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3 years ago

9

Solve for r , what is r equal to ?

1 answer:

Ivanshal [37]3 years ago

3 0

Answer:

$r= \sqrt[3]{\frac{3V}{4\pi}}$

Step-by-step explanation:

$V = \frac{4}{3} \pi r^3 \\\\3V = 4\pi r^3 \\\\r^3 = \frac{3V}{4\pi}\\\\\huge \purple {r= \sqrt[3]{\frac{3V}{4\pi}}}$

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Find all solutions of the equation in the interval [0, 2pi).

mina [271]

Answer:

x = 0 , π

Step-by-step explanation:

$-4 \sin x = 1 - cos^2 x$

Rewrite it by using the identity $\sin^2x + \cos^2x = 1$

$=> -4\sin x = \sin^2x$

Add 4sin x to both the sides.

$=> -4\sin x + 4\sin x = sin^2x + 4\sin x$

$=> \sin^2x + 4\sin x = 0$

Take sin x common from the expression in L.H.S.

$=> \sin x(\sin x + 4)=0$

Here , we can get two more equations to find x.

1) $\sin x(\sin x + 4)=0$

Divide both the sides by sin x

$=> \frac{\sin x(\sin x + 4)}{\sin x} = \frac{0}{\sin x}$

$=> \sin x + 4 = 0$

Substract 4 from both the sides.

$=> \sin x + 4 - 4 = 0 - 4$

$=> \sin x = -4$

$=> x = No \; Solution$

2) $\sin x(\sin x + 4)=0$

Divide both the sides by (sin x + 4)

$=> \frac{\sin x(\sin x + 4)}{\sin x + 4} = \frac{0}{\sin x + 4}$

$=> \sin x = 0$

$=> x = 0 \; , \pi$ over interval [0 , 2π).

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3 years ago

mojhsa [17]

Answer:

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Step-by-step explanation:

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3 years ago

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Kristof bought a new terrarium, shaped like a rectangular prism, for his pet snake. The terrarium has a length of 1.8 × 102 cm,

zepelin [54]

Answer:

Volume of rectangular prism in scientific notation is $2.574\cdot10^{6}$ cubic centimeters and in standard form $2574000\text{cm}^{3}$ .

Step-by-step explanation:

Since we know that volume of a rectangular prism is length*breadth*height.

Sides of our rectangular prism are given in scientific notation as $\text{length}=1.8*10^{2},$ $\text{width}=1.3*10^{2}$ and $\text{height}=1.1*10^{2}$ .

Let us substitute our values in volume formula,

$\text{ Volume of rectangular prism}=1.8\cdot 10^{2}\cdot 1.3\cdot 10^{2}\cdot 1.1\cdot 10^{2}$

Upon using exponent product property we will get,

$\text{ Volume of rectangular prism}=1.8\cdot1.3\cdot 1.1\cdot 10^{(2+2+2)}$

$\text{ Volume of rectangular prism}=2.574\cdot10^{6}\text{cm}^{3}$

Now let us convert our volume in standard form as,

$\text{ Volume of rectangular prism}=2.574\cdot1000000\text{cm}^{3}$

$\text{ Volume of rectangular prism}=2574000\text{cm}^{3}$

Therefore, volume of rectangular prism in scientific notation is $2.574\cdot10^{6}$ cubic centimeters and in standard form $2574000\text{cm}^{3}$ .

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3 years ago

Sams coordinates are (2,4) and the theaters coordinates are (5,-2.5) on a grid each unit represents 1 kilometer. Describe Sam's

Ostrovityanka [42]

The theater are relative to Sam 6.5 kilometers south, and 3 kilometers west.

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3 years ago

Use two unit multipliers to convert 4000 square inches to square feet.

tatiyna

Answer:

(4000 in^2) * (1 ft/12 in)^2 = 27 7/9 ft^2

Step-by-step explanation:

4,000 Square Inches =

27.777778 Square Feet

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3 years ago

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