Answer:
option A
Step-by-step explanation:
144 = 4 * 4 * 3 * 3 = 2 * 2 * 2 *2 * 3 * 3 = 2⁴* 3²
a¹² = a⁽³ˣ⁴⁾ = (a³)⁴
![\sqrt[4]{144a^{12}b^{3}} =\sqrt[4]{2^{4}*3^{2}*(a^{3})^{4}*b^{3}}\\\\=2*a^{3}\sqrt[4]{3*3*b^{3}}\\\\=2a^{3}\sqrt[4]{9b^{3}}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B144a%5E%7B12%7Db%5E%7B3%7D%7D%20%3D%5Csqrt%5B4%5D%7B2%5E%7B4%7D%2A3%5E%7B2%7D%2A%28a%5E%7B3%7D%29%5E%7B4%7D%2Ab%5E%7B3%7D%7D%5C%5C%5C%5C%3D2%2Aa%5E%7B3%7D%5Csqrt%5B4%5D%7B3%2A3%2Ab%5E%7B3%7D%7D%5C%5C%5C%5C%3D2a%5E%7B3%7D%5Csqrt%5B4%5D%7B9b%5E%7B3%7D%7D)
Answer:
Motorcycle will complete the 540 mile trip in 11.25 hr.
The car will complete it 2.25 hours less, or 9 hours.
The speed of the car therefore is 540/9 = 60 mph.
60t + 48t = 540
108t = 540
t = 5
So they will meet in 5 hours, after which time the motorcycle will have traveled 48*5 = 240 miles
and the car will have traveled 60*5 = 300 miles.
Hope this help
Step-by-step explanation:
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
(a+b+c)+3
(4+3+5)+3
Do the parenthesis because of PEMDAS
P=parenthesis
E= exponents
M= multiplication
A= addition
S=subtraction
(7+5)+3
12+3
=15
Answer: 15