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3 years ago

Wayne earns 7%

Mathematics

1 answer:

Ronch [10]3 years ago

7 0

Answer:

Step-by-step explanation:

3500 divided by 5 equals 700

700 times 7% equals 49

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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by

11111nata11111 [884]

Answer:

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is 8.217 cubic inches.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the open rectangular box ?

Solution :

Let the height be 'x'.

The length of the box is '11-2x'.

The breadth of the box is '7-2x'.

The volume of the box is $V=l\times b\times h$

$V=(11-2x)\times (7-2x)\times x$

$V=4x^3-36x^2+77x$

Derivate w.r.t x,

$V'(x)=4(3x^2)-2(36x)+77$

$V'(x)=12x^2-72x+77$

The critical point when V'(x)=0

$12x^2-72x+77=0$

Solve by quadratic formula,

$x=\frac{18+\sqrt{93}}{6},\frac{18-\sqrt{93}}{6}$

$x=4.607,1.392$

Derivate again w.r.t x,

$V''(x)=24x-72$

Now, $V''(4.607)=24(4.607)-72=38.568>0$ (+ve)

$V''(1.392)=24(1.392)-72=-38.592$ (-ve)

So, there is maximum at x=1.392.

The length of the box is $l=11-2x$

$l=11-2(1.392)=8.216$

The breadth of the box is $b=7-2x$

$b=7-2(1.392)=4.216$

The height of the box is h=1.392.

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is $V=l\times b\times h$

$V=8.216\times 4.216\times 1.392$

$V=48.217\ in.^3$

The volume of the box is 8.217 cubic inches.

5 0

3 years ago

The figure below shows the ideal pattern of movement of a herd of cattle, with the arrows showing the movement of the handler as

geniusboy [140]

Based on the theory, the distance from the starting point to the return point = Arc length = 109.9 feet.

<h3>What is the Length of an Arc?</h3>

The arc length of a circle can be calculated with the radius and central angle using the arc length formula.

Arc length = ∅/360 × 2πr

Since the sector formed is a quarter circle, then ∅ = 90°.

Raidus (r) = 70 ft

Distance from the starting point to the return point = arc length.

Arc length = ∅/360 × 2πr = 90/360 × 2π(70)

Arc length = 109.9 feet

Therefore, based on the theory, the distance from the starting point to the return point = Arc length = 109.9 feet.

Learn more about the arc length on:

brainly.com/question/2005046

#SPJ1

6 0

2 years ago

What is x? -3(52)=-3(x)+-3(2)

krek1111 [17]

Answer:

x = 50

Step-by-step explanation:

-3(52)=-3(x)+-3(2)

Divide both sides by -3

52 = x + 2

x = 50

8 0

3 years ago

These rational expressions all have the same denominator write the sum of their numerators over the common denominator 2x+1 + x

ale4655 [162]

So if all same you just simplify The top : 2x+1+x+4 2x+x+1+4 3x+5 The bottom all same just use one .x-3 3x+5/x-3

8 0

3 years ago

Read 2 more answers

A group of organs that work together together to perform a major function is called

Rasek [7]

Answer:

organ system

Step-by-step explanation:

Cells make up tissues, tissues make up organs, and organs make up organ systems.

8 0

3 years ago