Answer:
$4 and $3
Step-by-step explanation:
First, write out the equations as 70x + 29y = 367 and 70x + 45y = 415. Solve by using the elimination method by subtracting 70x from 70x. 45y minus 29y is equal to 16y. 415 minus 367 is 48. Divide 48 by 16, to get y is equal to get y is equal to three. Y represents pepperoni pizzas, so a pepperoni pizza costs $3. Plug a 3 into any equation for y and solve for x. 29 times 3 is 87. 367 minus 87 is 280. 280 divided by 70 is equal to 4, so x is equal to 4.
Currently the equation 6x - 2y = 18 is in standard form. Convert the standard form equation into a slope-intercept form and we can find the slope easily.
Solve for y.
6x - 2y = 18
-2y = 18 - 6x <-- Subtract 6x from each side. This is to isolate the 2y term
2y / -2 =
<-- Divide each side by 2. This it to
get rid of the 2 coefficient.
y = -9 + 3x
Rearrange the right-hand side a bit.
y = -9 + 3x becomes y = 3x - 9
Now it is in slope-intercept form.
The slope is the coefficient of the x variable.
So, 3 is the slope.
4 is the maximum depth of the trough so we expect the answer to be less than 4. As the cross section of the trough has the shape y = x², then the width of the water level at any depth y is 2x.
Let a to b be the water depth, σ is the weight density of the fluid (water), y is the depth of water at any level and the width of water at that level is w(x).
The fluid force against the walls of the trough equals :-
b
∫σyw(x) dx. . . . a = 0 and b is the desired depth, y = x², w(x) = 2x a
b
∫62.5 * x² *2x dx = 62.5 * 2 ∫x³ dx = 125 * ¼x⁴ = 31.25x⁴ 0
As the lower level as zero, we now have :-
31.25b⁴ = 779.423
b⁴ = 24.941536
b = 2.23476 ft . . . which is the required depth of water.
For this case we must simplify the following expression:
We convert the mixed number to an improper fraction:
So, by rewriting we have:
Answer: