Answer:
Mark the point of intersection S of circles R and P, and construct line QS.
Step-by-step explanation:
In the figure attached, the problem is shown. The construction of the tangent lines from point Q to circle P is almost done. The last step is to draw the lines that pass through point Q and the intersection of the circles.
So,
To what percent 34 is of 55, we first need to find the fraction equivalent.
34 out of 55 parts or 34/55
Divide 34 by 55.
34/55 = 0.61818...
Now, we move the decimal point 2 places to the right in order to convert it to a percent.
6.1818...
61.81818...
Rounded to the nearest hundredth: 61.82%
Rounded to the nearest tenth: 61.8%
Rounded to the nearest percent: 62%
Answer:
Therefore,
![r=\sqrt[3]{\frac{3V}{4\pi }}](https://tex.z-dn.net/?f=r%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B3V%7D%7B4%5Cpi%20%7D%7D)
is the required r
Step-by-step explanation:
Given:
Volume of inside of the sphere is given as

where r is the radius of the sphere
To Find:
r =?
Solution:
We have
......Given
![3\times V=4\pi r^{3} \\\\\therefore r^{3}=\frac{3V}{4\pi } \\\\\therefore r=\sqrt[3]{\frac{3V}{4\pi }} \textrm{which is the expression for r}](https://tex.z-dn.net/?f=3%5Ctimes%20V%3D4%5Cpi%20r%5E%7B3%7D%20%5C%5C%5C%5C%5Ctherefore%20r%5E%7B3%7D%3D%5Cfrac%7B3V%7D%7B4%5Cpi%20%7D%20%5C%5C%5C%5C%5Ctherefore%20r%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B3V%7D%7B4%5Cpi%20%7D%7D%20%5Ctextrm%7Bwhich%20is%20the%20expression%20for%20r%7D)
Therefore,
![r=\sqrt[3]{\frac{3V}{4\pi }}](https://tex.z-dn.net/?f=r%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B3V%7D%7B4%5Cpi%20%7D%7D)
is the required r
Answer:
Option D
Step-by-step explanation:
The questions which involve calculating the angles and the sides of a triangle either require the sine rule or the cosine rule. In this question, the two sides that are given are adjacent to each other the given angle is the included angle. This means that the angle B is formed by the intersection of the lines a and c. Therefore, cosine rule will be used to calculate the length of b. The cosine rule is:
b^2 = a^2 + c^2 - 2*a*c*cos(B).
The question specifies that c=71, B=123°, and a=65. Plugging in the values:
b^2 = 65^2 + 71^2 - 2(65)(71)*cos(123°).
Simplifying gives:
b^2 = 14293.0182932.
Taking square root on the both sides gives b = 119.6 (rounded to the one decimal place).
This means that the Option D is the correct choice!!!