All categories

4 years ago

What is the measure of an exterior angle of a rectangle of a regular 11-sided polygon?

Mathematics

2 answers:

Taya2010 [7]4 years ago

5 0

90 degrees because a rectangle has all right angles and a right angle is 90 degrees

horsena [70]4 years ago

4 0

$180 \div 11 =$

You might be interested in

Calculate the quotient. Simplify your results 2/7 divided 1 2/7

Elden [556K]

Answer:

1 4/7

Step-by-step explanation:

3 0

3 years ago

Help with q25 please. Thanks.

Westkost [7]

First, I'll make f(x) = sin(px) + cos(px) because this expression shows up quite a lot, and such a substitution makes life a bit easier for us.

Let's apply the first derivative of this f(x) function.

$f(x) = \sin(px)+\cos(px)\\\\f'(x) = \frac{d}{dx}[f(x)]\\\\f'(x) = \frac{d}{dx}[\sin(px)+\cos(px)]\\\\f'(x) = \frac{d}{dx}[\sin(px)]+\frac{d}{dx}[\cos(px)]\\\\f'(x) = p\cos(px)-p\sin(px)\\\\ f'(x) = p(\cos(px)-\sin(px))\\\\$

Now apply the derivative to that to get the second derivative

$f''(x) = \frac{d}{dx}[f'(x)]\\\\f''(x) = \frac{d}{dx}[p(\cos(px)-\sin(px))]\\\\ f''(x) = p*\left(\frac{d}{dx}[\cos(px)]-\frac{d}{dx}[\sin(px)]\right)\\\\ f''(x) = p*\left(-p\sin(px)-p\cos(px)\right)\\\\ f''(x) = -p^2*\left(\sin(px)+\cos(px)\right)\\\\ f''(x) = -p^2*f(x)\\\\$

We can see that f '' (x) is just a scalar multiple of f(x). That multiple of course being -p^2.

Keep in mind that we haven't actually found dy/dx yet, or its second derivative counterpart either.

-----------------------------------

Let's compute dy/dx. We'll use f(x) as defined earlier.

$y = \ln\left(\sin(px)+\cos(px)\right)\\\\y = \ln\left(f(x)\right)\\\\\frac{dy}{dx} = \frac{d}{dx}\left[y\right]\\\\\frac{dy}{dx} = \frac{d}{dx}\left[\ln\left(f(x)\right)\right]\\\\\frac{dy}{dx} = \frac{1}{f(x)}*\frac{d}{dx}\left[f(x)\right]\\\\\frac{dy}{dx} = \frac{f'(x)}{f(x)}\\\\$

Use the chain rule here.

There's no need to plug in the expressions f(x) or f ' (x) as you'll see in the last section below.

Now use the quotient rule to find the second derivative of y

$\frac{d^2y}{dx^2} = \frac{d}{dx}\left[\frac{dy}{dx}\right]\\\\\frac{d^2y}{dx^2} = \frac{d}{dx}\left[\frac{f'(x)}{f(x)}\right]\\\\\frac{d^2y}{dx^2} = \frac{f''(x)*f(x)-f'(x)*f'(x)}{(f(x))^2}\\\\\frac{d^2y}{dx^2} = \frac{f''(x)*f(x)-(f'(x))^2}{(f(x))^2}\\\\$

If you need a refresher on the quotient rule, then

$\frac{d}{dx}\left[\frac{P}{Q}\right] = \frac{P'*Q - P*Q'}{Q^2}\\\\$

where P and Q are functions of x.

-----------------------------------

This then means

$\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^2 + p^2\\\\\frac{f''(x)*f(x)-(f'(x))^2}{(f(x))^2} + \left(\frac{f'(x)}{f(x)}\right)^2 + p^2\\\\\frac{f''(x)*f(x)-(f'(x))^2}{(f(x))^2} +\frac{(f'(x))^2}{(f(x))^2} + p^2\\\\\frac{f''(x)*f(x)-(f'(x))^2+(f'(x))^2}{(f(x))^2} + p^2\\\\\frac{f''(x)*f(x)}{(f(x))^2} + p^2\\\\$

Note the cancellation of -(f ' (x))^2 with (f ' (x))^2

------------------------------------

Let's then replace f '' (x) with -p^2*f(x)

This allows us to form ( f(x) )^2 in the numerator to cancel out with the denominator.

$\frac{f''(x)*f(x)}{(f(x))^2} + p^2\\\\\frac{-p^2*f(x)*f(x)}{(f(x))^2} + p^2\\\\\frac{-p^2*(f(x))^2}{(f(x))^2} + p^2\\\\-p^2 + p^2\\\\0\\\\$

So this concludes the proof that $\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^2 + p^2 = 0\\\\$ when $y = \ln\left(\sin(px)+\cos(px)\right)\\\\$

Side note: This is an example of showing that the given y function is a solution to the given second order linear differential equation.

7 0

3 years ago

Wires manufactured for use in a computer system are specified to have resistances between .12 and .14 ohms. The actual measured

White raven [17]

Answer: a) 0.9544996

b) 0.9999366

Step-by-step explanation:

Given : The actual measured resistances of wires produced by company A have a normal probability distribution with mean $\mu=0.13$ ohm and standard deviation $s=0.005$ ohm.

Wires manufactured for use in a computer system are specified to have resistances between .12 and .14 ohms.

Let x be the random variable that represents the value of resistance in wires.

Using formula for z-score , $z=\dfrac{x-\mu}{s}$

The z-value at x= 0.12 will be

$z=\dfrac{0.12-0.13}{0.005}=-2$

The z-value at x= 0.14 will be

$z=\dfrac{0.14-0.13}{0.005}=2$

The p-value : $P(-2$

$=0.9772498-(1-P(z$

Hence, the probability that a randomly selected wire from company A’s production will meet the specifications = 0.9544996

b) Sample size : n= 4

Using formula for z-score , $z=\dfrac{x-\mu}{\dfrac{s}{\sqrt{n}}}$

The z-value at x= 0.12 will be

$z=\dfrac{0.12-0.13}{\dfrac{.005}{\sqrt{4}}}=-4$

The z-value at x= 0.14 will be

$z=\dfrac{0.14-0.13}{\dfrac{.005}{\sqrt{4}}}=4$

The p-value : $P(-4$

$=0.9999683-(1-P(z$

The probability that all four in a randomly selected system will meet the specifications = 0.9999366

3 0

4 years ago

Karen has 4h storybooks. Karen's storybook collection is 2/3 of what Mary's collection is. How many storybooks do they have in a

dedylja [7]

If half of Karen's collection (4) is 1/3 of Mary's, and half of Karen's collection is 2, then 2 x 3 is how many Mary has, right? Once you know how many books Mary has, you can add how many Karen has to get your answer.

7 0

4 years ago

What is the approximate area of a semicircle with radius of 16 meters? Use 3.14

hoa [83]

Answer:

803.4

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers