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:
5.25 feets
Step-by-step explanation:
Given that:
Height of Salem Sue = 38 feets
Height of Salem Sue's shadow = 57 feets long
Height of child standing next to the statue = 3.5 foot tall
Length of the child's shadow =?
Let lenght of child's shadow = s
IF;
38 Feets tall = 57 feets lenght
3.5 feets tall = s feets long
Cross multiply :
38 * s = 57 * 3.5
38s = 199.5
38s / 38 = 199.5 /38
s = 5.25
Hence, length of the child's shadow will be 5.25 feets long
If Ralph can make a one way journey to work with 1/16 of a tank of gas you have to double this to make the full journey.
You could also add 1/16 and 1/16 together
1/16+1/16=2/16
He would 2/16 of a tank of gas to get to work and back.
Answer:
x=−1/2+1/2√10 or -1/2+-1/2√10
Step-by-step explanation:
4x2+4x−2=7
Step 1: Subtract 7 from both sides.
4x2+4x−2−7=7−7
4x2+4x−9=0
For this equation: a=4, b=4, c=-9
4x2+4x+−9=0
Step 2: Use quadratic formula with a=4, b=4, c=-9.
x=
−b±√b2−4ac
2a
x=
−(4)±√(4)2−4(4)(−9)
2(4)
x=
−4±√160
8
x=
−1/2
+
1/2