All categories

2 years ago

Explain how to determine the diameter of any circle given the circumference.

Mathematics

1 answer:

Murrr4er [49]2 years ago

3 0

Answer:

circle of diagram (89).&"71

You might be interested in

What is the value of z in the equation 4×2-z=7?

sladkih [1.3K]

4×2-z=7
⇒ 8 - z = 7
⇒ 8 - 7 = z
⇒ 1 = z

3 0

2 years ago

There are three motors available to repair Ralph’s vacuum cleaner. Motor #1 has a 65% chance of breaking by the end of the week.

Orlov [11]

Answer:

0.619

Step-by-step explanation:

from the question we have the following data:

probability of motor 1 breaking = 65% = 0.65

probability of motor 2 breaking = 35% = 0.35

probability of motor 3 breaking = 5% = 0.05

since we have 3 motors the probability of any of them breaking down is = $\frac{1}{3}$

but what the question requires from us is the conditional probability of the first one being installed

we have to solve this questions using bayes theorem

such that:

$\frac{0.65*\frac{1}{3} }{0.65*\frac{1}{3}+0.35*\frac{1}{3}+0.05*\frac{1}{3} }$

= $\frac{0.2167}{0.2167+0.1167+0.0167}$

= $\frac{0.2167}{0.3501}$

= 0.618966

approximately 0.619

therefore the conditional probability ralph installed the first motor is 0.619

8 0

3 years ago

Dan needs to buy tomatoes to put on 30 Turkey sandwiches if the slices of one tomatoe can go on 4 sandwiches how many tomatoes s

Ipatiy [6.2K]

Dan should buy 8 tomatoes because then he can make 32 slices which is more than enough to put on the sandwiches.

8 0

3 years ago

Read 2 more answers

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

2 years ago

Read 2 more answers

The rectangular prism is to be sliced perpendicular to the shaded face and is to pass through point B, parallel to the front fac

kodGreya [7K]

The dimensions of the rectangular cross section will be 10 centimeters by 18 centimeters

Step-by-step explanation:

As ,we know

The rectangular cross section is parallel to the front face

Which clearly states that

The dimensions of the rectangular cross section is congruent with the dimensions of the front face

Lets assume that dimensions of the front face are 10 centimeters by 18 centimeters

Then ,The dimensions of the cross section will also be 10 centimeters by 18 centimeters

Hence we can say that the dimensions of the rectangular cross section will be 10 centimeters by 18 centimeters

4 0

3 years ago