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3 years ago

A circle centered at the origin contains the point

Mathematics

1 answer:

valentina_108 [34]3 years ago

6 0

Answer:

Yes, the distance from the origin to the point (8,√17) is 9 units.

Step-by-step explanation:

The equation of a circle centered at the origin with radius , r has equation:

${x}^{2} + {y}^{2} = {r}^{2}$

Since the circle passes through (0,-9), the radius is 9 units because (0,-9) is 9 units from the origin.

We substitute the radius to get:

${x}^{2} + {y}^{2} = {9}^{2}$

${x}^{2} + {y}^{2} = 81$

If (8,√17) lies on this circle, then it must satisfy this equation:

${8}^{2} + { (\sqrt{17} )}^{2} = 64 + 17 = 81$

This is True.

This means the distance from (8,√17) is 9 units from the origin.

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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:

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

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

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

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

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

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3 years ago

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vampirchik [111]

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Step-by-step explanation:

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iVinArrow [24]

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zaharov [31]

Answer:

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Step-by-step explanation:

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= ( 251 - 248 ) ÷ ( 2005 - 1965 )

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