Because of the symmetry, we can just go from x=0 to x=2 to find the area between
<span>y = x^2 and y = 4 </span>
<span>that area = ∫4-x^2 dx from 0 to 2 </span>
<span>= [4x - (1/3)x^3] from 0 to 2 </span>
<span>= 8 - 8/3 - 0 </span>
<span>= 16/3 </span>
<span>so when y = b </span>
<span>x= √b </span>
<span>and we have the area as </span>
<span>∫(b - x^2) dx from 0 to √b </span>
<span>= [b x - (1/3)x^3] from 0 to √b </span>
<span>= b√b - (1/3)b√b - 0 </span>
<span>(2/3)b√b = 8/3 </span>
<span>b√b =4 </span>
<span>square both sides </span>
<span>b^3 = 16 </span>
<span>b = 16^(1/3) = 2 cuberoot(2) </span>
<span>or appr 2.52</span>
Answer:
2:27
Step-by-step explanation:
the original ratio is '4 to 54' but both numbers divide by 2 so the answer is '2 to 27' also known as 2:27
Answer:
The domain of the transformed function is:
[0,∞)
Step-by-step explanation:
We know that the domain of a function is the set of all possible values where the function is defined i.e. the possible x-values.
Now we are given a parent function f(x) as:
Now, it is given that the function f(x) is transformed three units downward.
So, the resulting function g(x) is given as:
Hence, the function g(x) is defined for all x≥0.
( Since, the square root function is not defined for negative real numbers and for rest values it is defined)
Hence, the domain is given as:
[0,∞)
Answer:
The answer to your question is Midpoint = (0, 1)
Equation of the bisector y = 2x + 1
Step-by-step explanation:
Data
P (-4, 3)
Q (4, -1)
Process
1.- Find the midpoint
Xm = (-4 + 4)/2
Xm = 0/2
Xm = 0
Ym = (3 - 1)/2
Ym = 2/2
Ym = 1
Midpoint = (0, 1)
2.- Equation of the line
slope = (-1 - 3) / (4 + 4)
= -4/8
= -1/2
But the new line is perpendicular so the new slope is
m = 2
Equation of the new line
y - y1 = m(x - x1)
y - 1 = 2(x - 0)
y - 1 = 2x
y = 2x + 1
Answer:
4*10^18
Step-by-step explanation:
Easier to think of it as the factors out front (8 / 2) = 4
and subtract the exponents 30 - 12 = 18
= 4*10 ^18
