$A=P\left(1+\dfrac{t}{100}\right)^t\\\\P=\$14,300\\r=7\%\\t=4\\\\A=\$14,300\left(1+\dfrac{7}{100}\right)^4=\$14,300(1+0.07)^4\$14,300\cdot1.07^4\approx18,744.38$

5 0

3 years ago

How do you solve cos(pi/24) using Half-Angle formulas, and leaving in simplified form?

adoni [48]

$\cos \frac{\theta}{2}=\sqrt{\frac{1+\cos \theta}{2}}
\\
\\ \cos{\frac{\pi}{24}}=\cos{\frac{\frac{\pi}{12}}{2}}=\sqrt{\frac{1+\cos \frac{\pi}{12}}{2}}= \sqrt{ \frac{1}{2}+ \frac{\cos \frac{\pi}{12}}{2} } 
\\
\\ \cos{\frac{\pi}{12}}=\cos{\frac{\frac{\pi}{6}}{2}}=\sqrt{\frac{1+\cos \frac{\pi}{6}}{2}}= \sqrt{ \frac{1}{2}+ \frac{ \frac{ \sqrt{3} }{2} }{2} } =\sqrt{ \frac{2}{4}+ \frac{ \sqrt{3} }{4} } = \sqrt{\frac{ 2+\sqrt{3} }{4} } = 
\\
\\ =\frac{ \sqrt{2+\sqrt{3}} }{2} 
$

$\cos{\frac{\pi}{24}}= \sqrt{ \frac{1}{2}+ \frac{\cos \frac{\pi}{12}}{2} } = \sqrt{ \frac{1}{2}+ \frac{\frac{ \sqrt{2+\sqrt{3}} }{2}}{2} } = \sqrt{ \frac{2}{4}+ \frac{ \sqrt{2+\sqrt{3}} }{4}} } =\sqrt{ \frac{ 2+\sqrt{2+\sqrt{3}} }{4}} } 
\\
\\\cos{\frac{\pi}{24}}=\frac{\sqrt{2+\sqrt{2+\sqrt{3}}}} {2}$

6 0

3 years ago

A golden eagle flies 75 kilometers north in 1.5 hours. What is the eagle’s velocity? Question 3 options: A) 50 k/h B) 112.5 k/h

Roman55 [17]

Answer:

Option (c)

A golden eagle flies 75 kilometers north in 1.5 hours. Eagle’s velocity is 50 km/h r

Explanation:

Given, the distance of eagle is 75 kilometers north

Time is 1.5 hours

Velocity = $\frac{Distance}{Time}$