4 x 7 = 28
49 x 13 = 637
28/637
=4/91
Answer:
![\tan \dfrac{\theta}2 = \dfrac{1}2](https://tex.z-dn.net/?f=%5Ctan%20%5Cdfrac%7B%5Ctheta%7D2%20%3D%20%5Cdfrac%7B1%7D2)
Step by step Explanation:
![\sin \theta = \dfrac{\text{Perpendicular} }{\text{Hypotenuse}} = \dfrac{12}{15}\\\\\\\cos \theta = \dfrac{\text{Base}}{\text{Hypotenuse}}= \dfrac{9}{15}\\\\\text{Now,}\\\\\tan \dfrac{\theta}2 = \dfrac{\sin \tfrac{\theta}2}{\cos \tfrac{\theta}2}\\\\\\~~~~~~~~=\dfrac{2\cos \tfrac{\theta}2 \sin \tfrac{\theta}2 }{2\cos^2 \tfrac{\theta}2}~~~~~~;\left[\text{Multiply by}~ 2\cos\tfrac{\theta}2 \right]](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%20%3D%20%5Cdfrac%7B%5Ctext%7BPerpendicular%7D%20%7D%7B%5Ctext%7BHypotenuse%7D%7D%20%3D%20%5Cdfrac%7B12%7D%7B15%7D%5C%5C%5C%5C%5C%5C%5Ccos%20%5Ctheta%20%3D%20%5Cdfrac%7B%5Ctext%7BBase%7D%7D%7B%5Ctext%7BHypotenuse%7D%7D%3D%20%5Cdfrac%7B9%7D%7B15%7D%5C%5C%5C%5C%5Ctext%7BNow%2C%7D%5C%5C%5C%5C%5Ctan%20%5Cdfrac%7B%5Ctheta%7D2%20%3D%20%5Cdfrac%7B%5Csin%20%5Ctfrac%7B%5Ctheta%7D2%7D%7B%5Ccos%20%5Ctfrac%7B%5Ctheta%7D2%7D%5C%5C%5C%5C%5C%5C~~~~~~~~%3D%5Cdfrac%7B2%5Ccos%20%5Ctfrac%7B%5Ctheta%7D2%20%5Csin%20%5Ctfrac%7B%5Ctheta%7D2%20%7D%7B2%5Ccos%5E2%20%5Ctfrac%7B%5Ctheta%7D2%7D~~~~~~%3B%5Cleft%5B%5Ctext%7BMultiply%20by%7D~%202%5Ccos%5Ctfrac%7B%5Ctheta%7D2%20%5Cright%5D)
![=\dfrac{\sin \theta}{1+ \cos \theta}~~~~~~~~~~~~;[2 \sin x \cos x = \sin 2x ~ \text{and}~ 2\cos^2 x =1+\cos 2x]\\\\\\=\dfrac{\tfrac{12}{15}}{1+ \tfrac{9}{15}}\\\\\\=\dfrac{\tfrac{12}{15}}{\tfrac{24}{15}}\\\\\\=\dfrac{12}{15}\times \dfrac{15}{24}\\\\\\=\dfrac{12}{24}\\\\\\=\dfrac{1}2](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B%5Csin%20%5Ctheta%7D%7B1%2B%20%5Ccos%20%5Ctheta%7D~~~~~~~~~~~~%3B%5B2%20%5Csin%20x%20%5Ccos%20x%20%3D%20%5Csin%202x%20~%20%5Ctext%7Band%7D~%202%5Ccos%5E2%20x%20%3D1%2B%5Ccos%202x%5D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B%5Ctfrac%7B12%7D%7B15%7D%7D%7B1%2B%20%5Ctfrac%7B9%7D%7B15%7D%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B%5Ctfrac%7B12%7D%7B15%7D%7D%7B%5Ctfrac%7B24%7D%7B15%7D%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B12%7D%7B15%7D%5Ctimes%20%5Cdfrac%7B15%7D%7B24%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B12%7D%7B24%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D2)
Answer:
$27508
Step-by-step explanation:
The value of a truck v(x) in dollars after x years is modeled by the equation
.
Now, this is an exponential decay function, where the price of the truck is depreciating at an exponential rate.
So, after 2 years the value of the truck will become
dollars. (Answer)
Answer:
option-D
None of the above
Step-by-step explanation:
we are given
![x^2+20x+96](https://tex.z-dn.net/?f=x%5E2%2B20x%2B96)
we can find factors of 96
![96=12\times 8](https://tex.z-dn.net/?f=96%3D12%5Ctimes%208)
![20=12+8](https://tex.z-dn.net/?f=20%3D12%2B8)
![x^2+20x+96=x^2+(12+8)x+12\times 8](https://tex.z-dn.net/?f=x%5E2%2B20x%2B96%3Dx%5E2%2B%2812%2B8%29x%2B12%5Ctimes%208)
now, we can use formula
![x^2+(a+b)x+ab=(x+a)(x+b)](https://tex.z-dn.net/?f=x%5E2%2B%28a%2Bb%29x%2Bab%3D%28x%2Ba%29%28x%2Bb%29)
we get
![x^2+20x+96=(x+12)(x+8)](https://tex.z-dn.net/?f=x%5E2%2B20x%2B96%3D%28x%2B12%29%28x%2B8%29)
We can see that none of the factor matches
so, None of these
Answer: The answer is 21.25 pounds.
Step-by-step explanation: Given that the weight of Akoala is 20 pounds. Also, she is carrying her joey with her having weight 20 ounces. We need to find the combined weight of the adult Akoala and her joey in ounces.
For that, first we need to conver ounces to pounds.
We know
![1~\textup{pound}=16~\textup{ounces}\\\\\Rightarrow 1~\textup{ounce}=\dfrac{1}{16}~\textup{pounds}\\\\\Rightarrow 20~\textup{ounces}=\dfrac{1}{16}\times 20=\dfrac{5}{4}=1.25~\textup{pounds.}](https://tex.z-dn.net/?f=1~%5Ctextup%7Bpound%7D%3D16~%5Ctextup%7Bounces%7D%5C%5C%5C%5C%5CRightarrow%201~%5Ctextup%7Bounce%7D%3D%5Cdfrac%7B1%7D%7B16%7D~%5Ctextup%7Bpounds%7D%5C%5C%5C%5C%5CRightarrow%2020~%5Ctextup%7Bounces%7D%3D%5Cdfrac%7B1%7D%7B16%7D%5Ctimes%2020%3D%5Cdfrac%7B5%7D%7B4%7D%3D1.25~%5Ctextup%7Bpounds.%7D)
Therefore, the combined weight is given by
![W=20+1.25=21.25~\textup{pounds.}](https://tex.z-dn.net/?f=W%3D20%2B1.25%3D21.25~%5Ctextup%7Bpounds.%7D)
Thus, the answer is 21.25 pounds.