1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
USPshnik [31]
3 years ago
8

Write two equations. the first equation should express the area of the square (a as a function of the length (l of a side. the s

econd should express the volume (v as a function of the length (s of a side.
Mathematics
1 answer:
Sergeu [11.5K]3 years ago
6 0

Answer:

a = l²

v = s³

Step-by-step explanation:

The area of a rectangle is the product of its length and width. When that rectangle is a square, the length and width are the same. Here, they are given as "l". Then the area of the square is ...

a = l·l = l²

__

The volume of a cuboid is the product of its height and the area of its base. A cube of edge length s has a square base of side length s and a height of s. Then its volume will be ...

v = s·(s²) = s³

The two equations you want are ...

• a = l²

• v = s³

You might be interested in
Two integers a and b have a product of -48
ycow [4]
It’s c because I got it right on the test
3 0
3 years ago
Let f and g be the functions defined by f(x) = 10^ (x+2 / 3) and g(x) = log (x3 / 100) for all positive real numbers,
Vaselesa [24]

Answer:

F(x) and g(x) are not inverse functions.

Step-by-step explanation:

In order to calculate the inverse function of a function, we have to isolate X and after that, we change the variables.

As our function f(x) is a exponentian function, we can apply logarithm with base 10 (log) in both sides in order to isolate X. Remember that log10=1.

[tex]y=10^{(x+\frac{2}{3}) }\\\\log y=log 10^{(x+\frac{2}{3}) }\\log y = (x+\frac{2}{3}) . log10\\\frac{log Y}{log10} = (x+\frac{2}{3})\\\frac{log Y}{1} = (x+\frac{2}{3})\\log Y-\frac{2}{3}=x[/tex]

Now we change the variables.

F(x)=log x-\frac{2}{3}

F(x) and g(x) are not inverse functions.

4 0
3 years ago
If a bag contains 16 red, 6 yellow, 24 blue, and 8 white balloons, what is the part-to-whole ratio of yellow balloons to all bal
hichkok12 [17]
If a bag contains 16 red, 6 yellow, 24 blue, and 8 white balloons, that 1:7 part-to-whole ratio of yellow balloons to all balloons. There are 4 parts and 1 part is the part with the red balloons.

Your answer is: B) 1:7 

Have an amazing day and stay hopeful!

8 0
3 years ago
Read 2 more answers
Given the functions f(x) = 3x and g(x) = x² + 1, find [(gºf)(x)]- [(fºg)(x)].
Ipatiy [6.2K]

Answer:

6x^2 - 2

Step-by-step explanation:

plug in f(x) into the g(x) formula given

g(f(x)) = (3x)^2 + 1

simplify

= 9x^2+2

plug in g(x) into the f(x) formula given

f(g(x)) = 3(x^2+1)

distribute

= 3x^2 +3

set g(f(x)) - f(g(x))

(9x^2+2) - (3x^2+3)

carry the negative

9x^2+2-3x^2-3

simplify by combining like terms

6x^2-2

7 0
3 years ago
The total revenue for Dante's Villas is given as the function R(x)=700x−0.5x^2, where x is the number of villas rented. What num
yan [13]

The revenue function is,

R(x)=700x-0.5x^2

For maximum and minimum value, the first derivative of function is equal to 0.

Determine the first derivative of revenue function.

\begin{gathered} \frac{d}{dx}R(x)=\frac{d}{dx}(700x-0.5x^2) \\ R^{\prime}(x)=700-0.5\cdot2x \\ =700-x \end{gathered}

For maximum and minimum value, R'(x) = 0. So

\begin{gathered} 0=700-x \\ 700=x \end{gathered}

Since x = 700 corresponds to maximum or minimum value of revenue.

Determine the second derivative of revenue function.

\begin{gathered} \frac{d}{dx}R^{\prime}(x)=\frac{d}{dx}(700-x) \\ R^{\doubleprime}(x)=-1 \end{gathered}

Since second derivative of revenue function is less than 0 for every value of x. So x = 700 corresponds to maximum value of revenue.

So 700 villas rented to produce maximum revenue.

Answer: 700 villas

7 0
1 year ago
Other questions:
  • JL is a diameter of circle k. If tangents to circle I are constructed through points L and K what relationships would exist betw
    9·1 answer
  • Movies often use models to create special effects. In the movie Son of Godzilla, Godzilla appears to be 67 feet tall and was pla
    14·1 answer
  • Evalu<br> k(t) = 10t – 19<br> k(-7)=
    11·1 answer
  • Solve (1/81)^x*1/243=(1/9)^−3−1 by rewriting each side with a common base.
    10·1 answer
  • Which number is represented by point E on the graph?
    5·2 answers
  • Help meee pleasee !!!
    9·2 answers
  • What is the answer and steps to the following equation: 6(4-z)=2z
    11·2 answers
  • This subject is on integers
    9·1 answer
  • A grocery store sells long grain rice for 2.49 per pound. Write an expression for the cost of y pounds of long grain rice.
    8·1 answer
  • Which choice most effectively sets up the
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!