MATHEMATICS MIDDLE SCHOOL

Write 103 as a multiplication expression having repeated factors

Answers

Answer 1

Answer: 10³=10×10×10=1000 :)

Answer 2

Answer: 50 times 2 pluse 11.5 times 2

The missing value is the height, and it's equal to 746 centimeters, approximately.

Step-by-step explanation:

The complete question is

Find the missing dimension of the cylinder. Round your answer to the nearest whole number. Volume = 10,000π in. The radius is 16

A cylinder volume is defined by

$V= \pi r^(2) h$

Where $V=600,000 }cm^(3)$ and $r=16cm$ .

Replacing given values, we have

$600,000=\pi (16)^(2)h$

Solving for the height, we have

$h=(600,000)/(\pi 256) \approx (600,000)/(803.84) \approx 746$

Therefore, the missing value is the height, and it's equal to 746 centimeters, approximately.

Final answer:

To find the missing radius of a cylinder given its volume of 600,000 cm³, we use the formula r = √(V/π) assuming unit height, which upon calculation gives an approximate radius of 437 cm, rounded to the nearest whole number.

Explanation:

To find the missing radius of the cylinder when given the volume, we use the formula for the volume of a cylinder: V = πr²h, where V is the volume, r is the radius, and h is the height of the cylinder. As we are given the volume and need to find the radius (r), we rearrange the formula to solve for r:

r = √(V/πh)

Since the height (h) is not provided in the question itself, we must assume that it is either known or that the cylinder is such that the volume and radius alone are sufficient to determine the missing dimension (possibly a cylinder with unit height). In such a case, the formula simplifies to: r = √(V/π).

Using the provided volume of 600,000 cm³, the calculation would be:

r = √(600,000 cm³/π)

This equation can be input into a calculator to find the numerical value of r. Let's proceed with this:

r ≈ √(600,000 cm³/3.14159)

r ≈ √(191,000)

r ≈ 437 cm

This calculation gives us the approximate value for the radius, rounded to the nearest whole number. However, it is crucial to have the height of the cylinder to make an accurate calculation. In the absence of the height, the solution would need to treat the cylinder as having a unit height or some other given measurement.

Learn more about cylinder volume here:

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The paths of two runners cross at a stop sign. One runner is heading south at a constant rate of 6.5 miles per hour while the other runner is heading west at a constant rate of 7 miles per hour. How fast is the distance between them changing after 10 minutes?

Answers

Answer:

The distance between them changing after 10 minutes will be 9.553 mph.

Step-by-step explanation:

The paths of two runners cross at a stop sign (O). One runner is heading south at a constant rate of 6.5 miles per hour towards A while the other runner is heading west at a constant rate of 7 miles per hour towards B.

So, after 10 minutes the first runner covers a distance of $6.5 * (10)/(60) = 1.083$ miles and the second runner covers a distance of $7 * (10)/(60) = 1.167$ miles.

Therefore, after 10 minutes their distance will be $\sqrt{(1.083)^(2) + (1.167)^(2)} = 1.592$ miles.

Now, the distance between them is given by

AB² = OA² + OB²

Now, differentiating this equation with respect to time t (in hours) we get

$2(AB) (d(AB))/(dt) = 2(OA) (d(OA))/(dt) + 2(OB) (d(OB))/(dt)$

⇒ $(AB) (d(AB))/(dt) = (OA) (d(OA))/(dt) + (OB) (d(OB))/(dt)$

⇒ $1.592 * (d(AB))/(dt) = 1.083 * 6.5 + 1.167 * 7 = 15.208$

⇒ $(d(AB))/(dt) = 9.553$ mph.

Therefore, the distance between them changing after 10 minutes will be 9.553 mph. (Answer)

Final answer:

The distance between the two runners is not changing after 10 minutes.

Explanation:

To find the rate of change of the distance between the two runners, we can use the concept of relative velocity. The distance is changing due to the motion of both runners, so we need to find the rate at which each runner is approaching or moving away from the other. Since one runner is heading south and the other is heading west, their velocities are perpendicular to each other. We can use the Pythagorean theorem to find their combined velocity and then calculate the rate of change of the distance between them.

Let's consider the southward runner as Runner A and the westward runner as Runner B. The velocity of A is 6.5 miles per hour, and the velocity of B is 7 miles per hour. After 10 minutes, the distance traveled by A can be calculated as (6.5 miles/hour) * (10/60) hours = 1.083 miles. The distance traveled by B can be calculated as (7 miles/hour) * (10/60) hours = 1.167 miles.

Using the Pythagorean theorem, we can calculate the distance between the two runners after 10 minutes:

Distance = sqrt((1.083 miles)^2 + (1.167 miles)^2) ≈ 1.563 miles

To find the rate of change of the distance between them, we can differentiate the equation for the distance with respect to time:

d(Distance)/dt = (1/2)*((2*(1.083 miles)*(0))/(sqrt((1.083 miles)^2 + (1.167 miles)^2))) + (1/2)*((2*(1.167 miles)*(0))/(sqrt((1.083 miles)^2 + (1.167 miles)^2))) = 0

Therefore, the distance between the two runners is not changing after 10 minutes.

Learn more about Relative velocity here:

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What is the LCD of 1/2 and 2/17?
A.1
B.17
C.19
D.34

Answers

The lcd is 34. So D would be your answer

Answer:

Its 34

Step-by-step explanation:

Tommy has a pet monkey. Every day, his monkey eats 4 apples in the morning. The monkey also eats two bananas for every banana that Tommy eats.Write an equation to describe this situation where x is the number of bananas Tommy eats and y is the total number of pieces of fruit the monkey eats.

Answers

If you would like to write an equation to describe the following situation, you can do this like this:

4 apples in the morning ... 4
x ... the number of bananas Tommy eats
2 bananas for every banana that Tommy eats ... 2 * x
y ... the total number of pieces of fruit the monkey eats

The equation would be as follows: y = 4 + 2 * x.

David lives 3 2/3 miles from the lake. Mariel lives2 1/2 times as far from the lake as David does. How far from the lake does Mariel live?

A.6 1/6miles

B.6 1/3miles

C.7 1/3miles

D.9 1/6miles