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3 years ago

5

Rachel is a stunt driver. One time, during a gig where she escaped from a building about to explode, she drove to get to the saf

e zone at 24 meters per second. After 4 seconds of driving, she was 70 meters away from the safe zone.
Write this as a formula D(t):_+_

1 answer:

sergij07 [2.7K]3 years ago

8 0

Do you have any more information

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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

#LearnwithBrainly

6 0

3 years ago

The area of a parallelogram is 96 cm2. The height of the parallelogram is 4 cm less than the length of the base. What is the len

Valentin [98]

96/4=24 so the length of a standerd paralleegram is 24

4 0

3 years ago

Read 2 more answers

The Roman numeral which represents the number in standard form for 3,089 is?

Tresset [83]

MMMLXXXIX

~ hope this helps!

4 0

3 years ago

Solve the question below, please.

Ne4ueva [31]

Answer:

Adam: 52.26°

Step-by-step explanation:

Use Cosine Rule, $Cos(C) = \frac{a^2 + b^2 - c^2}{2ab}$ , to find the angle of both players.

✔️Angle of Carlos:

Let the angle be C,

a = 50 ft

b = 40 ft

c = 24 ft

Plug in the values into the equation

$Cos(C) = \frac{50^2 + 40^2 - 24^2}{2*50*40}$

$Cos(C) = \frac{3,524}{4,000}$

$C = Cos^{-1}(\frac{3,524}{4,000})$

C = 28.24° (nearest hundredth)

✔️Angle of Adam:

Let the angle be C,

a = 30 ft

b = 22 ft

c = 24 ft

Plug in the values into the equation

$Cos(C) = \frac{30^2 + 22^2 - 24^2}{2*30*22}$

$Cos(C) = \frac{808}{1,320}$

$C = Cos^{-1}(\frac{808}{1,320)}$

C = 52.26° (nearest hundredth)

6 0

3 years ago

Emily and Kylie are 140 miles apart, traveling towards each other. If Kylie travels 12 mph and Emily travels 8 mph how long unti

Bogdan [553]

Answer: 7 hr

Step-by-step explanation:

Given

Distance between Emily and Kylie is $140\ \text{miles}$

Speed of Emily $v_e=12\ mph$

Speed of Kylie $v_k=8\ mph$

Distance traveled by Emily $\Rightarrow d_e=12t$

Distance traveled by Kylie $\Rightarrow d_k=8t$

$\Rightarrow 12t+8t=140\\\Rightarrow 20t=140\\\Rightarrow t=7\ hr$

They will meet after 7 hour.

3 0

3 years ago