Help please with this question!!!

Mathematics

1 answer:

Vesnalui [34]3 years ago

7 0

1 - AB is the Hypotenuse, BC is the opposite, AC is the adjacent (next to)

AB is the Hypotenuse because it is across from the right angle. BC is the opposite because its on the opposite side of the angle. AC is next to (adjacent) of the angle.

2 - the ratio is 30/1 = 5/b

This is because S O/H C A/H T O/A or Sohcahtoa.

S is the sine, which is Opposite over Hypotenuse. C is the cosine, which is Adjacent over Hypotenuse, and T is tangent which is Opposite over Adjacent. So look at what we labeled, we need to find the adjacent side, or b, and we have the opposite side, 5. So what has opposite and adjacent? Tangent.

So we do tan(30)/1 = 5/b, and cross multiply.

Now the last question. Hypotenuse is always C. But the other two values don’t matter where you put them on the left side since its multiplication. So its 7.7^2 * 6^2 = c^2 which is 59.29 * 36 = C^2.
2134.44 = c^2. Square root sides so it is 46.2 = c. The answer is 46.2

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The population, P(t), of China, in billions, can be approximated by1 P(t)=1.394(1.006)t, where t is the number of years since th

vitfil [10]

Answer:

At the start of 2014, the population was growing at 8.34 million people per year.

At the start of 2015, the population was growing at 8.39 million people per year.

Step-by-step explanation:

To find how fast was the population growing at the start of 2014 and at the start of 2015 we need to take the derivative of the function with respect to t.

The derivative shows by how much the function (the population, in this case) is changing when the variable you're deriving with respect to (time) increases one unit (one year).

We know that the population, P(t), of China, in billions, can be approximated by $P(t)=1.394(1.006)^t$

To find the derivative you need to:

$\frac{d}{dt}\left(1.394\cdot \:1.006^t\right)=\\\\\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'\\\\1.394\frac{d}{dt}\left(1.006^t\right)\\\\\mathrm{Apply\:the\:derivative\:exponent\:rule}:\quad \frac{d}{dx}\left(a^x\right)=a^x\ln \left(a\right)\\\\1.394\cdot \:1.006^t\ln \left(1.006\right)\\\\\frac{d}{dt}\left(1.394\cdot \:1.006^t\right)=(1.394\cdot \ln \left(1.006\right))\cdot 1.006^t$

To find the population growing at the start of 2014 we say t = 0

$P(t)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^t\\P(0)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^0\\P(0)' = 0.00833901 \:Billion/year$

To find the population growing at the start of 2015 we say t = 1

$P(t)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^t\\P(1)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^1\\P(1)' = 0.00838904 \:Billion/year$