How do i solve this problem

In the diagram, the areas of and are in a ratio of 3 : 4. What are the coordinates of point C?

Radda [10]

9514 1404 393

Answer:

D. (4, -6)

Step-by-step explanation:

Since the heights of both triangles are the same (CD), their areas are proportional to their bases. That is ...

AC : CB = 3 : 4

In terms of coordinates, ...

4(C -A) = 3(B -C) . . . . multiply the ratios by 4(CB)

4C -4A = 3B -3C . . . .simplify

7C = 4A +3B . . . . . . . isolate C

C = (4A +3B)/7 . . . . . divide by 7

C = (4(1, -9) +3(8, -2))/7 = (28, -42)/7 . . . . substitute given coordinates

C = (4, -6)

8 0

3 years ago

Use a computer algebra system to plot the vector field F(x, y, z) = sin(x) cos2(y)i + sin3(y) cos4(z)j + sin5(z) cos6(x)k in the

Olenka [21]

By the divergence theorem,

$\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\iiint_{[0,\pi/2]^3}\mathrm{div}\vec F\cdot\mathrm dV$

We have

$\mathrm{div}\vec F(x,y,z)=\cos x\cos^2y+3\sin^2y\cos y\cos^4z+5\sin^4z\cos z\cos^6x$

Then the volume integral is

$\displaystyle\int_0^{\pi/2}\int_0^{\pi/2}\int_0^{\pi/2}\mathrm{div}\vec F\,\mathrm dx\,\mathrm dy\,\mathrm dz=\boxed{\frac{19\pi^2}{64}}$

7 0

4 years ago

For dinner last night, Vinnie ordered a large supreme pizza with extra anchovies. The regular price of the pizza is $24 but Vinn

MaRussiya [10]

Answer:

$20.94

Step-by-step explanation:

8 0

3 years ago

One centimeter is what times as long as one millimeter

Likurg_2 [28]

One centimeter equals 10 millimeters.

5 0

3 years ago

A new battery's voltage may be acceptable (A) or unacceptable (U). A certain flashlight requires two batteries, so batteries wil

klio [65]

Answer:

The probability that you test exactly 4 batteries is 0.0243.

Step-by-step explanation:

We are given that a new battery's voltage may be acceptable (A) or unacceptable (U). A certain flashlight requires two batteries, so batteries will be independently selected and tested until two acceptable ones have been found.

Suppose that 90% of all batteries have acceptable voltages.

Let the probability that batteries have acceptable voltages = P(A) = 0.90

So, the probability that batteries have unacceptable voltages = P(U) = 1 - P(A) = 1 - 0.90 = 0.10

Now, the probability that you test exactly 4 batteries is given by the three cases. Firstly, note that batteries will be tested until two acceptable ones have been found.

So, the cases are = P(AUUA) + P(UAUA) + P(UUAA)

This means that we have tested 4 batteries until we get two acceptable batteries.

So, required probability = (0.90 $\times$ 0.10 $\times$ 0.10 $\times$ 0.90) + (0.10 $\times$ 0.90 $\times$ 0.10 $\times$ 0.90) + (0.10 $\times$ 0.10 $\times$ 0.90 $\times$ 0.90)

= 0.0081 + 0.0081 + 0.0081 = <u>0.0243</u>

<u></u>

Hence, the probability that you test exactly 4 batteries is 0.0243.

3 0

3 years ago