Mathematics High School

A box with a square base of side a is three times higher than its width. Express the volume V of the box as a function of a.
V(a) = ?

Answers

Answer 1
volume of a box is length x width x height.
Here its bottom is square, with side= a (its side has length a)The box is three times higher.  This means 3 times a is its height.So putting it together:length= a, width =a  (square base)height= 3a  (three times higher than it is wide)V=a⋅a⋅3a=3a3
Answer 2

The volume V of a box with a square base of side a and a height that is three times its width is expressed as the function V(a) = 3a³.

To express the volume V of a box as a function of its base side length a, with the height being three times its width, we can use the formula for the volume of a rectangular prism, which is the product of its length, width, and height. As the base is a square with side a, both the length and the width of the base are a. Given that the box's height is three times its width (or length, since it is a square), the height will be 3a.

Therefore, the volume V of the box as a function of a is V(a) = a² × (3a) = 3a³.

Related Questions

Solve the inequality 6x - 8 > 4x + 26

x < 9

x < 17

x > 9

x > 17

Answers

6x > 4x+26+8
2x > 34

so,
x > 17 

Answer:

The Answer is D.  x > 17

Hope This Helps!

Farmer tom’s chickens and sheep are all in a jumble. he counts 48 heads and 134 legs, how many sheep does he have?

Answers

Chickens have 2 legs and sheep have 4 legs. If x is the number of chickens and y is the number of sheep, then we have the system of equations: x + y = 48, 2 x + 4 y = 134. We can solve this system : x = 48 - y, then we will put it into the 2nd equation: 2 * ( 48 - y ) + 4 y = 134, 96 - 2 y + 4 y = 134, 2 y = 134 - 96, 2 y = 38, y = 38 : 2, y = 19. Answer: Farmer Tom has 19 sheep.

A farmer wishes to enclose a pasture that is bordered on one side by a river (so one of the four sides wont require fencing) She has decided to create a rectangular shape for the area and will use barbed wire to create the enclosure there are 600 feet of wire availible for this project and she will use all the wire. what is the maximum area enclosed by the fence then find the maximum of the function. ...?

Answers

The area enclosed is (2x)(600-2x).(2x)(600−2x)=1200x−4x2
In order to maximize we need the derivative to be equal to 0.y′=1200−8x=0
1200=8x
x=150
Therefore the sides for maximum area are 150*300.
The area is: 45000

Answer:

Area is 45000 square feet.

Step-by-step explanation:

Let x be the length of fenced side parallel to the river side.

Let y be the length of other two sides.

Then,

[tex]x+ 2y 600[/tex]

So, we get [tex]x=600-2y[/tex]

Area of this rectangle = xy

= [tex]y(600-2y)[/tex]

[tex]x=-2y^{2}+600y[/tex]

Now attached is the graph of the area function, which is a parabola opening downward.

We can see ta the maximum area occurs when y=[tex]-600/[2(-2)][/tex] = 150

And [tex]x = 600-2(150)[/tex]

x =[tex]600-300=300[/tex]

Therefore, to maximize the area, the side parallel to the river is to be 300 feet long, and the other two fenced sides should be 150 feet long.

The area is = [tex]300\times150= 45000[/tex] square feet.

Using the 28/36 ratio, determine the maximum allowable recurring debt for someone with a monthly income of $4,850.
a. $388
b. $776
c. $970
d. $1,358

Answers

Answer:

The correct answer is A. $388

Step-by-step explanation:

The 28/36 Rule states that : A household should spend a maximum of 28% of its gross monthly income on total housing expenses and not more than 36% on total debt service.

Maximum expense on housing expense = 28% of 4850

                                                                    = $1358

Maximum expense on total debt service = 36% of 4850

                                                                    = $1746

Therefore, the maximum allowable recurring debt with a monthly income of $4,850 = 1746 - 1358 = $388

Hence, The option A is correct.


Answer:

a

Step-by-step explanation:

got it right on edge

The slope of a line is 0, and the y-intercept is 6. What is the equation of the line written in slope-intercept form? y = 6 y = 6x y = x + 6

Answers

the answer would be y=0x+6

Answer:

The answer is

y = 6

The first digit in the quotient of 6523÷7

Answers

931.857143 is ur answer. Ok

160 percent of 1,825 is? Rounded to nearest tenth
...?

Answers

2920 is 160 percent of 1825

A ball on a string moves around a complete circle, once a second, on a frictionless, horizontal table. The tension in the string is measured to be 6.0N . What would the tension be if the ball went around in only half a second?

Answers

The tension in the string balances out, and thus equals the centripetal force of the ball 

T = mv^2/r 

if it only takes half the time to finish one orbit it has to be moving at twice the original speed. 

And since v is squared T will increase by 4 

T' = m(2v)^2/r 

T' = 4mv^/r = 4T 

T' = 24.0 N

I hope my answer has come to your help. Have a nice day ahead and may God bless you always!
Final answer:

If the ball went around in half a second, the tension in the string would be 24.0 N.

Explanation:

To find the tension in the string if the ball went around in half a second, we can use the equation for centripetal force. The tension T in the string provides the centripetal force, which is equal to the mass of the ball times the square of its velocity divided by the radius of the circle:

T = (m * v^2) / r

In this case, the mass of the ball and the radius of the circle remain the same, but the velocity changes. Since the ball takes half the time to complete the circle, the velocity is twice as fast. Therefore, the tension in the string would be four times greater:

Tension = 4 * 6.0 = 24.0 N

Learn more about tension in string here:

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You travel 2,557 km in 190 days how far did you travel per hour

Answers

You travel 1.78 km per hour. I came up with this by takin 190 and multiplying it by 24(the amount of hours in a day). Then, I divided that by 2557 and came up with 1.78.
What it is asking for is a distance over time in HOURS. 
It isn't specific about the distance units so, we can assume km is OKAY to use!

Now we need to convert 190 days to hours. Let's set up some conversion factors. 

1 Day = 24 Hours

[tex] \frac{190 days}{1} * \frac{24 hours}{1 day} [/tex]

I recommend setting up conversions like the way I did above. To do so simply make the units cancel out. Similar to how 3/3 cancel out, units also cancel out in the same way. So when you are trying to figure out whether or not you divide or multiply by the conversion factor simply use this method. Say we had 190 hours, the hours unit would need to be on the bottom, and the days on top. It'd be 1/24, thus you would divide by 24. 

[tex] \frac{190 days}{1} * \frac{24 hours}{1 day} [/tex] = 4560 hours.

Now what it is asking for his a rate of distance per hour. This rate is also called speed. Remember in the statement it said how far per hour. Meaning when dividing the units should look like this: [tex] \frac{km}{hour} [/tex]

[tex] \frac{2557km}{4560hour} [/tex] = 0.5607[tex] \frac{km}{hour} [/tex]

The answer is: 
0.5607[tex] \frac{km}{hour} [/tex]
 

Lets say I had an 80% in a class, yet I got a 100% percent on the midterm, which is 10% of my grade. What would my new grade be?

Answers

you can do a quick calculation of the grades with their weighted percent!!

if you assume that your grade combines to 100% total, and the midterm that's 10% of your grade has yet to be factored in, this would mean that you've received 90% of your grades. in this 90%, you got an 80.

so, at 90% you scored an 80%. at 10% you scored a 100%. you need to combine the two of these to represent how your assignments/tests/homework combine to 100% (90 of that finished, 10 of that coming from your midterm). create an addition problem that represents this, converting percents to decimals:

(0.90)(0.80) + (0.10)(1.00) = .82, or 82%

your final grade would be an 82% in the class.

what capital letters are reflect symmetry

Answers

The letters O and X are reflective. 
The following capital letters are symmetrical:
A
B
C
D
E
H
I
M
O
T
U
V
W
X
Y



Is 3.4 a rational or irrational number? Please explain why, thanks.

Answers

Rational, 3.4 can be written as a fraction and is noncontinuous
"An irrational number can be written as a decimal, but not as a fraction. An irrational number has endless non-repeating digits to the right of the decimal point."

Answer:

Yes it is a rational number

I just did it and I passed

Which absolute value function, when graphed, will be narrower than the graph of the parent function, f(x) = |x|? f(x) = |x| – 3 f(x) = |x + 2| f(x) = 0.5|x| f(x) = 4|x|

Answers

That would be f(x) = 4|x|. Reason is, the bigger the number that's multiplied by |x|, the narrower the graph will be. The opposite is true for the smaller the number, & so f(x) = .5|x| will be wider.
Hope this helps!

f(x) = 4|x| is the function narrower than the parent function , Option D is the correct answer.

What is an absolute function ?

An Absolute function is a function that returns a positive value at any given point.

It is given that

The parent function is

f(x) = |x|

To find the function which will be narrower , it will be plotted to check

It is the known fact that when a function is multiplied by a number greater than 1 , the resulting function gets narrower , This can be easily identified from the graph.

f(x) = 4|x| is the function narrower than the parent function , Option D is the correct answer.

To know more about Absolute Function

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Which arrangement shows 4.09,4 2/3 ,21/4 and 4.7 in order from least to greatest?

Answers

4.09 < 4 2/3 < 4.7 < 21/4

6-4x verbal expression

Answers

Four multiplied by "x" subtracted from six
Six minus four multiplied by x

An organic farm uses 3/7 of the land to grow potatoes and 2/5 of the land to grow spinach. The remaining land is used to grow tomato plants. What fraction of the land is used to grow tomato plants?

Answers

Fraction of the land is used to grow tomato plants=1-(fraction of the land to grow potatoes + fraction of the land to grow spinach)


Land used for to grow tomato plants=1-(3/7 + 2/5)
=1-(15+14)35
=1-29/35
=(35-29)/35
=6/35

Answer: this organic far uses 6/35 of the land to grow tomato plants.

HELP!!!
what is the value of x in the following equation:
1/4 x + 1/4 x = 4/5 ?
A. 8/5
B.5/8
C.2/5
D.3/5

Answers

the value of x in this equation is 2/5

What are the constant terms in the expression? 8m−5n+2+m−148m−5n+2+m−14 Drag and drop the constant terms into the box.

Answers

2

Is is the only integer that is alone.
2, 2, and -14 are the constant terms. They never change. The other terms change when 'm' and 'n' change.

what is a term without a variable

Answers

A term without a variable is called a constant term, and the degree of that term is 0 Hope that helps you I knew this was 0 beciase i study this a long time ago

Solve the system of equations.

5x + y = 9
3x + 2y = 4

Answers

y=-5x+9

3x+2(-5x+9)=4
3x-10x+18=4
-7x=4-18
-7x=-14
x=2

5(2)+y=9
10+y=9
y=9-10
y=-1

The answer is (2,-1) :)

Four points A, B, C, and D are coplanar, but only two at a time are collinear. Suppose a line is drawn through each pair of points. How many lines can you draw? ...?

Answers

Based on the given details above, the number of lines that can be drawn through each pair of points would be six: Four sides and two diagonals. When we say coplanar points, these are points that lie in the same plane. This is made up of three or more points. Hope this answer helps. 

Thirteen and eight tenths

Answers

13 8/10

hope this helps you

It takes for three gardeners 90 minutes to weed a garden. If the job is to be done in only 15 minutes, how many more gardeners need to be put on the jobs?

Answers

3 gardeners :90 minutes
? Gardeners : 15 minutes
1 gardener : 270 minutes
? Gardeners : 270/15
18 gardeners
The answer is 15 gardeners.
Thus, 15 gardeners would be needed if the job is to be done in only 15 minutes.

Find the slope of the line that passed through points a and d
A) -7/2
B) -2/7
C) 0
D) 2/7

Answers

Simple...

you have: Find the slope of the line that passed through points A and D.

A is located at: (-3,-2)

B is located at (4,0)

Using [tex] \frac{ y_{1}- y_{2} }{ x_{1}- x_{2} } [/tex] to find slope-->>>

[tex] \frac{-2-0}{-3-4} = \frac{-2}{-7} = \frac{2}{7} [/tex]

m=[tex] \frac{2}{7} [/tex]

Thus, your answer.

Answer:

The answer is m=2/7 or answer choice D

Step-by-step explanation:

A store is having a clearance sale where merchandise on the sales rack is reduced by 80% from the original price. If a jacket was originally priced at $76, what is the sale price.

Answers

76 - 80% = 15.2 
$15.20 is your answer :)

At the grocery store, you buy a carton of milk for $1.95, a loaf of bread for $0.85, and a box of cereal for $2.05. Use mental math to find the total cost of the groceries

Answers

total cost is 4.85 dollars to do this simply add them together

license plates in a particular state display two letters followed by three numbers, such as AT-887 or BB-013. How many different license plates can be manufactured for this state?

Answers

10^3*26^2
10 values 0-9 which can repeat
26 letters which can repeat

What is the measure of angle B?

A. 32
B. 62
C. 120
D. 31

Answers

I hope this helps you
so we can narrow it down to a or D .so if 5*31 =155 155-35=120 .180-120=60 60+58=118 180-118=62 31*2=62(answer is 31) and sorry for the long problem.its how I think.if you need more help with answers,m message and follow me .

tinku is fond of collecting spiders and insects. He knows spiders have 8 legs and insects have 6 legs. he counted 36 legs. How many of each does he have in hi collection?

Answers

Let, number of spiders = x
number of insects = y

6x + 8y = 36

remember, legs can't be in fraction or decimal.

So, only (3, 2) fits with that.

So, there are 3 spiders & 2 insects in his collection.

Hope this helps!

John has 15 more music cds than micheal together they have a total of 55 cds

Answers

Michael has 40 CDs. 40+15=55. 
Other Questions
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