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notsponge [240]

1 year ago

8

Cindy bought a new lamp for $40.00. She later saw the lamp on sale for 25% less than what she had originally paid. What was the

lamp selling for the second time she saw it?

1 answer:

baherus [9]1 year ago

7 0

Answer: acute rigth angle

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This box has the same length , width, and height as the 2 basketballs. Which expression gives the volume of the empty space enci

Solnce55 [7]

Don't you just grab the volume of the box and subtract the volume of the basketballs.

8 0

2 years ago

Read 2 more answers

PLEASE HELP ASAP<br> Prove that x+a is a factor of (x+a)^5 + (x+c)^5 + (a-c)^5

Brums [2.3K]

$P(x)=(x+a)^5 + (x+c)^5 + (a-c)^5$

If $x+a$ is a factor of $P(x)$ , then $-a$ is a root of $P(x)$ .

Therefore

$(-a+a)^5+(-a+c)^5+(a-c)^5=0\\\\0^5+(-1(a-c))^5+(a-c)^5=0\\\\(-1)^5(a-c)^5+(a-c)^5=0\\\\-(a-c)^5+(a-c)^5=0\\\\0=0$

6 0

2 years ago

Use green's theorem to compute the area inside the ellipse x252+y2172=1. use the fact that the area can be written as ∬ddxdy=12∫

Pavel [41]

The area of the ellipse $E$ is given by

$\displaystyle\iint_E\mathrm dA=\iint_E\mathrm dx\,\mathrm dy$

To use Green's theorem, which says

$\displaystyle\int_{\partial E}L\,\mathrm dx+M\,\mathrm dy=\iint_E\left(\frac{\partial M}{\partial x}-\frac{\partial L}{\partial y}\right)\,\mathrm dx\,\mathrm dy$

( $\partial E$ denotes the boundary of $E$ ), we want to find $M(x,y)$ and $L(x,y)$ such that

$\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1$

and then we would simply compute the line integral. As the hint suggests, we can pick

$\begin{cases}M(x,y)=\dfrac x2\\\\L(x,y)=-\dfrac y2\end{cases}\implies\begin{cases}\dfrac{\partial M}{\partial x}=\dfrac12\\\\\dfrac{\partial L}{\partial y}=-\dfrac12\end{cases}\implies\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1$

The line integral is then

$\displaystyle\frac12\int_{\partial E}-y\,\mathrm dx+x\,\mathrm dy$

We parameterize the boundary by

$\begin{cases}x(t)=5\cos t\\y(t)=17\sin t\end{cases}$

with $0\le t\le2\pi$ . Then the integral is

$\displaystyle\frac12\int_0^{2\pi}(-17\sin t(-5\sin t)+5\cos t(17\cos t))\,\mathrm dt$

$=\displaystyle\frac{85}2\int_0^{2\pi}\sin^2t+\cos^2t\,\mathrm dt=\frac{85}2\int_0^{2\pi}\mathrm dt=85\pi$

###

Notice that $x^{2/3}+y^{2/3}=4^{2/3}$ kind of resembles the equation for a circle with radius 4, $x^2+y^2=4^2$ . We can change coordinates to what you might call "pseudo-polar":

$\begin{cases}x(t)=4\cos^3t\\y(t)=4\sin^3t\end{cases}$

which gives

$x(t)^{2/3}+y(t)^{2/3}=(4\cos^3t)^{2/3}+(4\sin^3t)^{2/3}=4^{2/3}(\cos^2t+\sin^2t)=4^{2/3}$

as needed. Then with $0\le t\le2\pi$ , we compute the area via Green's theorem using the same setup as before:

$\displaystyle\iint_E\mathrm dx\,\mathrm dy=\frac12\int_0^{2\pi}(-4\sin^3t(12\cos^2t(-\sin t))+4\cos^3t(12\sin^2t\cos t))\,\mathrm dt$

$=\displaystyle24\int_0^{2\pi}(\sin^4t\cos^2t+\cos^4t\sin^2t)\,\mathrm dt$

$=\displaystyle24\int_0^{2\pi}\sin^2t\cos^2t\,\mathrm dt$

$=\displaystyle6\int_0^{2\pi}(1-\cos2t)(1+\cos2t)\,\mathrm dt$

$=\displaystyle6\int_0^{2\pi}(1-\cos^22t)\,\mathrm dt$

$=\displaystyle3\int_0^{2\pi}(1-\cos4t)\,\mathrm dt=6\pi$

3 0

2 years ago

Anna bought 8 tetras and 2 rainbow fish for her aquarium. The rainbow fish cost $6 more than the tetras. She paid a total of $

____ [38]

Answer:

C, D, and E

Step-by-step explanation:

When trying to solve for the cost of each item you will find a rainbow fish is $8.50 and a tetra is $2.50. If you use that information to solve the other answer choices C, D, and E would be correct

5 0

2 years ago

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The Chang family is on their way home from a cross-country road trip. During the trip, the function D(t) = 2,280 - 60t can be us

nordsb [41]

Answer:

C

Step-by-step explanation:

I took the test and got it correct.

7 0

2 years ago