Answer this problem. Simplify a. 63.19 b. 25.84 c. 81.49 d. 94.57

If 1900 square centimeters of material are available to make a box with a square base and an open top, find the largest possible

Evgen [1.6K]

Answer:

Volume = $7969$ cubic centimeter

Step-by-step explanation:

Let the length of each side of the base of the box be A and the height of the box be H.

Area of material required to make the box is equal to is $A^2 + 4*A*H.$

$A^2 + 4*A*H = 1900$

Rearranging the above equation, we get -

$`H = \frac{(1900 - A^2)}{(4*A)}$

Volume of box is equal to product of base area of box and the height of the box -

$V = A*A* H$

Substituting the given area we get -

$\frac{A^2*(1900 - A^2)}{4A} = \frac{(1900*A - A^3)}{4}$

For maximum volume

$\frac{dV}{dA} =0$

$\frac{ 1900}{4} - \frac{3*A^2}{4} = 0$

$A^2 = \frac{1900}{3}$

Volume of the box

= $\frac{\frac{1900}{3}*(1900 - \frac{1900}{3}) }{4 * \sqrt{\frac{1900}{3} } }$

= $7969$ cubic centimeter

3 0

3 years ago

Rachel has developed a plan to start paying off her credit card debt, and has stopped making purchases with her credit card. She

Ann [662]

Present value of annuity PV = P(1 - (1 + r/t)^-nt) / (r/t)
where: p is the monthly payment, r is the APR = 14.12% = 0.1412, t is the number of payments in one year = 12, n is the number of years = 2.
1,120.87 = P(1 - (1 + 0.1412/12)^(-2 x 12)) / (0.1412 / 12)
0.1412(1120.87) = 12P(1 - (1 + 0.1412/12)^-24)
P = 0.1412(1120.87) / 12(1 - (1 + 0.1412/12)^-24) = $53.88

Minimum monthly payment = 3.15% of 1120.87(1 + 0.1412/12) = 0.0315 x 1120.87(1 + 0.1412/12) = $35.72

Therefore, his first payment will be greater than the minimum payment by 53.88 - 35.72 = $18.16

5 0

3 years ago

Read 2 more answers

the birth rate in a certain country in 1994 was 14,6 birthd per thousand population. in 2004 the birth rate was 14.32 per thousa

amm1812

Answer:

$y(x)=-0.028x+14.6$

Step-by-step explanation:

Birth Rate in 1994 = 14.6 births per thousand population.

Birth Rate in 2004 = 14.32 births per thousand population.

A linear equation is of the form: y=mx+c

Where:

x=years after 1994
y=the birth rate
m=Yearly Birth Rate

First, we determine the birth rate per year

$m=\dfrac{14.32-14.6}{10-0}\\=\dfrac{-0.28}{10}\\m=-0.028$

Therefore, a linear equation that relates y in terms of x is of the form:

$y(x)=-0.028x+c$

When x=0, y=14.6

14.6=-0.028(0)+c

c=14.6

Therefore, the linear equation that relates y in terms of x is:

$y(x)=-0.028x+14.6$

4 0

3 years ago

Anyone know the answer?

Brut [27]

Check out the picture I've got the full explanations on there
Hope it's clear

4 0

3 years ago

What best describes the area of a polygon

never [62]

Answer:

The area of any regular polygon is given by the formula: Area = (a x p)/2, where a is the length of the apothem and p is the perimeter of the polygon. Plug the values of a and p in the formula and get the area. As an example, let's use a hexagon (6 sides) with a side (s) length of 10.

The area of a polygon is the two-dimensional set of all points surrounded by the sides of the polygon.

If you're looking for an equation, it varies based on the number of sides and the shape of the polygon.

Step-by-step explanation:

Apothem

A regular polygon is equilateral (it has equal sides) and equiangular (it has equal angles). To find the area of a regular polygon, you use an apothem — a segment that joins the polygon’s center to the midpoint of any side and that is perpendicular to that side (segment HM in the following figure is an apothem).

6 0

3 years ago