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svetoff [14.1K]
2 years ago
5

Find the circumference of the circle. Round your answer to the nearest hundredth.

Mathematics
1 answer:
Alex Ar [27]2 years ago
7 0

Answer:

circumference = 25.13 \ cm

Step-by-step explanation:

circumference = 2 \pi r = 2 \pi 4 = 8 \pi =25.13 \ cm

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Find the exact value by using a half-angle identity. sin(5pi/12)
anzhelika [568]

Find <span>tan<span>(<span><span>5π</span>12</span>)</span></span> and sin ((5pi)/12)
Answer: <span>±<span>(2±<span>√3</span>)</span>and±<span><span>√<span>2+<span>√3</span></span></span>2</span></span>

Explanation:

Call tan ((5pi/12) = t. 
Use trig identity: <span><span>tan2</span>a=<span><span>2<span>tana</span></span><span>1−<span><span>tan2</span>a</span></span></span></span>
<span><span>tan<span>(<span><span>10π</span>12</span>)</span></span>=<span>tan<span>(<span><span>5π</span>6</span>)</span></span>=−<span>1<span>√3</span></span>=<span><span>2t</span><span>1−<span>t2</span></span></span></span>
<span><span>t2</span>−2<span>√3</span>t−1=0</span>

<span>D=<span>d2</span>=<span>b2</span>−4ac=12+4=16</span>--> <span>d=±4</span>

<span>t=<span>tan<span>(<span><span>5π</span>12</span>)</span></span>=<span><span>2<span>√3</span></span>2</span>±<span>42</span>=2±<span>√3</span></span>

Call <span><span>sin<span>(<span><span>5π</span>12</span>)</span></span>=<span>siny</span></span>
Use trig identity: <span><span>cos2</span>a=1−2<span><span>sin2</span>a</span></span>
<span><span>cos<span>(<span><span>10π</span>12</span>)</span></span>=<span>cos<span>(<span><span>5π</span>6</span>)</span></span>=<span><span>−<span>√3</span></span>2</span>=1−2<span><span>sin2</span>y</span></span>
<span><span><span>sin2</span>y</span>=<span><span>2+<span>√3</span></span>4</span></span>
<span><span>siny</span>=<span>sin<span>(<span><span>5π</span>12</span>)</span></span>=±<span><span><span>√<span>2+<span>√3</span></span></span>2</span></span></span>

5 0
3 years ago
Find the product. (-2x^2 )^3 ·3 x
jeka94

Assignment: \bold{Solve \ \left(-2x^2\right)^3\cdot \:3x}

<><><><><>

Answer: \boxed{\bold{-24x^7}}

<><><><><>

Explanation: \downarrow\downarrow\downarrow

<><><><><>

[ Step One ] Rewrite \bold{\left(-2x^2\right)^3}

\bold{-2^3\left(x^2\right)^3}

[ Step Two ] Rewrite Equation

\bold{-2^3\cdot \:3x^6x}

[ Step Three ] Apply Exponent Rule

Note: \bold{Exponent \ Rule \ \:a^b\cdot \:a^c=a^{b+c}: \ x^6x=\:x^{6+1}=\:x^7}

\bold{-2^3\cdot \:3x^7}

[ Step Four ] Refine

\bold{-24x^7}

<><><><><><><>

\bold{\rightarrow Rhythm \ Bot \leftarrow}

4 0
3 years ago
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Answer the following questions, using the simulation: a. Determine the spring constant, k, of Spring 1, by using Hooke’s Law. Ta
Akimi4 [234]

At high noon, you can feel warm air coming from inland. During noon, especially in spring and summer, the radiation caused by the Sun warms the land surface more compared to the sea surface. This is because heat is directly applied on the land surface compared to the ocean.

4 0
3 years ago
By what percent did the price change, if… a the price was $100 and now it is $250?
elena-s [515]
It had a 150% increase in price

100* 1.5 = 150
150+100 = 250
7 0
3 years ago
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A rectangle with an area of 5/8 ft² is dilated by a factor of 8. What is the area of the dilated rectangle?
gulaghasi [49]

Answer:

40 ft²

Step-by-step explanation:

Let the length of the original rectangle be L and original Breadth be B

it is given that the original area  is 5/8 ft²

i.e.

Original Length x Original Breadth = Original Area, or,

LB = 5/8 ft² ------------------(1)

Given that the dilation factor is 8,

Hence,

New Length = 8L and New Breadth = 8B

THerefore,

New Area = 8L x 8B

= 64 LB  (from (1) above , we know that LB = 5/8 ft², substitute into expression)

= 64 (5/8)

= 40 ft²

4 0
3 years ago
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