = N0 × eʳᵗ to answer the remaining questions:

- The initial size of the culture is:

N0 = N / eʳᵗ = 500 / ₑ(0.0513×10) ≈ 222.11 (rounded to 2 decimal places)

- The doubling period is the time it takes for the population to double. Find this by setting N = 2N0 and solving for t:

2N0 = N0 × eʳᵗ

2 = eʳᵗ

ln(2) = rt

t = ln²/ᵣ

t ≈ 13.53 (rounded to 2 decimal places)

So the doubling period is approximately 13.53 minutes.

- The population after 100 minutes is:

N = N0 × eʳᵗ = 222.11 × ₑ(0.0513×100) ≈ 5807.76 (rounded to 2 decimal places)

- To find when the population reaches 13000, we can solve N = 13000 for t:

13000 = N0 × eʳᵗ

13000 = 222.11 × ₑ(0.0513t)

58.56 = ₑ(0.0513t)

ln(58.56) = 0.0513t

t ≈ 44.59 (rounded to 2 decimal places)

So the population will reach 13000 after approximately 44.59 minutes.

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The measure of 5 is 110°.

Given, Lines n and p are parallel to each other and have transversal t.

To find: The value of angle 5.

Therefore, the sum of these angles will be 180

Angle 4 = angle 5

Now, they are alternate interior angles.

Therefore,

angle 5 = 110

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Answer:

h = 5t²+ 25t

from projectiles

h = u²sin²∆ / 2g

taking the angle to be ∆

and range is u²sin2∆/g

Therefore integrate the equation h= 5t²+25t

R = 5t³/3 + 25t²/2 + t

Answer:

356.89$

Step-by-step explanation:

259.9 + 62.99 = 322.98, 8.25% + 2.25 = 10.5 tax rate... So 322.98 + 10.5% = 356.89$

a. In the integrand ∫[x/(6x² + 5)²]dx, we make the substitution u =  (6x² + 5)

b. Writing the integrand ∫[x/(6x² + 5)²]dx in the form ∫f(u)du, f(u) = u²/12

Integration is the reverse of differentiation

a. Since we want to find the substitution in order to evaluate the following integrand ∫[x/(6x² + 5)²]dx, we proceed as follows

In the integrand ∫[x/(6x² + 5)²]dx, we see that the other function is the polynomial in the denominator which is (6x² + 5). So, we make the substitution u =  (6x² + 5)

b. To rewrite the integrand in terms of u so that ∫[x/(6x² + 5)²]dx is int he form ∫f(u)du, we proceed as  follows

Since  integrand ∫[x/(6x² + 5)²]dx and u = 6x² + 5. Differentiation u with respect to x, we have that

du/dx = d(6x² + 5)/dx

= d(6x²)/dx + d5/dx

= 12x + 0

= 12x

So, du/dx = 12x

xdx = du/12

So, substituting this into the integrand, we have that

∫[x/(6x² + 5)²]dx = ∫[x/u²]dx

= ∫[xdx/u²]

= ∫[du/12/u²]

=  ∫[du/12u²]  

So, comparing  ∫[f(u)du]  = ∫[du/12u²]  

So, f(u) = u²/12

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Answer:

[tex]f(u)=\dfrac{1}{12u^5}[/tex]

Step-by-step explanation:

Integration by substitution is a technique used to simplify the integration of complex functions. It involves writing part of the function in terms of a new variable u, where u is some function of x.

Given integral:

[tex]\displaystyle \int \dfrac{x}{(6x^2+5)^5}\; \text{d}x[/tex]

Substitute u for 6x² + 5.

Differentiate u with respect to x and rearrange the equation to isolate dx:

[tex]\dfrac{\text{d}u}{\text{d}x}=12x \implies \text{d}x=\dfrac{1}{12x}\; \text{d}u[/tex]

Substitute the expressions for u and dx into the original expression to rewrite the original integral in terms of u and du:

[tex]\begin{aligned}\displaystyle \int \dfrac{x}{(6x^2+5)^5}\; \text{d}x &= \int \dfrac{x}{u^5} \cdot \dfrac{1}{12x}\; \text{d}u\\\\&= \int \dfrac{1}{12u^5}\; \text{d}u\\\\\end{aligned}[/tex]

Therefore:

[tex]f(u)=\dfrac{1}{12u^5}[/tex]

The lengths of the legs are 7.7 units and 6.4 units

To determine the lengths of the legs of the triangle, we have that;

We need to know the different trigonometric identities. These identities are expressed as;

From the information given, we have that;

Using the sine identity;

sin θ = opposite/hypotenuse

Substitute the values

sin 40 = x/10

cross multiply the values, we get;

x = 6. 4 units

Using the cosine identity;

cos 40 = y/10

y = 7. 7 units

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The length of the other two legs are 6.4 and 7.6

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

Since the hypotenuse is 10, we are going to find the other legs of the right triangle using the trig functions.

sin40 = opp/hyp

0.643 = opp/10

opp = 0.643 × 10

opp = 6.4

Cos 40 = adj/hyp

0.766 = adj/10

adj = 0.766 × 10

adj = 7.6

Therefore the length of other two legs are 6.4 and 7.6

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The interest paid for the loan is $1748

Given that there is a 6.1% interest rate for a loan of $28,654 in student loan debt pay in the first year,

We need to find the interest paid for the same.

So,

Simple Interest = principal × time × rate / 100

= 28654 × 1 × 6.1 / 100

= 28654 × 0.061

= 1747.894

= 1748

Hence the interest paid for the loan is $1748

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This is an exercise in parametric equations, which are a way of representing a curve or surface on the plane or in space using arbitrary values or a constant called a parameter instead of using an independent variable. In the case of circles, the points (x,y) can be expressed from a single variable θ, which is called a parameter. The parametric equations of a circle with radius r ≥ 0 and center (h,k) are given by x = h + rcosθ y = k + rsinθ, where 0 < θ < 2π. The parametric equation of a circle can be expressed from the angle θ of the point through the circle with respect to the x-coordinate axis. The parametric equations of the conics, including the circumference, can be deparameterized to obtain the canonical equation.

The parametric equation of a circle can be expressed from the angle θ of the point through the circle with respect to the x-coordinate axis. The angle can be expressed in radians (θ∈[0,2π]) or sexagesimal degrees (θ∈[0º,360º]). The parametric equation of a circle with center C=(-1,3) and radius r=2 cm is defined by x = -1 + 2cosθ and y = 3 + 2sinθ.

The parametric equations of a curve are expressed from the variable (or parameter) t, such that x = x(t) and y = y(t). Each value of t determines a point (x,y) in the plane. The parametric equations of a circle with radius r ≥ 0 and center (h,k) are given by x = h + rcosθ y = k + rsinθ, where 0 < θ < 2π. The parametric equation of a circle centered at the origin and with radius r is x² + y² = r².

The parametric equations for a curve are not unique. They represent the same circle with center at (0,0) and radius R. The parametric equations of the conics, including the circumference, can be deparameterized to obtain the canonical equation. To go from the parametric to the Cartesian equations, the parameter t must be eliminated. The parametric equations of a point on a circle of radius r at an angle θ are x = rcos(θ) and y = rsin(θ).

cos²(t) + sin²(t) = 1

Multiplying both sides by 25, we get:

25 cos²(t) + 25 sin²(t) = 25

Which is equivalent to:

x² + y² = 25

Therefore, we can write:

x(t) = 5 cos(t), y(t) = 5 sin(t)

This means that for every value of t in the interval 0≤t≤2π, we can get a point on the circle.

Answer:

8/27

Step-by-step explanation:

There are a total of 27 students in the class, and 8 of them are accounting majors. Therefore, the probability of the first student selected being an accounting major is 8/27.

After the first student is selected, there will be 26 students remaining, out of which 6 are art majors. Therefore, the probability of the second student selected being an art major, given that the first student was an accounting major, is 6/26.

To find the probability of both events occurring together, we need to multiply the individual probabilities:

P(accounting major first) * P(art major second | accounting major first)

= (8/27) * (6/26)

= 48/702

= 8/117

The range of the equation y = |x| is

∞ > x ≥ 0

The absolute value function x returns the distance between x and 0 on the number line regardless of the sign of x

Plotting a graph of y = | x| also have it that the smallest possible value of |x| is 0 which occurs when x = 0

for any other value of x, the unction y = |x | will be positive

hence we can say that the range of |x| is [0, ∞).

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Answer:

5

Step-by-step explanation:

v - e + f =2

5 - 8 + f = 2

f = 2 - 5 + 8

= 5

The plane traveled approximately 15,806 feet from point A to point B.

tan(angle) = opposite side / adjacent side

Let x be the horizontal distance from Qasim to point A and y be the horizontal distance from Qasim to point B. Then:

tan(16°) = 7200 / x

tan(38°) = 7200 / y

We can solve for x and y:

x = 7200 / tan(16°)

y = 7200 / tan(38°)

Now, we can calculate x and y:

x ≈ 7200 / 0.2878

= 25016.6 feet

y = 7200 / 0.7813

= 9210.7 feet

Finally, to find the distance the plane traveled from point A to point B, we take the difference between y and x:

distance = y - x

= 9210.7 - 25016.6

= -15805.9 feet

we take the absolute value:

distance = 15806 feet (rounded to the nearest foot)

approximately 15,806 feet from point A to point B.

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You'll need to build Excel formulas using =SUM() function on specified cells in order to calculate total assets, total liabilities, revenue, and expenses. To calculate net income, subtract total expense from total revenue. Calculate Equity by summing common stock, retained earnings, and net income, then subtracting dividends. Finally, sum total liabilities and total equity.

To answer these questions, you are required to have Excel skills and basic understanding of business accounting principles. Let's break it down per section:

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The Equivalent measurements of a given quantity can be useful in a variety of situations, such as when you need to convert between different units of volume

2 1/2 gallons is equal to various measurements depending on the context, but here are a few common conversions:

- 10 pints: There are 2 pints in a quart, and 4 quarts in a gallon, so 2 1/2 gallons would be 2 x 4 + 2 = 10 pints.

- 20 cups: There are 2 cups in a pint, 2 pints in a quart, and 4 quarts in a gallon, so 2 1/2 gallons would be 2 x 4 x 2 + 2 = 20 cups.

- 640 fluid ounces: There are 8 fluid ounces in a cup, 2 cups in a pint, 2 pints in a quart, and 4 quarts in a gallon, so 2 1/2 gallons would be 4 x 2 x 2 x 8 x 2.5 = 640 fluid ounces.

Knowing the equivalent measurements of a given quantity can be useful in a variety of situations, such as when you need to convert between different units of volume, or when you need to mix ingredients in a recipe.

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