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3 years ago

Given f(x) =x^2 -10x+22 what is the domain of f

Mathematics

1 answer:

fomenos3 years ago

7 0

Answer:

$f(x) = x^2 -10x +22$

And we want to find the domain. And that represent the possible values for x. Since we have a quadratic function we have that the domain would be all the reals, and we can write:

$D= [x \in R]$

Where D represent the domain and R the set of the real numbers.

Step-by-step explanation:

For this case we have the following function:

$f(x) = x^2 -10x +22$

And we want to find the domain. And that represent the possible values for x. Since we have a quadratic function we have that the domain would be all the reals, and we can write:

$D= [x \in R]$

Where D represent the domain and R the set of the real numbers.

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Miley drove 288 miles in 4 1/2 hours.what was mileys average speed in miles per hour?

Norma-Jean [14]

1/2 of an hour is = 30
288 / 4.30=67
The answer is 67 miles per hour.

8 0

3 years ago

How to know if a function is periodic without graphing it ?

zhenek [66]

A function $f(t)$ is periodic if there is some constant $k$ such that $f(t+k)=f(k)$ for all $t$ in the domain of $f(t)$ . Then $k$ is the "period" of $f(t)$ .

Example:

If $f(x)=\sin x$ , then we have $\sin(x+2\pi)=\sin x\cos2\pi+\cos x\sin2\pi=\sin x$ , and so $\sin x$ is periodic with period $2\pi$ .

It gets a bit more complicated for a function like yours. We're looking for $k$ such that

$\pi\sin\left(\dfrac\pi2(t+k)\right)+1.8\cos\left(\dfrac{7\pi}5(t+k)\right)=\pi\sin\dfrac{\pi t}2+1.8\cos\dfrac{7\pi t}5$

Expanding on the left, you have

$\pi\sin\dfrac{\pi t}2\cos\dfrac{k\pi}2+\pi\cos\dfrac{\pi t}2\sin\dfrac{k\pi}2$

and

$1.8\cos\dfrac{7\pi t}5\cos\dfrac{7k\pi}5-1.8\sin\dfrac{7\pi t}5\sin\dfrac{7k\pi}5$

It follows that the following must be satisfied:

$\begin{cases}\cos\dfrac{k\pi}2=1\\\\\sin\dfrac{k\pi}2=0\\\\\cos\dfrac{7k\pi}5=1\\\\\sin\dfrac{7k\pi}5=0\end{cases}$

The first two equations are satisfied whenever $k\in\{0,\pm4,\pm8,\ldots\}$ , or more generally, when $k=4n$ and $n\in\mathbb Z$ (i.e. any multiple of 4).

The second two are satisfied whenever $k\in\left\{0,\pm\dfrac{10}7,\pm\dfrac{20}7,\ldots\right\}$ , and more generally when $k=\dfrac{10n}7$ with $n\in\mathbb Z$ (any multiple of 10/7).

It then follows that all four equations will be satisfied whenever the two sets above intersect. This happens when $k$ is any common multiple of 4 and 10/7. The least positive one would be 20, which means the period for your function is 20.

Let's verify:

$\sin\left(\dfrac\pi2(t+20)\right)=\sin\dfrac{\pi t}2\underbrace{\cos10\pi}_1+\cos\dfrac{\pi t}2\underbrace{\sin10\pi}_0=\sin\dfrac{\pi t}2$

$\cos\left(\dfrac{7\pi}5(t+20)\right)=\cos\dfrac{7\pi t}5\underbrace{\cos28\pi}_1-\sin\dfrac{7\pi t}5\underbrace{\sin28\pi}_0=\cos\dfrac{7\pi t}5$

More generally, it can be shown that

$f(t)=\displaystyle\sum_{i=1}^n(a_i\sin(b_it)+c_i\cos(d_it))$

is periodic with period $\mbox{lcm}(b_1,\ldots,b_n,d_1,\ldots,d_n)$ .

4 0

3 years ago

Plz answer the question attached

Agata [3.3K]

Answer:

y = -2x + 5

Step-by-step explanation:

To find the slope, you need to pick two points and put into the slope formula. It doesn't matter which ones, you will get the right answer regardless. I used (-3, 11) and (2, 1).

$m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\m=\frac{11 -1 }{-3 -2 } \\m=\frac{10 }{-5 } \\m=-2$

Now that you have the slope, you can plug it into point-slope form to find the equation in slope-intercept form. You will also need to plug one of the given points. Again, it doesn't matter which one.

$y-y_{1}=m(x-x_{1} )\\y-1=-2(x-2)\\y-1=-2x+4\\y=-2x+5$

4 0

3 years ago

4/5 n = 9/10<br>solve n

Alex787 [66]

N =9/8
n = 1 1/8

Hope this helpsb☺

6 0

3 years ago

I took $6.00 off an $11.00 item. What % got taken off. How do I figure that out?

jeka94

Answer:

54.5454%

Step-by-step explanation:

6/11=0.545454545454 and that as a percentage is 54.5454%

8 0

3 years ago