Answer:
(2/3)y
Step-by-step explanation:
Given that :
Age gap between father and daughter = y
2/3 of the difference in their ages expressed as in terms of y ;
2/ 3 * y
(2/3)y
<span>
5*n+(3/4)*n = 2 // - 2
5*n+(3/4)*n-2 = 0
23/4*n-2 = 0 // + 2
23/4*n = 2 // : 23/4
n = 2/23/4
n = 8/23
</span>
Answer:
(a) ![y = \frac{4}{x^2}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B4%7D%7Bx%5E2%7D)
(b) ![x = \frac{2}{5}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B2%7D%7B5%7D)
Step-by-step explanation:
Given
Variation: Inverse proportional.
This is represented as:
![y\ \alpha\ \frac{1}{x^2}](https://tex.z-dn.net/?f=y%5C%20%5Calpha%5C%20%5Cfrac%7B1%7D%7Bx%5E2%7D)
See attachment for table
Solving (a):
First convert variation to equation
![y = k\frac{1}{x^2}](https://tex.z-dn.net/?f=y%20%3D%20k%5Cfrac%7B1%7D%7Bx%5E2%7D)
From the table:
![(x,y) = (1,4)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%3D%20%281%2C4%29)
So, we have:
![4 = k * \frac{1}{1^2}](https://tex.z-dn.net/?f=4%20%3D%20k%20%2A%20%5Cfrac%7B1%7D%7B1%5E2%7D)
![4 = k * \frac{1}{1}](https://tex.z-dn.net/?f=4%20%3D%20k%20%2A%20%5Cfrac%7B1%7D%7B1%7D)
![4 = k * 1](https://tex.z-dn.net/?f=4%20%3D%20k%20%2A%201)
![4 = k](https://tex.z-dn.net/?f=4%20%3D%20k)
![k = 4](https://tex.z-dn.net/?f=k%20%3D%204)
Substitute 4 for k in ![y = k\frac{1}{x^2}](https://tex.z-dn.net/?f=y%20%3D%20k%5Cfrac%7B1%7D%7Bx%5E2%7D)
![y = 4 * \frac{1}{x^2}](https://tex.z-dn.net/?f=y%20%3D%204%20%2A%20%5Cfrac%7B1%7D%7Bx%5E2%7D)
![y = \frac{4}{x^2}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B4%7D%7Bx%5E2%7D)
Solving (b): x when y = 25.
Substitute 25 for y in ![y = \frac{4}{x^2}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B4%7D%7Bx%5E2%7D)
![25 = \frac{4}{x^2}](https://tex.z-dn.net/?f=25%20%3D%20%5Cfrac%7B4%7D%7Bx%5E2%7D)
Cross Multiply
![25 * x^2 = 4](https://tex.z-dn.net/?f=25%20%2A%20x%5E2%20%3D%204)
Divide through by 25
![x^2 = \frac{4}{25}](https://tex.z-dn.net/?f=x%5E2%20%3D%20%5Cfrac%7B4%7D%7B25%7D)
Take positive square roots of both sides
![x = \sqrt{\frac{4}{25}](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%7B%5Cfrac%7B4%7D%7B25%7D)
![x = \frac{2}{5}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B2%7D%7B5%7D)
Step-by-step explanation:
given= in triangle PQR,<R=90⁰ QR=61 FEET RP=90 FEET
by using pythagoras therom ;
(hypotenuse)²=(side1)² +(side2)²
(PQ)²=(PR)²+(QR)²
(PQ)²=(90)² + (61)²
(PQ)²=8100 + 3721
(PQ)²=11821
<em>T</em><em>A</em><em>K</em><em>I</em><em>N</em><em>G</em><em> </em><em>S</em><em>Q</em><em>U</em><em>A</em><em>R</em><em>E</em><em> </em><em>R</em><em>O</em><em>O</em><em>T</em><em>S</em><em> </em><em>O</em><em>N</em><em> </em><em>B</em><em>O</em><em>T</em><em>H</em><em> </em><em>S</em><em>I</em><em>D</em><em>E</em><em>S</em><em>,</em><em> </em><em>W</em><em>E</em><em> </em><em>G</em><em>E</em><em>T</em><em>;</em>
PQ= 108 feet
<P = thita
sin ⁰ = opposite/hypotenuse
sin⁰ =QR/PQ
SIN⁰ =61/108
SIN⁰ =0.56
there amgle P measures 0.56 degree
Answer:
Step-by-step explanation:
The explicit formula for the nth term is a%5Bn%5D=216%2A%281%2F6%29% where n starts at n=1. The 16th term is when n = 16, so.