Need some math help

Mathematics

1 answer:

Blababa [14]2 years ago

3 0

Answer:

why do you need help if it gives you the value?

Step-by-step explanation:

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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

Classify the figure in as many ways as possible.

Dima020 [189]

The answer is D.

This figure has 4 sides which makes it a quadrilateral.

This figure has 2 sets of parallel sides which makes it a parallelogram.

This figure has 4 equal sides which makes it a rhombus.

This figure has 4 right angles which makes it a rectangle.

And this figure has both 4 equal sides and 4 equal angles which makes it a square.

To make it easier, all squares are: quadrilaterals, parallelograms, rhombuses, rectangles and of course squares.

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3 years ago

What is the volume of this pyramid? 945 cm³ 1260 cm³ 1890 cm³ 2520 cm³ A pyramid with a right triangular base. The right triangu

notsponge [240]

Answer:

The volume of the pyramid is $1,260\ cm^{3}$