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3241004551 [841]

3 years ago

11

The endpoints of a segment are (4,2) and (-2,2). What are the endpoints of the segment after it has been translated 6 units down

?

1 answer:

Yuki888 [10]3 years ago

4 0

(4,-4) and (-2,-4)

hope that helps!

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Find the missing measure

mr_godi [17]

Answer:

Step-by-step explanation:

5 0

3 years ago

Find an approximate equation y=ab^x with the coordinates (0, 4) (3, 95)

bogdanovich [222]

We have $y=ab^{x}$

Plug in $(0, 4)$ :
$4=ab^{0}$ ⇒ $4=a$
So we now have $a$

Plug in $(3, 95)$ :
$95=4b^{3}$
⇒ $b^{3}=\frac{95}{4}$
⇒ $b=\sqrt[3]{\frac{95}{4}}$
which is approximately 2.874

So we get
$y=4(\sqrt[3]{\frac{95}{4}})^{x}$
or, in decimal form,
$y=4*2.874^{x}$

7 0

2 years ago

Let R be the shaded region in the first quadrant enclosed by the y-axis and the graphs of y=sinx and y=cosx.

julsineya [31]

<span>since sin and cos = each other at pi/4; take your integrals from 0 to pi/4
</span><span>[S] cos(t) dt - [S] sin(t) dt ;[0,pi/4]
</span>
<span>to revolve it around the x axis;
we do a sum of areas [S] 2pi [f(x)]^2 dx
</span>
<span>take the cos first and subtract out the sin next; like cutting a hole out of a donuts.
</span><span>pi [S] cos(x)^2 dx - [S] sin(x)^2 dx ; [0,pi/4]
</span>
<span>cos(2t) = 2cos^2 - 1
cos^2 = (1+cos(2t))/2
</span>
<span>1/sqrt(2) - (-1/sqrt(2) +1)
1/sqrt(2) + 1/sqrt(2) -1
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3 0

2 years ago

Identify the initial amount a and the rate of growth r (as a percent) of the exponential function y = 12(1.05)t. Evaluate the fu

aleksandrvk [35]

Answer

Exponential function is in the form of : $y =a(1+r)^x$ .....[1]

where a is the initial amount and r is the growth rate and (1+r) is the growth factor.

Given the function: $y = 12(1.05)^t$

On comparing with equation [1] we have;

Initial amount(a) = 12

1+r = 1.05

Subtract 1 from both sides we get;

$r = 0.05$ or 5%

Growth (r) = 0.05 or 5%

Now, evaluate the function for t = 5 we have;

Substitute the value of t=5 in the given function we have;

$y = 12(1.05)^{5}$

$y = 12 \cdot 1.27628156 = 15.3153787$

Therefore, the value of function when t=5 to the nearest tenth is 15.3

7 0

2 years ago

Find a potential function for F or determine that F is not conservative. (If F is not conservative, enter NOT CONSERVATIVE.) F =

xxMikexx [17]

For $F$ to be conservative, we need to have

$\dfrac{\partial f}{\partial x}=\cos z$

$\dfrac{\partial f}{\partial y}=10y$

$\dfrac{\partial f}{\partial z}=-x\sin z$

Integrate the first PDE with respect to $x$ :

$\displaystyle\int\frac{\partial f}{\partial x}\,\mathrm dx+\int\cos z\,\mathrm dx\implies f(x,y,z)=x\cos z+g(y,z)$

Differentiate with respect to $y$ :

$\dfrac{\partial f}{\partial y}=10y=\dfrac{\partial g}{\partial y}\implies g(y,z)=5y^2+h(z)$

Now differentiate $f$ with respect to $z$ :

$\dfrac{\partial f}{\partial z}=-x\sin z=-x\sin z+\dfrac{\mathrm dh}{\mathrm dz}\implies\dfrac{\mathrm dh}{\mathrm dz}=0\implies h(z)=C$

So we have

$f(x,y,z)=x\cos z+5y^2+C$

so $F$ is indeed conservative.

8 0

3 years ago