Answer:
A=49 degree
a=13.5
b=11.7
Step-by-step explanation:
1/64 is the answer as a fraction
1/4 is the same as 1 * 0.25
Answer:
The bird has to fly 7.5 m
Step-by-step explanation:
Please see diagram in attached image.
Notice that there is a right angle triangle that defines the situation, and you know two elements of such triangle;
1) one acute angle (
), and
2) the side opposite to that angle.
What you need to find is the side adjacent to the angle, which is what the bird needs to fly horizontally to be above the fish. We named that "x".
The trig function that relates such triangle elements is the tangent:

which rounded to the nearest tenth is: 7.5 m
Answer:
17.5% per annum
Step-by-step explanation:
<u>Given:</u>
Money invested = $20,000 at the age of 20 years.
Money expected to be $500,000 at the age of 40.
Time = 40 - 20 = 20 years
<em>Interest is compounded annually.</em>
<u>To find:</u>
Rate of growth = ?
<u>Solution:</u>
First of all, let us have a look at the formula for compound interest.

Where A is the amount after T years compounding at a rate of R% per annum. P is the principal amount.
Here, We are given:
P = $20,000
A = $500,000
T = 20 years
R = ?
Putting all the values in the formula:
![500000 = 20000 \times (1+\frac{R}{100})^{20}\\\Rightarrow \dfrac{500000}{20000} =(1+\frac{R}{100})^{20}\\\Rightarrow 25 =(1+\frac{R}{100})^{20}\\\Rightarrow \sqrt[20]{25} =1+\frac{R}{100}\\\Rightarrow 1.175 = 1+0.01R\\\Rightarrow R \approx17.5\%](https://tex.z-dn.net/?f=500000%20%3D%2020000%20%5Ctimes%20%281%2B%5Cfrac%7BR%7D%7B100%7D%29%5E%7B20%7D%5C%5C%5CRightarrow%20%5Cdfrac%7B500000%7D%7B20000%7D%20%3D%281%2B%5Cfrac%7BR%7D%7B100%7D%29%5E%7B20%7D%5C%5C%5CRightarrow%2025%20%3D%281%2B%5Cfrac%7BR%7D%7B100%7D%29%5E%7B20%7D%5C%5C%5CRightarrow%20%5Csqrt%5B20%5D%7B25%7D%20%3D1%2B%5Cfrac%7BR%7D%7B100%7D%5C%5C%5CRightarrow%201.175%20%3D%201%2B0.01R%5C%5C%5CRightarrow%20R%20%5Capprox17.5%5C%25)
So, the correct answer is
<em>17.5% </em>per annum and compounding annually.