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mamaluj [8]
3 years ago
10

Formulate a system of equations to represent this situation, with f = the amount of money that Frank spent and r = the amount of

money that Rachel spent. Frank and Rachel spent a total of $15.75. If Rachel spends twice as much money as Frank, how much money did they each spend?
A)
B)
C)
D)
Mathematics
1 answer:
dem82 [27]3 years ago
4 0

Answer:

A

Step-by-step explanation:

I just did it

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A rectangular room measures 224 square feet. One side of the room is 14 feet long. What is the perimeter of the room?
rusak2 [61]

Answer: The perimeter is 60 feet

Step-by-step explanation:

224/14=16

16+14+16+14=60 feet

The perimeter is 60 feet

3 0
3 years ago
Calculus 3 help please.​
Reptile [31]

I assume each path C is oriented positively/counterclockwise.

(a) Parameterize C by

\begin{cases} x(t) = 4\cos(t) \\ y(t) = 4\sin(t)\end{cases} \implies \begin{cases} x'(t) = -4\sin(t) \\ y'(t) = 4\cos(t) \end{cases}

with -\frac\pi2\le t\le\frac\pi2. Then the line element is

ds = \sqrt{x'(t)^2 + y'(t)^2} \, dt = \sqrt{16(\sin^2(t)+\cos^2(t))} \, dt = 4\,dt

and the integral reduces to

\displaystyle \int_C xy^4 \, ds = \int_{-\pi/2}^{\pi/2} (4\cos(t)) (4\sin(t))^4 (4\,dt) = 4^6 \int_{-\pi/2}^{\pi/2} \cos(t) \sin^4(t) \, dt

The integrand is symmetric about t=0, so

\displaystyle 4^6 \int_{-\pi/2}^{\pi/2} \cos(t) \sin^4(t) \, dt = 2^{13} \int_0^{\pi/2} \cos(t) \sin^4(t) \,dt

Substitute u=\sin(t) and du=\cos(t)\,dt. Then we get

\displaystyle 2^{13} \int_0^{\pi/2} \cos(t) \sin^4(t) \, dt = 2^{13} \int_0^1 u^4 \, du = \frac{2^{13}}5 (1^5 - 0^5) = \boxed{\frac{8192}5}

(b) Parameterize C by

\begin{cases} x(t) = 2(1-t) + 5t = 3t - 2 \\ y(t) = 0(1-t) + 4t = 4t \end{cases} \implies \begin{cases} x'(t) = 3 \\ y'(t) = 4 \end{cases}

with 0\le t\le1. Then

ds = \sqrt{3^2+4^2} \, dt = 5\,dt

and

\displaystyle \int_C x e^y \, ds = \int_0^1 (3t-2) e^{4t} (5\,dt) = 5 \int_0^1 (3t - 2) e^{4t} \, dt

Integrate by parts with

u = 3t-2 \implies du = 3\,dt \\\\ dv = e^{4t} \, dt \implies v = \frac14 e^{4t}

\displaystyle \int u\,dv = uv - \int v\,du

\implies \displaystyle 5 \int_0^1 (3t-2) e^{4t} \,dt = \frac54 (3t-2) e^{4t} \bigg|_{t=0}^{t=1} - \frac{15}4 \int_0^1 e^{4t} \,dt \\\\ ~~~~~~~~ = \frac54 (e^4 + 2) - \frac{15}{16} e^{4t} \bigg|_{t=0}^{t=1} \\\\ ~~~~~~~~ = \frac54 (e^4 + 2) - \frac{15}{16} (e^4 - 1) = \boxed{\frac{5e^4 + 55}{16}}

(c) Parameterize C by

\begin{cases} x(t) = 3(1-t)+t = -2t+3 \\ y(t) = (1-t)+2t = t+1 \\ z(t) = 2(1-t)+5t = 3t+2 \end{cases} \implies \begin{cases} x'(t) = -2 \\ y'(t) = 1 \\ z'(t) = 3 \end{cases}

with 0\le t\le1. Then

ds = \sqrt{(-2)^2 + 1^2 + 3^2} \, dt = \sqrt{14} \, dt

and

\displaystyle \int_C y^2 z \, ds = \int_0^1 (t+1)^2 (3t+2) \left(\sqrt{14}\,ds\right) \\\\ ~~~~~~~~ = \sqrt{14} \int_0^1 \left(3t^3 + 8t^2 + 7t + 2\right) \, dt \\\\ ~~~~~~~~ = \sqrt{14} \left(\frac34 t^4 + \frac83 t^3 + \frac72 t^2 + 2t\right) \bigg|_{t=0}^{t=1} \\\\ ~~~~~~~~ = \sqrt{14} \left(\frac34 + \frac83 + \frac72 + 2\right) = \boxed{\frac{107\sqrt{14}}{12}}

8 0
1 year ago
Area= 60 cm width 5cm what is the length and width
Anna [14]

Answer:

length = 12 cm | width = 5 cm

Step-by-step explanation:

You already know the width is 5 cm. So now just divide 5 from 60 to get the length of 12 cm.

3 0
2 years ago
Read 2 more answers
Please help ASAP. Find the volume of the trapezoid as a simplified expression. If correct I will give brainliest.
Leokris [45]

Answer:

2x^2*(2x^3+8x^2+2x)      or

4x^5+16x^4+4x^3

Step-by-step explanation:

A=[2x^3-x+(8x^2+3x)]*4x^2/2=2x^2*(2x^3+8x^2+2x)

or A=4x^5+16x^4+4x^3

6 0
3 years ago
Help on this thx for helping if you did
vichka [17]
To evaluate two fractions being divided, you must turn the right fraction into a reciprocal. That means you must put the bottom number at the top and then put the top number on the bottom (you’re basically switching them).

8/13 / 3/2

Now, once you turned the other number into a reciprocal, you multiply across. The top number times the other top number and do this to the bottom numbers, too.

8/13 * 3/2 = 24/26

You found the answer, 24/26. But as you can see, it’s not one of the choices. That’s because you need to simplify.

24/26 / 2/2 = 12/13

12/13 is your answer, or choice C!

I hope this helped. Comment below if you have any questions.
6 0
3 years ago
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