"Simplest form is the one <span>algebraic expression that has no like terms and no parentheses is in this form. This is actually the simplest way of describing an algebraic expression. I hope that this is the answer that you were looking for and it has actually come to your desired help.</span>
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
.055 is the answer to this problem
Height of another tree that cast a shadow which is 20ft long is 5 feet approximately
<h3><u>Solution:</u></h3>
Given that tree with a height of 4 ft casts a shadow 15ft long on the ground
Another tree that cast a shadow which is 20ft long
<em><u>To find: height of another tree</u></em>
We can solve this by setting up a ratio comparing the height of the tree to the height of the another tree and shadow of the tree to the shadow of the another tree
![\frac{\text {height of tree}}{\text {length of shadow}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%20%7Bheight%20of%20tree%7D%7D%7B%5Ctext%20%7Blength%20of%20shadow%7D%7D)
Let us assume,
Height of tree = ![H_t = 4 feet](https://tex.z-dn.net/?f=H_t%20%3D%204%20feet)
Length of shadow of tree = ![L_t = 15 feet](https://tex.z-dn.net/?f=L_t%20%3D%2015%20feet)
Height of another tree = ![H_a](https://tex.z-dn.net/?f=H_a)
Length of shadow of another tree = ![L_a = 20 feet](https://tex.z-dn.net/?f=L_a%20%3D%2020%20feet)
Set up a proportion comparing the height of each object to the length of the shadow,
![\frac{\text {height of tree}}{\text {length of shadow of tree}}=\frac{\text { height of another tree }}{\text { length of shadow of another tree }}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%20%7Bheight%20of%20tree%7D%7D%7B%5Ctext%20%7Blength%20of%20shadow%20of%20tree%7D%7D%3D%5Cfrac%7B%5Ctext%20%7B%20height%20of%20another%20tree%20%7D%7D%7B%5Ctext%20%7B%20length%20of%20shadow%20of%20another%20tree%20%7D%7D)
![\frac{H_{t}}{L_{t}}=\frac{H_{a}}{L_{a}}](https://tex.z-dn.net/?f=%5Cfrac%7BH_%7Bt%7D%7D%7BL_%7Bt%7D%7D%3D%5Cfrac%7BH_%7Ba%7D%7D%7BL_%7Ba%7D%7D)
Substituting the values we get,
![\frac{4}{15} = \frac{H_a}{20}\\\\H_a = \frac{4}{15} \times 20\\\\H_a = 5.33](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B15%7D%20%3D%20%5Cfrac%7BH_a%7D%7B20%7D%5C%5C%5C%5CH_a%20%3D%20%5Cfrac%7B4%7D%7B15%7D%20%5Ctimes%2020%5C%5C%5C%5CH_a%20%3D%205.33)
So the height of another tree is 5 feet approximately
Answer:
|−0.658| < |−0.653|.
Step-by-step explanation: