780, or C, is correct. Since 9.75 is 1/80th of the actual measurement, we can set up an equation like this:
9.75 = 1/80x
Then multiply each side by 80:
780 = x
The actual building's height is 780 ft.
We can check this answer by plugging in 780 for x in the original equation:
9.75 = 1/80(780)
9.75 = 9.75
Check! <span>✓</span>
Let, total number of T-shirts are x.
Number of blue T-shirts = (2/3)x = 2x/3 .
Number of blue shirts on sale = (3/5)(2x/3) = 2x/5 .
Number of medium sized blue shirts on sale = (1/5)(2x/5) = 2x/25 .
Fraction of the shop's T-shirts are blue T-shirts that are on sale and are size medium =
= 2/25 . ( Number of medium sized blue shirts on sale divided by total number of T-shirts )
Hence, this is the required solution.
Answer:
Step-by-step explanation:
Given that:
The differential equation; ![(x^2-4)^2y'' + (x + 2)y' + 7y = 0](https://tex.z-dn.net/?f=%28x%5E2-4%29%5E2y%27%27%20%2B%20%28x%20%2B%202%29y%27%20%2B%207y%20%3D%200)
The above equation can be better expressed as:
![y'' + \dfrac{(x+2)}{(x^2-4)^2} \ y'+ \dfrac{7}{(x^2- 4)^2} \ y=0](https://tex.z-dn.net/?f=y%27%27%20%2B%20%5Cdfrac%7B%28x%2B2%29%7D%7B%28x%5E2-4%29%5E2%7D%20%5C%20y%27%2B%20%5Cdfrac%7B7%7D%7B%28x%5E2-%204%29%5E2%7D%20%5C%20y%3D0)
The pattern of the normalized differential equation can be represented as:
y'' + p(x)y' + q(x) y = 0
This implies that:
![p(x) = \dfrac{(x+2)}{(x^2-4)^2} \](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%5Cdfrac%7B%28x%2B2%29%7D%7B%28x%5E2-4%29%5E2%7D%20%5C)
![p(x) = \dfrac{(x+2)}{(x+2)^2 (x-2)^2} \](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%5Cdfrac%7B%28x%2B2%29%7D%7B%28x%2B2%29%5E2%20%28x-2%29%5E2%7D%20%5C)
![p(x) = \dfrac{1}{(x+2)(x-2)^2}](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%5Cdfrac%7B1%7D%7B%28x%2B2%29%28x-2%29%5E2%7D)
Also;
![q(x) = \dfrac{7}{(x^2-4)^2}](https://tex.z-dn.net/?f=q%28x%29%20%3D%20%5Cdfrac%7B7%7D%7B%28x%5E2-4%29%5E2%7D)
![q(x) = \dfrac{7}{(x+2)^2(x-2)^2}](https://tex.z-dn.net/?f=q%28x%29%20%3D%20%5Cdfrac%7B7%7D%7B%28x%2B2%29%5E2%28x-2%29%5E2%7D)
From p(x) and q(x); we will realize that the zeroes of (x+2)(x-2)² = ±2
When x = - 2
![\lim \limits_{x \to-2} (x+ 2) p(x) = \lim \limits_{x \to2} (x+ 2) \dfrac{1}{(x+2)(x-2)^2}](https://tex.z-dn.net/?f=%5Clim%20%5Climits_%7Bx%20%5Cto-2%7D%20%28x%2B%202%29%20p%28x%29%20%3D%20%20%5Clim%20%5Climits_%7Bx%20%5Cto2%7D%20%28x%2B%202%29%20%5Cdfrac%7B1%7D%7B%28x%2B2%29%28x-2%29%5E2%7D)
![\implies \lim \limits_{x \to2} \dfrac{1}{(x-2)^2}](https://tex.z-dn.net/?f=%5Cimplies%20%20%5Clim%20%5Climits_%7Bx%20%5Cto2%7D%20%20%5Cdfrac%7B1%7D%7B%28x-2%29%5E2%7D)
![\implies \dfrac{1}{16}](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B1%7D%7B16%7D)
![\lim \limits_{x \to-2} (x+ 2)^2 q(x) = \lim \limits_{x \to2} (x+ 2)^2 \dfrac{7}{(x+2)^2(x-2)^2}](https://tex.z-dn.net/?f=%5Clim%20%5Climits_%7Bx%20%5Cto-2%7D%20%28x%2B%202%29%5E2%20q%28x%29%20%3D%20%20%5Clim%20%5Climits_%7Bx%20%5Cto2%7D%20%28x%2B%202%29%5E2%20%5Cdfrac%7B7%7D%7B%28x%2B2%29%5E2%28x-2%29%5E2%7D)
![\implies \lim \limits_{x \to2} \dfrac{7}{(x-2)^2}](https://tex.z-dn.net/?f=%5Cimplies%20%20%5Clim%20%5Climits_%7Bx%20%5Cto2%7D%20%20%5Cdfrac%7B7%7D%7B%28x-2%29%5E2%7D)
![\implies \dfrac{7}{16}](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B7%7D%7B16%7D)
Hence, one (1) of them is non-analytical at x = 2.
Thus, x = 2 is an irregular singular point.
Perimeter is
2 • width+ 2•length=
2• (4x-4)+2•(2x+5)=
Distribute multiplication in parentheses
8x-8+4x+10=
Combine like terms
12x+2
The least number of buses needed to carry 710 passengers is 5.
Option A)5 is the correct answer.
<h3>What is the least number of buses needed to carry 710 passengers? </h3>
Given that;
- Number of passengers n = 710
- Least number of buses need B = ?
To get the least number of buses, we say;
Number of buses B = 710 ÷ 150
Number of buses B = 4.7 ≈ 5
The least number of buses needed to carry 710 passengers is 5.
Option A)5 is the correct answer.
Learn to solve more word problems here: brainly.com/question/2610134
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