It will be irrational. The sum of any irrational and rational number will ALWAYS result in a irrational answer. Khan Academy has a video on this if you want to watch it.

3 0

2 years ago

a spherical balloon is deflated at a rate of 256pi/3 cm^3/sec. at what rate is the radius of the balloon changing when the radiu

Hunter-Best [27]

What you need to look for is $\frac { dr }{ dt }$ when r=8.

Now:

$Volume\quad of\quad a\quad sphere:\\ \\ V=\frac { 4 }{ 3 } \pi { r }^{ 3 }$

$\therefore \quad \frac { dV }{ dr } =\frac { 4 }{ 3 } \pi \cdot 3{ r }^{ 2 }=4\pi { r }^{ 2 }\\ \\ \therefore \quad \frac { dr }{ dV } =\frac { 1 }{ \frac { dV }{ dr } } =\frac { 1 }{ 4\pi { r }^{ 2 } }$

$And:\\ \\ \frac { dV }{ dt } =-\frac { 256\pi }{ 3 } \\ \\ Therefore:\\ \\ \frac { dr }{ dt } =\frac { dr }{ dV } \cdot \frac { dV }{ dt }$

$\\ \\ =\frac { 1 }{ 4\pi { r }^{ 2 } } \cdot -\frac { 256\pi }{ 3 } \\ \\ =-\frac { 256 }{ 12 } \cdot \frac { \pi }{ \pi } \cdot \frac { 1 }{ { r }^{ 2 } }$

$\\ \\ =-\frac { 64 }{ 3{ r }^{ 2 } } \\ \\ When\quad r=8,\\ \\ \frac { dr }{ dt } =-\frac { 64 }{ 3\cdot { 8 }^{ 2 } } =-\frac { 1 }{ 3 } \\ \\ Answer:\quad -\frac { 1 }{ 3 } \quad cm/sec$

3 0

3 years ago

If frank has 24 pennies 62 nickles 55 dimes 16 quarters and 19 fifty cent pieces how much money does he have

Nitella [24]

Answer:

Frank has $22.34.

Step-by-step explanation:

24 pennies - 0.01 x 24 = 0.24

62 nickels - 0.05 x 62 = 3.10

55 dimes - 0.10 x 55 = 5.50

16 quarters - 0.25 x 16 = 4.00

19 half dollar (50cent) - 0.50 x 19 = 9.50

0.24 + 3.10 + 5.50 + 4.00 + 9.50 = 22.34

8 0

3 years ago

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Given the function F(x), you can get a picture of the graph of its inverse F -1(x) by flipping the original graph of F(x) over t

Xelga [282]

The inverse of a function is found by switching the x and the y in the equation and solving for the new y. Therefore, when you have a function plotted on an x/y coordinate plane, you can find its inverse by switching the x and y coordinates and plotting the new points. This process makes the function and the inverse be symmetrical about the line y = x. Your choice is C.

7 0

3 years ago

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