What is the length of an arc cut off by an angle of 3 radians on a circle of radius 8 inches?

The surface area of a cone with diameter 28 cm and height 22 cm in terms of pi is:

        c.     561.1 pi cm²

The diameter of cone= 28 cm

Radius of cone is half the diameter this means that:

Radius(r) of cone= 14 cm

Also, height(h) of cone= 22 cm

We know that the surface area of cone is given by:

[tex]Surface\ Area=\pi r(r+\sqrt{h^2+r^2})[/tex]

Now as we know the value of h and r hence we will substitute these values in the formula to get:

        [tex]Surface\ Area=\pi \times 14(14+\sqrt{(14)^2+(22)^2})\\\\\\Surface\ Area=14\pi (14+26.07681)\\\\\\surface\ Area=14\pi\times 40.07681\\\\\\Surface\ Area=561.07534\pi cm^2[/tex]

  Hence, the surface area of cone is:  561.1π cm²

Answer:

The answer is D. 6

Step-by-step explanation:

By determining the cost per song, which is $0.78, we can calculate that downloading ten songs from the website would cost $7.80.

To determine the cost to download ten songs, we first need to calculate the cost per song. We are given that six song downloads cost $4.68. By dividing this total cost by the number of songs, we find the cost per song:

Cost per song = Total cost for six songs / Number of songs

= $4.68 / 6

= $0.78 per song

Now, to find the cost of ten songs, we multiply the cost per song by ten:

Total cost for ten songs = Cost per song * Number of songs

= $0.78 * 10

= $7.80

Therefore, it would cost $7.80 to download ten songs from the website.

The measure of side a is 14.

We have,

We use the trigonometric identites:

Sin function

Now,

Sin A = Perpendicular / Hypotenuse

Sin 34 = a / 25

0.56 = a / 25

a = 0.56 x 25

a =  14

Thus,

The measure of side a is 14.

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Answer:

B. [tex]x=62[/tex]; [tex]y=30[/tex]

Step-by-step explanation:

We have been given two similar triangles. We are asked to find the value of x and y for the given triangles.

[tex]\Delta SWK\sim \Delta EBT[/tex]

We know that the measure of corresponding angles of two similar triangles are equal.

[tex]m\angle S=m\angle E[/tex]

[tex]m\angle W=m\angle B[/tex]

[tex]m\angle K=m\angle T[/tex]

[tex]110=2x-14[/tex]

[tex]2x-14=110[/tex]

[tex]2x-14+14=110+14[/tex]

[tex]2x=124[/tex]

[tex]\frac{2x}{2}=\frac{124}{2}[/tex]

[tex]x=62[/tex]

[tex]m\angle S=m\angle E[/tex]

[tex]40=m\angle E[/tex]

Using angle sum property, we will get:

[tex]m\angle E+m\angle B+m\angle T=180[/tex]

[tex]40+y+110=180[/tex]

[tex]y+150=180[/tex]

[tex]y+150-150=180-150[/tex]

[tex]y=30[/tex]

Therefore, option B is the correct choice.

We want to make a 4 players team, and there are total 8 players. As we know the order of selection does not matter in a team of players, only the combination of players matters.

So we would use concept of Combinations and It will be choose 4 out of 8 players.

The formula for Combination is given as follows :-

[tex]nCr = \frac{n!}{r!*(n-r)!} \\\\ Choose \;4 \;out \;of \;8 \;players \\\\ 8C4 = \frac{8!}{4!*(8-4)!} = \frac{8!}{4!*4!} \\\\ 8C4 = \frac{8*7*6*5*4*3*2*1}{(4*3*2*1)*(4*3*2*1)} = \frac{8*7*6*5}{4*3*2*1} =\frac{1,680}{24} = 70 \;combinations[/tex]

Hence, Total number of different teams = 70 combinations.

The expression that represents the situation is 40 + 3p.

The correct option is D.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

The essay is worth 40 points and each correctly answered multiple-choice question is worth 3 points.

If Rasha answered p multiple-choice questions correctly, she would earn a total of 40 + 3p points.

Therefore, the correct expression is D.

40 + 3p.

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Final answer:

To find the product of (5.2 · [tex]10^-^6[/tex]) and (8 · 10³), multiply the base numbers and add the exponents. The result is 41.6 × [tex]10^-^3[/tex], which simplifies to 4.16 × 10^-2.

Explanation:

The student asked to find the product of two numbers expressed in scientific notation: (5.2 · [tex]10^-^6[/tex]) and (8 · 10³). When multiplying numbers in scientific notation, you multiply the base numbers and add the exponents.

Step-by-Step Solution:

Simplified Result:

This can further be simplified by writing 41.6 × [tex]10^-^3[/tex]as 4.16 × [tex]10^-^2[/tex], by moving one decimal place to the left in the base number and increasing the exponent by 1 to balance it.

The perimeter of the triangle will be 48  cm. The correct option is D.

A perimeter is the total length of the boundary or outer edge of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.

For example, the perimeter of a rectangle is the sum of the lengths of all four sides, while the perimeter of a circle is the distance around its circumference. The perimeter is usually measured in units such as meters, centimeters, inches, or feet, depending on the context of the problem.

Whenever we have two tangents outside the circle and they are in contact with each other, it means their lengths are the same

The perimeter of the triangle will be calculated as,

Perimeter = sum of all the sides

Perimeter = ( 11 + 11 + 7 + 7 + 6 + 6 )

Perimeter = 48 cm

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The estimated answer would be =14000

Answer:

Step-by-step explanation:

To find the answer we must use the diagram, we see that among 8 possible results, there's one possible outcome to hit HHH.

So, to find the amount of people that are expected to hit HHH, we just have to  multiply each percentage assigned to the HHH outcome:

[tex](0.7)(0.5)(0.3)=0.105[/tex]

Now, we see that a 10.5% of the people will be expected to hit HHH.

The approximate number of people would be:

[tex]25(0.105) \approx 3[/tex]

Therefore, almost 3 persons are expected to hit HHH.

By using basic property of inverse function we got that if f(x) and it’s inverse function are both plotted on the same coordinate plane, then their point of intersection is (3,3)

Function is relation between a set to another set with a property that every element of first set has a unique image in second set.

Here graph of f(x) is given and we have to find the point of intersection of function and it's inverse function

We know that a function and it's inverse function are mirror image of each other with respect to line y=x hence they intersect only at y=x line

By drawing y=x line with the given graph we got that f(x) intersect y=x line at (3,3) hence inverse function will intersect at (3,3)

By using basic property of inverse function we got that if f(x) and it’s inverse function are both plotted on the same coordinate plane, then their point of intersection is (3,3)

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When the graph of a function and its inverse function are plotted on the same coordinate plane, the point of intersection is the point where the two graphs intersect. Therefore, the point of intersection is (x, y).

When the graph of a function and its inverse function are plotted on the same coordinate plane, the point of intersection is the point where the two graphs intersect.

Let's say the point of intersection is (x, y).

This means that both f(x) and f-1(x) have the same x-coordinate, which is x, and the same y-coordinate, which is y.

Therefore, the point of intersection is (x, y).

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Final answer:

The amplitude of a wave is the coefficient A in the equation y(x, t) = A sin(kx - ωt + φ), and the period T can be calculated using T = 2π/ω, where ω is the angular frequency. Additional properties like wavelength and speed can be found using related equations involving the wave number and frequency.

Explanation:

To find the amplitude and period from the equation of a wave, look at the standard form of a sinusoidal wave function, which is generally y(x, t) = A sin(kx - ωt + φ). Here, the amplitude can be directly read from the equation as the coefficient A, which represents the maximum displacement from the rest position. As for the period, it can be derived from the angular frequency using the formula T = 2π/ω, where T is the period and ω is the angular frequency.

The wavelength (λ) and speed (v) of the wave can also be determined from the properties of the wave. The wavelength is related to the wave number by the equation λ = 2π/k, and the speed can be calculated if the frequency (f) is known, using the equation v = λf.

For example, if the amplitude is provided as 30 V/m and the frequency is given as 2.0 MHz, the period (T) would then be 5.0 × 10-7 s based on the relationship between frequency and period, T = 1/f.

Answer:

mean is 578.3 deviation 261.9

Step-by-step explanation:

The equivalent expression of [tex]2^{\frac{1}{3} }[/tex] in radical forms is ∛2

Radical are expression that uses a root, such as square root, cube root . They are numbers represented in radical symbols.

Therefore,

[tex]2^{\frac{1}{3} }[/tex] in radical form can be represented as follows:

Using indices rule

[tex]a^{\frac{1}{b} } = \sqrt[b]{a}[/tex]

Therefore,

[tex]2^{\frac{1}{3} } = \sqrt[3]{2}[/tex]

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Answer:

A)

Step-by-step explanation: