Answer:
18
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
here [ a, b ] = [ 1, 5 ]
f(b) = f(5) = 3 × 5² = 75
f(a) = f(1) = 3 × 1² = 3, hence
average rate of change = 
= 
= 18
The length side AB is 64 ft , Option D is the correct answer.
<h3>What is a Right triangle ?</h3>
A triangle that has one angle 90 degree is called Right angled Triangle.
From the figure it can be seen that
The triangle CDE is a right Triangle
Applying Pythagoras theorem to find the length of CE
CE² = 12² + 16²
CE = 20 ft
As both the triangles are similar therefore the ratio of the sides will be equal
BC : CD = AC : CE
48 / 12 = AC / 20
AC = 80ft
As Triangle ABC is also a right angled triangle
Applying Pythagoras theorem to find the length of AB
AC² = BC² +AB²
6400 = 48² +AB²
AB² = 4096
AB = 64 ft
Therefore Option D is the correct answer.
To know more about Right Triangle
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So,
If you do some simple division, you will find how much each cm costs in each cake.
20cm cake = 67.5 cents/cm
25cm cake = 93.75 cents/cm
Assuming that you cannot order fractions of cakes, the best deal would be to order 5 of the 20cm cakes.
Cost = 13.50 * 5 = $67.50
You will have to pay $67.50 for the cakes if you want the best deal.
Answer:
15
Step-by-step explanation:
Answer:
Time,t that it will elapse before the concerntration of the dye in the tank reaches1% of its original value is 460.52 seconds
Step-by-step explanation:
Let Q(t) = amount of dye for all time,t.
Let Q'= rate in - rate out.
But Q/200 = concerntration of dye
Therefore rate out= Q/200 ×2.
Q'/Q = - 1/100
Dividing by Q gives
Ln/Q/ + c = -1/100t + c1
Integrating both sides with respect to t
Ln/Q/ = -1/100t + c2.
c1 and c1 are just another constants
Q= c3e^-t/100
Exponentiating both sides will cause the absolute values to get absorbed into the constants giving rise to a new constant c3
200= c3-0/100
c3= 200
2= 200e^-t/100
Ln1/100= - t/100
Ln0.01 = - t/ 100
Cross multiply
t= Ln0.01 × 100
t = 4.6052 ×100
t = 460.52seconds
