Dr /dt = 7

A = pi r^2

dA / dr = 2pir

dA/dt = dA/dr * dr/dt = 2pir * 7 = 14pir

when r = 12 rate of change of the area = 14*pi*12 = 168pi

= 527.79 cm^2 / minute to nearest hundredth

5 0

3 years ago

If the ratio of the length of segment AC to the length of segment CB is 3:1, what is the y-coordinate of point C?

Yuki888 [10]

Answer:

The coordinates of point C are (8,8.5)

Step-by-step explanation:

The picture of the question in the attached figure

Let

$(C_x,C_y)$ ----> coordinates of point C

we have that

The horizontal distance AB is equal to

$AB_x=10-2=8\ units$

The vertical distance AB is equal to

$AB_y=10-4=6\ units$

Find the horizontal coordinate of point C

we know that

$\frac{AC}{CB}=\frac{3}{1}$

$\frac{AC_x}{CB_x}=\frac{3}{1}$

$AC_x=3CB_x$ ----> equation A

$AC_x+CB_x=8$ ----> equation B

substitute equation A in equation B

$3CB_x+CB_x=8$

$4CB_x=8\\CB_x=2$

$AC_x=3(2)=6$

The x-coordinate of point C is equal to the x-coordinate of point A plus the horizontal distance between the point A and point C

$C_x=A_x+AC_x=2+6=8$

Find the vertical coordinate of point C

we know that

$\frac{AC}{CB}=\frac{3}{1}$

$\frac{AC_y}{CB_y}=\frac{3}{1}$

$AC_y=3CB_y$ ----> equation A

$AC_y+CB_y=6$ ----> equation B

substitute equation A in equation B

$3CB_y+CB_y=6$

$4CB_y=6\\CB_y=1.5$

$AC_y=3(1.5)=4.5$

The y-coordinate of point C is equal to the y-coordinate of point A plus the vertical distance between the point A and point C

$C_y=A_y+AC_y=4+4.5=8.5$

therefore

The coordinates of point C are (8,8.5)

5 0

3 years ago

Which trinomials are perfect square trinomials?

lora16 [44]

Perfect square is
a²+2ab+b²

so just take the square root of the end ones and add then double to get middle term

A.
m+10=10m, doubled is 20m
nope

B.
m+5=5m, doubled is 10m, yep

C.
m+2√15=fancy thing that won't get to 36m

D.
m+12=12m, doubled is 24m, yep

B and D

3 0

3 years ago

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