Answer:
460 miles, 1 week
Step-by-step explanation:
249 per week + 0.25 per mile
180 per week + 0.4 per mile
after 460 miles in 1 week the cost will be the same
Answer:
2.67 inches.
Step-by-step explanation:
Assuming that we represent the size of the squares with the letter y, such that after the squares are being cut from each corner, the rectangular length of the box that is formed can now be ( 23 - 2y), the width to be (13 - 2y) and the height be (x).
The formula for a rectangular box = L × B × W
= (23 -2y)(13-2y) (y)
= (299 - 46y - 26y + 4y²)y
= 299y - 72y² + 4y³
Now for the maximum volume:
dV/dy = 0
This implies that:
299y - 72y² + 4y³ = 299 - 144y + 12y² = 0
By using the quadratic formula; we have :
![= \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a}](https://tex.z-dn.net/?f=%3D%20%5Cdfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2%20-4ac%7D%7D%7B2a%7D)
where;
a = 12; b = -144 and c = 299
![= \dfrac{-(-144) \pm \sqrt{(-144)^2 -4(12)(299)}}{2(12)}](https://tex.z-dn.net/?f=%3D%20%5Cdfrac%7B-%28-144%29%20%5Cpm%20%5Csqrt%7B%28-144%29%5E2%20-4%2812%29%28299%29%7D%7D%7B2%2812%29%7D)
![= \dfrac{144 \pm \sqrt{20736 -14352}}{24}](https://tex.z-dn.net/?f=%3D%20%5Cdfrac%7B144%20%5Cpm%20%5Csqrt%7B20736%20-14352%7D%7D%7B24%7D)
![= \dfrac{144 \pm \sqrt{6384}}{24}](https://tex.z-dn.net/?f=%3D%20%5Cdfrac%7B144%20%5Cpm%20%5Csqrt%7B6384%7D%7D%7B24%7D)
![= \dfrac{144 \pm79.90}{24}](https://tex.z-dn.net/?f=%3D%20%5Cdfrac%7B144%20%5Cpm79.90%7D%7B24%7D)
![= \dfrac{144 + 79.90}{24} \ \ OR \ \ \dfrac{144 - 79.90}{24}](https://tex.z-dn.net/?f=%3D%20%5Cdfrac%7B144%20%2B%2079.90%7D%7B24%7D%20%5C%20%5C%20%20OR%20%20%5C%20%5C%20%20%20%5Cdfrac%7B144%20-%2079.90%7D%7B24%7D)
![= 9.33 \ \ OR \ \ 2.67](https://tex.z-dn.net/?f=%3D%209.33%20%5C%20%5C%20%20OR%20%20%5C%20%5C%202.67)
Since the width is 13 inches., it can't be possible for the size of the square to be cut to be 9.33
Thus, the size of the square to be cut out from each corner to obtain the maximum volume is 2.67 inches.
Answer:
35-22=x
35-22=13
Step-by-step explanation:
Include units if necessary:
$35-$22=$13
14,18 and 22 is already an even number
Answer:
see explanation
Step-by-step explanation:
Calculate AC and AB using the distance formula
d = ![\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%5E2%2B%28y_%7B2%7D-y_%7B1%7D%29%5E2%20%20%20%20%7D)
with (x₁, y₁ ) = A(1,8) and (x₂, y₂ ) = C(4,2)
AC = ![\sqrt{(4-1)^2+(2-8)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%284-1%29%5E2%2B%282-8%29%5E2%7D)
= ![\sqrt{3^2+(-6)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B3%5E2%2B%28-6%29%5E2%7D)
= ![\sqrt{9+36}](https://tex.z-dn.net/?f=%5Csqrt%7B9%2B36%7D)
=
=
= 3![\sqrt{5}](https://tex.z-dn.net/?f=%5Csqrt%7B5%7D)
Repeat with
(x₁, y₁ ) = A(1, 8) and (x₂, y₂ ) = B(2, 6)
AB = ![\sqrt{(2-1)^2+(6-8)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%282-1%29%5E2%2B%286-8%29%5E2%7D)
= ![\sqrt{1^2+(-2)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B1%5E2%2B%28-2%29%5E2%7D)
= ![\sqrt{1+4}](https://tex.z-dn.net/?f=%5Csqrt%7B1%2B4%7D)
= ![\sqrt{5}](https://tex.z-dn.net/?f=%5Csqrt%7B5%7D)
So AB =
and AC = 3![\sqrt{5}](https://tex.z-dn.net/?f=%5Csqrt%7B5%7D)
Thus
AC = 3AB