how to find angle when 3 sides are given but only 1 angle?

Step-by-step explanation:

We can use the formula for the volume of a right circular cone, which is V = (1/3)πr^2h, where V is the volume, r is the radius of the base, h is the height, and π is the constant pi.

We are given that the volume of the cone is 162 cubic inches and the height is 6 inches, so we can substitute these values into the formula and solve for the radius:

162 = (1/3)πr^2(6)

Simplifying:

54 = πr^2

Dividing both sides by π:

r^2 = 54/π

Taking the square root of both sides:

r = sqrt(54/π) ≈ 4.115

Therefore, the radius of the base of the cone is approximately 4.115 inches.

To find the diameter of the base, we can multiply the radius by 2:

d = 2r ≈ 8.23

Therefore, the diameter of the base of the cone is approximately 8.23 inches.

The equation for the polynomial in this problem is given as follows:

[tex]y = \frac{1}{16}(x^4 - 17x^2 + 16)[/tex]

We are given the roots for each function, hence the factor theorem is used to define the functions.

The function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

The roots for this problem are given as follows:

Hence the polynomial is:

y = a(x + 4)(x + 1)(x - 1)(x - 4)

y = a(x² - 16)(x² - 1)

[tex]y = a(x^4 - 17x^2 + 16)[/tex]

When x = 0, y = 1, hence the leading coefficient a is given as follows:

a = 1/16.

Thus the equation is:

[tex]y = \frac{1}{16}(x^4 - 17x^2 + 16)[/tex]

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The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of periods is given as follows:

5 + 6 + 4 = 15.

The frequency of each class is given as follows:

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Answer:

Step-by-step explanation:

It has been moved 7 units down.

Answer:

approximately $ 1019

or $ 1019.42

Step-by-step explanation:

multiply # of hours worked times the hourly wage.

Step-by-step explanation:

U wrote this a little weird so i hope i got the right equation lol.

is (7 1/3) * x = (1.6)/(6/11) the right equation? if so,

(im gonna rewrite 7 and 1/3 as 22/3)

22/3x = (1.6)/(6/11) >simplify right side of equation

22/3x = 2.933333... >divide by 22/3

x = 0.4

The probability P(Z < -0.75) is approximately 0.2266.

P(x < 86) ≈ 0.2266 (rounded to four decimal places).

To find the indicated probability P(x < 86), we can standardize the normal distribution using the Z-score formula:

Z = (X - μ) / σ,

where X is the value of interest, μ is the mean, and σ is the standard deviation.

In this case, X = 86, μ = 89, and σ = 4. Plugging these values into the formula, we get:

Z = (86 - 89) / 4 = -0.75.

Now, we need to find the probability associated with this Z-score. We can look up this value in the standard normal distribution table or use a calculator. The probability P(Z < -0.75) is approximately 0.2266.

Therefore, P(x < 86) ≈ 0.2266 (rounded to four decimal places).

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Step-by-step explanation:

To solve the equation d÷2 = 108, we can use inverse operations to isolate the variable d on one side of the equation. Since the variable d is being divided by 2, we can multiply both sides of the equation by 2 to get rid of the division:

d÷2 = 108

Multiplying by 2:

2(d÷2) = 2 × 108

Simplifying:

d = 216

Therefore, the solution to the equation d÷2 = 108 is d = 216. We can check this solution by substituting it back into the original equation:

d÷2 = 108

216÷2 = 108

108 = 108

The left-hand side is equal to the right-hand side, so the solution is correct.

Answer: d = 216

Step-by-step explanation:

       To solve this equation, we will isolate the d variable using inverse operations. Multiplication is the inverse operation of division.

Given:

    d ÷ 2 = 108 ​

Multiply both sides of the equation by 2:

    d = 2 * (108)

    d = 216

a.) the net present value of Project A over a 4-year life with a salvage value, assuming a minimum rate of return of 12%, is -$4,837.60.

b.) Project B has a higher net present value than Project A, making it the project with the greatest net present value.

a. To calculate the net present value (NPV) of Project A, we need to discount the cash flows and salvage value at the minimum rate of return of 12% using the given table for the present value of $1 at compound interest:

Year 12%

1 0.893

2 0.797

3 0.712

4 0.636

First, let's calculate the present value of the cash flows:

PV_cash_flows = $18,000 * (0.712 + 0.636 + 0.636 + 0.636) = $18,000 * 2.620 = $47,160.

Next, let's calculate the present value of the salvage value:

PV_salvage_value = $18,400 * 0.636 = $11,702.40.

Now, let's calculate the net present value:

NPV = PV_cash_flows - Initial investment + PV_salvage_value

= $47,160 - $63,700 + $11,702.40

= $-4,837.60.

Therefore, the net present value of Project A over a 4-year life with a salvage value, assuming a minimum rate of return of 12%, is -$4,837.60.

b. Project B has a computed net present value (NPV) of $2,720 over a 4-year life. Comparing the NPV of Project A (-$4,837.60) with that of Project B ($2,720), we can conclude that Project B provides the greatest net present value.

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Answer:

Step-by-step explanation:

You can write an equation based upon where the curve has "zeroes" or when the curve touches/goes through the x axis.

Take opposite sign

Bounces off at -2 , this means there is a multiplicity

(x+2)²

Goes through at +1

(x-1)

Put it together:

y = (x+2)²(x-1)

The exact area of the shaded region is 9π.

We must first compute the area of the shaded zone and then calculate the radii of the circles in order to establish the precise size of the shaded region.

Given that the huge circle's diameter is 12, we know that its radius, which is 6, is equal to half of its diameter.

The center's of the three circles combine to form an equilateral triangle since each circle is tangent to the other two circles. The radius of the inscribed circle in an equilateral triangle is equal to one-third of the triangle's height. Consequently, each smaller circle's radius is 6/3, or 2.

Three sectors make up the shaded area, each of which has a Centre angle of 120 degrees (360 degrees divided by three). the region of

36π - 27π = 9π. Therefore, the exact area of the shaded region is 9π.

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To find the value of [tex]\sf f(8) \\[/tex] for the function [tex]\sf f(x) = \frac{1}{2}x^2 - \left(\frac{1}{4}x + 3\right) \\[/tex], we substitute [tex]\sf x = 8 \\[/tex] into the function.

[tex]\sf f(8) = \frac{1}{2}(8)^2 - \left(\frac{1}{4}(8) + 3\right) \\[/tex]

Simplifying inside the parentheses:

[tex]\sf f(8) = \frac{1}{2}(64) - \left(\frac{1}{4}(8) + 3\right) \\[/tex]

[tex]\sf f(8) = 32 - \left(2 + 3\right) \\[/tex]

[tex]\sf f(8) = 32 - 5 \\[/tex]

Finally, subtracting:

[tex]\sf f(8) = 27 \\[/tex]

Therefore, the value of [tex]\sf f(8) \\[/tex] is 27.

Answer:

f(8) = 27

Step-by-step explanation:

to evaluate f(8) substitute x = 8 into f(x)

f(8) = [tex]\frac{1}{2}[/tex] × 8² - ( [tex]\frac{1}{4}[/tex] (8) + 3)

     = [tex]\frac{1}{2}[/tex] × 64 - (2+ 3)

     = 32 - 5

     = 27

The correct statements concerning the roots of unity are: B. nth roots of unity are evenly spaced on the unit circle.OC. 1 is always the nth root of unity. Option B and C

B. nth roots of unity are evenly spaced on the unit circle.

This statement is true. The nth roots of unity are the solutions to the equation z^n = 1, where z is a complex number. These roots are evenly spaced around the unit circle in the complex plane. If we represent the roots as points on the unit circle, their angular separation is 2π/n radians.

OC. 1 is always the nth root of unity.

This statement is true. The number 1 is always a solution to the equation z^n = 1. In fact, it is the principal root of unity. For any positive integer n, 1 raised to any power is always 1, so it satisfies the equation.

The incorrect statements are:

A. -1 is the nth root of unity when n is odd.

This statement is false. -1 is the nth root of unity only when n is even. For example, -1 is the square root of unity (n=2) since (-1)^2 = 1. However, when n is odd, -1 is not a root of unity because (-1)^n = -1, not 1.

D. -1 is always the nth root of unity.

This statement is also false. As mentioned earlier, -1 is not always the nth root of unity. It is only a root when n is even.

In summary, the correct statements are that nth roots of unity are evenly spaced on the unit circle, and 1 is always the nth root of unity. The incorrect statements are that -1 is the nth root of unity when n is odd and that -1 is always the nth root of unity. Option B and C

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Step-by-step explanation:

Let's solve this problem step by step.

Let's assume the speed at which salmon normally swim, with no current, is 'n' miles per hour.

When the salmon swims downstream (with the current), it is helped by the current's speed, so its effective speed is the sum of its normal swimming speed and the current's speed. Therefore, when swimming downstream, the salmon's speed is (n + 5) miles per hour.

When the salmon swims upstream (against the current), it faces resistance from the current, so its effective speed is the difference between its normal swimming speed and the current's speed. Therefore, when swimming upstream, the salmon's speed is (n - 5) miles per hour.

We are given that the salmon can swim 25 miles downstream in the same amount of time it takes to swim 15 miles upstream. Let's set up an equation to represent this information:

Time taken to swim downstream = Time taken to swim upstream

Distance / Speed downstream = Distance / Speed upstream

25 / (n + 5) = 15 / (n - 5)

To solve this equation, we can cross-multiply:

25(n - 5) = 15(n + 5)

25n - 125 = 15n + 75

25n - 15n = 75 + 125

10n = 200

n = 20

Therefore, the salmon normally swims at a speed of 20 miles per hour with no current.

Answer:

13:20 52:80

Step-by-step explanation:

divide 52 by 13=4

multiply 20 by 4=80

The length of a rectangle is 6 in., longer than its width. If the perimeter of a rectangle is 76 in. then its length is 22 and width is 16.

The solution to the question is as follows:

let the width of the rectangle is x in.

Then, ATQ,

The length of the rectangle will be x+6

Now,perimeter of the rectangle=2(l+b)=76(given)

2(l+b)=76

2(x+x+6)=76

2(2x+6)=76

4x+12=76

4x=76-12

4x=64

x=64/4

x=16

If x=16,then width of rectangle=16

length of rectangle=x+6=16+6=22

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The airline uses different airplanes that can be used to match specific flight requirements. Different Planes can provide different services, depending on the airline's needs and passenger preferences.Thus, the fleet mix is an essential part of an airline's overall strategy

An airline uses different airplanes that are suited for a specific flight mission or type of passengers.

The airline's fleet is designed to match specific flight requirements, such as short-haul vs. long-haul flights, high-density passenger traffic, or specialized services.

The table below provides data on the different planes used by the airline.

Plane Number of Seats Seat Width (inches) Wi-Fi First-Class Seats SkyBus 280 120 20.3 No No SkyBus 580 225 20.6 Yes Yes Grigson A-2 70 19.9 No No Grigson A-5 130 20.5 Yes No SkyDancer 350 20.2 Yes YesThe table indicates that the airline uses five types of planes in its operations.

The planes have varying numbers of seats, seat width, Wi-Fi capability, and first-class seats. SkyBus 280 has a seating capacity of 120 passengers, a seat width of 20.3 inches, no Wi-Fi, and no first-class seats.

SkyBus 580 has 225 seats, a seat width of 20.6 inches, Wi-Fi, and first-class seats. Grigson A-2 has 70 seats, a seat width of 19.9 inches, no Wi-Fi, and no first-class seats.

Grigson A-5 has 130 seats, a seat width of 20.5 inches, Wi-Fi, and no first-class seats. Finally, SkyDancer has 350 seats, a seat width of 20.2 inches, Wi-Fi, and first-class seats.

In conclusion, the airline uses different airplanes that can be used to match specific flight requirements. Different planes can provide different services, depending on the airline's needs and passenger preferences.

Thus, the fleet mix is an essential part of an airline's overall strategy.

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Answer:

[tex] {(2pq)}^{3} = 8 {p}^{3} {q}^{3} [/tex]

The correct answer is A.

Answer:

Option B, Surface Area = 24p²q²

Step-by-step explanation:

The surface area of a cube can be expressed as a monomial by using the formula:

Surface Area = 6s²

Where "s" represents the length of one side of the cube.

It is given that the length of one side of the cube is 2pq. Plug this into the formula above. We get,

=> Surface Area = 6(2pq)²

Applying the power of a product rule for exponents we get,

=> Surface Area = 6(2pq)²

=> Surface Area = 6(2²p²q²)

=> Surface Area = 6(4p²q²)

=> Surface Area = 24p²q²

Thus, option B is the correct option.

Answer:

Step-by-step explanation:

(4i+8)-(5i-5) = 4i + 8 - 5i + 5 = -i+13

Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.

To estimate [tex]\sf f'(1) \\[/tex] using a positive difference quotient for the function [tex]\sf f(x) = 3\log(x) \\[/tex], we can use the following formula:

[tex]\sf f'(1) \approx \frac{f(1+h) - f(1)}{h}\\[/tex]

where [tex]\sf h \\[/tex] is a small positive value. Let's choose [tex]\sf h = 0.001 \\[/tex] for our estimation.

First, let's evaluate [tex]\sf f(1) \\[/tex]:

[tex]\sf f(1) = 3\log(1) = 3\cdot 0 = 0 \\[/tex]

Next, let's evaluate [tex]\sf f(1+h) \\[/tex]:

[tex]\sf f(1+h) = 3\log(1+h) \\[/tex]

Substituting [tex]\sf h = 0.001 \\[/tex]:

[tex]\sf f(1+0.001) = 3\log(1.001) \\[/tex]

Now, we can calculate the positive difference quotient:

[tex]\sf f'(1) \approx \frac{f(1+h) - f(1)}{h} = \frac{3\log(1.001) - 0}{0.001} \\[/tex]

Using a calculator, we find:

[tex]\sf f'(1) \approx 0.434 \\[/tex]

Therefore, [tex]\sf f'(1) \approx 0.434 \\[/tex] (rounded to three decimal places).

From the graph of [tex]\sf f(x) = 3\log(x) \\[/tex], we would expect the estimate [tex]\sf f'(1) \\[/tex] to be greater than [tex]\sf f'(1) \\[/tex] since the graph of [tex]\sf f(x) \\[/tex] is increasing at [tex]\sf x = 1 \\[/tex].

The ball is approximately 160.59 yards from the center of the green.

To solve this problem, we can use the law of cosines. Let's label the positions as follows:

Center of the fairway: F

Center of the green: G

Golfer's ball: B

We're given that the distance between the marker in the fairway (F) and the center of the green (G) is 120 yards. The golfer walks off 30 yards from the marker to reach his ball (B).

Let's find the distance between the ball (B) and the center of the green (G):

Using the law of cosines, we have:

BG² = BF² + FG² - 2 * BF * FG * cos(100°)

Given:

BF = 30 yards (distance walked by the golfer)

FG = 120 yards (distance between the marker and the green)

Angle FGB (formed by the marker, the ball, and the green) = 100°

Substituting these values into the formula, we get:

BG² = 30² + 120² - 2 * 30 * 120 * cos(100°)

Now, let's calculate:

BG² = 900 + 14,400 - 2 * 30 * 120 * cos(100°)

To find cos(100°), we can use a calculator or a trigonometric table. The value of cos(100°) is approximately -0.173648.

BG² = 900 + 14,400 - 2 * 30 * 120 * (-0.173648)

BG² = 900 + 14,400 + 10,483.68

BG² = 25,783.68

Taking the square root of both sides, we find:

BG ≈ √(25,783.68) ≈ 160.59 yards

Therefore, the ball is approximately 160.59 yards from the center of the green.

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Hello!

number = x

3 * x - 2 = 25

3x - 2 = 27

3x = 27

x = 27/3

x = 9

the number is 9

The number is:

Work/explanation:

Let t be the number. 3 times a number t is 3t. Then if we decrease by 2, it's the same as subtracting 2. So, 3t - 2.

Now this equals 25:

3t - 2 = 25

So now we have a little equation to solve.

Add 2 on each side

3t = 27

Divide each side by 3

t = 9

Answer: 2−(56x+

3

1

​

)=

9

8

​

11

​

Step-by-step explanation:

The time that the rocket will hit the ground, to the nearest 100th of second, is 23.26 seconds.The equation that relates the height of a rocket, y in feet, to the time after launch, x in seconds is given as y=-16x²+261x+146.

Using this equation, to find the time that the rocket will hit the ground, to the nearest 100th of second we need to find when y = 0 as the height of the rocket will be zero when it hits the ground.

So, we can solve for x as follows:y = -16x²+261x+146Put y = 0 and solve for x.0 = -16x²+261x+146

Rearrange and factor the equation to get the values of x.0 = 16x²-261x-146Using the quadratic formula, we can solve for x as follows:x = (-b ± √(b²-4ac))/2a

Where a = 16, b = -261, and c = -146.x = (-(-261) ± √((-261)²-4(16)(-146)))/(2(16))

Simplify x = (261 ± √(109881))/32x = (261 ± 331.7)/32

The solutions are:x = 23.25625 secondsx = 10.14375 seconds

However, the time that the rocket will hit the ground is when x = 23.25625 seconds (to the nearest 100th of second). Therefore, the time that the rocket will hit the ground, to the nearest 100th of second, is 23.26 seconds. Answer: \boxed{23.26}.

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Answer:

Therefore, the roots of the given equation are x = 2, x = 1, and x = -3.

Step-by-step explanation:

This problem involves finding the zeros (or roots) of a polynomial equation, which are the values of x that make the equation equal to zero. The given equation is cubic, meaning it has a degree of 3 and can have up to three real roots.

One way to find the roots of this equation is to use the Rational Root Theorem, which states that any rational root of a polynomial equation with integer coefficients must have the form p/q, where p is a factor of the constant term (in this case 18) and q is a factor of the leading coefficient (in this case 3). However, this method only works for finding rational roots, and there may be irrational or complex roots as well.

Another method is to use a graphing calculator or software to graph the equation and visually locate the x-intercepts, which are the points where the graph crosses the x-axis and the value of y is zero. From the graph, we can see that there are three real roots: one positive, one negative, and one between -2 and -1.

A third method is to use numerical methods (such as Newton's method or the Bisection method) to estimate the roots to a desired level of accuracy. However, this method involves iterative calculations and can be time-consuming.

Without using a graphing calculator, we can try to factor the given equation by using the Rational Root Theorem. The possible rational roots are ±1, ±2, ±3, ±6, ±9, ±18 (all factors of 18 divided by all factors of 3). We can test these roots by substituting them into the equation and seeing if the result equals zero.

Testing x = 1 gives:

3(1)^3 - 2(1)^2 - 13(1) + 18 = 3 - 2 - 13 + 18 = 6, which is not zero.

Testing x = -1 gives:

3(-1)^3 - 2(-1)^2 - 13(-1) + 18 = -3 - 2 + 13 + 18 = 26, which is not zero.

Testing x = 2 gives:

3(2)^3 - 2(2)^2 - 13(2) + 18 = 3(8) - 2(4) - 13(2) + 18 = 0, which means x = 2 is a root.

Using polynomial division, we can factor out (x - 2) from the cubic polynomial to obtain a quadratic polynomial that can be factored:

(3x^3 - 2x^2 - 13x + 18) / (x - 2) = 3x^2 + 4x - 9

Factoring the quadratic gives:

3x^2 + 4x - 9 = (3x - 3)(x + 3)

Setting each factor equal to zero and solving for x gives:

3x - 3 = 0, so x = 1

x + 3 = 0, so x = -3

Answer:

C) 24 in

Step-by-step explanation:

We can use Pythagorean theorem:

a²+b²=c²

18²+b²=30²

324 + b² = 900

b² = 576

b = 24

Missing side length is C) 24 in

a) The exponential function for the number of bacteria after t minutes is given as follows: [tex]y = 5800e^{-0.103585t}[/tex]

b) The number of bacteria after 18 minutes is given as follows: 899 bacteria.

The format of the exponential function is given as follows:

[tex]y = A(0)e^{-kt}[/tex]

In which:

The initial population is given as follows:

A(0) = 5800

Hence:

[tex]y = 5800e^{-kt}[/tex]

After 11 minutes, there are 1856 bacteria left, hence the decay rate k is obtained as follows:

[tex]1856 = 5800e^{-11k}[/tex]

[tex]e^{-11k} = \frac{1856}{5800}[/tex]

[tex]k = -\frac{\ln{\left(\frac{1856}{5800}\right)}}{11}[/tex]

k = 0.103585.

Hence the function is:

[tex]y = 5800e^{-0.103585t}[/tex]

After 18 minutes, the population is given as follows:

[tex]y = 5800e^{-0.103585(18)}[/tex]

y = 899 bacteria.

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Answer:

Step-by-step explanation:

This graph is an upside down exponential graph moved up one unit. The growth factor is 3; therefore, the equation for this graph is

[tex]f(x)=-(3)^x+1[/tex]

Answer:

  f(x) = -(3^x) +3

Step-by-step explanation:

You want an equation for the curve shown in the graph.

A function that has a horizontal asymptote and rapidly changes is often an exponential function.

The location of the horizontal asymptote tells you the vertical translation. Here, the function is translated upward 3 units.

The direction of the rapid change tells you the sign of the leading coefficient. Here, it is negative.

The location of the point 1 unit different from the horizontal asymptote tells you the horizontal translation. Here, the x-value of (0, 2) is 0, so there is no horizontal translation.

The point 1 horizontal unit away from the point just found tells you the base of the exponent. Here, the point (1, 0) is 3 units different from the horizontal asymptote, so the base of the exponent is 3.

Putting these values together, we have ...

  f(x) = -(3^x) +3

__

Additional comment

The attached graph confirms this equation.

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