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3 years ago

1. Find the diameter of a ball that rolls 100 feet after 60 revolutions.

Mathematics

1 answer:

Andre45 [30]3 years ago

7 0

Answer:

Correct option: C (it is missing the point)

0.53

Step-by-step explanation:

When a ball rolls one revolution, the distance travelled is the length of its circunference, that is:

Circunference = pi * diameter

So, to solve this question, we can use a rule of three:

1 revolution -> pi * d

60 revolutions -> 100 feet

100 = 60 * pi * d

d = 100 / (60 * pi) = 0.53 feet

Correct option: C (it is missing the point).

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Simplify the expression 2x(4 + x - 9 + 3x)

sammy [17]

The answer is d 8x^2 - 10

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3 years ago

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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= $s=32.66$

5 0

3 years ago

HURRY !!

LekaFEV [45]

Answer:

B. In step 2, marquis should have interpreted the results as x _< - 9.2, which means that x is less than or equal to -9.2

Step-by-step explanation:

Step 1 is correct.

Step 2.

-9.2 >= x

Subtract x from both sides.

-x - 9.2 >= 0

Add 9.2 to both sides.

-x >= 9.2

Divide both sides by -1. When you multiply or divide both sides of an inequality, the inequality sign changes direction.

x <= -9.2

The first error is in Step 2.

Answer:

B. In step 2, marquis should have interpreted the results as x _< - 9.2, which means that x is less than or equal to -9.2

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3 years ago

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In a 45 45 90 right triangle the length of the hypotenuse is 15/2 what is length on one of the legs

Nikitich [7]

Hi there!

For any 45 45 90 right triangle, the length of the hypotenuse is always the square root of 2 times one of the legs.

To get the lengths of the leg, let's divide the length of the hypotenuse by the square root of 2.

We get the following:

$\frac{15}{ 2 \sqrt{2} }$

When simplifying fractions like this, we want to avoid having radicals on the bottom. In order to remove the radical from the denominator, let's multiply the numerator and the denominator by the square root of 2.

We get the following:

$\frac{15 \sqrt{2} }{4}$

That's your answer.

Have an awesome day! :)

- collinjun0827, Junior Moderator

8 0

3 years ago

What is 1 /7 as a decimal rounded to 3 decimal places?

Nostrana [21]

Answer:

0.143

Step-by-step explanation:

You need to convert 1/7 to have a denominator of either 100 or 10. We can do 100.

1/7 = ?/100

then you need to divide 100/7 to find the scale factor which in this case is 14.286

then you can insert it into the equation

1/7 = 1 * 14.286/100

you end up with

14.286/100

then you can dived the two

0.14286 is what you end up with

but since it says rounded to the 3rd decimal place you go to the 3rd which is 2.

To round it you look at the 4th number which is 8.

<em>5 and above give it a shove up</em>

So now its 0.143

Hope this helped :)

7 0

3 years ago