Anybody got some answers?

Mathematics

1 answer:

kiruha [24]3 years ago

4 0

I don’t know if this is right but this is what I figured.
37.245508982

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Kerry is comparing the fuel efficiency of two cars, Car A and Car B. Car A lists gas mileage as 32.4 miles per gallon for highwa

andrezito [222]

Okay. To find the miles per gallon of B, we have to divide 100 by 2.6. 100/2.6 is 38.4615385 or about 38.5 miles per gallon when rounded to the nearest tenth. Car B goes approx. 38.5 miles per gallon.

6 0

2 years ago

Can anyone explain those marked steps in case (iii)

Tema [17]

$\cos\dfrac{3x}2=\cos\left(\dfrac\pi2+\dfrac x2\right)$
$\implies \dfrac{3x}2=2n\pi+\dfrac\pi2+\dfrac x2$

follows from the fact that the cosine function is $2\pi$ -periodic, which means $\cos x=\cos(2\pi+x)$ . Roughly speaking, this is the same as saying that a point on a circle is the same as the point you get by completing a full revolution around the circle (i.e. add $2\pi$ to the original point's angle with respect to the horizontal axis).

If you make another complete revolution (so we're effectively adding $4\pi$ ) we get the same result: $\cos x=\cos(4\pi+x)$ . This is true for any number of complete revolutions, so that this pattern holds for any even multiple of $\pi$ added to the argument. Therefore $\cos x=\cos(2n\pi+x)$ for any integer $n$ .

Next, because $\cos(-x)=\cos x$ , it follows that $\cos x=\cos(2n\pi-x)$ is also true for any integer $n$ . So we have

$\implies \dfrac{3x}2=2n\pi\pm\left(\dfrac\pi2+\dfrac x2\right)$

The rest follows from considering either case and solving for $x$ .