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2 years ago

What is the volume of the rectangular prism? . choices: (63yd^3) (7yd^3) (22.5yd^3) (189yd^3)

Mathematics

1 answer:

Alexxx [7]2 years ago

4 0

Answer: (7yd^3)

Step-by-step explanation:

Width= $3*\frac{1}{3}$

Length= $7*\frac{1}{3}$

Height= $9*\frac{1}{3}$

Width= 1

Length= 2.33333333333...

Height= 3

1*2.33333333333*3= 6.99999999999

6.99999999999 is round up to 7

So that would be (7yd^3)

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Consider the line integral Z C (sin x dx + cos y dy), where C consists of the top part of the circle x 2 + y 2 = 1 from (1, 0) t

pashok25 [27]

Direct computation:

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$\vec r(t)=(x(t),y(t))=(\cos t,\sin t)$

with $0\le t\le\pi$ , and the line segment by

$\vec s(t)=(1-t)(-1,0)+t(2,-\pi)=(3t-1,-\pi t)$

with $0\le t\le1$ . Then

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)$

$=\displaystyle\int_0^\pi(-\sin t\sin(\cos t)+\cos t\cos(\sin t)\,\mathrm dt+\int_0^1(3\sin(3t-1)-\pi\cos(-\pi t))\,\mathrm dt$

$=0+(\cos1-\cos2)=\boxed{\cos1-\cos2}$

Using the fundamental theorem of calculus:

The integral can be written as

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)=\int_C\underbrace{(\sin x,\cos y)}_{\vec F}\cdot\underbrace{(\mathrm dx,\mathrm dy)}_{\vec r}$

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This requires

$\dfrac{\partial f}{\partial x}=\sin x\implies f(x,y)=-\cos x+g(y)$

$\dfrac{\partial f}{\partial y}=\cos y=\dfrac{\mathrm dg}{\mathrm dy}\implies g(y)=\sin y+C$

So we have

$f(x,y)=-\cos x+\sin y+C$

which means $\vec F$ is indeed conservative. By the fundamental theorem, we have

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)=f(2,-\pi)-f(1,0)=-\cos2-(-\cos1)=\boxed{\cos1-\cos2}$

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3 years ago

Cloud [144]

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3 years ago

What is the volume of the rectangular prism? . choices: (63yd^3) (7yd^3) (22.5yd^3) (189yd^3)​

What is the volume of the rectangular prism? . choices: (63yd^3) (7yd^3) (22.5yd^3) (189yd^3)