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gizmo_the_mogwai [7]
2 years ago
9

Somebody Please Help!!!

Mathematics
1 answer:
Finger [1]2 years ago
4 0

Answer:

11) 153, 85, 238 12) 12, 15, 27

Step-by-step explanation:

To find the area of these shapes, you have to cut them into two seperate shapes as shown the in the image: Shape 1 and Shape 2

11) Let Shape 1 be the rectangle: 17×9=153

let Shape 2 be the triangle: \frac{1}{2}×10×8.5=42.5×2=85

Total area: 153 + 85 = 238

12) Let cut this shape vertically where you'll have a rectangle thats 3 by 4 and a rectangle that's 5 by 3

Shape 1: 3×4=12

Shape 2: 5×3=15

Total area: 15 + 12 = 27

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ira [324]
Let x = 6 = 2y so
3(6 - 2y) + 14y = 8 so
18 - 6y + 14y = 8 so
8y = -10 and
y =  \frac{ - 10}{8} =   - \frac{5}{4}  \\  \\ since \: x = 6 - 2y \\ 6  - 2( \frac{ - 5}{4}) = x  \: so \\ x = 6 +  \frac{10}{4} =  \frac{24}{4} +  \frac{10}{4} =  \frac{34}{4} =  \frac{17}{2}

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3 years ago
Find the value of x in the triangle shown below
pantera1 [17]

Answer:

48 (i might be wrong)

Step-by-step explanation:

180-66-66=48

7 0
2 years ago
100 divided by 235 ?
Alina [70]

Answer:

100 divided by 235=0.425

6 0
2 years ago
Mr. Win owns a toy store. He wants to display 12 new motion toys in the store window. Each toy uses 3 batteries. If N represents
Assoli18 [71]

Answer: See explanation

Step-by-step explanation:

You didn't state the sentences but let me help out based on the information given.

Number of new motion toys = 12

Number of batteries used by each toy = 3

Since N represents the total number of batteries he need, the value of N will be:

= Number of toys × Number of batteries used by each toy

= 12 × 3

= 36

That means N equals 36.

7 0
3 years ago
Find the mass and the center of mass of a wire loop in the shape of a helix (measured in cm: x = t, y = 4 cos(t), z = 4 sin(t) f
Sholpan [36]

Answer:

<u>Mass</u>

\sqrt{17}(\displaystyle\frac{8\pi^3}{3}+32\pi)

<u>Center of mass</u>

<em>Coordinate x</em>

\displaystyle\frac{(\displaystyle\frac{(2\pi)^4}{4}+32\pi)}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}

<em>Coordinate y</em>

\displaystyle\frac{16\pi}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}

<em>Coordinate z</em>

\displaystyle\frac{-16\pi}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}

Step-by-step explanation:

Let W be the wire. We can consider W=(x(t),y(t),z(t)) as a path given by the parametric functions

x(t) = t

y(t) = 4 cos(t)

z(t) = 4 sin(t)  

for 0 ≤ t ≤ 2π

If D(x,y,z) is the density of W at a given point (x,y,z), the mass  m would be the curve integral along the path W

m=\displaystyle\int_{W}D(x,y,z)=\displaystyle\int_{0}^{2\pi}D(x(t),y(t),z(t))||W'(t)||dt

The density D(x,y,z) is given by

D(x,y,z)=x^2+y^2+z^2=t^2+16cos^2(t)+16sin^2(t)=t^2+16

on the other hand

||W'(t)||=\sqrt{1^2+(-4sin(t))^2+(4cos(t))^2}=\sqrt{1+16}=\sqrt{17}

and we have

m=\displaystyle\int_{W}D(x,y,z)=\displaystyle\int_{0}^{2\pi}D(x(t),y(t),z(t))||W'(t)||dt=\\\\\sqrt{17}\displaystyle\int_{0}^{2\pi}(t^2+16)dt=\sqrt{17}(\displaystyle\frac{8\pi^3}{3}+32\pi)

The center of mass is the point (\bar x,\bar y,\bar z)

where

\bar x=\displaystyle\frac{1}{m}\displaystyle\int_{W}xD(x,y,z)\\\\\bar y=\displaystyle\frac{1}{m}\displaystyle\int_{W}yD(x,y,z)\\\\\bar z=\displaystyle\frac{1}{m}\displaystyle\int_{W}zD(x,y,z)

We have

\displaystyle\int_{W}xD(x,y,z)=\sqrt{17}\displaystyle\int_{0}^{2\pi}t(t^2+16)dt=\\\\=\sqrt{17}(\displaystyle\frac{(2\pi)^4}{4}+32\pi)

so

\bar x=\displaystyle\frac{\sqrt{17}(\displaystyle\frac{(2\pi)^4}{4}+32\pi)}{\sqrt{17}(\displaystyle\frac{8\pi^3}{3}+32\pi)}=\displaystyle\frac{(\displaystyle\frac{(2\pi)^4}{4}+32\pi)}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}

\displaystyle\int_{W}yD(x,y,z)=\sqrt{17}\displaystyle\int_{0}^{2\pi}4cos(t)(t^2+16)dt=\\\\=16\sqrt{17}\pi

\bar y=\displaystyle\frac{16\sqrt{17}\pi}{\sqrt{17}(\displaystyle\frac{8\pi^3}{3}+32\pi)}=\displaystyle\frac{16\pi}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}

\displaystyle\int_{W}zD(x,y,z)=4\sqrt{17}\displaystyle\int_{0}^{2\pi}sin(t)(t^2+16)dt=\\\\=-16\sqrt{17}\pi

\bar z=\displaystyle\frac{-16\sqrt{17}\pi}{\sqrt{17}(\displaystyle\frac{8\pi^3}{3}+32\pi)}=\displaystyle\frac{-16\pi}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}

3 0
2 years ago
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