Answer:
-11.3
Step-by-step explanation:
Combine the negative terms, obtaining -3.5 - 12.8, or -16.3.
Next, combine 5 and this last result: -16.3 + 5 = -11.3
Answer:
30 mph
Step-by-step explanation:
Let d = distance (in miles)
Let t = time (in hours)
Let v = average speed driving <u>to</u> the airport (in mph)
⇒ v + 15 = average speed driving <u>from</u> the airport (in mph)
Using: distance = speed x time
![\implies t=\dfrac{d}{v}](https://tex.z-dn.net/?f=%5Cimplies%20t%3D%5Cdfrac%7Bd%7D%7Bv%7D)
Create two equations for the journey to and from the airport, given that the distance one way is 18 miles:
![\implies t=\dfrac{18}{v} \ \ \textsf{and} \ \ t=\dfrac{18}{v+15}](https://tex.z-dn.net/?f=%5Cimplies%20t%3D%5Cdfrac%7B18%7D%7Bv%7D%20%20%5C%20%5C%20%5Ctextsf%7Band%7D%20%5C%20%5C%20%20t%3D%5Cdfrac%7B18%7D%7Bv%2B15%7D)
We are told that the total driving time is 1 hour, so the sum of these expressions equals 1 hour:
![\implies \dfrac{18}{v} +\dfrac{18}{v+15}=1](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B18%7D%7Bv%7D%20%2B%5Cdfrac%7B18%7D%7Bv%2B15%7D%3D1)
Now all we have to do is solve the equation for v:
![\implies \dfrac{18(v+15)}{v(v+15)} +\dfrac{18v}{v(v+15)}=1](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B18%28v%2B15%29%7D%7Bv%28v%2B15%29%7D%20%2B%5Cdfrac%7B18v%7D%7Bv%28v%2B15%29%7D%3D1)
![\implies \dfrac{18(v+15)+18v}{v(v+15)}=1](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B18%28v%2B15%29%2B18v%7D%7Bv%28v%2B15%29%7D%3D1)
![\implies 18(v+15)+18v=v(v+15)](https://tex.z-dn.net/?f=%5Cimplies%2018%28v%2B15%29%2B18v%3Dv%28v%2B15%29)
![\implies 18v+270+18v=v^2+15v](https://tex.z-dn.net/?f=%5Cimplies%2018v%2B270%2B18v%3Dv%5E2%2B15v)
![\implies v^2-21v-270=0](https://tex.z-dn.net/?f=%5Cimplies%20v%5E2-21v-270%3D0)
![\implies (v-30)(v+9)=0](https://tex.z-dn.net/?f=%5Cimplies%20%28v-30%29%28v%2B9%29%3D0)
![\implies v=30, v=-9](https://tex.z-dn.net/?f=%5Cimplies%20v%3D30%2C%20v%3D-9)
As v is positive, v = 30 only
So the average speed driving to the airport was 30 mph
(and the average speed driving from the airport was 45 mph)
The formula to solve a cylinder is V=πr²h
So, round pi to 3.14
We must plug in for the radius (r) in this equation. To do this, we must half up the diameter, 5. 5/2 = 2.5
6 is height
V=3.14 * 2.5² * 6
V=117.81 we must round though to tenth, and that would be:
Answer V=117.8m³
Answer:
<em><u>First box/top box is 2 because 8 - 6 = 2</u></em>
<em><u>Second box/bottom box is 1 because 8 - 7 = 1</u></em>
Calculation of relative maxima and minima of a function f (x) in a range [a, b]:
We find the first derivative and calculate its roots.
We make the second derivative, and calculate the sign taken in it by the roots of the first derivative, and if:
f '' (a) <0 is a relative maximum
f '' (a)> 0 is a relative minimum
Identify intervals on which the function is increasing, decreasing, or constant. G (x) = 1- (x-7) ^ 2
First derivative
G '(x) = - 2 (x-7)
-2 (x-7) = 0
x = 7
Second derivative
G '' (x) = - 2
G '' (7) = - 2 <0 is a relative maximum
answer:
the function is increasing at (-inf, 7)
the function is decreasing at [7, inf)