By formula, given the equation of a line in slope intercept form and coordinates of the point, a formula yields the distance between them.
Answer: 54-7n
Step-by-step explanation:
When we talk about mathematical language, the <u>difference </u>between two numbers, quantities or terms is the <u>substraction operation.</u>
For example, the <u>difference</u> between a and b is:
a-b
On the other hand, if we read a numer c <u>times</u> a number n, this means both numbers are multiplied.
For example:
c <u>times</u> n is:
(c)(n)
So, according to the explained above, “the difference of fifty-four and seven times a number n” is:
54-7n
Answer:
![x^{21/5}](https://tex.z-dn.net/?f=x%5E%7B21%2F5%7D)
Step-by-step explanation:
Step 1: Convert
into exponential form
![((x^7)^{1/5})^{3}](https://tex.z-dn.net/?f=%28%28x%5E7%29%5E%7B1%2F5%7D%29%5E%7B3%7D)
Step 2: Mulitply the 2 exponents together
![(x^{7/5})^{3}](https://tex.z-dn.net/?f=%28x%5E%7B7%2F5%7D%29%5E%7B3%7D)
Step 3: Multiply the exponents again
= ![x^{21/5}](https://tex.z-dn.net/?f=x%5E%7B21%2F5%7D)
It is given that
![\csc (\theta)=\frac{\sqrt[]{170}}{10}](https://tex.z-dn.net/?f=%5Ccsc%20%28%5Ctheta%29%3D%5Cfrac%7B%5Csqrt%5B%5D%7B170%7D%7D%7B10%7D)
We know that
![\sin (\theta)=\frac{1}{\csc (\theta)}](https://tex.z-dn.net/?f=%5Csin%20%28%5Ctheta%29%3D%5Cfrac%7B1%7D%7B%5Ccsc%20%28%5Ctheta%29%7D)
![\text{Substitute }\csc (\theta)=\frac{\sqrt[]{170}}{10},\text{ we get}](https://tex.z-dn.net/?f=%5Ctext%7BSubstitute%20%7D%5Ccsc%20%28%5Ctheta%29%3D%5Cfrac%7B%5Csqrt%5B%5D%7B170%7D%7D%7B10%7D%2C%5Ctext%7B%20we%20get%7D)
![\sin (\theta)=\frac{1}{\frac{\sqrt[]{170}}{10}}](https://tex.z-dn.net/?f=%5Csin%20%28%5Ctheta%29%3D%5Cfrac%7B1%7D%7B%5Cfrac%7B%5Csqrt%5B%5D%7B170%7D%7D%7B10%7D%7D)
![\sin (\theta)=\frac{10}{\sqrt[]{170}}](https://tex.z-dn.net/?f=%5Csin%20%28%5Ctheta%29%3D%5Cfrac%7B10%7D%7B%5Csqrt%5B%5D%7B170%7D%7D)
![\sin (\theta)=\frac{\sqrt[]{10}\sqrt[]{10}}{\sqrt[]{17\times10}}](https://tex.z-dn.net/?f=%5Csin%20%28%5Ctheta%29%3D%5Cfrac%7B%5Csqrt%5B%5D%7B10%7D%5Csqrt%5B%5D%7B10%7D%7D%7B%5Csqrt%5B%5D%7B17%5Ctimes10%7D%7D)
![\sin (\theta)=\frac{\sqrt[]{10}}{\sqrt[]{17}}](https://tex.z-dn.net/?f=%5Csin%20%28%5Ctheta%29%3D%5Cfrac%7B%5Csqrt%5B%5D%7B10%7D%7D%7B%5Csqrt%5B%5D%7B17%7D%7D)
![\sin (\theta)=\sqrt[]{\frac{10}{17}}](https://tex.z-dn.net/?f=%5Csin%20%28%5Ctheta%29%3D%5Csqrt%5B%5D%7B%5Cfrac%7B10%7D%7B17%7D%7D)
Hence the required value is