66 results

cube - solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges

1 over 14 cubed

1 over 14 cubed
14 cubed means we raise 14 to the power of 3:
14^3
1 over 14 cubed is written as:
1/14^3
To simplify this, we [URL='https://www.mathcelebrity.com/powersq.php?sqconst=+6&num=14%5E3&pl=Calculate']evaluate 14^3[/URL] = 2744
So we have:
[B]1/2744[/B]

2/5 the cube of a number

2/5 the cube of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The cube of a number means we raise x to the power of 3:
x^3
2/5 of the cube means we multiply x^3 by 2/5:
[B](2x^3)/5[/B]

4 multiplied by the cube of p is reduced by 5

4 multiplied by the cube of p is reduced by 5
The cube of p means we raise p to the 3rd power:
p^3
4 multiplied by the cube of p
4p^3
reduced by 5:
[B]4p^3 - 5[/B]

4 times a number cubed decreased by 7

4 times a number cubed decreased by 7
A number is denoted as an arbitrary variable, let's call it x
x
Cubed means raise x to the third power
x^3
Decreased by 7 means subtract 7
x^3 - 7

4 times of the sum of the cubes of x and y

4 times of the sum of the cubes of x and y
The cube of x means we raise x to the 3rd power:
x^3
The cube of y means we raise y to the 3rd power:
y^3
The sum of the cubes means we add:
x^3 + y^3
4 times the sum of the cubes:
[B]4(x^3 + y^3)[/B]

5 more than twice the cube of a number

5 more than twice the cube of a number.
Take this algebraic expression in pieces.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The cube of a number means we raise it to a power of 3
x^3
Twice the cube of a number means we multiply x^3 by 2
2x^3
5 more than twice the cube of a number means we multiply 2x^3 by 5
5(2x^3)
Simplifying, we get:
10x^3

5 more than twice the cube of a number

5 more than twice the cube of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
The cube of a number means we raise x to the power of 3:
x^3
Twice the cube means we multiply x^3 by 2
2x^3
Finally, 5 more than twice the cube means we add 5 to 2x^3:
[B]2x^3 + 5[/B]

64 divided by the cube of y

64 divided by the cube of y
The cube of y means y raised to the 3rd power:
y^3
64 divided by this:
[B]64/y^3[/B]

7 subtracted from x cubed

7 subtracted from x cubed
x cubed means x raised to the 3rd power
x^3
7 subtracted from this
[B]x^3 - 7[/B]

7 times the cube of the sum of x and 8

7 times the cube of the sum of x and 8
Take this algebraic expression in 3 parts:
[LIST=1]
[*]The sum of x and 8 means we add 8 to x: x + 8
[*]The cube of this sum means we raise the sum to the 3rd power: (x + 8)^3
[*]7 times this cubed sum means we multiply (x + 8)^3 by 7:
[/LIST]
[B]7(x + 8)^3[/B]

A company makes a puzzle that is made of 53 small plastic cubes. The puzzles are shipped in boxes th

A company makes a puzzle that is made of 53 small plastic cubes. The puzzles are shipped in boxes that each contain 52 puzzles. That boxes are loaded into trucks that each contain 53 boxes. What is the total number of small plastic cubes in each truck?
1 truck has 53 boxes, and each box contains 52 puzzles, and each puzzle has 53 small plastic cubes.
We have 53 * 52 * 53 = [B]146,068 plastic cubes[/B]

A cube has an edge that is x cm long. What is the capacity of C(x)?

A cube has an edge that is x cm long. What is the capacity of C(x)?
Capacity is another word for volume, or the amount an object will hold. Given a side x, the capacity (volume) of a cube is:
C(x) = [B]x^3[/B]

A cube is 1 meter long.What is the total length of all its edges?

A cube is 1 meter long.What is the total length of all its edges?
A cube has 12 edges.
12 edges x 1 meter for each edge = [B]12 meters[/B]

A cubical storage box has edges that are 2 feet 4 inches long. What is the volume of the storage box

A cubical storage box has edges that are 2 feet 4 inches long. What is the volume of the storage box?
Since 1 foot = 12 inches, we have:
2 feet 4 inches = 2(12) + 4
2 feet 4 inches = 24 + 4
2 feet 4 inches = 28 inches
We type [URL='https://www.mathcelebrity.com/cube.php?num=28&pl=Side&type=side&show_All=1']cube side = 28[/URL] into our search engine to get:
V = [B]21952 cubic inches[/B]

A cubicle is 6 1?2 feet by 8 3?4 feet. What is the area of the cubicle?

A cubicle is 6 1?2 feet by 8 3?4 feet. What is the area of the cubicle?
Area of a cube is length times width:
A = 8 & 3/4 * 6 & 1/2
We need to convert these to improper fractions.
[LIST]
[*]8 & 3/4 [URL='https://www.mathcelebrity.com/fraction.php?frac1=8%263%2F4&frac2=3%2F8&pl=Simplify']converted to an improper fraction[/URL] is 35/4
[*]6 & 1/2 [URL='https://www.mathcelebrity.com/fraction.php?frac1=6%261%2F2&frac2=3%2F8&pl=Simplify']converted to an improper fraction[/URL] is 13/2
[/LIST]
Multiply the improper fractions together:
A = 35/4 * 13/2
[URL='https://www.mathcelebrity.com/fraction.php?frac1=35%2F4&frac2=13%2F2&pl=Multiply']Using our fraction multiplier[/URL], we get:
[B]455/8 sq ft[/B]
If you want to convert this to a mixed fraction, we [URL='https://www.mathcelebrity.com/fraction.php?frac1=455%2F8&frac2=3%2F8&pl=Simplify']type this in our calculator [/URL]and get:
[B]56 & 7/8 sq ft[/B]

A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the pro

A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the probability that the number rolled is greater than 3 and the coin toss is heads? Write your answer as a fraction in simplest form
Let's review the vitals of this question:
[LIST]
[*]The probability of heads on a fair coin is 1/2.
[*]On a fair die, greater than 3 means either 4, 5, or 6. Any die roll face is a 1/6 probability.
[*]So we have a combination of outcomes below:
[/LIST]
Outcomes
[LIST=1]
[*]Heads and 4
[*]Heads and 5
[*]Heads and 6
[/LIST]
For each of the outcomes, we assign a probability. Since the coin flip and die roll are independent, we multiply the probabilities:
[LIST=1]
[*]P(Heads and 4) = 1/2 * 1/6 = 1/12
[*]P(Heads and 5) = 1/2 * 1/6 = 1/12
[*]P(Heads and 6) = 1/2 * 1/6 = 1/12
[/LIST]
Since we want any of those events, we add all three probabilities
1/12 + 1/12 + 1/12 = 3/12
This fraction is not simplified. S[URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F12&frac2=3%2F8&pl=Simplify']o we type this fraction into our search engine, and choose Simplify[/URL].
We get a probability of [B]1/4[/B].
By the way, if you need a decimal answer or percentage answer instead of a fraction, we type in the following phrase into our search engine:
[URL='https://www.mathcelebrity.com/perc.php?num=1&den=4&pcheck=1&num1=+16&pct1=+80&pct2=+35&den1=+90&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']1/4 to decimal[/URL]
Alternative Answers:
[LIST]
[*]For a decimal, we get [B]0.25[/B]
[*]For a percentage, we get [B]25%[/B]
[/LIST]

A spherical water tank holds 11,500ft^3 of water. What is the diameter?

A spherical water tank holds 11,500ft^3 of water. What is the diameter?
The tank holding amount is volume. And the volume of a sphere is:
V = (4pir^3)/3
We know that radius is 1/2 of diameter:
r =d/2
So we rewrite our volume function:
V = 4/3(pi(d/2)^3)
We're given V = 11,500 so we have:
4/3(pi(d/2)^3) = 11500
Multiply each side by 3/4
4/3(3/4)(pi(d/2)^3) = 11,500*3/4
Simplify:
pi(d/2)^3 = 8625
Since pi = 3.1415926359, we divide each side by pi:
(d/2)^3 = 8625/3.1415926359
(d/2)^3 = 2745.42
Take the cube root of each side:
d/2 = 14.0224
Multiply through by 2:
[B]d = 28.005[/B]

C varies directly as the cube of a and inversely as the 4th power of B

C varies directly as the cube of a and inversely as the 4th power of B
The cube of a means we raise a to the 3rd power:
a^3
The 4th power of B means we raise b to the 4th power:
b^4
Varies directly means there exists a constant k such that:
C = ka^3
Also, varies inversely means we divide by the 4th power of B
C = [B]ka^3/b^4[/B]
Varies [I]directly [/I]as means we multiply by the constant k.
Varies [I]inversely [/I]means we divide k by the term which has inverse variation.
[MEDIA=youtube]fSsG1OB3qdk[/MEDIA]

c varies jointly as the square of q and cube of p

c varies jointly as the square of q and cube of p
The square of q means we raise q to the 2nd power:
q^2
The cube of p means we raise p to the rdd power:
p^3
The phrase [I]varies jointly[/I] means there exists a constant k such that:
[B]c = kp^3q^2[/B]

Cube

Free Cube Calculator - Solves for Volume (Capacity), Lateral Area,Surface Area, and the value of a side for a cube.

cube root of a number and 7

cube root of a number and 7
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Cube root of a number means we raise x to the 1/3 power:
x^1/3
And 7 means we add 7:
[B]x^1/3 + 7[/B]

Cube the difference of b and c

Cube the difference of b and c
the difference of b and c:
b - c
Cubing means raising to the power of 3:
[B](b - c)^3[/B]

Divide x cubed by the quantity x minus 7

Divide x cubed by the quantity x minus 7
x cubed means we raise x to the power of 3:
x^3
We divide this by x - 7:
[B]x^3/(x - 7)[/B]

Equation and Inequalities

Free Equation and Inequalities Calculator - Solves an equation or inequality with 1 unknown variable and no exponents as well as certain absolute value equations and inequalities such as |x|=c and |ax| = c where a and c are constants. Solves square root, cube root, and other root equations in the form ax^2=c, ax^2 + b = c. Also solves radical equations in the form asqrt(bx) = c. Also solves open sentences and it will solve one step problems and two step equations. 2 step equations and one step equations and multi step equations

Erik is rolling two regular six-sided number cubes. What is the probability that he will roll an eve

Erik is rolling two regular six-sided number cubes. What is the probability that he will roll an even number on one cube and a prime number on the other?
P(Even on first cube) = (2,4,6) / 6 total choices
P(Even on first cube) = 3/6
P(Even on first cube) = 1/2 <-- [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F6&frac2=3%2F8&pl=Simplify']Using our fraction simplify calculator[/URL]
P(Prime on second cube) = (2,3,5) / 6 total choices
P(Prime on second cube) = 3/6
P(Prime on second cube) = 1/2 <-- [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F6&frac2=3%2F8&pl=Simplify']Using our fraction simplify calculator[/URL]
Since each event is independent, we have:
P(Even on the first cube, Prime on the second cube) = P(Even on the first cube) * P(Prime on the second cube)
P(Even on the first cube, Prime on the second cube) = 1/2 * 1/2
P(Even on the first cube, Prime on the second cube) = [B]1/4[/B]

Factoring and Root Finding

Free Factoring and Root Finding Calculator - This calculator factors a binomial including all 26 variables (a-z) using the following factoring principles:

* Difference of Squares

* Sum of Cubes

* Difference of Cubes

* Binomial Expansions

* Quadratics

* Factor by Grouping

* Common Term

This calculator also uses the Rational Root Theorem (Rational Zero Theorem) to determine potential roots

* Factors and simplifies Rational Expressions of one fraction

* Determines the number of potential*positive* and *negative* roots using Descarte’s Rule of Signs

* Difference of Squares

* Sum of Cubes

* Difference of Cubes

* Binomial Expansions

* Quadratics

* Factor by Grouping

* Common Term

This calculator also uses the Rational Root Theorem (Rational Zero Theorem) to determine potential roots

* Factors and simplifies Rational Expressions of one fraction

* Determines the number of potential

H minus 6 all cubed

H minus 6 all cubed
H minus 6
h - 6
All cubed means raise the entire expression to the 3rd power
(h - 6)^3

How many cubic inches are in a cubic foot?

How many cubic inches are in a cubic foot?
Volume of a cube with 12 inch (1 foot sides) = 12 * 12 * 12 = [B]1728 cubic inches[/B]

If V is the volume of a cube whose side is s, express s in terms of V:

If V is the volume of a cube whose side is s, express s in terms of V:
We know the Volume (V) of a cube with side length s is:
V = s^3
Take the cube root of each side:
V^1/3 = (s^3)^1/3
s = [B]V^1/3[/B]

K varies inversely with square root of m and directly with the cube of n.

K varies inversely with square root of m and directly with the cube of n.
[LIST]
[*]We take a constant c as our constant of proportionality.
[*]The word inversely means we divide
[*]The word directly means we multiply
[/LIST]
[B]k = cn^3/sqrt(m)[/B]

mcubemultipliedbyntothefourthpower

mcubemultipliedbyntothefourthpower
m cubed means we raise m to the 3rd power:
m^3
n to the fourth power:
n^4
Multiply both expressions together:
[B]m^3n^4[/B]

Number Property

Free Number Property Calculator - This calculator determines if an integer you entered has any of the following properties:

* Even Numbers or Odd Numbers (Parity Function or even-odd numbers)

* Evil Numbers or Odious Numbers

* Perfect Numbers, Abundant Numbers, or Deficient Numbers

* Triangular Numbers

* Prime Numbers or Composite Numbers

* Automorphic (Curious)

* Undulating Numbers

* Square Numbers

* Cube Numbers

* Palindrome Numbers

* Repunit Numbers

* Apocalyptic Power

* Pentagonal

* Tetrahedral (Pyramidal)

* Narcissistic (Plus Perfect)

* Catalan

* Repunit

* Even Numbers or Odd Numbers (Parity Function or even-odd numbers)

* Evil Numbers or Odious Numbers

* Perfect Numbers, Abundant Numbers, or Deficient Numbers

* Triangular Numbers

* Prime Numbers or Composite Numbers

* Automorphic (Curious)

* Undulating Numbers

* Square Numbers

* Cube Numbers

* Palindrome Numbers

* Repunit Numbers

* Apocalyptic Power

* Pentagonal

* Tetrahedral (Pyramidal)

* Narcissistic (Plus Perfect)

* Catalan

* Repunit

Please help me!! I don't understand!

I don't understand this word problem: If each of these shapes in Figure 1 were separated and filled with water, could the sphere that contains the cube hold all of the water? [I]Assume in the second image the corners of the cube touch the sphere so the diagonal from one corner of the cube to the opposite diagonal corner is the diameter of the sphere. [IMG]https://classroom.ucscout.org/courses/1170/files/191225/preview?verifier=mT7v59BhdVHalyprWq0KmBEItbf4CPWFqOgwoEa8[/IMG][IMG]https://classroom.ucscout.org/courses/1170/files/191494/preview?verifier=nsLscsxToebAVXTSYsoMr7rwIl536LrCJSDGPaHp[/IMG][/I]
Could you guys help me please?

Please help me!! I don't understand!

Figure 1, we have a cone, cylinder, and cube. Let's get the volume of each
Cone volume = pir^2h/3
radius = s/2
h = s
Cone Volume = pi(s/2)^2(s)/3
Cone Volume = pis^3/12
Volume of cube = s^3
Volume of cylinder = pir^2h
Volume of cylinder = pi(s/2)^2s
Volume of cylinder = pis^3/2
But Figure 2 has no sizes? For sides, height, etc. So I cannot answer the question until I have that.

Prove that the difference of two consecutive cubes is never divisible by 3

Take two consecutive integers:
n, n + 1
The difference of their cubes is:
(n + 1)^3 - n^3
n^3 + 3n^2 + 3n + 1 - n^3
Cancel the n^3
3n^2 + 3n + 1
Factor out a 3 from the first 2 terms:
3(n^2 + n) + 1
The first two terms are always divisible by 3 but then the + 1 makes this expression not divisible by 3:
3(n^2 + n) + 1 = 1 (mod 3)
[MEDIA=youtube]hFvJ3epqmyE[/MEDIA]

ratio of x cubed and the sum of y and 5

ratio of x cubed and the sum of y and 5
x cubed means we raise x to the power of 3:
x^3
The sum of y and 5:
y + 5
ratio of x cubed and the sum of y and 5
[B]x^3/(y + 5)[/B]

S varies jointly with t cubed and v

S varies jointly with t cubed and v
Varied jointly means there exists a constant k such that:
[B]s = kt^3v[/B]

Start with t and cube it.

Start with t and cube it.
Cubing a variable means raising it to the power of 3:
[B]t^3[/B]

sum of the cube of x and half of y

sum of the cube of x and half of y
The cube of x means we raise x to the 3rd power:
x^3
half of y means we divide y by 2:
y/2
sum of the cube of x and half of y means we add y/2 to x^3
[B]x^3 + y/2[/B]

Sum of the First (n) Numbers

Free Sum of the First (n) Numbers Calculator - Determines the sum of the first (n)

* Whole Numbers

* Natural Numbers

* Even Numbers

* Odd Numbers

* Square Numbers

* Cube Numbers

* Fourth Power Numbers

* Whole Numbers

* Natural Numbers

* Even Numbers

* Odd Numbers

* Square Numbers

* Cube Numbers

* Fourth Power Numbers

take away 1 from the cube of e

The cube of e is e^3.
Take away 1 means subtract 1
e^3 - 1

Ted tossed a number cube and rolled a die. How many possible outcomes are there?

Ted tossed a number cube and rolled a die. How many possible outcomes are there?
A number cube has 6 possible outcomes
A die has 6 possible outcomes.
We have 6 * 6 = [B]36 possible outcomes[/B].

the cube of c decreased by a^2

the cube of c decreased by a^2
The cube of means we raise the variable c to the power of 3:
c^3
The phrase [I]decreased by[/I] means we subtract:
[B]c^3 - a^2[/B]

The cube of g plus the square of m

The cube of g plus the square of m
The cube of g means we raise g to the 3rd power:
g^3
The square of m means we raise m to the 2nd power:
m^2
The word [I]plus[/I] means we add them both
[B]g^3 + m^2[/B]

the cube of t is less than 12

the cube of t is less than 12
The cube of t
t^3
is less than 12, we use the operator <
t^3 < 12

The cube of the difference of 5 times the square of y and 7 divided by the square of 2 times y

The cube of the difference of 5 times the square of y and 7 divided by the square of 2 times y
Take this in algebraic expression in parts:
[U]Term 1[/U]
[LIST]
[*]The square of y means we raise y to the 2nd power: y^2
[*]5 times the square of y: 5y^2
[/LIST]
[U]Term 2[/U]
[LIST]
[*]2 times y: 2y
[*]The square of 2 times y: (2y)^2 = 4y^2
[*]7 divide by the square of 2 times y: 7/4y^2
[/LIST]
[U]The difference of these terms is written as Term 1 minus Term 2:[/U]
[LIST]
[*]5y^2/4y^2
[/LIST]
[U]The cube of the difference means we raise the difference to the power of 3:[/U]
[B](5y^2/4y^2)^3[/B]

the cube of the difference of 5 times x and 4

the cube of the difference of 5 times x and 4
Take this algebraic expression in pieces:
5 times x:
5x
The difference of 5x and 4 means we subtract 4 from 5x:
5x - 4
We want to cube this difference, which means we raise the difference to the power of 3.
[B](5x - 4)^3[/B]

the cube of the product of 3 and x

the cube of the product of 3 and x
The product of 3 and x:
3x
Cube this product means raise it to the power of 3:
(3x)^3 = [B]27x^3[/B]

the cube of the sum of 2a and 3b

the cube of the sum of 2a and 3b
Sum of 2a and 3b:
(2a + 3b)
The cube of the sum mean we raise the sum to the power of 3:
[B](2a + 3b)^3[/B]

The cube of x is less than 15

The cube of x is less than 15
The cube of x means we raise x to the 3rd power:
x^3
Less than 15 means we setup the following inequality
[B]x^3 < 15[/B]

the difference of 5 and the cube of the sum of x and y

the difference of 5 and the cube of the sum of x and y
The sum of x and y:
x + y
The cube of the sum of x and y means we raise x + y to the 3rd power:
(x + y)^3
The difference of 5 and the cube of the sum of x and y
[B]5 - (x + y)^3[/B]

The product of a number and its square is less than 8

Let the number be x.
Let the square be x^2.
So we have (x)(x^2) = x^3 < 8
Take the cube root of this, we get x = 2

the quotient of the cube of a number x and 5

the quotient of the cube of a number x and 5
[LIST]
[*]A number means an arbitrary variable, let's call it x
[*]The cube of a number means raise it to the 3rd power, so we have x^3
[*]Quotient means we have a fraction, so our numerator is x^3, and our denominator is 5
[/LIST]
[B]x^3
----
5[/B]

The sum of 3w and 5 cubed

The sum of 3w and 5 cubed
The sum of 3w and 5:
3w + 5
The word [I]cubed[/I] means we raise 3w + 5 to the power 3:
[B](3w + 5)^3[/B]

the sum of b cubed and five

the sum of b cubed and five
b cubed
b^3
the sum of this and five
[B]b^3 + 5[/B]

the sum of the cube of a number and 12

the sum of the cube of a number and 12
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The cube of a number means we raise x to the power of 3:
x^3
Finally, we take the sum of x^3 and 12. Meaning, we add 12 to x^3. This is our final algebraic expression.
[B]x^3 + 12[/B]

the sum of x and its cube

the sum of x and its cube
The cube of x means we raise x to the power of 3:
x^3
The sum of x and it's cube means we add x^3 to x:
[B]x + x^3[/B]

the total of 3 times the cube of u and the square of u

the total of 3 times the cube of u and the square of u
[U]The cube of u means we raise u to the power of 3:[/U]
u^3
[U]The square of u means we raise u to the power of 2:[/U]
u^2
The total of both of these is found by adding them together:
[B]u^3 + u^2[/B]

The volume of a cube is 64. Its surface area is

Volume of a cube is s^3 where s is the length of one side.
V = 64
s^3 = 64
Take the cube root of each side:
s = 4 since 4^3 = 64
Surface Area of a cube is 6s^2. With s = 4, we have:
SA = 6(4)^2
SA =6(16)
SA =[B] 96
[MEDIA=youtube]nDSA2NDO9to[/MEDIA][/B]

Twice x increased by the cube of y equals z

Twice x increased by the cube of y equals z
[LIST]
[*]Twice x means we multiply x by 2: 2x
[*]Increased this by the cube of y which is y^3. So we have 2x + y^3
[*]Now, we set this entire expression equal to z: 2x + y^3 = z
[/LIST]

u cubed equals nine

u cubed equals nine
u cubed means we raise u to the 3rd power:
u^3
We set this equal to 9:
[B]u^3 = 9[/B]

Variation Equations

Free Variation Equations Calculator - This calculator solves the following direct variation equations and inverse variation equations below:

* y varies directly as x

* y varies inversely as x

* y varies directly as the square of x

* y varies directly as the cube of x

* y varies directly as the square root of x

* y varies inversely as the square of x

* y varies inversely as the cube of x

* y varies inversely as the square root of x

* y varies directly as x

* y varies inversely as x

* y varies directly as the square of x

* y varies directly as the cube of x

* y varies directly as the square root of x

* y varies inversely as the square of x

* y varies inversely as the cube of x

* y varies inversely as the square root of x

Write an equation that relates the quantities. G varies jointly with t and q and inversely with the

Write an equation that relates the quantities. G varies jointly with t and q and inversely with the cube of w . The constant of proportionality is 8.25 .
[LIST]
[*]Varies jointly or directly means we multiply
[*]Varies inversely means divide
[*]The cube of w means we raise w to the 3rd power: w^3
[/LIST]
Using k = 8.25 as our constant of proportionality, we have:
[B]g = 8.25qt/w^3[/B]

x cubed plus x squared decreased by 7

x cubed plus x squared decreased by 7
[U]x cubed means we raise x to the power of 3:[/U]
x^3
[U]x squared means we raise x to the power of 2:[/U]
x^2
[U]x cubed plus x squared[/U]
x^3 + x^2
[U]Decreased by 7:[/U]
[B]x^3 + x^2 - 7[/B]

X varies directly with the cube root of y when x=1 y=27. Calculate y when x=4

X varies directly with the cube root of y when x=1 y=27. Calculate y when x=4
Varies directly means there is a constant k such that:
x = ky^(1/3)
When x = 1 and y = 27, we have:
27^1/3(k) = 1
3k = 1
To solve for k, we[URL='https://www.mathcelebrity.com/1unk.php?num=3k%3D1&pl=Solve'] type in our equation into our search engine[/URL] and we get:
k = 1/3
Now, the problem asks for y when x = 4. We use our variation equation above with k = 1/3 and x = 4:
4 = y^(1/3)/3
Cross multiply:
y^(1/3) = 4 * 3
y^(1/3) =12
Cube each side:
y^(1/3)^3 = 12^3
y = [B]1728[/B]

z is jointly proportional to the square of x and the cube of y

z is jointly proportional to the square of x and the cube of y
The square of x means we raise x to the power of 2:
x^2
The cube of y means we raise y to the power of 3:
y^3
The phrase [I]jointly proportional[/I] means we have a constant k such that:
[B]z = kx^2y^3[/B]