All categories

3 years ago

11. A carousel has a diameter of 50 feet. To the nearest foot, how far does a child

Mathematics

2 answers:

aliya0001 [1]3 years ago

6 0

Answer:

1256 ft

Step-by-step explanation:

The circumference of a circle tell us how long is the line which enclose the circle. So, after 1 revolution a child seated near the outer edge travels a distance equal to the circumference of the carousel. If 8 revolutions are made the distance travelled will be 8 times the circumference.

Circumference = π · diameter = π · 50 ft = 157 ft

Distance travelled = 8 · 157 ft = 1256 ft

Ivan3 years ago

5 0

Answer:

1257 ft.

50 x 3.14 = 157.1

8 x 157.1 = 1257

You might be interested in

Help needed ASAP! Please

Marina CMI [18]

It is infinitely many solutions I hope this helps

4 0

3 years ago

Read 2 more answers

Evaluate the following integral (Calculus 2) Please show step by step explanation!

Nuetrik [128]

Answer:

$4\ln \left| \dfrac{1}{3}\sqrt{9+(\ln x)^2} + \dfrac{1}{3}\ln x \right|+\text{C}$

Step-by-step explanation:

Fundamental Theorem of Calculus

$\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))$

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given indefinite integral:

$\displaystyle \int \dfrac{4}{x\sqrt{9+(\ln(x))^2}}\:\:\text{d}x$

Rewrite 9 as 3²:

$\implies \displaystyle \int \dfrac{4}{x\sqrt{3^2+(\ln(x))^2}}\:\:\text{d}x$

Integration by substitution

$\boxed{\textsf{For }\sqrt{a^2+x^2} \textsf{ use the substitution }x=a \tan\theta}$

$\textsf{Let } \ln x=3 \tan \theta$

$\begin{aligned}\implies \sqrt{3^2+(\ln x)^2} & =\sqrt{3^2+(3 \tan\theta)^2}\\ & = \sqrt{9+9\tan^2 \theta}\\ & = \sqrt{9(1+\tan^2 \theta)}\\ & = \sqrt{9\sec^2 \theta}\\ & = 3 \sec\theta\end{aligned}$

Find the derivative of ln x and rewrite it so that dx is on its own:

$\implies \ln x=3 \tan \theta$

$\implies \dfrac{1}{x}\dfrac{\text{d}x}{\text{d}\theta}=3 \sec^2\theta$

$\implies \text{d}x=3x \sec^2\theta\:\:\text{d}\theta$

Substitute everything into the original integral:

$\begin{aligned} \implies \displaystyle \int \dfrac{4}{x\sqrt{9+(\ln(x))^2}}\:\:\text{d}x & = \int \dfrac{4}{3x \sec \theta} \cdot 3x \sec^2\theta\:\:\text{d}\theta\\\\ & = \int 4 \sec \theta \:\: \text{d}\theta\end{aligned}$

Take out the constant:

$\implies \displaystyle 4 \int \sec \theta\:\:\text{d}\theta$

$\boxed{\begin{minipage}{7 cm}\underline{Integrating $\sec kx$}\\\\$\displaystyle \int \sec kx\:\text{d}x=\dfrac{1}{k} \ln \left| \sec kx + \tan kx \right|\:\:(+\text{C})$\end{minipage}}$

$\implies 4\ln \left| \sec \theta + \tan \theta \right|+\text{C}$

$\textsf{Substitute back in } \tan\theta=\dfrac{1}{3}\ln x :$

$\implies 4\ln \left| \sec \theta + \dfrac{1}{3}\ln x \right|+\text{C}$

$\textsf{Substitute back in } \sec\theta=\dfrac{1}{3}\sqrt{9+(\ln x)^2}:$

$\implies 4\ln \left| \dfrac{1}{3}\sqrt{9+(\ln x)^2} + \dfrac{1}{3}\ln x \right|+\text{C}$

Learn more about integration by trigonometric substitution here:

brainly.com/question/28157322

brainly.com/question/28156093

8 0

2 years ago

Ever bought 6 pounds and 7 ounces of pomegranates 5 pounds of melon and 15 ounces of lemon what is the combined weight of the fr

DaniilM [7]

Answer:

12 pounds, 6 ounces.

Step-by-step explanation:

First, add up both the pounds. 6+5=11 . Then, add up the ounces. 7+15=22 To simplify, since ounces make up pounds, and 16 ounces are in one pound, you would do 22 divided by 16. This will end in a decimal so take the highest number of 16 that can go into 22, which is 1. Subtract 16 from 22 to get the new number of ounces. This would be 6. Then, add 1 to the number of pounds. This would be 12. The simplified/combined answer is 12 pounds and 6 ounces.

4 0

3 years ago

A company was able to increase its staff from 127 employees to 204

alekssr [168]

The percentage increase in staff was 60.6%.

8 0

3 years ago

What is the image point of (-1, -7) after a translation left 3 units and up 2 units?

3241004551 [841]

Answer:

(-4,-5)

Step-by-step explanation: