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yan [13]
3 years ago
7

A tunnel is in the shape of a parabola. The maximum height is 50 m and it is 10 m wide at the base, as shown below. A parabola o

pening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 50 meters and its width from left to right is 10 meters. What is the vertical clearance 2 m from the edge of the tunnel?
Mathematics
1 answer:
Valentin [98]3 years ago
3 0

The 3 known points of the parabola are the origin (0,0) and the bottom left and right points ( -5,-50) (5,-50)

The general form of a parabola that goes through the origin is:  

y = ax^2  

We need to solve for a:

-50 = a(5)^2  

-50 = 25a  

a = -50/25

a = -2

Now the equation of the parabola is y = (-2)x^2.

To solve for the vertical clearance (y) 2 meters from the edge

Subtract the distance from the edge 2 meters from the original edge which is 5 meters, 5-2 = 3.

Now replace x with 3 and solve for y:

y = (-2)3^2

y = -2(9)

y = -18

The clearance would then 50 - 18 = 32 meters.

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4 0
3 years ago
Use the sum and difference identities to find the exact values of the sine, cosine, and tangent of the angle. . 165 = 135 + 30
Serhud [2]
So lets get to the problem 

<span>165°= 135° +30° </span>

<span>To make it easier I'm going to write the same thing like this </span>
<span>165°= 90° + 45°+30° </span>

<span>Sin165° </span>
<span>= Sin ( 90° + 45°+30° ) </span>
<span>= Cos( 45°+30° )..... (∵ Sin(90 + θ)=cosθ </span>
<span>= Cos45°Cos30° - Sin45°Sin30° </span>

<span>Cos165° </span>
<span>= Cos ( 90° + 45°+30° ) </span>
<span>= -Sin( 45°+30° )..... (∵Cos(90 + θ)=-Sinθ </span>
<span>= Sin45°Cos30° + Cos45°Sin30° </span>


<span>Tan165° </span>
<span>= Tan ( 90° + 45°+30° ) </span>
<span>= -Cot( 45°+30° )..... (∵Cot(90 + θ)=-Tanθ </span>
<span>= -1/tan(45°+30°) </span>
<span>= -[1-tan45°.Tan30°]/[tan45°+Tan30°] </span>

<span>Substitute the above values with the following... These should be memorized </span>
<span>Sin 30° = 1/2 </span>
<span>Cos 30° =[Sqrt(3)]/2 </span>
<span>Tan 30° = 1/[Sqrt(3)] </span>
<span>Sin45°=Cos45°=1/[Sqrt(2)] </span>
<span>Tan 45° = 1</span>
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4 years ago
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Burka [1]
The answer to your question would be B.
I hope this helped:D

7 0
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Furkat [3]

Answer:

4/5 is greater than 3/8, so this sign: >

3 0
4 years ago
Read 2 more answers
Kara bought two birthday gifts for her twin nephews. Each gift cost $12.50. Sales tax was
mixas84 [53]

Answer:

$27.12

Step-by-step:

So, we first need to learn how much money the tax is. We can find it like this

8.5 8.5x12.50

------ x 12.50 = ----------------

100 100

106.25

= ------------- = 1.0625 ~~ $1.06

100

The tax is $1.06

So now, the only thing left is to add

12.50 + 1.06 = $13.56

13.56x2 = $27.12 (for both gifts)

In total, both gifts cost $27.12 with tax.

In total, both gifts cost

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