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3 years ago

Simplify... thank you

Mathematics

1 answer:

loris [4]3 years ago

6 0

First simplify the radical then simplify the fraction then get the root iut of the denominator, you should get the second one

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At the beginning of the school year, the 7th grade class at Oak Hill Middle School has 480 students. There are 270 girls and 210

Dimas [21]

Answer:

Part 1: 43.75%

Part 2: 44.07%

Step-by-step explanation:

Hello!

(Pt.1) First, set up a ratio $210/480$ . Next, you use long division I got the percent 43.75. After that, you subtract 6 from the girls group, (because of them moving away and then more coming back.) and 2 from the boys group. Then, you subtract those from the school "population" and you get 472 as the final population. So then you set up another ratio, $208/472$ . I got a percent of 44.07% from that.

Thanks For Reading!

7 0

2 years ago

58:27

Nina [5.8K]

Answer:

the answer is C, 18 inches width and 7 inches height

5 0

3 years ago

Read 2 more answers

You hit a golf ball 90 yards. It travels three-fourths of the distance to the hole. Write an equation you can use to find the di

artcher [175]

Answer:

90=3/4 + d

Explanation :

Where:

90 represents the yard

3/4 represents distance travelled by ball

d represents distance from tee to the hole.

Hence:

90=3/4 + d

7 0

3 years ago

Read 2 more answers

Find the absolute extrema for f(x,y)=4-x^2-y^4+1/2y^2 over the closed disk D:x^2+y^2 is less than or equal to 1

algol [13]

Find the critical points of $f(x,y)$ :

$\dfrac{\partial f}{\partial x}=-2x=0\implies x=0$

$\dfrac{\partial f}{\partial y}=y-4y^3=y(1-4y^2)=0\implies y=0\text{ or }y=\pm\dfrac12$

All three points lie within $D$ , and $f$ takes on values of

$\begin{cases}f(0,0)=4\\f\left(0,-\frac12\right)=\frac{65}{16}\\f\left(0,\frac12\right)=\frac{65}{16}\end{cases}$

Now check for extrema on the boundary of $D$ . Convert to polar coordinates:

$f(x,y)=f(\cos t,\sin t)=g(t)=4-\cos^2-\sin^4t+\dfrac12\sin^2t=3+\dfrac32\sin^2t-\sin^4t$

Find the critical points of $g(t)$ :

$\dfrac{\mathrm dg}{\mathrm dt}=3\sin t\cos t-4\sin^3t\cos t=\sin t\cos t(3-4\sin^2t)=0$

$\implies\sin t=0\text{ or }\cos t=0\text{ or }\sin t=\pm\dfrac{\sqrt3}2$

$\implies t=n\pi\text{ or }t=\dfrac{(2n+1)\pi}2\text{ or }\pm\dfrac\pi3+2n\pi$

where $n$ is any integer. There are some redundant critical points, so we'll just consider $0\le t< 2\pi$ , which gives

$t=0\text{ or }t=\dfrac\pi3\text{ or }t=\dfrac\pi2\text{ or }t=\pi\text{ or }t=\dfrac{3\pi}2\text{ or }t=\dfrac{5\pi}3$

which gives values of

$\begin{cases}g(0)=3\\g\left(\frac\pi3\right)=\frac{57}{16}\\g\left(\frac\pi2\right)=\frac72\\g(\pi)=3\\g\left(\frac{3\pi}2\right)=\frac72\\g\left(\frac{5\pi}3\right)=\frac{57}{16}\end{cases}$

So altogether, $f(x,y)$ has an absolute maximum of 65/16 at the points (0, -1/2) and (0, 1/2), and an absolute minimum of 3 at (-1, 0).

5 0

3 years ago

Find all the powers of 4 in the range 4 through 1000

marissa [1.9K]

Powers of 4 are like 4^1, 4^2, 4^3 and so on
remember that 4^x means 4 times itself x times for example
4^3=4 times iteslef 3 times=4 times 4 times 4

so the multipules of the powers of 4 are just 4 times of the previous
so we will list

4^1=4
4^2=16
4^3=64
4^4=256
4^5=1024

1024 is already more than 1000 so the list stops and is
1,16,64,256

8 0

3 years ago