The area of a circle is 113.10 what is the radius

Karlene is keeping track of her calcium intake for a nutrition challenge at school. So far, she

swat32

Idk uh uh uuu uuu uh did ui I’m

5 0

3 years ago

What is an equation in slope-intercept form of the line that passes through (6, 10) and is parallel to the graph of y=13 x−1 ?

nadezda [96]

10=13(6)+b
10=78+b
b=-68
y=13x-68

7 0

3 years ago

Write an equation for an exponential growth function where the initial population is 74 and the population quadruples during eac

Liono4ka [1.6K]

If the population quadruples every period say hour, that means the "rate of growth" is 300%, so whatever the current amount, increased by 3 times as much is 4 times the current amount, or a quadrupled amount.

$\bf \qquad \textit{Amount for Exponential Growth}\\\\
A=I(1 + r)^t\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
I=\textit{initial amount}\to &74\\
r=rate\to 300\%\to \frac{300}{100}\to &3.00\\
t=\textit{elapsed time}\\
\end{cases}
\\\\\\
A=74(1+3)^t\implies A=74(4)^t$

6 0

3 years ago

What is x if y Is 5 x^2 (2y +5)=240

UkoKoshka [18]

X^2(2y+5)=240
x^2(2(5)+5)=240
x^2+(10+5)=240
x^2+15=240
minus 15 both sides
x^2=225
sqrt both sides
x=15

6 0

3 years ago

[10 points] A manufacturer wants to design an open box having a square base and a surface area of 108 square inches. What dimens

MissTica

Answer:

6 inches square by 3 inches high

Step-by-step explanation:

For a given surface area, the volume of an open-top box is maximized when it has the shape of half a cube. If the area were than of the whole cube, it would be 216 in² = 6×36 in².

That is, the bottom is 6 inches square, and the sides are 3 inches high.

_____

Let x and h represent the base edge length and box height, respectively. Then we have ...

x² +4xh = 108 . . . . box surface area

Solving for height, we get ...

h = (108 -x²)/(4x) = 27/x -x/4

The volume is the product of base area and height, so is ...

V = x²h = x²(27/x -x/4) = 27x -x³/4

We want to maximize the volume, so we want to set its derivative to zero.

dV/dx = 0 = 27 -(3/4)x²

x² = (4/3)(27) = 36

x = 6

h = 108/x² = 3

The box is 6 inches square and 3 inches high.

_____

Comment on maximum volume, minimum area

In the general case of an open-top box, the volume is maximized when the cost of the bottom and the cost of each pair of opposite sides is the same. Here, the "cost" is simply the area, so the area of the bottom is 1/3 the total area, 36 in².

If the box has a closed top, then each pair of opposite sides will have the same cost for a maximum-volume box. If costs are uniform, the box is a cube.

7 0

3 years ago