Answer:![43.54 ft^3/min](https://tex.z-dn.net/?f=43.54%20ft%5E3%2Fmin)
Step-by-step explanation:
Given
Thickness of oil slick=0.07 foot
radius of slick=110 ft
![\frac{\mathrm{d} r}{\mathrm{d} t}=0.9 ft/s](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20r%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D0.9%20ft%2Fs)
Let V be the volume of oil slick
so, ![V=0.07\pi \cdot r^2](https://tex.z-dn.net/?f=V%3D0.07%5Cpi%20%5Ccdot%20r%5E2)
rate of oil flowing is
![\frac{\mathrm{d} V}{\mathrm{d} t}=0.07\times 2\pi \cdot r\frac{\mathrm{d} r}{\mathrm{d} t}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20V%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D0.07%5Ctimes%202%5Cpi%20%5Ccdot%20r%5Cfrac%7B%5Cmathrm%7Bd%7D%20r%7D%7B%5Cmathrm%7Bd%7D%20t%7D)
![\frac{\mathrm{d} V}{\mathrm{d} t}=0.07\times 2\pi \times 110\times 0.9=43.54 ft^3/min](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20V%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D0.07%5Ctimes%202%5Cpi%20%5Ctimes%20110%5Ctimes%200.9%3D43.54%20ft%5E3%2Fmin)
First, factor out the common factor 5.
<span>15y^2-50y+35 =
= 5(3y^2 - 10y + 7)
Now we need to factor the trinomial.
3 can be factored as 3 * 1
7 can be factored as 1 * 7 or (-1) * (-7)
Since the middle term is negative, we need to use -1 and -7 as the factors of 7
= 5(3y - 7)(y - 1)
</span>
Step-by-step explanation:
Solution,
According to question,
Length= 12 cm
Breadth= (12-2) cm= 10 cm
Now,
By using the formula of area of rectangle, we get
Area of rectangle= Length×breadth
Area of rectangle=12 cm×10 cm
Area of rectangle=120 cm²
Hence, the area of the rectangle is 120 cm².
If a bag contains 16 red, 6 yellow, 24 blue, and 8 white balloons, that 1:7 part-to-whole ratio of yellow balloons to all balloons. There are 4 parts and 1 part is the part with the red balloons.
Your answer is: B) 1:7
Have an amazing day and stay hopeful!
Answer:
See below.
Step-by-step explanation:
The converse of the Pythagorean Theorem tells us that if the sum of the square of the two shorter lengths is equivalent to the square of the longest length, then the triangle is indeed a right triangle.
We have the side lengths (x²-1), (2x), and (x²+1).
We can see that our hypotenuse will be (x²+1), since it will always yield the largest value for x.
So, we can use the Pythagorean Theorem:
![a^2+b^2=c^2](https://tex.z-dn.net/?f=a%5E2%2Bb%5E2%3Dc%5E2)
Substitute (x²-1) and (2x) for a and b, and substitute (x²+1) for c:
![(x^2-1)^2+(2x)^2\stackrel{?}{=}(x^2+1)^2](https://tex.z-dn.net/?f=%28x%5E2-1%29%5E2%2B%282x%29%5E2%5Cstackrel%7B%3F%7D%7B%3D%7D%28x%5E2%2B1%29%5E2)
Square each expression:
![(x^4-2x^2+1)+(4x^2)\stackrel{?}{=}(x^4+2x^2+1)](https://tex.z-dn.net/?f=%28x%5E4-2x%5E2%2B1%29%2B%284x%5E2%29%5Cstackrel%7B%3F%7D%7B%3D%7D%28x%5E4%2B2x%5E2%2B1%29)
Combine like terms:
![x^4+(-2x^2+4x^2)+1\stackrel{?}{=}(x^4+2x^2+1)](https://tex.z-dn.net/?f=x%5E4%2B%28-2x%5E2%2B4x%5E2%29%2B1%5Cstackrel%7B%3F%7D%7B%3D%7D%28x%5E4%2B2x%5E2%2B1%29)
Add:
![x^4+2x^2+1\stackrel{\checkmark}{=}x^2+2x^2+1](https://tex.z-dn.net/?f=x%5E4%2B2x%5E2%2B1%5Cstackrel%7B%5Ccheckmark%7D%7B%3D%7Dx%5E2%2B2x%5E2%2B1)
We can see that the resulting equations are equivalent, proving that the triangle is indeed a right triangle.
And we're done!