Mathematics College

A rectangular box has the dimensions shown in the diagram. The volume of the box is given by the function V(x) = x3 – 4x, where x is the height in inches.

What is the height of the box if the volume is 15 in.3?

There is a rectangular box with length x+2 in. , width x-2 in. , and height x in.

height = in.

Answers

Answer 1

Answer:

[tex]Height =3[/tex]

Step-by-step explanation:

Given

[tex]Length = x + 2[/tex]

[tex]Width = x - 2[/tex]

[tex]Height = x[/tex]

[tex]Volume = 15[/tex]

Required

Find the height

The volume is calculated as thus:

[tex]Volume = Length * Width * Height[/tex]

This gives

[tex]15 = (x + 2) * (x - 2) * x[/tex]

Apply difference of two squares

[tex]15 =(x^2 - 4 ) * x[/tex]

[tex]15 = x^3 - 4x[/tex]

Subtract 15 from both sides

[tex]x^3 - 4x - 15 = 0[/tex]

Using a calculator to factorize, we have:

[tex](x-3)(x^2+3x+5) = 0[/tex]

Split

[tex]x - 3 = 0[/tex] or [tex]x^2 + 3x + 5 = 0[/tex]

[tex]x = 3[/tex] or [tex]x^2 + 3x + 5 = 0[/tex]

x has complex roots for [tex]x^2 + 3x + 5 = 0[/tex]

Hence:

[tex]x = 3[/tex]

Recall that:

[tex]Height = x[/tex]

[tex]Height =3[/tex]

Related Questions

how to prove it's an identity
sin y + sin 3y + sin 5y + sin 7y = 4 cos y cos 2y sin 4y

Answers

Answer:

0.9777102203

Step-by-step explanation:

the identity is 0.9777102203

mathew paid a total of $68.00 for 8 pepporoni pizzas

Answers

Answer:

Each pizza cost $8.50

Step-by-step explanation:

You are taking a trip at the same time as another
family. Your family traveled 1.900 miles in 2 days,
their family traveled 2.700 miles in 3 days. Who is
traveling fastera

Answers

Answer:

My family is traveling faster, since it is traveling at the rate of 950 miles per day, while the other family travels at 900 miles per day.

Step-by-step explanation:

Since I am taking a trip at the same time as another family, and my family traveled 1,900 miles in 2 days, while their family traveled 2,700 miles in 3 days, to determine who is traveling faster the following calculation must be performed:

1,900 / 2 = 950

2,700 / 3 = 900

Thus, my family is traveling faster, since it is traveling at the rate of 950 miles per day, while the other family travels at 900 miles per day.

Adrian is walking along the edge of a circular pool. The distance from one end of the pool to the other and through its center is
24 feet
What distance, rounded to the nearest hundredth of a foot, did Adrian cover to complete one lap of the pool by walking along its
edge?
O A
452.39 feet
ов.
37.70 feet
Ос.
75.40 feet
OD
150.80 feet

Answers

Answer:

Step-by-step explanation:

Help Me As quick as possible

Answers

Answer:

(A)

Step-by-step explanation:

Answer:

C and D are greater than 250.

Step-by-step explanation:

a = 225

b = 41 1/6

c = 500

d = 281 1/4

Find ALL solutions:

x^4 + 8x = 0

Answers

Answer:

x = 0 or x = -2

Step-by-step explanation:

x^4+8x=0

Step 1: Factor left side of equation.

x(x+2)(x2−2x+4)=0

Step 2: Set factors equal to 0.

x=0 or x+2=0 or x2−2x+4=0

x=0 or x=−2

Answer:

x= 0, -2, 1+i[tex]\sqrt{3}[/tex], 1-i[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Hope it helps ;)

Evaluate the following expression (2.3)-3(1,1)

Answers

Answer:

2.3 - ( 3, 1)

Step-by-step explanation:

1) Simplify 3 × (1, 1) 3 × (1, 1) to 3× 1, 13 × 1,1.

2.3 - ( 3 × 1, 1 )

2) Simplify 3 × 1 to 3.

2.3 - ( 3, 1)

Therefor, the answer is 2.3 - ( 3, 1).

The value of the expression is an illustration of equivalent equations

The value of 2.3 - 3(1.1) is -1

How to determine the value of the expression

The expression is given as:

2.3 - 3(1.1)

Open the bracket

2.3 - 3(1.1) = 2.3 - 3.3

Evaluate the difference

2.3 - 3(1.1) = -1

Hence. the value of 2.3 - 3(1.1) is -1

Answers

I think it’s 25 but I’m not too sure

Which number line represents the solution to

W - 2 < 8 ?

Answers

Answer:

w<10

number - A

(<) means "open circle to the left."

Find the areas of these parallelograms, drawn on a centimetre grid.
b)
a)

Answers

Answer:

a-16cm

b-12cm if not iwill look again

Step-by-step explanation:

Area of the parallelograms are :(a) = 16 cm² and (b) = 12 cm² which is drawn on a centimeter grid.

What is Parallelogram?

A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal. A parallelogram is a square and a rhombus is a square.

The formula to calculate the area of a parallelogram can thus be given as,

Area of parallelogram = b × h square units

where b is the length of the base and h is the height or altitude

For parallelogram (a),

length of the base = 4 cm

the height or altitude = 4 cm

Area of parallelogram (a) = b × h = 4 × 4

Area of parallelogram (a) = 16 cm²

For parallelogram (b),

length of the base = 2 cm

the height or altitude = 6 cm

Area of parallelogram (b) = b × h = 2 × 6

Area of parallelogram (b) = 12 cm²

Learn more about parallelograms here:

brainly.com/question/11220936

#SPJ2

What is the measure of Angle A?
A
6x - 20
3x +4

Answers

Answer:

A=152°

Step-by-step explanation:

6x-20=3x+4

3x=24

x=8

6x-20=6(8)-20=48-20=28

A=180-28=152

Please help 30 points will give brainliest

Answers

Answer:

60°

Step-by-step explanation:

48 bilyenin 8de 1 i kaç tanedir

Answers

Answer:

Huh-

Step-by-step explanation:

please help I appreciate it also have a good day!

Answers

17 to the power of 1

17 to the power of 1 its soo easy

Help, I don’t understand this DeltaMath question

In ΔHIJ, the measure of ∠J=90°, the measure of ∠I=52°, and JH = 4.2 feet. Find the length of IJ to the nearest tenth of a foot.

Answers

I can use the angle and the length of JH to find the length of IJ.

To do this, I look at the relationship IJ and JH have to the 52 degree angle. JH is opposite to angle I, and IJ is adjacent to angle I. Because the two side lengths are opposite and adjacent, I use the tangent function to solve this.

Tangent of an angle = the length of the opposite side / the length of the adjacent side. This is just another way to say tan(x)=opposite/adjacent

Now I can fill in what I know...
tan(52)=4.2/x
Now, I want to isolate x.
tan(52) = 4.2/x
x(tan(52))=4.2
x=4.2/tan(52)

Now I put 4.2/tan(52) into a calculator and get x = 3.3 ft

Hope this helps!

There is a $250 entrance fee for each band to enter the competition. A total of $8000 was collected. How many bands competed in this competition? PLEASE HELPPPPPPPPPPPPPPPPPPPPPP

Answers

32 because $250 x 4 = $1000, and $8000/$1000 =8, so 4 x 8 = 32

32!! 8000 divided by 250 is 32! So you have 32 bands

6) What would be the next three terms in the sequence 1, 3, 9, 27.....? *
2 points

Answers

81

explanation: you are multiplying by 3 each time. 27*3 is 81.

it’s 81!!!!!!!!!!!!!

allowing 20% discount on the Marked price of a watch value of the Watch will be rupees 2376 of vat of 10% is added find its marked price

Answers

Answer:

brainly.in/question/15492399

Here your question has been answered.

Hope this helps you, Do mark me as brainliest.

what is the answer to 2x+7=-3x+37

Answers

Answer:

Step-by-step explanation:

Answer: x=6

Step-by-step explanation:

hope this helps!

PLEASE
Find the mean, median, mode, and range of the following data set.

4, 3, 2, 4, 6, 6, 4, 3, 3, 4, 5

Mean:

Median:

Mode:

Range:

Answers

Answer:

Mean: 4

Median: 4

Mode: 4

Range: 4

Hope this helps

mean: 4

median: 4

mode: 4

range: 4

2 3 3 3 4 4 4 4 5 6 6

What is the equation of a circle with the center(-9,-5) and radius equals 9

Answers

Answer:

(x+9)^2+(y+5)^2=81

Step-by-step explanation:

(x-h)^2+(y-k)^2=r^2

(h,k)=center

r=radius

so if you just insert the center (-9,-5) and the r with 9

(x-(-9))^2+(y-(-5))^2=9^2

(x+9)^2+(y+5)^2=81

Hope that helps :)

Answer:

(x + 9)^2 + (y + 5)^2 = 81

Step-by-step explanation:

Hope this helps

If right I’ll mark brainiest

Answers

Answer:

1.5s - 0.5

Step-by-step explanation:

-2.9a + 6.8 + 4.4a - 7.3

6.8 - 7.3 = -0.5

-2.9a + 4.4a = 1.5a

1.5s - 0.5

Answer:

1.5a

Step-by-step explanation:

The diagram shows three angles at a point.
Not drawn accurately
168
x 123
Work out the value of x.

Answers

Angle x has a size of 69.

What exactly is a phrase?

One or more terms in an equation can be added, subtracted, multiplied, or divided.

When we simplify an expression, we always merge similar terms in the expression.

If an expression has two sides, we also preserve all similar terms on one side of the expression.

Example:

An expression is 1 + 3x + 4y = 7.

3 + 4 is a formula.

A formula is 2 x 4 + 6 x 7 - 9.

There is an expression: 33 + 77 - 88.

We can determine the angle in a circle given two angles of 168 degrees and 123 degrees.

168°+123°+x°=360°

291°+x°=360°

291°-x°=360 °

x=69°

To know more about expression visit:

brainly.com/question/3118662

#SPJ1

explain natural substance

Answers

Answer:

This is your answer ☺️

Biotic materials. Wood: rattan, bamboo, bark
Natural fiber: silk, wool, cotton, flax, hemp, jute, kapok, kenaf, moss

the difference of d and 7 divided by 2

Answers

Answer:

(D- 7) ÷ 2

Substitute D

(8 - 7) ÷ 2

1 ÷ 2

0.5

when five is subtracted from
4 times a number and the
remainder is divided by 3, the
result become 7. what is the
number?

Answers

Hope it helps u mate.......

The temperature overnight in Sitka, Alaska was 12 below zero. How should this be written?

Answers

Answer:

-12°

Step-by-step explanation:

it is negative because it it below zero.

Finding angle measure pls help

Answers

58

Hope it’s right
Best luck with your studying

Can someone give me the answer please

Answers

Answer:

<-.....-8 -7 -6 -5 -4 -3 -2 -1 0................->

The values of the number decreases

Step-by-step explanation:

вычислите: 7/8:(-2 1/4):5/6:(2 1/2):(-6/25)

Answers

Answer:

= 3087 / 320

Step-by-step explanation:

Other Questions

Mary is content with middle class life and looks forward to the future. hii if you answer this ill give you brainlist Helppppp im in a test so hurry help with this question plz In order to request the records of a prior case for review and possible reconsideration, the Supreme Court of the United States issues which of the selections listed below to the lower courts? DOES THIS LOOK GODD??The people of ZincWritten by: Ava.NCharacters by: Ava. NOne of the most desolate days of Zincs was in 2000 on Friday, Jan 1. It was a new years day, everybody was having fun, running around playing, and singing. The Zinc always invited people that came into their village. The people of Zink were the nicest and smartest of the village. They didn't even know what was going to happen next when they invited Zandar. Zandar the ruler of kings. He wore a black robe, and went straight to the church on Friday, Jan 1. I was there. I knew what he looked liked and I didnt like him at first. Napkin followed him to the church, trying to stay behind him but not too close but not too far. He took off his robe, then some weird muscler cats came out of nowhere. Man those are some big cats, I wonder if they're just here to worship their gods or something. Napkin whispered. Is the ship here yet? Zandar mumbled Yes my king. The minion bowed his head in approval, to the king. A starved cat wobbled up the stairs with bloat pink eyes. My king may you spare us some food. The starving swollen cat whimpered. My people are bringing some food right now and it's filled with crates of bread and fish. Tell all your friends to come over and get some bread and fish. The more friends you bring the more bread and fish you get. Zandar said in a happy tone. Yes my lord! I shall hurry off and get all my family and friends. The starving cat, not looking starving anymore, ran off behind an open alley. I can see the crates from here, you may go get more cats. Zandar hesitated. For our feast.A few minutes later, a large number of boxes, and crates were everywhere around the church. It never smelled like fish or bread anywhere, it was mostly smelled like powder. Napkin snuck behind the church getting to one of the boxes. The smells stinged his nose, making him almost sneeze. He tried all his strength to open one of the boxes. AHH! Napkin screamed. What was that! Zandar whispered, biting his lip hard. Almost making it bleed. Probably just some kids chasing each other. One of the minions said.Napkin ran in front of the church, almost rolling over on his back.HE HAS GUNS! Napkin screamed.It felt like the whole village turned quiet for one second. Zandar let his claws out, gripping them to the church, almost breaking the stone cobbla. His eyes were furious. Africa ran to bite his brother on the neck grabbing his scruff. Sorry for my little brother, he just had too much milk today! Africa apologized I'm telling the truth! Please listen to me! You'll all die! Napkin was trying to struggle to get out of his brothers grip. Zandar smiled evilly at Napkin, being pulled away by his brother. Napkin could not hear what Zandar was saying to his Minions but...Happy New year! Zandar laughed.The pulling of Napkins brother stopped. Napkin ran as fast as he could, seeing bodys drop left and right of him. Hearing bullet guns drop. He stopped running pushing the dirt and gravel in the air, running back to his brother.No! Napkin yelled. Pushing his head against the dead body of his brother. He felt pain in his head and in his stomach. Zandar punched on Napkin. He rolled over hitting the gravel upside down making his nose bleed. Zander's hand unleashed his long claws in the air. Swinging down, if flet slow in Napkins brain. He rolled over and ran as fast as he could. Getting from under Zandar.Everyone I know is dead, everyone I talked to is dead, EVERYONE.. Napkin thought in his head tears rolling down from his eyes running away from the church. Anywhere away from him, ANYWHERE!Chapter 1: The Invitation Napkin sprinted from the bushes chasing the rabbit. Sweat came down from his fur trying not to lose the rabbit. Mouse brain! Napkin yelled. A hawk had grabbed the rabbit with their sharp talons, flying off into the distance. Dang it. Napkin kicked dirt across the grass. That's the third one today! I'm going to start to get dizzy at some point in the day. Napkin walked to the right bank of a river, drinking some water. Got to stay hydrated I guess? Napkin felt a pain in his left shoulder, he fell back on his stomach, looking near the left of his eye seeing blood flow down his left shoulder. He stood shaking in pain as he looked up, seeing a black figure approaching him out of the blushes, walking towards him in the river. He couldn't keep his eyes open any longer, his eyelids got heavier and heavier. select all the statements that are true (YOO SOMEONE) Solve the problem:Kiram has 5 ziploc bags. He puts an equal number of marbles (X).Then he realized that heneeded to add 2 more marbles for each bag. If the total number of marbles is 30 how manymarbles in each bag? answer the 3 questions (brainliest) im not sure if the first ones right Fruit-O-Rama sells dried pineapple for $0.25 per ounce. Mags spent a total of $2.65 on pineapple. How many ounces did she buy [tex]the \: surface \: area \: of \: a \: cube \: is \: 24 \: cm \: fimd \: the \: volume[/tex] 330 is what percent of 20? how to the eath turn Please Help. Thank You! Writing a rapI have to write a rap for music and this is what I need to do:1. Choose a topic and pick a title for your rap2. Write the lyrics3. Explain the purpose of this rap(Anything would be helpful even just a topic to write the rap about) If a day of the week is randomly selected, what's the probability that the day contains the letter "a" in its name?Round your answer to four decimal places (if necessary). EXPOSITORY WRITING write a paragraph explaining how life in the west was different from life in the west. Weston is shopping for a new backpack. The backpack he wants costs$25.95. The sales tax in Weston's city is 6%. Write two expressions torepresent the price of the backpack, b, plus 6% of the cost. One expressionshould be a sum and the other should be a product. (Be sure to write two.) pls help the teacher said its not 14 I dont know express 75 as a product of three factors