The answer is in the attachment below:
Answer:
![sin(b^\circ) = \dfrac{3}{5}](https://tex.z-dn.net/?f=sin%28b%5E%5Ccirc%29%20%3D%20%5Cdfrac%7B3%7D%7B5%7D)
Step-by-step explanation:
We are given a
where ![\angle K = 90^\circ](https://tex.z-dn.net/?f=%5Cangle%20K%20%3D%2090%5E%5Ccirc)
![tan(b^\circ) = \dfrac{3}{4}\\cos(b^\circ) = \dfrac{4}{5}](https://tex.z-dn.net/?f=tan%28b%5E%5Ccirc%29%20%3D%20%5Cdfrac%7B3%7D%7B4%7D%5C%5Ccos%28b%5E%5Ccirc%29%20%3D%20%5Cdfrac%7B4%7D%7B5%7D)
As per trigonometric rules,
![tan(\theta) = \dfrac{Perpendicular}{Base}](https://tex.z-dn.net/?f=tan%28%5Ctheta%29%20%3D%20%5Cdfrac%7BPerpendicular%7D%7BBase%7D)
![cos(\theta) = \dfrac{Base}{Hypotenuse}](https://tex.z-dn.net/?f=cos%28%5Ctheta%29%20%3D%20%5Cdfrac%7BBase%7D%7BHypotenuse%7D)
Comparing the given value of tangent and cosine:
Perpendicular = 3 units
Base = 4 units
Hypotenuse = 5 units
Also, we know that:
![sin(\theta) = \dfrac{Perpendicular}{Hypotenuse}](https://tex.z-dn.net/?f=sin%28%5Ctheta%29%20%3D%20%5Cdfrac%7BPerpendicular%7D%7BHypotenuse%7D)
![\Rightarrow sin(b^\circ) = \dfrac{3}{5}](https://tex.z-dn.net/?f=%5CRightarrow%20sin%28b%5E%5Ccirc%29%20%3D%20%5Cdfrac%7B3%7D%7B5%7D)
Now, it is given that the triangle is dilated by a scale factor of
.
i.e. all the sides will become half of its initial values.
New Perpendicular = 1.5 units
New Base = 2 units
New Hypotenuse = 2.5 units
Using the formula for sine:
![sin(\theta) = \dfrac{Perpendicular}{Hypotenuse}](https://tex.z-dn.net/?f=sin%28%5Ctheta%29%20%3D%20%5Cdfrac%7BPerpendicular%7D%7BHypotenuse%7D)
![\Rightarrow sin(b^\circ)= \dfrac{1.5}{2.5}\\\Rightarrow sin(b^\circ)= \dfrac{15}{25}\\\Rightarrow sin(b^\circ)=\dfrac{3}{5}](https://tex.z-dn.net/?f=%5CRightarrow%20%20sin%28b%5E%5Ccirc%29%3D%20%5Cdfrac%7B1.5%7D%7B2.5%7D%5C%5C%5CRightarrow%20%20sin%28b%5E%5Ccirc%29%3D%20%5Cdfrac%7B15%7D%7B25%7D%5C%5C%5CRightarrow%20%20%20sin%28b%5E%5Ccirc%29%3D%5Cdfrac%7B3%7D%7B5%7D)
The compound interest formula is
FV=P(1+(r/n))^n*t
FV= future value
P= principal or amount of $ deposited
r= annual interest rate in decimal form
n= number of times compounded per year
t= time in years
Therefore 8000(1+(.12/12))^12*7 which equals $18453.78
Answer:
-144
Step-by-step explanation:
x=-48 times 3
Step-by-step explanation:
![first \: take \: square \: root \: of \: \sqrt{7} then \: multiply \: by \: 73 \: and \: you \: will \: get \: answer](https://tex.z-dn.net/?f=first%20%5C%3A%20%20take%20%5C%3A%20%20square%20%5C%3A%20%20root%20%5C%3A%20%20of%20%5C%3A%20%20%20%5Csqrt%7B7%7D%20%20then%20%20%5C%3A%20multiply%20%20%5C%3A%20by%20%20%5C%3A%2073%20%5C%3A%20%20and%20%20%5C%3A%20you%20%20%5C%3A%20will%20%20%5C%3A%20get%20%5C%3A%20%20answer)