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o-na [289]
3 years ago
5

The perimeter of a triangle is 65 centimeters. The second side is twice the first and the third side is 3 and 1/2 times the firs

t side. Find the length of each side. (Hint: P = a + b + c)
Mathematics
1 answer:
Harlamova29_29 [7]3 years ago
4 0
X=first number
2x= second side
3.5x= third side


X+2x+3.5x=65

6.5 x= 65
Divide both sides by 6.5

X=10. First side
2x= 20. Second side

3.5x= 35 = third side

10, 20, 35

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What is the inverse of y = 2x^2 – 8?
Novosadov [1.4K]
y = 2x^2 - 8 \\ 2x^2 = y + 8 \\ x^2 = \frac{y+8}{2}  \\ x = \sqrt{\frac{y+8}{2}}  \\  f^{-1} (x)=\sqrt{\frac{x+8}{2}}
6 0
3 years ago
Use the shell method to compute the volume of the solids obtained by rotating the region enclosed by the graphs of the functions
Marina CMI [18]

Answer:

44.18 cubic unit

Step-by-step explanation:

The intersection of the curve y = x^2 and y = 8-x^2 is

x^2 = 8 - x^2

2x^2 = 8

x^2 = 4

x = \pm 2

Since we are rotating the region where x \geq 0.5 we will use the intersection x = 2 and y = 4

Using the shell method with x ranges from 0.5 to 2. The volume of the shell would be

V = \int\limits^2_{0.5} {2\pi x h} \, dx

where h is the difference between the y-coordinates of the curves, in other words

h = 8 - x^2 - x^2 = 8 - 2x^2

Plug h into the V integral and we have

V = \int\limits^2_{0.5} {2\pi x (8 - 2x^2)} \, dx\\V = 4\pi\int\limits^2_{0.5} {(4x - x^3)} \, dx\\V = 4\pi[2x^2 - x^4/4]^2_{0.5}\\V = 4\pi(2*2^2 - 2^4/4 - 2*0.5^2 + 0.5^4/4)\\V = 4\pi(8 - 4 - 0.5 + 0.015625) \approx 44.18

7 0
3 years ago
Using the image, determine the length of each arc.
Over [174]

Answer:

GIF=1.239 R

HET= 3.769 R

Step-by-step explanation:

Assuming the image is the shown below, we can use the following formula to find the length of arc L_{arc}:

L_{arc}=2 \pi R (\frac{\theta}{360 \°})

Where \theta is the angle in the arc and R is the radius of the circle.

Since we are not given the value of R, we will only work with this.

For GIF:

L_{arc-GIF}=2 \pi R (\frac{71\°}{360 \°})

L_{arc-GIF}=1.239 R

For HET:

We firstly need to find the value of this angle, taking into account the whole circumference is 360 \°:

360 \°=71 \°+53 \°+HET+20 \°

Finding HET:

HET=216 \°

Now, let's calculate the length of arc:

L_{arc-HET}=2 \pi R (\frac{216\°}{360 \°})

L_{arc-HET}=3.769 R

5 0
4 years ago
Please help for 18 points
Gnom [1K]

Answer:

9 per game.

Step-by-step explanation:

45y/5x

I'm not so sure what the equation would look like

8 0
3 years ago
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The equation of line t is y= -8/7x + 5. line u is perpendicular to t. what is the slope of line u?
liq [111]

Answer:

slope = 7/8

Step-by-step explanation:

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thus

slope of line t = -8/7

flip and change signs

7/8

8 0
3 years ago
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