For this case we have the following number:
What we must do is rewrite the number as the product of two numbers.
We have then:
From here, we write the number as the multiplication of a whole number and a power of base ten.
We have then:
Where,
: whole number
: power of base 10
Answer:
The distance written as a whole number multiplied by a power of ten is:
Let
h: height of the water
r: radius of the circular top of the water
V: the volume of water in the cup.
We have:
r/h = 3/10
So,
r = (3/10)*h
the volume of a cone is:
V = (1/3)*π*r^2*h
Rewriting:
V (t) = (1/3)*π*((3/10)*h(t))^2*h(t)
V (t) =(3π/100)*h(t)^3
Using implicit differentiation:
V'(t) = (9π/100)*h(t)^2*h'(t)
Clearing h'(t)
h'(t)=V'(t)/((9π/100)*h(t)^2)
the rate of change of volume is V'(t) = 2 cm3/s when h(t) = 5 cm.
substituting:
h'(t) = 8/(9π) cm/s
Answer:
the water level is rising at a rate of:
h'(t) = 8/(9π) cm/s
John get paid in a week in which he makes 48 toy cars = $312
<u>Step-by-step explanation</u>:
Step 1 :
- Pay for each first 40 toy cars = $6
- Pay for each additional toy car = increase in 50% of $6
Step 2 :
50% of $6 = (50/100)$6 = $3
Pay for each additional toy car = (50% of $6) + $6
= $3 + $6 = $9
Step 3 :
Pay for total of 48 cars = pay for 1st 40 cars + pay for additional 8 cars
= $6(40) + $9(8)
= $240 + $72
Pay for total of 48 cars = $312