A region with a 15 mile diameter has a population density of about 5000 people per square mile. Find the number of people who li
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Answer:
see explanation
Step-by-step explanation:
Given that M is directly proportional to r³ then the equation relating them is
M = kr³ ← k is the constant of proportion
To find k use the condition when r = 4, M = 160, thus
160 = k × 4³ = 64k ( divide both sides by 64 )
2.5 = k
M = 2.5r³ ← equation of variation
(a)
When r = 2, then
M = 2.5 × 2³ = 2.5 × 8 = 20
(b)
When M = 540, then
540 = 2.5r³ ( divide both sides by 2.5 )_
216 = r³ ( take the cube root of both sides )
r = = 6
It is given in the question that
Ann, Chang, and Kareem sent a total of 89 text messages over their cell phones during the weekend. Ann sent 9 fewer messages than Chang. Kareem sent 3 times as many messages as Ann.
Let number of messages Chang sent be x. And Ann sent 9 fewer than Chang, so Ann sent (x-9) messages. And Kareem sent 3 times as many messages as Ann, so Kareem sent 3(x-9) messages.
And the total messages are 89. That is
Combining like terms
So Chang sent 25 messages, Ann sent
And Kareem sent