(30 points)

Mathematics

1 answer:

Drupady [299]3 years ago

7 0

dilation and a rotation

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Maya can run 18 miles in 3 hours, and she can bike 18 miles in 2 hours.

Aloiza [94]

Answer:

Step-by-step explanation:

if it is two hours then half of it is 9

so 18 + 9 = 27 which is how many miles she biked

6 is the number of miles she ran

so u times it by 1.5

27 + 9 = 36

4 0

3 years ago

Read 2 more answers

Find the exact value of each of the following. In each case, show your work and explain the steps you take to find the value.

mote1985 [20]

Answer: a) $\frac{1}{2}$

b) 1

c) 2

Step-by-step explanation:

(a) sin 17π/6

It is known that the value of sin x repeat after an interval of $2\pi\ or\ 360^{\circ}$

∴ $\sin\frac{17\pi}{6}=\sin2\frac{5\pi}{6}=\sin(2\pi+\frac{5}{6}\pi)=\sin{\frac{5}{6}\pi}=\sin(\pi-\frac{\pi}{6})=\sin(\frac{\pi}{6})=\frac{1}{2}$

[Since the value of sin x is positive in 2nd quadrant]

(b) tan 13π/4

It is known that the value of sin x repeat after an interval of $\pi\ or\ 180^{\circ}$

∴ $\tan\frac{13\pi}{4}=\tan(3\pi+\frac{\pi}{4})=\tan{\frac{\pi}{4}}=1$

(c) sec 11π/3

$\text{Since, }\sec(x)=\frac{1}{\cos x}$

$\cos(\frac{11\pi}{3})=cos(\frac{5\pi}{3}+2\pi)=\cos(\frac{5\pi}{3})=\cos(6\pi-\frac{\pi}{3})=\cos(\frac{\pi}{3})=\frac{1}{2}\\\Rightarrow\sec(\frac{11\pi}{3})=\frac{1}{\cos(\frac{11\pi}{3})}=2$