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Anestetic [448]

3 years ago

15

Which equation could be used to solve the problem? Larry skated 7200 feet in 3 minutes. How many feet per minute did he skate (x

)? A. 7200 feet • 3 minutes = x B. 7200 feet + 3 minutes = x C. 7200 feet ÷ 3 minutes = x D. 3 minutes ÷ 7200 feet = x please help

1 answer:

kari74 [83]3 years ago

7 0

A. 7200 feet ÷ 3 minutes = x

Hope it helps!

And happy Pi Day! :D

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Why is exponential functions important to know when owning a business ?

Ronch [10]

Answer:

You need to know your math!

Step-by-step explanation:

If your gonna start a business you have to know your math, sure you can hire people but people work for cash, so when you start out on your own with your business you need to know your math so you can keep the business running. Hope this helps! :)

4 0

3 years ago

How many centimeters in 60 inches?

ivann1987 [24]

152.4cm. 2.54cm = 1in. 60in x (2.54cm/1in) = 152.4cm.

7 0

3 years ago

I'm having trouble with #2. I've got it down to the part where it would be the integral of 5cos^3(pheta)/sin(pheta). I'm not sur

Butoxors [25]

$\displaystyle\int\frac{\sqrt{25-x^2}}x\,\mathrm dx$

Setting $x=5\sin\theta$ , you have $\mathrm dx=5\cos\theta\,\mathrm d\theta$ . Then the integral becomes

$\displaystyle\int\frac{\sqrt{25-(5\sin\theta)^2}}{5\sin\theta}5\cos\theta\,\mathrm d\theta$
$\displaystyle\int\sqrt{25-25\sin^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$
$\displaystyle5\int\sqrt{1-\sin^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$
$\displaystyle5\int\sqrt{\cos^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$

Now, $\sqrt{x^2}=|x|$ in general. But since we want our substitution $x=5\sin\theta$ to be invertible, we are tacitly assuming that we're working over a restricted domain. In particular, this means $\theta=\sin^{-1}\dfrac x5$ , which implies that $\left|\dfrac x5\right|\le1$ , or equivalently that $|\theta|\le\dfrac\pi2$ . Over this domain, $\cos\theta\ge0$ , so $\sqrt{\cos^2\theta}=|\cos\theta|=\cos\theta$ .

Long story short, this allows us to go from

$\displaystyle5\int\sqrt{\cos^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$

to

$\displaystyle5\int\cos\theta\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$
$\displaystyle5\int\dfrac{\cos^2\theta}{\sin\theta}\,\mathrm d\theta$

Computing the remaining integral isn't difficult. Expand the numerator with the Pythagorean identity to get

$\dfrac{\cos^2\theta}{\sin\theta}=\dfrac{1-\sin^2\theta}{\sin\theta}=\csc\theta-\sin\theta$

Then integrate term-by-term to get

$\displaystyle5\left(\int\csc\theta\,\mathrm d\theta-\int\sin\theta\,\mathrm d\theta\right)$
$=-5\ln|\csc\theta+\cot\theta|+\cos\theta+C$

Now undo the substitution to get the antiderivative back in terms of $x$ .

$=-5\ln\left|\csc\left(\sin^{-1}\dfrac x5\right)+\cot\left(\sin^{-1}\dfrac x5\right)\right|+\cos\left(\sin^{-1}\dfrac x5\right)+C$

and using basic trigonometric properties (e.g. Pythagorean theorem) this reduces to

$=-5\ln\left|\dfrac{5+\sqrt{25-x^2}}x\right|+\sqrt{25-x^2}+C$

4 0

3 years ago

Read 2 more answers

I need help please !!!!!!

garri49 [273]

Answer:

And the probability that the first die shows an odd number is 1/2, as is the probability that the second does. Since the dice fall independently, P(both are odd) = P(first is odd)*P(second is odd) = (1/2)*(1/2) = 1/4. Therefore P(at least one is even) = 1 - 1/4 = 3/4.

7 0

3 years ago

Read 2 more answers

The length of a kitchen wall is 24 2/3 feet long. A border will be placed along the wall of the kitchen. If the border strips ar

krek1111 [17]

Total length of the kitchen wall = 24 2/3 feet.

Let us convert 24 2/3 feet into improper fracion.

24 2/3 = (24*3+2)/3 = 74/3 feet.

Length of each strip = 1 3/4 feet.

Let us convert 1/3/4 feet in improper fracion.

1 3/4 feet = (1*4+3)/4 = 7/4 feet.

Total number of strips required = (Total length of the kitchen wall) ÷ (Length of each strip)

= 74/3 feet ÷ 7/4 feet.

Let us convert division sign into multiplication, we get

74/3 × 4/7.

Multiplying across, we get

296/21.

On dividing 296 by 21, we get 14.09 approximately.

14.09 represents more than 14.

So, we can round it to the next whole number, that is 15.

Therefore, 15 strips of border are needed.

5 0

3 years ago