If the diameter of the circle above is 20 mm, what is the area of the circle? A. 100 mm2 B. 400 mm2 C. 20 mm2 D. 10 mm2

Mathematics

2 answers:

baherus [9]3 years ago

5 0

Answer:

100π.

Step-by-step explanation:

cestrela7 [59]3 years ago

3 0

Answer:

The answer is 100π.

Step-by-step explanation:

Since the diameter of the circle is 20mm, the radius of the circle is 20/2 = 10mm.

The formula for area of a circle is π*r^2. If we substitute r for 10, we get the final answer as 100π or about 314.16.

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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

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

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