Answer:
[tex]\frac{da}{dt}=-95.2m/s^2[/tex]
Step-by-step explanation:
From the question we are told that:
Slant height [tex]h=13ft[/tex]
Velocity [tex]v=\frac{dx}{dt}=8[/tex]
Distance [tex]d=12ft[/tex]
Generally the equation for area is mathematically given by
[tex]A=0.5*x*sqrt(169 - x^2)[/tex]
Differentiating
[tex]\frac{da}{dx}=\frac{169-2 x^2}{(2 sqrt(169-x^2))}[/tex]
Multiplying through by dx/dt
[tex]\frac{da}{dx}*\frac{dx}{dt}=\frac{169-2 x^2}{(2 \sqrt{169-x^2})}*\frac{dx}{dt}[/tex]
[tex]\frac{da}{dt}=\frac{169-2x^2}{(2 \sqrt{169-x^2})}*\frac{dx}{dt}[/tex]
[tex]\frac{da}{dt}=\frac{169-(2*12^{2})}{2*\sqrt{(169-12^{2})}}*8[/tex]
[tex]\frac{da}{dt}=-95.2m/s^2[/tex]
Find the distance traveled by a particle with position (x, y) as t varies in the given time interval.
x = 3 sin^2(t), y = 3 cos^2(t), 0< t<3pi
What is the length of the curve?
The length of the curve (and thus the total distance traveled by the particle along the curve) is
[tex]\displaystyle\int_0^{3\pi}\sqrt{x'(t)^2+y'(t)^2}\,\mathrm dt[/tex]
We have
x(t) = 3 sin²(t ) ==> x'(t) = 6 sin(t ) cos(t ) = 3 sin(2t )
y(t) = 3 cos²(t ) ==> y'(t) = -6 cos(t ) sin(t ) = -3 sin(2t )
Then
√(x'(t) ² + y'(t) ²) = √(18 sin²(2t )) = 18 |sin(2t )|
and the arc length is
[tex]\displaystyle 18 \int_0^{3\pi} |\sin(2t)| \,\mathrm dt[/tex]
Recall the definition of absolute value: |x| = x if x ≥ 0, and |x| = -x if x < 0.
Now,
• sin(2t ) ≥ 0 for t ∈ (0, π/2) U (π, 3π/2) U (2π, 5π/2)
• sin(2t ) < 0 for t ∈ (π/2, π) U (3π/2, 2π) U (5π/2, 3π)
so we split up the integral as
[tex]\displaystyle 18 \left(\int_0^{\pi/2} \sin(2t) \,\mathrm dt - \int_{\pi/2}^\pi \sin(2t) \,\mathrm dt + \cdots - \int_{5\pi/2}^{3\pi} \sin(2t) \,\mathrm dt\right)[/tex]
which evaluates to 18 × (1 - (-1) + 1 - (-1) + 1 - (-1)) = 18 × 6 = 108.
please help find the solution to the system of equations
Answer:
x = 2 y = 3
Step-by-step explanation:
-2x + 7 = 5x - 7
-7x + 7 = -7
-7x = -14
x = 2
y = -2(2) + 7
y = -4 + 7
y = 3
There are two rectangles Jared is examining. He knows the width of the first rectangle measures
2.48 cm, and the length is twice its width.
Jared also knows that the width of the second rectangle is equal to the length of the first rectangle,
and that the area of the second rectangle is 9.92. Given this information, find the length of the
second rectangle for Jared.
1st rectangle:
width: 2.48cm
length: 4.96
2nd rectangle:
width: 4.96 (equals to the length of the 1st rectangle)
area: 9.92
length: 9.92/4.96 = 2
Solve the initial-value problem using the method of undetermined coefficients.
y'' − y' = xe^x, y(0) = 6, y'(0) = 5
First check the characteristic solution. The characteristic equation to this DE is
r ² - r = r (r - 1) = 0
with roots r = 0 and r = 1, so the characteristic solution is
y (char.) = C₁ exp(0x) + C₂ exp(1x)
y (char.) = C₁ + C₂ exp(x)
For the particular solution, we try the ansatz
y (part.) = (ax + b) exp(x)
but exp(x) is already accounted for in the second term of y (char.), so we multiply each term here by x :
y (part.) = (ax ² + bx) exp(x)
Differentiate this twice and substitute the derivatives into the DE.
y' (part.) = (2ax + b) exp(x) + (ax ² + bx) exp(x)
… = (ax ² + (2a + b)x + b) exp(x)
y'' (part.) = (2ax + 2a + b) exp(x) + (ax ² + (2a + b)x + b) exp(x)
… = (ax ² + (4a + b)x + 2a + 2b) exp(x)
(ax ² + (4a + b)x + 2a + 2b) exp(x) - (ax ² + (2a + b)x + b) exp(x)
= x exp(x)
The factor of exp(x) on both sides is never zero, so we can cancel them:
(ax ² + (4a + b)x + 2a + 2b) - (ax ² + (2a + b)x + b) = x
Collect all the terms on the left side to reduce it to
2ax + 2a + b = x
Matching coefficients gives the system
2a = 1
2a + b = 0
and solving this yields
a = 1/2, b = -1
Then the general solution to this DE is
y(x) = C₁ + C₂ exp(x) + (1/2 x ² - x) exp(x)
For the given initial conditions, we have
y (0) = C₁ + C₂ = 6
y' (0) = C₂ - 1 = 5
and solving for the constants here gives
C₁ = 0, C₂ = 6
so that the particular solution to the IVP is
y(x) = 6 exp(x) + (1/2 x ² - x) exp(x)
A rectangle auditorium seats 1260 people. The number of seats in each row exceeds the number of rows by 12. Find the number of seats in each row
Answer:
Easy, all you ha
Step-by-step explanation:
A square steel bar has a length of 5.1 ft and a 2.7 in by 2.7 in cross section and is subjected to axial tension. The final length is 5.10295 ft . The final side length is 2.69953 in . What is Poisson's ratio for the material
Answer:
The Poisson's ratio for the material is 0.0134.
Step-by-step explanation:
The Poisson's ratio ([tex]\nu[/tex]), no unit, is the ratio of transversal strain ([tex]\epsilon_{t}[/tex]), in inches, to axial strain ([tex]\epsilon_{a}[/tex]), in inches:
[tex]\nu = -\frac{\epsilon_{t}}{\epsilon_{a}}[/tex] (1)
[tex]\epsilon_{a} = l_{a,f}-l_{a,o}[/tex] (2)
[tex]\epsilon_{t} = l_{t,f}-l_{t,o}[/tex] (3)
Where:
[tex]l_{a,o}[/tex] - Initial axial length, in inches.
[tex]l_{a,f}[/tex] - Final axial length, in inches.
[tex]l_{t,o}[/tex] - Initial transversal length, in inches.
[tex]l_{t,f}[/tex] - Final transversal length, in inches.
If we know that [tex]l_{a,o} = 61.2\,in[/tex], [tex]l_{a,f} = 61.235\,in[/tex], [tex]l_{t,o} = 2.7\,in[/tex] and [tex]l_{t,f} = 2.69953\,in[/tex], then the Poisson's ratio is:
[tex]\epsilon_{a} = 61.235\,in - 61.2\,in[/tex]
[tex]\epsilon_{a} = 0.035\,in[/tex]
[tex]\epsilon_{t} = 2.69953\,in - 2.7\,in[/tex]
[tex]\epsilon_{t} = -4.7\times 10^{-4}\,in[/tex]
[tex]\nu = - \frac{(-4.7\times 10^{-4}\,in)}{0.035\,in}[/tex]
[tex]\nu = 0.0134[/tex]
The Poisson's ratio for the material is 0.0134.
Which equation represents a slope of −4 and y-intercept of (0,2)?
y = −4x + 2
y = −2x
y = −2x − 4
y = 4x + 2
Answer:
y=-4x+2
Step-by-step explanation:
Hi there!
We want to find out which equation represents a line with a slope of -4 and a y intercept of (0,2)
The most common way to write the equation of the line is in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept
We have everything we need to plug into the equation, let's just label the values to avoid confusion
m=-4
b=2 (when you substitute the y intercept as b, b is the value of y in the point)
Now substitute into the equation
y=-4x+2
Hope this helps!
Flying against the wind, an airplane travels 7760 kilometers in 8 hours. Flying with the wind, the same plane travels 3690 kilometers in 3 hours. What is the rate of the plane in still air and what is the rate of the wind
Answer:
1100 and 130 (km/h)
Step-by-step explanation:
1. if the velocity of the wind is 'w' and the velocity of the plane in still air is 'p', then
2. it is possible to make up two equations:
the fly against the wind: (p-w)*8=7760;
the fly with the wind: (p+w)*3=3690.
3. if to solve the system made up, then:
[tex]\left \{ {{3(p+w)=3690} \atop {8(p-w)=7760}} \right. \ => \ \left \{ {{p+w=1230} \atop {p-w=970}} \right. \ => \ \left \{ {{p=1100} \atop {w=130}} \right.[/tex]
4. the required rate of the plane in still air is p=1100 km/h; the rate of the wind is w=130 km/h.
the average temperature at the south pole is -49.62and the average temperature at north pole is -34.68. how much higher is the average temperature at the north pole than at the south pole
solve 3 1/5 = y - 12/25
3 1/5 = y - 12/25
31/5+y = -12/25
31+y = -12/25×5
31+y = -12/5
y = -12/5-31
y = -143/5
y = -28.6
HOPE IT HELPS
The point of a square pyramid is cut off, making each lateral face of the pyramid a trapezoid with the dimensions shown. A trapezoid has a base of 3 inches, height of 1 inches, and top side length of 1 inch:
What is the area of one trapezoidal face of the figure?
There are five cities in a network. The cost of building a road directly between i and j is the entry ai,j in the matrix below. An infinite entry indicates that there is a mountain in the way and the road cannot be built. Determine the least cost of making all the cities reachable from each other.
0 3 5 11 9
3 0 3 9 8
5 3 0 [infinity] 10
11 9 [infinity] 0 7
9 9 10 7 0
Solution :
Given :
There are five cities in a network and the cost of [tex]\text{building}[/tex] a road directly between [tex]i[/tex] and [tex]j[/tex] is the entry [tex]a_{i,j}[/tex]
[tex]a_{i,j}[/tex] refers to the matrix.
Road cannot be built because there is a mountain.
The given matrix :
[tex]\begin{bmatrix}0 & 3 & 5 & 11 & 9\\ 3 & 0 & 3 & 9 & 8\\ 5 & 3 & 0 & \infty & 10\\ 11 & 9 & \infty & 0 & 7\\ 9 & 8 & 10 & 7 & 0\end{bmatrix}[/tex]
The matrix on the left above corresponds to the weighted graph on the right.
Using the [tex]\text{Kruskal's algorithm}[/tex] we can select the cheapest edge that is not creating a cycle.
Starting with 2 edges of weight 3 and the edge of weight 5 is forbidden but the edge is 7 is available.
The edge of the weight 8 completes a minimum spanning tree and total weight 21.
If the edge of weight 8 had weight 10 then either of the edges of weight 9 could be chosen the complete the tree and in this case there could be 2 spanning trees with minimum value.
Needddd annnsssweeerrr
Answer:
90in2
Step-by-step explanation:
3x5x6=90
Answer:
C.90
Step-by-step explanation:
first multiply 3 and 5 which is 15 then times it with 6 which equals 90
find area of shaded region
Answer:
The answer is 21.98. I just took area of the whole circle and subtracted it with the area of two circles in it
Answer:
21. 99
Step-by-step explanation:
[tex]s = \pi \times {r}^{2} \\ s1 = 3.14 \times 9 = 28.27 \\ s2 = 3.14 \times 1 = 3.14 \\ a = 28.27 - (3.14 \times 2) = 28.27 - 6.28 = 21.99[/tex]
Which of the following is an advantage of using systematic random sampling?
Systematic random sampling reduces sampling variability.
Systematic random sampling does not require a finite population size.
Systematic random sampling could inadvertently miss patterns in the population.
Systematic random sampling uses clusters, which are close in proximity, making data collection easier.
This is a question that asks about the advantages of a systematic random sampling. Thus, we first take a look at the types of sampling, and then we see the advantage of systematic random sampling.
Samples may be classified as:
Convenient: Sample drawn from a conveniently available pool.
Random: Basically, put all the options into a hat and drawn some of them.
Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.
Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.
Systematic:
One of the bigger advantages is that the systematic sampling eliminate clusters, which means that the last option is wrong.
Inadvertently missing patterns is a problem in systematic sampling, and not an advantage, thus the third option is also wrong.
It also does not reduce sampling variability, thus the first option is wrong.
From this, it can be concluded that the correct option is:
Systematic random sampling does not require a finite population size.
For another example of systematic random sampling, you can check https://brainly.com/question/21100042
trong một thùng có chứa 3 bi đỏ 4 bi đen
Answer:
The FitnessGram™ Pacer Test is a multistage aerobic capacity test that progressively gets more difficult as it continues. The 20 meter pacer test will begin in 30 seconds. Line up at the start. The running speed starts slowly, but gets faster each minute after you hear this signal. [beep] A single lap should be completed each time you hear this sound. [ding] Remember to run in a straight line, and run as long as possible. The second time you fail to complete a lap before the sound, your test is over.ep explanation:
10. In a group of 50 people, there are two types of professionals, engineers and managers. If 36 of them are engineers and 24 of them are managers, how many persons are both managers and engineers?
Step-by-step explanation:
The photo above is the Venn diagram
Now, the number of persons that are both managers and engineers= n
Since, Total number of persons is 50
Therefore, 50= M+n+E
M only = 36-n
E only = 24-n
Therefore, 50= 36 - n + n + 24 - n
50 = 36+24-n
50 = 60 - n
60 - n = 50
-n = 50 - 60
-n = - 10
Therefore, n = 10
Therefore, the number of persons that are both Managers and Engineers is 10persons.
What is the common difference for this arithmetic sequence?
-6,-1,4,9,14,...
A. 6
B. 4
C. 5
D. 3
SUBMIT
Answer:
5 is the answer to your question
Step-by-step explanation:
the numbers are increasing by +5
Solve |2x – 3| = 4x Question 18 options: A) x = 1∕2 B) x = –3∕2 or x = 1∕2 C) x = –3∕2 D) No solutions
Answer:
A
Step-by-step explanation:
If x>3/2, 2x-3>0(2x-3)=4x, x=-3/2 which isn't possible as x>3/2
If x<3/2, 2x-3<0-(2x-3)=4x, x=1/2.
Hence the answer is x=1/2
Doyle Company issued $500,000 of 10-year, 7 percent bonds on January 1, 2018. The bonds were issued at face value. Interest is payable in cash on December 31 of each year. Doyle immediately invested the proceeds from the bond issue in land. The land was leased for an annual $125,000 of cash revenue, which was collected on December 31 of each year, beginning December 31, 2018
Answer:
f
Step-by-step explanation:
What is the measure of b, in degrees
Answer:
B) 32
Step-by-step explanation:
(sin 74) / 10 = (sin c) / 10
c = 74
180 - 74 -74
= 32
a) Everyone on the team talks until the entire team agrees on one decision. O b) Everyone on the team discusses options and then votes. O c) The team passes the decision-making responsibility to an outside person. O di The team leader makes a decision without input from the other members.
Answer:
a) Everyone on the team talks until the entire team agrees on one decision.
Step-by-step explanation:
Option B consists of voting and not everyone would like the outcome. Option C is making an outsider the decision maker, which can't be helpful since he / she won't have as strong opinions as the team itself. Option D is just plain wrong as it defeats the purpose of team work and deciding as one team. So, I believe option A makes the most sense
A diameter perpendicular to a chord
that chord
Select one:
a. is parallel to
b. bisects
c. is equal to
dùng tiền gửi ngân hàng trả tiền cho người bán 100.000.000
Answer:
Sorry, i dont know
Step-by-step explanation:
I dont know the answer to this question.....
Figure A is a scale image of figure B. Figure A maps to figure B with a scale factor of 2/3. What is the value of x?
9514 1404 393
Answer:
x = 7
Step-by-step explanation:
10.5 maps to x with a scale factor of 2/3:
x = 10.5 × 2/3
x = 7
ALL I NEED HELP WITH IS WITH PART D, HOW DO I GET THAT
Use the function f(x) = −16x^2 + 22x + 3 to answer the questions.
Part A: Completely factor f(x). (2 points)
Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph. (4 points)
Step-by-step explanation:
Step 1: Factor the equation
[tex]f(x) = -16x^{2} + 22x + 3\\f(x) = -(8x + 1)(2x - 3)[/tex]
Step 2: Find the x-intercepts of the graph of f(x)
[tex]-8x - 1 + 1 = 0 + 1\\-8x / -8 = 1 / -8\\x = -1/8[/tex]
[tex]2x - 3 + 3 = 0 + 3\\2x / 2 = 3 / 2\\x = 3/2[/tex]
Step 3: Describe the end behavior of the graph of f(x)
Since the function is to the power of 2, that means that it is a parabola. And since the leading coefficient is negative, means that the arrows will be pointing down therefore, the end behavior of this graph is as x goes to infinity, f(x) goes to negative infinity and as x goes to negative infinity, f(x) goes to negative infinity.
Step 4: What are the steps you would use to graph f(x)
The first step that I would do is factor the equation. Then I would find the x-intercepts of the graph and plot them on the graph. I would then plug in 0 for all of the x values to get the y intercept. After doing that I would get the vertex using the vertex formula plotting it on the graph. Finally, I would connect all of the dots together to form the graph of the equation.
Answer:
The person above me is correct!
help me with this questions please!
9514 1404 393
Answer:
r = 18
Step-by-step explanation:
Let d represent the number of districts. The given information lets us write two equations:
3d = 27 . . . . . the number of state senators
d +r = 27 . . . . the number of representatives
The first equation tells us ...
d = 27/3 = 9
The the second equation tells us ...
r = 27 -d = 27 -9 = 18
The number of at-large representatives is r = 18.
Evaluate lim
x→0+
√x ln x
Answer:
vr
Step-by-step explanation:
konho bi m
Cars arrive at an automatic car wash system every 10 minutes on average. The cars inter-arrival times are exponentially distributed. Washing time for each is 6 minutes per car and is purely deterministic (i.e., the waiting line system is M/D/c). Assuming that the car wash has a single bay to serve the cars, what is the average number of cars waiting in line (L.)?
Answer:
the average number of cars waiting in line L[tex]q[/tex] is 0.45
Step-by-step explanation:
Given the data in the question;
Cars arrive at an automatic car wash system every 10 minutes on average.
Car arrival rate λ = 1 per 10 min = [ 1/10 × 60 ]per hrs = 6 cars per hour
Washing time for each is 6 minutes per car
Car service rate μ = 6min per car = [ 1/6 × 60 ] per hrs = 10 cars per hour
so
P = λ/μ = 6 / 10 = 0.6
Using the length of queue in M/D/1 system since there is only one service bay;
L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ P² / ( 1 - P ) ]
so we substitute
L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ (0.6)² / ( 1 - 0.6 ) ]
L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ 0.36 / 0.4 ]
L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ 0.9 ]
L[tex]q[/tex] = 0.45
Therefore, the average number of cars waiting in line L[tex]q[/tex] is 0.45
What is the equation of a parabola that has a vertical axis, passes through the point (–1, 3), and has its vertex at (3, 2)? x= –y216+6y16–4116 y= –x216+6x16–4116 y=x216–6x16+4116 x=y216–6y16+4116
Answer:
y=x216–6x16+4116
Step-by-step explanation:
plato :)
The equation of the parabola is in option (C) if the parabola that has a vertical axis, passes through the point (–1, 3), and has its vertex at (3, 2) option (C) is correct.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
(x - h)² = 4a(y - k)
(h, k) is the vertex of the parabola:
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
It is given that:
The equation of a parabola that has a vertical axis, passes through the point (–1, 3)
The vertex of the parabola is at (3, 2)
As we know, in the standard form of the parabola (h, k) represents the vertex of the parabola.
h = 3
k = 2
Plug the above point in the equation:
[tex]\rm y\ =\ \dfrac{x^{2}}{16}-\dfrac{6x}{16}+\dfrac{41}{16}[/tex]
x = 3
y = 2
[tex]\rm 2\ =\ \dfrac{3^{2}}{16}-\dfrac{6(3)}{16}+\dfrac{41}{16}[/tex]
= 9/16 - 18/16 + 41/16
= (9-18+41)/16
= 32/16
2 = 2 ( true)
The equation of the parabola is:
[tex]\rm y\ =\ \dfrac{x^{2}}{16}-\dfrac{6x}{16}+\dfrac{41}{16}[/tex]
Thus, the equation of the parabola is in option (C) if the parabola that has a vertical axis, passes through the point (–1, 3), and has its vertex at (3, 2) option (C) is correct.
Learn more about the parabola here:
brainly.com/question/8708520
#SPJ2
