Ask question

Ask question

All categories

3 years ago

12

Ticket Prices for a Science museum are $18 for adults and $12 for students. If $162 is collected from a group of 12 people, How

many adults and students are in the group?

1 answer:

vova2212 [387]3 years ago

3 0

Answer:

Step-by-step explanation:

You might be interested in

Can someone help please

myrzilka [38]

<h3>Answer: 15x^(7/3) - 8x^(7/4) + x + 9000</h3>

=========================================================

Explanation:

If you know the cost function C(x), to find the marginal cost, we apply the derivative.

Marginal cost = derivative of cost function

Marginal cost = C ' (x)

Since we're given the marginal cost, we'll apply the antiderivative (aka integral) to figure out what C(x) is. This reverses the process described above.

$\text{Cost} = \text{antiderivative of marginal cost}\\\\\displaystyle C(x) = \int \left(35x^{4/3} - 14x^{3/4} + 1\right)dx\\\\$

$C(x) = \frac{1}{1+4/3}*35x^{4/3+1} - \frac{1}{1+3/4}*14x^{3/4+1} + x + D\\\\C(x) = \frac{1}{7/3}*35x^{7/3} - \frac{1}{7/4}*14x^{7/4} + x + D\\\\C(x) = \frac{3}{7}*35x^{7/3} - \frac{4}{7}*14x^{7/4} + x + D\\\\C(x) = 15x^{7/3} - 8x^{7/4} + x + D\\\\$

D represents a fixed constant. I would have used C as the constant of integration, but it's already taken by the cost function C(x).

To determine the value of D, we plug in x = 0 and C(x) = 9000. This is because we're told the fixed costs are $9000. This means that when x = 0 units are made, you still have $9000 in costs to pay. This is the initial value. You'll find that all of this leads to D = 9000 because everything else zeros out.

Therefore, we go from this

$C(x) = 15x^{7/3} - 8x^{7/4} + x + D\\\\$

to this

$C(x) = 15x^{7/3} - 8x^{7/4} + x + 9000\\\\$

which is the final answer.

3 0

2 years ago

Tristán wants to build a square garden in his backyard if the garden is going to be 64 ft2 how many feet of material will he nee

Alex777 [14]

Answer:

Tristan will need 32 feet of material for the perimeter of the garden.

Step-by-step explanation:

Given that

Area of square garden = A = 64 square feet

Perimeter = P = ?

We know that for calculation of perimeter, length of side of square is required which is not directly given in the question. The area will be used to calculate length of side and then length will be used to calculate the perimeter.

So,

$Area = A = s^2$

s is for side

Putting the value of area

$64 = a^2$

Taking square root on both sides

$\sqrt{s^2} = \sqrt{64}\\s = 8\ feet$

The length of side is 8 feet.

Perimeter will be:

$P = 4*s\\P = 4*8\\P = 32\ feet$

Hence,

Tristan will need 32 feet of material for the perimeter of the garden.

3 0

3 years ago

Solve x 2 + 9x + 8 = 0 by completing the square. What are the solutions?

Sindrei [870]

So firstly, what two terms have a product of 8x^2 and a sum of 9x? That would be x and 8x. Replace 9x with x + 8x: $x^2+x+8x+8=0$

Next, factor x^2 + x and 8x + 8 separately. Make sure that they have the same quantity on the inside: $x(x+1)+8(x+1)=0$

Now you can rewrite the equation as $(x+8)(x+1)=0$

Now using zero product property, solve for x:

$x+8=0\\ x=-8\\ \\ x+1=0\\ x=-1$

<u>In short, the solutions are {-1,-8}, or C.</u>

4 0

3 years ago

What is the place value of 2 in 1025

tresset_1 [31]

Tens place value, like twenty five

5 0

3 years ago

The area of a triangle is 6.75 m to the 2 power. If the base of the triangle is 3 m, what is the height of the triangle?

4vir4ik [10]

<span>The area of a triangle is 6.75 m^2

=> (1/2) x base x height=</span>6.75 m^2
=>(1/2) x 3 x <span>height = </span>6.75
=><span>height = (</span>6.75x2)/3= 4.1

so the height is 4.1m

6 0

3 years ago

Read 2 more answers