Answer:
<h2>
sin2P ≈ 1</h2>
Step-by-step explanation:
Given SinP + SinQ = 7/5...1 and
∠P + ∠Q = 90°... 2
From compound angle; SinP +SinQ =
... 3
Substituting equation 2 into 3 we will have;
SinP +SinQ =
= 7/5
![2sin45^{0} cos\frac{P-Q}{2}=7/5](https://tex.z-dn.net/?f=2sin45%5E%7B0%7D%20cos%5Cfrac%7BP-Q%7D%7B2%7D%3D7%2F5)
since P = 90-Q from equation 1, then;
![2sin45^{0} cos\frac{90-Q-Q}{2}=7/5\\2sin45^{0} cos\frac{90-2Q}{2}=7/5\\2(\frac{1}{\sqrt{2} } ) cos\frac{90-2Q}{2}=7/5\\cos\frac{90-2Q}{2} = 7/5* \frac{\sqrt{2} }{2} \\cos\frac{90-2Q}{2} = \frac{7\sqrt{2}}{10}\\\frac{90-2Q}{2} = cos^{-1} \frac{7\sqrt{2}}{10}\\\frac{90-2Q}{2} = 8.15\\90-2Q = 16.30\\2Q = 90-16.3\\2Q = 73.7\\Q = 36.85^{0} \\\\P = 90-36.85\\P = 53.15^{0}](https://tex.z-dn.net/?f=2sin45%5E%7B0%7D%20cos%5Cfrac%7B90-Q-Q%7D%7B2%7D%3D7%2F5%5C%5C2sin45%5E%7B0%7D%20cos%5Cfrac%7B90-2Q%7D%7B2%7D%3D7%2F5%5C%5C2%28%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D%20%29%20cos%5Cfrac%7B90-2Q%7D%7B2%7D%3D7%2F5%5C%5Ccos%5Cfrac%7B90-2Q%7D%7B2%7D%20%3D%207%2F5%2A%20%5Cfrac%7B%5Csqrt%7B2%7D%20%7D%7B2%7D%20%5C%5Ccos%5Cfrac%7B90-2Q%7D%7B2%7D%20%3D%20%20%5Cfrac%7B7%5Csqrt%7B2%7D%7D%7B10%7D%5C%5C%5Cfrac%7B90-2Q%7D%7B2%7D%20%3D%20cos%5E%7B-1%7D%20%5Cfrac%7B7%5Csqrt%7B2%7D%7D%7B10%7D%5C%5C%5Cfrac%7B90-2Q%7D%7B2%7D%20%3D%208.15%5C%5C90-2Q%20%3D%2016.30%5C%5C2Q%20%3D%2090-16.3%5C%5C2Q%20%3D%2073.7%5C%5CQ%20%3D%2036.85%5E%7B0%7D%20%5C%5C%5C%5CP%20%3D%2090-36.85%5C%5CP%20%3D%2053.15%5E%7B0%7D)
To get sin2P; Accoding to the trig identity;
Sin2P = 2SinPCosP
Sin2P = 2Sin53.15cos53.15
sin2P = 0.9598
sin2P ≈ 1
Answer:
b no
Step-by-step explanation:
c^2 =![\sqrt{a {}^{2} +b {}^{2}} 9 + 25 \: is \: not =81](https://tex.z-dn.net/?f=%20%5Csqrt%7Ba%20%7B%7D%5E%7B2%7D%20%20%2Bb%20%7B%7D%5E%7B2%7D%7D%20%3C%2Fp%3E%3Cp%3E9%20%2B%2025%20%5C%3A%20is%20%5C%3A%20not%20%20%3D81)
<h2><u>
Answer:</u></h2><h2><u>
</u>
![\boxed{t=27}](https://tex.z-dn.net/?f=%5Cboxed%7Bt%3D27%7D)
<u>
</u></h2><h2><u>
</u></h2><h2><u>
Solution Steps:</u></h2>
______________________________
<h3>1.) Multiply both sides of the equation by 3:</h3>
× ![3=t](https://tex.z-dn.net/?f=3%3Dt)
× ![-3=-33](https://tex.z-dn.net/?f=-3%3D-33)
<em> - We do this because we need to get x alone and separate from fraction from. </em>
<u>Equation at the end of Step 1:</u>
- <u />
<u />
<h3>2.) Add 33 to both sides:</h3>
Cancels Out
<em> - We do this to cancel out an extra numbers in order to get only x alone with 1 number on the opposite side of the equal. </em>
______________________________
Answer:
2
+7x-15
Step-by-step explanation:
I presume f(x)=x+5 and g(x) =2x-3 and the question is f(x)*g(x)
f(x)*g(x)
(x+5)(2x-3)
distribute
2
+10x-3x-15
2
+7x-15
The correct option is Option 4: ![2a^2b^3 + 10ab^4](https://tex.z-dn.net/?f=2a%5E2b%5E3%20%2B%2010ab%5E4)
Step-by-step explanation:
Given
Length of box = l = ab
Width of box = w = a+5b
Height of box = h = 2b^2
The volume of a box is given by:
![V = Length*Width*Height\\V = l*w*h](https://tex.z-dn.net/?f=V%20%3D%20Length%2AWidth%2AHeight%5C%5CV%20%3D%20l%2Aw%2Ah)
Putting the values
![V = (ab)(a+5b)(2b^2)\\ = (ab)(2b^2)(a+5b)\\=(2ab^3)(a+5b)\\Distributive property\\=(2ab^3*a) + (2ab^3*5b)\\=2a^2b^3 + 10ab^4](https://tex.z-dn.net/?f=V%20%3D%20%28ab%29%28a%2B5b%29%282b%5E2%29%5C%5C%20%3D%20%28ab%29%282b%5E2%29%28a%2B5b%29%5C%5C%3D%282ab%5E3%29%28a%2B5b%29%5C%5CDistributive%20property%5C%5C%3D%282ab%5E3%2Aa%29%20%2B%20%282ab%5E3%2A5b%29%5C%5C%3D2a%5E2b%5E3%20%2B%2010ab%5E4)
Hence,
The correct option is Option 4: ![2a^2b^3 + 10ab^4](https://tex.z-dn.net/?f=2a%5E2b%5E3%20%2B%2010ab%5E4)
Keywords: Volume, Polynomials
Learn more about polynomials at:
#LearnwithBrainly