Answer:
dx/dt = 0,04 m/sec
Step-by-step explanation:
Area of the circle is:
A(c) =π*x² where x is a radius of the circle
Applying differentiation in relation to time we get:
dA(c)/dt = π*2*x* dx/dt
In this equation we know:
dA(c)/dt = 0,5 m²/sec
And are looking for dx/dt then
0,5 = 2*π*x*dx/dt when the area of the sheet is 12 m² (1)
When A(c) = 12 m² x = ??
A(c) = 12 = π*x² ⇒ 12 = 3.14* x² ⇒ 12/3.14 = x²
x² = 3,82 ⇒ x = √3,82 ⇒ x = 1,954 m
Finally plugging ths value in equation (1)
0,5 = 6,28*1,954*dx/dt
dx/dt = 0,5 /12.28
dx/dt = 0,04 m/sec
The correct answer is Choice A.
If you plot the points on a graph, you will see that there is a slope of -1 and the y-intercept is (0, 3).
This matches the equation of y = -x + 3 in Choice A.
There is a missing graph in the problem given. However, we can simply solve the equation using the given data.
Items to be sold: scarves and hats. Minimum of 20 items sold in all.
Scarves sell for 10 each and hats sell for 20 each. Must sell at least 300 worth of merchandise to make profit.
Let s represent scarves and h represent hats.
10s + 20h <u>></u> 300
s + h <u>></u> 20
We use inequality because the problem states "at least".
s + h = 20
10s + 20h = 300
s = 20 - h
10(20-h) + 20h = 300
200 - 10h + 20h = 300
10h = 300 - 200
10h = 100
h = 100/10
h = 10
s = 20 - h
s = 20 - 10
s = 10
s + h <u>></u> 20
10 + 10 <u>></u> 20
10s + 20h <u>></u> 300
10(10) + 20(10) <u>></u> 300
100 + 200 <u>></u> 300
