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jenyasd209 [6]
2 years ago
15

A. Use this diagram of a right triangle to derive and prove the Pythagorean Identity, based on sin θ and cos θ. Start with what

you know about the relationship among a (adjacent side), o (opposite side), and h (hypotenuse). Using the diagram and the labeled components, define sine and cosine. Incorporate these definitions in your equation. In your response, include all steps and calculations.
B. With respect to , the adjacent side of the triangle has a length of 6 cm and the opposite side has a length of 3 cm. Find the value of the hypotenuse . Then, use these values to confirm the Pythagorean Identity for this triangle.
Mathematics
1 answer:
Taya2010 [7]2 years ago
5 0
0x - 12 so she is wrong. 2x hope this helps
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Solve the linear system using substitution
levacccp [35]
Hello there!

3x - y = 3
-x + y = 3

We need to solve 3x - y = 3 for y

Let start by adding -3x to both sides

3x - y = 3

3x - 3x - y = 3 - 3x

-y = 3 - 3x
We cannot leave the variable with a negative sign. We must multiply both sides by -1

-y * -1= (3 - 3x)-1

y = 3x - 3

Substitute 3x -3 for y in -x+y=3

-x + y = 3

-x + 3x - 3 = 3

2x - 3 = 3

2x = 3 + 3

2x = 6

x = 6/2

x = 3

Now substitute 3 for x in y=3x -3

y = 3x - 3

y = 3(3) - 3

y= 9 - 3

y= 6

Thus,

The answer is x=3 and y=6

It is always my pleasure to help students like you :)

As always, I am here to help!


7 0
3 years ago
A tunnel is in the shape of a parabola. The maximum height is 16 m and it is 16 m wide at the base, as shown below.
NeX [460]
Vertex at the origin and opening down → y=ax^2
Width: w=16
x=w/2→x=16/2→x=8
x=8, y=-16→y=ax^2→-16=a(8)^2→-16=a(64)→-16/64=a(64)/64→-1/4=a→a=-1/4

y=ax^2→y=-(1/4)x^2

7 m from the edge of the tunnel → x=w/2-7=8 m-7 m→x=1 m
x=1→y=-(1/4)x^2=-(1/4)(1)^2=-(1/4)(1)→y=-1/4

Vertical clearance: 16-1/4=16-0.25→Vertical clearance=15.75 m

Please, see the attached file.

Answer: Third option 15.75 m

3 0
3 years ago
Read 2 more answers
A washer and a dryer cost $552 combined. The washer costs $98 less than the dryer. What is the cost of the dryer?
Sedaia [141]

552-98 = 450

454/2 = 227

washer cost $227

 227+98 = 325

dryer cost $325

 

5 0
3 years ago
If a new college graduate wants a car costing $21,000, how much must be saved annually over the next four years if the funds ear
fgiga [73]
I'm assuming the funds earn 5% yearly?

Call x the amount he saves every year.  The first year's deposit will be multiplied by 1.05 three times, the next will be multiplied by 1.05 twice, the third will be multiplied by 1.05 once, and the fourth will not generate interest (as it will immediately be used to buy the car).

Therefore, x(1.05^3+1.05^2+1.05+1)=21000, so 4.31x=21000.  Dividing by 4.31, we see that x is approximately equal to 4872.
8 0
3 years ago
Solve: 3(5x - 8) = 6x + 39
soldier1979 [14.2K]

Steps to solve:

3(5x - 8) = 6x + 39

~Distribute left side

15x - 24 = 6x + 39

~Add 24 to both sides

15x = 6x + 63

~Subtract 6x to both sides

9x = 63

~Divide 9 to both sides

x = 7

Best of Luck!

6 0
3 years ago
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