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2 years ago

A kids toy ball is in the shape of a sphere and has a diameter of 9 millimeters. What is the volume of the toy ?

Mathematics

2 answers:

Vlad [161]2 years ago

5 0

Answer:

381.7 ... hope this helped

Step-by-step explanation:

Solving forV

≈

381.70351

Katena32 [7]2 years ago

3 0

Answer:

381.7 mm cubed

Step-by-step explanation:

To find the volume of a sphere is V=4 /3πr³

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Since they give you the diameter, you have to divide by 2, so:

9 ÷ 2 = 4.5

When you plug in 4.5, you get you answer.

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Have a good day :)

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Consider the curve defined by the equation y=6x2+14x. Set up an integral that represents the length of curve from the point (−2,

torisob [31]

Answer:

32.66 units

Step-by-step explanation:

We are given that

$y=6x^2+14x$

Point A=(-2,-4) and point B=(1,20)

Differentiate w.r. t x

$\frac{dy}{dx}=12x+14$

We know that length of curve

$s=\int_{a}^{b}\sqrt{1+(\frac{dy}{dx})^2}dx$

We have a=-2 and b=1

Using the formula

Length of curve= $s=\int_{-2}^{1}\sqrt{1+(12x+14)^2}dx$

Using substitution method

Substitute t=12x+14

Differentiate w.r t. x

$dt=12dx$

$dx=\frac{1}{12}dt$

Length of curve= $s=\frac{1}{12}\int_{-2}^{1}\sqrt{1+t^2}dt$

We know that

$\sqrt{x^2+a^2}dx=\frac{x\sqrt {x^2+a^2}}{2}+\frac{1}{2}\ln(x+\sqrt {x^2+a^2})+C$

By using the formula

Length of curve= $s=\frac{1}{12}[\frac{t}{2}\sqrt{1+t^2}+\frac{1}{2}ln(t+\sqrt{1+t^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}[\frac{12x+14}{2}\sqrt{1+(12x+14)^2}+\frac{1}{2}ln(12x+14+\sqrt{1+(12x+14)^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}(\frac{(12+14)\sqrt{1+(26)^2}}{2}+\frac{1}{2}ln(26+\sqrt{1+(26)^2})-\frac{12(-2)+14}{2}\sqrt{1+(-10)^2}-\frac{1}{2}ln(-10+\sqrt{1+(-10)^2})$

Length of curve= $s=\frac{1}{12}(13\sqrt{677}+\frac{1}{2}ln(26+\sqrt{677})+5\sqrt{101}-\frac{1}{2}ln(-10+\sqrt{101})$

Length of curve= $s=32.66$

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3 years ago

Which statement holds true for a skewed histogram showing a distribution of the weights of students in a class?

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3 years ago

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Your friend has $90 when he goes to the fair. He spends $5 to enter the fair and $15 on food. Rides at the fair cost $1.50 per r

Maksim231197 [3]

Answer: Option 'B' is correct.

Step-by-step explanation:

Since we have given that ,

Total money he takes while going to the fair = $90

Money he spends to enter the fair = $5

Money he spends on food =$15

Total he spent now is given by

$\$5+\$15=\$20$

Now, he spend on rides at the fair i.e. 1.50 per ride .

Let the number of rides be x

So, cost incurred on rides = 1.5x

So, the spending money can be expressed as

$20+1.50x$

Now, remaining money left to him after spending on x rides too is

$90-(1.50x+20)\\\\=90-1.50x-20\\\\=70-1.5x$

Let f(x) denotes the function used to determine the money he has left over after rides .

So it becomes

$f(x)=70-1.50x\\\\f(x)=-1.50x+70$

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2 years ago

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