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3 years ago

8

Dave builds a wheelchair ramp with 1 metre of wood. He wants the vertical height of the ramp to be 50 centimetres. What does the

angle of elevation need to be?

1 answer:

Yakvenalex [24]3 years ago

7 0

Answer:

$\theta=30^{o}$

Step-by-step explanation:

1 m is 100 cm

The hypotenuse is 100 cm and the opposite side is 50 cm

$sin \theta=\frac {50}{100}$

$\theta=30^{o}$

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The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there a

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Answer:

24761 mosquitoes

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Step-by-step explanation:

Let the equation that shows the population of the mosquitoes after x days,

$A=P(1+r)^x$

Where,

P = Initial population,

r = rate of increasing per day,

Here, A = 1000, when x = 0,

$1000=P(1+r)^0\implies P = 1000$

A = 1900 when x = 1,

$1900 = P(1+r)^1\implies 1900 = 1000(1+r)\implies 1.9 = 1 + r\implies r = 0.9$

Thus, the required function that represents the population after x days,

$A=1900(1+0.9)^x=1900(1.9)^x$

If x = 4,

The number of mosquito after 4 days,

$A=1900(1.9)^4 = 24760.99\approx 24761$

If A = 60,000,

$60000 = 1900(1.9)^x$

$\frac{600}{19}=1.9^x$

Taking log both sides,

$\log(\frac{600}{19})=x\log 1.9$

$\implies x = \frac{\log(\frac{600}{19})}{\log 1.9}=5.378\approx 5.4$

Thus, there will 60,000 mosquitoes after 5 days.

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