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3 years ago

If the ratio of radius of two spheres is 4:7, the ratio of their volume is?

Mathematics

1 answer:

Kazeer [188]3 years ago

6 0

Answer:

64 : 343

Step-by-step explanation:

First use the radii to find the volume

1) Radius of first sphere is 4 (taken from 4:7 ratio)

Insert it into the equation for volume of a sphere: V=4 /3πr^3

V = (4/3)(π)(4^3)

V = (4/3)(π)(64)

V = 256/3 π

Volume of the first sphere = 256/3 π

2) Radius of the second sphere is 7 (also taken from 4:7 ratio)

Insert it into the equation for volume of a sphere: V=4 /3πr^3

V = (4/3)(π)(7^3)

V = (4/3)(π)(343)

V = 1372/3 π

Volume of the second sphere = 1372/3 π

Next, calculate the ratio by dividing the two numbers

256/3 π ÷ 1372/3 π

Answer should be 64 : 343

The simple way to do this problem is to just cube the numbers:

4:7 becomes 4^3 : 7^3 = 64 : 343

Either way works.

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Answer:

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Step-by-step explanation:

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3 years ago

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a. For what values of x does f (x )equals 3 x plus 3 sine x have a horizontal tangent line? b. For what values of x does f (x )

laila [671]

Answer:

(a)Therefore the value of x= $\pi$

(b) Therefore the value of x $=\frac{\pi}{2}$

Step-by-step explanation:

Horizontal tangent line: The first order derivative of a function gives the slope of the tangent of the function. The slope of horizontal line is zero.If the slope of tangent line is zero then the tangent line is called horizontal tangent line.

(a)

Given function is,

$f(x)= 3x+3sin x$

Differential with respect to x

$f'(x)=3+3cos x$

For horizontal tangent line, f'(x)=0

3+ 3 cos x= 0

⇒3 cos x=-3

⇒cos x=-1

⇒x = 180° $=\pi$

Therefore the value of x= $\pi$

(b)

Given that, the slope is 3.

Then,f'(x)=3

3+ 3 cos x= 3

⇒3 cos x= 3-3

⇒cos x=0

⇒x = 90° $=\frac{\pi}{2}$

Therefore the value of x $=\frac{\pi}{2}$

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3 years ago

What is the range of y=−x^2−2x+3? x≤−4 x≤4 x≥−4 x≥4

saveliy_v [14]

Answer:

Domain: (−∞,∞),{x|x∈R}

Range: (−∞,4],{y|y≤4

Hope this helps

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3 years ago

How would i graph f(2x)=2x+3

SpyIntel [72]

See the attached, the line going vertically is at -0.7.

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3 years ago

Find the component form of the vector v ⃗ with ‖v ⃗ ‖=4√3 when drawn in standard position v ⃗ lies in Quadrant II and makes a 30

nydimaria [60]

The answer:

first of all, we should know that the expression of a vector V (a, b) can be written as follow:

V = r (Vx i + Vyj), where r is the length of the vector, it is r = sqrt(V²x + V²y)
Vx is the component lying on the x-axis and Vy on the y-axis

v ⃗ lies in Quadrant II, means Vx is less than 0 (negative)

so Vx= -r sin30° and Vy= rcos30°

r= ‖v ⃗ ‖=4√3

so we have v = - 4√3sin30° i + 4√3 cos30° j

the components are

v(- 4√3sin30°, 4√3 cos30°) = (-2√3, 4√3 cos30°)

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3 years ago

If the ratio of radius of two spheres is 4:7, the ratio of their volume is?​

If the ratio of radius of two spheres is 4:7, the ratio of their volume is?