Select all the correct answers.
1 answer:
Answer:
The inequality x3 − 14x2 + 48x − 1,680 ≤ 0 can be used to find pool’s length.
⇒The water level in the pool cannot exceed 14 feet.
Step-by-step explanation:
The question is on inequalities
Given;
Length= x ft
depth= x-6 ft
Width= x-8 ft
volume ≤ 1680 ft³
Forming the inequality to find length x of the pool
Volume= base area × depth
base area × depth ≤ volume
x(x-8) × (x-6) = 1680
(x²-8x )(x-6) = 1680
x(x²-8x) -6 (x²-8x)=1680
x³-8x²-6x²+48x=1680
x³-14x²+48x=1680
x³-14x²+48x-1680 ≤ 0
⇒The water level in the pool cannot exceed 14 feet...why?
taking the value of x at maximum to be 17 according to the graph, then maximum depth will be;
d=x-6 = 17-6=11 ft
⇒11 ft is less than 14ft
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Answer:
(a) A(x) = 100x + 1100
(b) x = 2.5 USD
(c) A(x) = 100x + 1100 and x = -1.5 USD
Step-by-step explanation:
(a) Since there's a linear relation between weekly sales A(x) and the discount, we can model it as the following expression
A(x) = mx + b
where x is the discount, m is the slope and b is the intersect of the linear equation. We can solve for slope first
To solve for b, we can just plug in m = 100, x = 0 and A(0) = 1100
1100 = 100*0 + b
b = 1100
Therefore A(x) = 100x + 1100
With discount x, the actual price would then be p - x. Where p is the original undiscounted pricing ($16 in this case)
And with sale A(x), the revenue would then be
To find the maximum value of this, we can take the 1st derivative and set it to 0
R' = -200x + 100p - 1100 = 0
200x = 100p - 1100
when p = $16 then x = 0.5*16 - 5.5 = 8 - 5.5 = 2.5 USD
(c) when the price p is $8 then A(x) would sill be 100x + 1100 because it doesn't depend on p, but the discount. But to maximize the revenue, x will need to be
0.5p - 5.5 = 0.5*8 - 5.5 = 4 - 5.5 = -1.5 USD
So the Pizza owner would need to raise the price by 1.5 USD because originally the pizza is already inexpensive.
To find the number of solutions of a system of linear equations you need to identify the slope (m) in each equation:
-If the slope is the same in both lines the system has no solution
-If the slope is different in the lines the system has one solution
-If the equation are the same (incluided the value of b) the system has infinitely many solutions
You have the next equations:
Write the equations in slope-intercept form y=mx+b (solve for y).
First equation:
Second equation: