Need help! Stuck in this question.

Solve the following formula for m C = amt m = Answer as expression

d1i1m1o1n [39]

M=c/at

Divide both sides by a and t to isolate m. Then the solution is just m=c/at

4 0

3 years ago

A rectangle box with a square base and no top needs to be made using 300ft^2 of material. Find the dimensions of the box with th

Yuri [45]

The dimensions of the box are 10 ft and 5 ft

The maximum volume is 500 ft³

Step-by-step explanation:

A rectangle box with

A square base and no top
It needs to be made using 300 ft² of material
It has greatest volume

Surface area of a box without top (SA) = perimeter of base × height + area of the base

Volume of a box (V) = base area × height

Assume that the length of the side of the square base is x and the height of the box is y

∵ It needs to be made using 300 ft² of material

∴ The surface area of the box is 300 ft²

∵ Its base is a square of side length x ft

∴ Perimeter of the base = 4 × x = 4 x

∴ Area of the base = x²

∵ The height of the box = y ft

∵ SA = perimeter of base × height + area of the base

∵ SA = (4x)(y) + x²

∴ SA = 4xy + x²

∵ SA of the box = 300 ft²

- Equate the two expressions of SA

∴ 4xy + x² = 300

Now let us find y in terms of x

- Subtract x² from both sides

∴ 4xy = 300 - x²

- Divide each term by 4x to find y

∴ $y=\frac{75}{x}-\frac{1}{4}x$

∵ V = area of the base × height

∴ V = x² × y = x²y

- Substitute y by the equation of it above

∴ $V=x^{2}(\frac{75}{x}-\frac{1}{4}x)$

∴ $V=75x-\frac{1}{4}x^{3}$

∵ The volume of the box is greatest

- That means differentiate V and equate it by 0

∵ $\frac{dV}{dx}=75-\frac{3}{4}x^{2}$

∵ $\frac{dV}{dx}=0$ ⇒ greatest volume

∴ $75-\frac{3}{4}x^{2}=0$

- Subtract 75 from both sides

∴ $-\frac{3}{4}x^{2}=-75$

- Divide both sides by $-\frac{3}{4}$

∴ x² = 100

- Take √ for both sides

∴ x = 10

Substitute the value of x in the equation of y

∵ $y=\frac{75}{10}-\frac{1}{4}(10)$

∴ y = 5

The dimensions of the box are 10 ft and 5 ft

∵ $V=75x-\frac{1}{4}x^{3}$

∵ x = 10

∴ $V=75(10)-\frac{1}{4}(10)^{3}$

∴ $V=750-\frac{1}{4}(1000)$

∴ V = 750 - 250

∴ V = 500 ft³

The maximum volume is 500 ft³

Learn more:

You can learn more about the volume in brainly.com/question/6443737

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6 0

3 years ago

A right triangle has a hypotenuse of 70 feet and a leg of 35 feet. What is the length of the other leg? Select one:

saveliy_v [14]

H = 70ft.
P = 35ft.
B = ?

H^2 = P^2 + B^2
70×70 = (35×35) + B^2
B^2 = 4900-1225
B = √3675
B = 35√3 ft.

3 0

3 years ago

If the train that Megan is riding covers 180 miles in 3 hours, how fast is the train traveling?

Anettt [7]

Answer:

60 mph

Step-by-step explanation:

3 0

3 years ago

32 people volunteers to donate blood. n dident have he health requirment so they couldent donate the rest of the volunteers dona

Vesna [10]

Answer:

the equation representing total amount of blood donated is $470(32-n)=15040-470n \ ml$ .

Step-by-step explanation:

Total number of volunteers = 32

number of volunteers couldn't donate blood = $n$ .

So Number of volunteers who donated blood can be calculated by subtracting number of volunteers couldn't donate blood from Total number of volunteers.

Framing in equation form we get;

So, the number of remaining volunteers who donated blood = $32-n$ .

Each of these volunteers donated blood = 470 ml

Now Total Amount of Blood donated is equal to Amount each of these volunteers donated blood times the number of volunteers who donated blood.

Framing in the equation form we get;

total amount of blood donated milliliters = $470(32-n)=15040-470n \ ml$

Hence the equation representing total amount of blood donated is $470(32-n)=15040-470n \ ml$ .

4 0

3 years ago