Choose the appropriate trigonometric ratio and solve for x. Round your answer to the nearest tenth.

The area of one petal of the polar curve r = 5 sin 2θ would be 25π/4.

Supposing that there is no direct formula available for deriving the area, we can derive the area of that region by dividing it into smaller pieces, whose area can be known directly.

Then summing all those pieces' area gives us the area of the main big region.

The polar curve r = 5sin 2θ

When r = 0, θ = 0, π/2 which corresponds to one loop.

We need the limits to provide r=0 or cos(5x) =0 so:

Therefore the area of the region enclosed by this curve is

[tex]A = \dfrac{1}{2} \int\limits^a_b {r^{2} } \, d\theta \\\\\\A = \dfrac{1}{2} \int\limits^{\pi /2}_0 {25sin^{2}2\theta } \, d\theta \\\\\\A = \dfrac{1}{2} \times 25\int\limits^{\pi /2}_0 {sin^{2}2\theta } \, d\theta \\\\\\A = \dfrac{1}{2} \times 25\int\limits^{\pi /2}_0 \dfrac {1-cos^{2}4\theta } {2}\, d\theta\\ \\\\A = \dfrac{25}{2}( \theta - \dfrac {sin4\theta} {2})\, d\theta |^{\pi /2}_0\\\\\\A = \dfrac{25}{2} \times \dfrac{\pi }{2} \\\\\\A = \dfrac{25\pi }{4}[/tex]

Thus, the area of one petal of the polar curve r = 5sin 2θ would be 25π/4.

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Answer: Explanation:The slope-intercept form of a linear equation is: y=mx+bWhere m is the slope and b is the y-intercept value.We can subtract 5x from each side of the equation to put the equation in slope intercept form while keeping the equation balanced:−5x+5x+y=−5x+40+y=−5x+4y=−5x+4Therefore:The slope is: m=−5The y-intercept is: b=4 or (0,4)

Step-by-step explanation:

Answer:

Slope m=-5  Y intercept=4 (-5,4)

Step-by-step explanation:

To get the slope you will need Rise over Run. 5/1 which is slope

which will make x=0 and y=4  which is y intercept.

The triangles are similar triangles, and the values of HK and GH are (b) 4 and 2√5, respectively

The triangles are similar triangles, and they are represented by the following similarity ratio:

GK : HK = HK : JK

From the question, we have:

GK = 2 and JK = 8

So, we have:

2 : HK = HK : 8

Express as fractions

[tex]\frac{2}{HK} = \frac{HK}{8}[/tex]

Cross multiply

HK² = 16

Take the positive square root of both sides

HK = 4

The length GH is calculated using the following Pythagoras theorem

GH² = GK² + HK²

This gives

GH² = 2² + 4²

Evaluate the squares

GH² = 20

Solve for GH

GH = 2√5

Hence, the values of HK and GH are (b) 4 and 2√5, respectively

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Answer:

5.5 km/h

Step-by-step explanation:

→ 5% of 110

→ (5/100) × 110

→ 0.05 × 110

→ 5.5 km/h

Answer:

The ratio is 1:4 or 1 computer for every 4 sixth graders.

Step-by-step explanation:

20 for 80 = 20:80

20:80 divided by 10:10 = 2:8

2:8 divided by 2:2 = 1:4

Answer:

2/4

Step-by-step explanation:

2/4 does not equel a whole number instead it only reaches 1/2

Step-by-step explanation:

I am not sure i understand the text you put there.

what I think is clear is to find the expected number of the appearances of the number 3 when spinning the spinner 100 times.

to do this we start by checking the given information.

and we see that the given table based on the result of in total 50 spins (7+8+9+7+11+8).

when spinning the spinner additional times, we can expect the same structure of distribution of the individual possible results as before. we just scale everything to the new size of the overall sample.

before, with 50 spins, we saw the number 3 9 times.

so, with 100 spins, which is 2×50, we expect to see the number 3 then 2×9 = 18 times.

Answer:

i

Step-by-step explanation:

i = [tex]\sqrt{-1}[/tex] ⇒ i² = ([tex]\sqrt{-1}[/tex] )² = - 1 , then

[tex]i^{5}[/tex]

= i² × i² × i

= - 1 × - 1 ×i

= 1 × i

= i

Answer:

i think that the answer is b

Step-by-step explanation:

lmk if im wrong

Answer:

Step-by-step explanation:

Answer:

The answer is A

Step-by-step explanation:

Hope this helps

Answer:

50

Step-by-step explanation:

100% - 8% = 92%

Proportions:

46 ⇒ 92%

A ⇒ 100%

A = 46*100/92

A = 4600/92

A = 50

Answer:

A 95% confidence interval for the mean μ of a population is computed from a random sample and found to be 9 ±3. We may conclude that A. there is a 95% probability that μ is between 6 and 12.

Step-by-step explanation:

hope it helps

Answer:

P(2 red in 5 offspring) = 26.4%

P(no more than 2 red flowers) = 65.9%

Step-by-step explanation:

P(red) = 25%

P(white) = 75%

P(2 red in 5 offspring) = 5C2 P(red)*P(red)*P(white)*P(white)*P(white)

= 10 * 0.25 * 0.25 * 0.75 * 0.75 * 0.75 = 26.4%

P(no more than 2 red flowers) = P(1 red in 5 offspring) + P(2 red in 5 offspring)

= 5C1 P(red)*P(white)^4 + 0.2637

= 5 * 0.25 * 0.75* 0.75 * 0.75 * 0.75 + 0.2637

= 0.6592 = 65.9%

Answer: d. the correct decision has been made

Step-by-step explanation:

Answer:

$3.88

Step-by-step explanation:

Answer:

A: 12

Step-by-step explanation:

Using the pythagoreom theorem, a^2+b^2=c^2. We can plug in the lengths of 5 and 13 which is 5^2+b^2=13^2. Now we can square the numbers to get 25+b^2=169. Subtract 25 from 169 to get 144. Now find the square root of 144 which is 12.

what is the question tho?

Step-by-step explanation:

short step

(-isin(π/6)+2×5cos(π/6) ei π/4)

I/2+5√3 4√-1

The product of the trigonometric expressions will be 10 (cos 75° + i sin 75°).

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The trigonometric expressions are given below.

2 [cos(45°) + i sin(45°)] and 5 [cos(30°) + i sin(30°)]

Then the product of the trigonometric expressions is given as,

⇒ 2 [cos(45°) + i sin(45°)] × 5 [cos(30°) + i sin(30°)]

⇒ 10 [(cos 45° × cos 30° + sin 45° × sin 30° × i²) + i (sin 45° × cos 30° + cos 45° × sin 30°)]

⇒ 10 [cos (45° + 30°) + i sin (45° + 30°)]

⇒ 10 (cos 75° + i sin 75°)

The product of the trigonometric expressions will be 10 (cos 75° + i sin 75°).

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Answer:

2hours 20minutes

Step-by-step explanation:

hope this helps

Answer:

10

Step-by-step explanation:

Its outside the graph

Answer:

A and C

Step-by-step explanation:

Because the numbers are smaller so you need to look for a bigger number than what the number you have is.

Answer:

The gradient is 20

Step-by-step explanation:

Gradient = Change in Charge / change in hours worked.

Gradient = 200 - 80/ 6 - 0

= 120/ 6

= 20

b. The gradient of the line represents the amount the plumber charges per hour

Answer:

∠A≅∠X          AB≅XZ

∠B≅∠Z          AC≅XY

∠C≅∠Y          BC≅ZY

ΔABC≅ΔZXY

Step-by-step explanation:

congruent is identical in form so if the angle has one dash than look for the identical version on the other triangle

Answer:

Your answer is B) Function 1 has the smaller minimum value of -14.

Step-by-step explanation:

Method 1: Looking at the Function 1 and 2 points.

Method 2:

I have graphed functions 1 and 2 onto desmos to help determine which one has the smaller minimum.

Answer:

a = 9

Step-by-step explanation:

45 = 4(a + 3) – 3

Add 3 to both sides.

48 = 4(a + 3)

Divide both sides by 4.

12 = a + 3

Subtract 3 from both sides.

9 = a

a = 9

Answer: a = 9

The volume of the solid generated by revolving the region bounded by the given curve and lines y = 2x, y = 2, x = 0 about the x-axis will be  

V = 8π/3

When the integration is done in the three dimensions in the three coordinates x,y and z then we will call it as a volume integration.

I set y=2x = y=2 to find where the intersect each others so I can have my boundaries for integration.

You goal is to find the area so you can integrate around that area. We're revolving around the x-axis so the area will be a circle.

V = ∫A(x)dx =  ∫(πr²)dr

Since we have two different radius, we subtract them from each others.

∫(πr₂² - πr₁²)dr

∫(π(2)² - π(2x)²)dr

∫(4π - 4πx²)dr

4π∫(1 - x²)dr

integrate from 0 to 1 since that's where our boundary is.

V = 4π∫(1 - x²)dr = 8π/3

Hence the volume of the solid generated by revolving the region bounded by the given curve and lines y = 2x, y = 2, x = 0 about the x-axis will be V = 8π/3

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