Answer:
See below
Step-by-step explanation:
It has something to do with the<em> </em><u><em>Weierstrass substitution</em></u>, where we have
First, consider the double angle formula for tangent:
Therefore,
Once the double angle identity for sine is
we know 
, but sure, we can derive this formula considering the double angle identity
Recall
Thus,
Similarly for cosine, consider the double angle identity
Thus,
Hence, we showed 
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![5\cos(x) =12\sin(x) +3, x \in [0, 2\pi ]](https://tex.z-dn.net/?f=5%5Ccos%28x%29%20%3D12%5Csin%28x%29%20%2B3%2C%20x%20%5Cin%20%5B0%2C%202%5Cpi%20%5D)
Solving
Just note that
and 
is not defined for 
Answer:
<h3>55 secs</h3>
Step-by-step explanation:
Given the elevation h (in feet) of the balloon modeled by the function h(x)=−6x+330, we can calculate the time it takes the balloon to reach the ground. The hot air balloon hits the ground at h(x) = 0.
Substitute h(x) = 0 into the modeled expression and find x as shown;
h(x)=−6x+330
0 = −6x+330
6x = 330
Divide both sides by 6
6x/6 = 330/6
x = 55 seconds
Hence the hot air balloon hits the ground after 55 seconds
Answer:
y=3
y=9
Step-by-step explanation:
y=3×0+3
=3
y=3×1+3
=9
The value of x is 1.
The value of y is 4.
Solution:
Given TQRS is a rhombus.
<u>Property of rhombus:
</u>
Diagonals bisect each other.
In diagonal TR
⇒ 3x + 2 = y + 1
⇒ 3x – y = –1 – – – – (1)
In diagonal QS
⇒ x + 3 = y
⇒ x – y = –3 – – – – (2)
Solve (1) and (2) by subtracting
⇒ 3x – y – (x – y) = –1 – (–3)
⇒ 3x – y – x + y = –1 + 3
⇒ 2x = 2
⇒ x = 1
Substitute x = 1 in equation (2), we get
⇒ 1 – y = –3
⇒ –y = –3 – 1
⇒ –y = –4
⇒ y = 4
The value of x is 1.
The value of y is 4.
Answer:
It would take alot of time for be to fill everything out so the simple solution is, complementary angles add up to 90 degrees and supplementary add up to 180 degrees. Simply for complementary do 90 - m<1 = m<2, and for supplementary 180 - m<3 = m<4.
