111.28 1/8=0.125 0.125*890.20=111.275 money can only have 2 decimals so round up and $111.28 is your answer.
Answer: The person's speed is 8 miles per hour.
Step-by-step explanation:
To solve we want to convert the
and
proportionally for the number of miles per hour. We know that multiplying a fraction by its reciprocal will equal 1. So let's do that for the value of the hour.
×![\frac{64}{1} =\frac{64}{64} =1](https://tex.z-dn.net/?f=%5Cfrac%7B64%7D%7B1%7D%20%3D%5Cfrac%7B64%7D%7B64%7D%20%3D1)
Since we multiplied that to the number of hours we must also do that for the number of miles.
×![\frac{64}{1} =\frac{64}{8} =8](https://tex.z-dn.net/?f=%5Cfrac%7B64%7D%7B1%7D%20%3D%5Cfrac%7B64%7D%7B8%7D%20%3D8)
Answer:
![Laura = 0.60](https://tex.z-dn.net/?f=Laura%20%3D%200.60)
![Billy = 0.50](https://tex.z-dn.net/?f=Billy%20%3D%200.50)
0.60 > 0.50
Step-by-step explanation:
Given
![Laura = 60\ shades](https://tex.z-dn.net/?f=Laura%20%3D%2060%5C%20shades)
![Billy = 50\ shades](https://tex.z-dn.net/?f=Billy%20%3D%2050%5C%20shades)
Required
Represent using decimal number and compare
From the question, we understand that there are 100th grids;
So:
![Laura = \frac{60}{100}](https://tex.z-dn.net/?f=Laura%20%3D%20%5Cfrac%7B60%7D%7B100%7D)
![Laura = 0.60](https://tex.z-dn.net/?f=Laura%20%3D%200.60)
![Billy = \frac{50}{100}](https://tex.z-dn.net/?f=Billy%20%3D%20%5Cfrac%7B50%7D%7B100%7D)
![Billy = 0.50](https://tex.z-dn.net/?f=Billy%20%3D%200.50)
Comparing both decimals;
Since 0.60 is greater than 0.50, we have:
0.60 > 0.50
F(x) = 18-x^2 is a parabola having vertex at (0, 18) and opening downwards.
g(x) = 2x^2-9 is a parabola having vertex at (0, -9) and opening upwards.
By symmetry, let the x-coordinates of the vertices of rectangle be x and -x => its width is 2x.
Height of the rectangle is y1 + y2, where y1 is the y-coordinate of the vertex on the parabola f and y2 is that of g.
=> Area, A
= 2x (y1 - y2)
= 2x (18 - x^2 - 2x^2 + 9)
= 2x (27 - 3x^2)
= 54x - 6x^3
For area to be maximum, dA/dx = 0 and d²A/dx² < 0
=> 54 - 18x^2 = 0
=> x = √3 (note: x = - √3 gives the x-coordinate of vertex in second and third quadrants)
d²A/dx² = - 36x < 0 for x = √3
=> maximum area
= 54(√3) - 6(√3)^3
= 54√3 - 18√3
= 36√3.
Answer:
Y= 2e^(5t)
Step-by-step explanation:
Taking Laplace of the given differential equation:
s^2+3s-10=0
s^2+5s-2s-10=0
s(s+5)-2(s+5) =0
(s-2) (s+5) =0
s=2, s=-5
Hence, the general solution will be:
Y=Ae^(-2t)+ Be^(5t)………………………………(D)
Put t = 0 in equation (D)
Y (0) =A+B
2 =A+B……………………………………… (i)
Now take derivative of (D) with respect to "t", we get:
Y=-2Ae^(-2t)+5Be^(5t) ....................... (E)
Put t = 0 in equation (E) we get:
Y’ (0) = -2A+5B
10 = -2A+5B ……………………………………(ii)
2(i) + (ii) =>
2A+2B=4 .....................(iii)
-2A+5B=10 .................(iv)
Solving (iii) and (iv)
7B=14
B=2
Now put B=2 in (i)
A=2-2
A=0
By putting the values of A and B in equation (D)
Y= 2e^(5t)