It is given in the question that
A rectangular box has a square base with an edge length of x cm and a height of h cm. The volume of the box is given by
![V = x^2h cm^3](https://tex.z-dn.net/?f=V%20%3D%20x%5E2h%20cm%5E3)
And the edge length of the base is 12 cm, the edge length of the base is decreasing at a rate of 2 cm/min, the height of the box is 6 cm, and the height is increasing at a rate of 1 cm/min.
Here we differentiate V with respect to t, and we use product rule, that is
![V = 2xh(dx/dt)+ x^2(dh/dt)](https://tex.z-dn.net/?f=V%20%3D%202xh%28dx%2Fdt%29%2B%20x%5E2%28dh%2Fdt%29)
Substituting the given values , we will get
[/tex]
![dV/dt = -288+144 = -144cm^3/min](https://tex.z-dn.net/?f=dV%2Fdt%20%3D%20-288%2B144%20%3D%20-144cm%5E3%2Fmin)
So at that moment, the volume is decreasing at the rate of
![144 cm^3/min](https://tex.z-dn.net/?f=144%20cm%5E3%2Fmin)
First, we need to make the equation given to be in the form;
y=mx + b
where m is the slope and b is the intercept
8y - 3x = -8
Add 2x to both-side of the equation
8y = 3x - 8
Divide through the equation by 8
y = 3/8 x -1
comparing the above with y =mx + b
m = 3/8
slope of parallel equations are equal
From the options given the only equation with slope 3/8 is;
y= 3/8 x + 8
![y=\frac{3}{8}x\text{ + 8}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7B8%7Dx%5Ctext%7B%20%2B%208%7D)
The above equation of the line is parallel to 8y - 3x = -8
Answer:
Step-by-step explanation:
The equation 0.15 x + 150 ≥ 450 will help Teagan determine how much he has to sell today ⇒ A
Step-by-step explanation:
The given is:
- The computer store pays its employees $150 per day plus a commission of 15% of their sales
- Teagan wants to make at least $450 today
We need to find which equation will help Teagan to determine how much he has to sell today
Assume that he has to sell by $x today
∵ The store pays $150 per day plus a commission of 15%
of their sales
∵ Teagan's total sales = x
- Multiply 15% by x, then add the product by 150
∴ Teagan makes = 15% × x + 150
∵ 15% × x =
× x = 0.15 x
∴ Teagan makes = 0.15 x + 150
∵ Teagan wants to make at least $450 today
- At least means ≥
∴ Teagan makes ≥ 450
- Substitute Teagan makes by 0.15 x + 150
∴ 0.15 x + 150 ≥ 450
The equation 0.15 x + 150 ≥ 450 will help Teagan determine how much he has to sell today
Learn more:
You can learn more about the linear inequality in brainly.com/question/6703816
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Step-by-step explanation:
decrease value is 1353
value 31,647