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3 years ago

Find the length of arc AB.

Mathematics

1 answer:

guajiro [1.7K]3 years ago

5 0

Answer:

11.17

Step-by-step explanation:

arc length = 2πr(θ/360)

= 2π(8)(80/360)

= 11.1701072...

= 11.17 to nearest hundredth

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98 POINTS MATH!

patriot [66]

Let $a$ be the length of the leg with one tick mark and $b$ the length of the leg with two tick marks.

In the upper triangle, the law of cosines says

$6^2=a^2+b^2-2ab\cos43^\circ$

In the lower triangle, it says

$4^2=a^2+b^2-2ab\cos(4y-5)^\circ$

Subtract the second equation from the first to eliminate $a^2+b^2$ :

$6^2-4^2=-2ab(\cos43^\circ-\cos(4y-5)^\circ)$

$10=ab(\cos(4y-5)^\circ-\cos43^\circ)$

$a$ and $b$ are lengths so they must both be positive. 10 is also positive, so in order to preserve the sign on both sides of this equation, we must have

$\cos(4y-5)^\circ-\cos43^\circ>0$

$\cos(4y-5)^\circ>\cos43^\circ$

Now we have to be a bit careful. If $x$ is an acute angle, then as $x$ gets larger, the value of $\cos x$ gets smaller. So if we have two angles $\theta$ and $\varphi$ , with $0^\circ$ , then we would have $\cos\theta>\cos\varphi$ .

This means in our inequality, taking the inverse cosine of both sides would reverse the inequality:

$(4y-5)^\circ$

We know that $(4y-5)^\circ$ is an angle in a triangle, so it must be some positive measure:

$(4y-5)^\circ>0^\circ\implies y>\dfrac54^\circ$

So we must have

$\dfrac54^\circ$

6 0

3 years ago

The formula to find the period of orbit of a satellite around a planet is T^2=(4pi^2/GM)r^3 where r is the orbit's mean radius,

Natalija [7]

The answer is $r= \sqrt[3]{GMT^{2}/4 \pi^{2}}$

$T^{2} = \frac{4 \pi^{2}}{GM} r^{3}$

Move $\frac{4 \pi^{2} }{GM}$ to the other side of the equation:
$T^{2} /\frac{4 \pi^{2} }{GM} = r^{3} \\ 
T^{2} *\frac{GM}{4 \pi^{2} } = r^{3}$

Rearrange:
$r^{3} = T^{2} *\frac{GM}{4 \pi^{2} } \\ 
r^{3}= \frac{T^{2} *GM}{4 \pi^{2} } \\ 
r^{3}= \frac{GMT^{2}}{4 \pi^{2} } \\ 
r^{3} = GMT^{2}/4 \pi^{2}$

Since $x^{3}= \sqrt[3]{x}$ , then
$r^{3} = GMT^{2}/4 \pi^{2} \\ 
r= \sqrt[3]{GMT^{2}/4 \pi^{2}}$

3 0

4 years ago

Read 2 more answers

An archaeologist is categorizing the artifacts he has discovered. Two-thirds of the artifacts are shards of pottery. One-eighth

Reika [66]

Answer:

Personal items=15

Step-by-step explanation:

We are given:

Total number of artifacts = 72.

We are told that 2/3 of total artifacts are shards of pottery.

$\text{Shards of pottery}=72*\frac{2}{3} =24*2=48$