A sailor is on the top deck of a ship that is anchored near shore, 200 feet from a lighthouse. The sailor can see the top of the lighthouse by looking up at a 21° angle of elevation and can see the bottom of the lighthouse by looking down at a 14° angle of depression.

How tall is the lighthouse?

Enter your answer in the box. Round to the nearest tenth of a foot.

Answer:

  -1/2

Step-by-step explanation:

You want to know the exact value of sin(-5π/6).

The reference angle is the smallest angle its terminal side makes with the x-axis. The angle -5π/6 is a 3rd-quadrant angle, whose reference angle is ...

  -5π/6 +π = π/6

You know that the signs of the sine and cosine trig functions are negative in the 3rd quadrant. Since you have memorized the short table of trig functions (first attachment), you know the value you're looking for is ...

  sin(-5π/6) = -sin(π/6) = -1/2

__

Additional comment

The second attachment shows the functions that are positive in the different quadrants. The ones not listed are negative.

The third attachment shows the coordinates on the unit circle as (cos, sin). The angle 7π/6 is the same as the angle -5π/6.

The fourth attachment shows you can put your calculator in radian mode and have it tell you the answer.

Answer:

I have provided the answers on the original image you provided.

Step-by-step explanation:

For f(x) = -2x² + 8x + 1

To find the y-intercept, set x = 0 and determine the value for f(x). This will work out to +1 so the y-intercept is (0, 1)

To find the vertex y-value. Note that we are given the x value as 2. Substitute 2 for x in the function expression. This will give you a value of 9. So the vertex is (2, 9)

The coefficient of x² is negative so it will be a maximum vertex and therefore opens downward

For g(x) = 3x² + 6x -4

To find the x value of the vertex, differentiate with respect to x and set this first derivative equal to zero

First derivate of g(x), g'(x) = 6x + 6

Set 6x + 6 =0 to get x = -1

The axis of symmetry is nothing but the x value of the vertex and therefore x = -1

The coefficient of x² is positive. So the vertex will be a minimum and it will be an upward opening parabola

I hope that helps

Answer:

The amplitude of the function y=2*sin(x) is 2. The amplitude is the maximum value of the function, and in this case, the maximum value of y is 2.

The period of the function y=2*sin(x) is 2π. The period is the distance in the x-axis between two points at which the function has the same value. And in this case, the function reaches the maximum value of 2 at x = π/2, and the next time it reaches the same value is x = 3π/2, which is a distance of 2π in the x-axis.

Answer:

3rd one is the answer

Step-by-step explanation:

x=7*2/5

Answer:

[tex]\frac{5}{8}[/tex]

Step-by-step explanation:

3 [tex]\frac{3}{8}[/tex] - 2[tex]\frac{6}{8}[/tex]

I can rewrite3 [tex]\frac{3}{8}[/tex]

2 [tex]\frac{8}{8}[/tex] + [tex]\frac{3}{8}[/tex]   ([tex]\frac{8}{8}[/tex] means the same as 1)

2[tex]\frac{11}{8}[/tex] - 2 [tex]\frac{6}{8}[/tex] = [tex]\frac{5}{8}[/tex]

238

14x17, the answer is 238 for your question plus it's an easy one you could've just multiplied and got your answer even from a calculator..

The total amount of money Williams will pay if he downloaded 45 song is 36.5 dollars.

The total cost if he download s song is 14 + 0.50s.

William signed up for a streaming music service that costs $14 per month. The service allows William to listen to unlimited music, but if he wants to download songs for offline listening, the service charges $0.50 per song.

Therefore, the amount of money Williams will save to download 45 songs is as follows:

Using equation,

y = 14 + 0.50x

where

Therefore,

y = 14 + 0.50(45)

y = 14 + 22.5

y = 36.5 dollars

If he downloaded s songs,

total cost = 14 + 0.50s

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The value of x is given as follows:

x = 1.5.

The measure of each segment is given as follows:

The segment addition postulate is a geometry axiom that states that a line segment, divided into a number of smaller segments, has the length given by the sum of the lengths of the segments.

For this problem, we have that segment WY is divided into two smaller segments, WX and XY.

This means that the equation to find the value of x is presented as follows:

WY = WX + XY

7x - 3 = 9x - 11 + 4x - 1

13x - 12 = 7x - 3

6x = 9

x = 1.5.

Hence the segment lengths are given as follows:

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Answer:

-------------------------------

Let the time Kyle ran be x, then he walked for (x + 1) hours.

He ran 12x km and walked 5(x + 1) km thus in total 42 km.

Set up and equation and solve for x:

Total time was:

Answer:

run = 10

rise = 20

Slope in simple: 2/1

Step-by-step explanation:

Rise over run = 20/10 --> 2/1

a) To calculate the after-tax cost of debt, we first need to calculate the pre-tax cost of debt, which is the coupon interest rate. In this case, the bond has a coupon interest rate of 8%. We then need to multiply this by (1-tax rate) to get the after-tax cost of debt. In this case, the firm is in a 40% tax bracket, so:

After-tax cost of debt = 8% x (1 - 40%) = 4.8%

b) To calculate the cost of preferred stock, we need to know the dividend yield, which is the annual dividend payment per share divided by the price per share. In this case, the preferred stock does not have any dividends, so its cost of capital is 0%.

c) To calculate the cost of new common stock, we need to know the dividend yield, which is the annual dividend payment per share divided by the price per share. We also need to know the rate of growth in dividends. In this case:

Dividend yield = Dividend per share / Price per share

Dividend yield = 7 / 90 = 0.0778

Cost of new common stock = (Dividend per share / Price per share) + (Dividend growth rate)

Cost of new common stock = 0.0778 + 0.06 = 13.78%

d) To calculate the firm's weighted average cost of capital (WACC), we need to use the capital structure weights and the costs of each type of capital. In this case:

WACC = (Weight of debt x After-tax cost of debt) + (Weight of preferred stock x Cost of preferred stock) + (Weight of new common stock x Cost of new common stock)

Note: These weights can be calculated from the proportion of each source of financing in the firm's capital structure.

WACC = (0.354.8%) + (00%) + (0.65*13.78%) = 7.63%.

The firm's weighted average cost of capital using retained earnings and the capital structure weights is 7.63%.

Cost of capital is the minimum rate of return or profit a company must earn before generating value. It's calculated by a business's accounting department to determine financial risk and whether an investment is justified.

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Answer:

36,552

Step-by-step explanation:

To estimate the product of 481.68 and 76.25 to the nearest whole number, we can round both numbers to the nearest whole number first. 481.68 can be rounded to 482 and 76.25 can be rounded to 76.

Then, we can calculate the product of 482 and 76 to get the estimated result:

482 * 76 = 36,552

Therefore, the estimated product of 481.68 and 76.25 to the nearest whole number is 36,552.

Answer:

36,552

Step-by-step explanation:

To estimate the product of 481.68 and 76.25, you can round each number to the nearest whole number. 481.68 rounds to 482, and 76.25 rounds to 76.

The product of 482 and 76 is approximately 36,552. Therefore, the product of 481.68 and 76.25 is approximately 36,552.

Answer:

Inequality Form:

x≤ −9/11

Interval Notation:

(−∞,−9/11]

Answer: He will have to plant 14 rows

Step-by-step explanation:

-11 because

(gof)(x) = 18x2 - 123x + 193. Substitute x = 4. (gof)(4) = 18(4)2 - 123(4) + 193. (gof)(4) = -11. Solution: The solution is (gof)(4) = -11.

Step-by-step explanation:

when x=10

3x+5y=20

3×10+5y=20

30+5y=20

5y=20-30

5y=-10

y=-10/5

y=-2

Answer:

Step-by-step explanation:

turn 3/4 into 6/8

there you can see 2 3/8 - 6/8 is less than two (the answer is 1 5/8 im pretty sure)

Answer: 18, 28, 38, 48, 58

Step-by-step explanation:

Answer:

18, 28, 38, 48, 58

Step-by-step explanation:

I think this is pretty self explanatory.

Answer:

6x+48

Step-by-step explanation:

u multiply what is in the bracket by 6

[tex]\huge\text{Hey there!}[/tex]

[tex]\text{In order to solve for this particular equation, you have to DISTRIBUTE 6}\\\text{within the PARENTHESES}}[/tex]

[tex]\text{REMEMBER: if you have a variable by itself, it is understood to be an invisible 1}[/tex]

[tex]\text{Anywho! Let us answer your given question}[/tex]

[tex]\mathsf{6(x + 8)}[/tex]

[tex]\mathsf{= 6(x) + 6(8)}[/tex]

[tex]\mathsf{= 6x + 48}[/tex]

[tex]\huge\text{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\mathsf{6x + 48}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer: 63 inches tall

Step-by-step explanation:

The counter in the photograph appears 4 inches tall, and it is actually 3.5 feet tall, or 42 inches tall.

Therefore, the scale of the photograph is  [tex]42 inches/4inches = 10.5 inches[/tex]

The shoplifter in the photograph appears [tex]6[/tex] inches tall, so in real life, they are [tex]6 inches[/tex] * [tex]10.5 inches[/tex] [tex]= 63 inches[/tex] tall

So the shoplifter is [tex]63 inches[/tex] tall.

The height of BC is calculated from the knowledge of similar triangles to be 2.76 m

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

Examining the figure shows that pair of equivalent sides are

AE and DE, AC and BC.

The solution is worked out using the proportion as follows

AE / DE = AC / BC

5 / 0.92 = (5 + 10) / BC

5 * BC = 0.92 * 15

BC = 2.76 m

hence  BC = 2.76 m

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Check the picture below.

A. Work shows that as the probability of success approaches 0, the standard deviation decreases and approaches 0.

The standard deviation for the binomial distribution with a probability of success p = 0.017 for 20 trials would be 0.282. The standard deviation for a binomial distribution can be calculated using the formula =√np(1−p).

Inserting the values for n = 20, p = 0.017 gives us an answer of 0.282. As the probability of success approaches 0, the standard deviation decreases and approaches 0.

This is because as the probability of success approaches 0, the number of successes in the trials approaches 0, so there is less variation in the number of successes and the standard deviation approaches 0.

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Solving for x in the proportion 4/5 / x = 2 / 74/4 gives

The given proportion is 4/5 / x = 2 / 74/4

Using the equation 4/5 / x = 2 / 74/4, x is solved by making it the subject of the formula and this means placing x alone at the left hand side of the equation. this is achieved by

cross multiplying

4/5 / x = 2 / 74/4

4/5 * 74/4 = 2x

74/5 = 2x

dividing through by 2

x = 37/5

x = 7 2/5

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Answer:

the 3rd oneeeeeeeeeeeeeeeeeeeeeeeeeeee

The ratio of the lengths of  ( AD, IH ) is 2:1

A chord that passes through the center of the circle is known as diameter of he circle. Chords IH and EF are diameters of our given circle.

Point A is the center of this circle.

In the given diagram we have EF is the diameter of the circle.

BC is the chord of the circle and Diameter and chord length will vary.

AD is the radius of the circle and IH is the diameter of the circle.

Diameter of the circle IH is 2 times the radius AD

So,

The Answer is option B

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Answer:

5

Step-by-step explanation:

set everything equal to a to solve for a.

a + 1 - 2 = 4

a + 1 = 6

a = 5

so your answee would be 5.

we can check this by plugging back in.

5+1-2=4

Using the given points, Observing the values at x=0, We get y-intercept = 2units , Using formula for slope we have , m = -1 and the equation is

x+y-2=0.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics. A set of two or more linear equations with two or more variables each constitutes a system of linear equations, all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy all of the system's equations is necessary to identify the one and only solution to a system of linear equations.

A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis. This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points satisfy x = 0 because of this.

In mathematics, the slope or gradient of a line is a number that indicates the line's steepness as well as its X and Y directions.

at x=0, we find y-intercept,

from the table,

y-intercept (c) = 2 units.

slope = [tex]\frac {y_2 - y_1}{x_2-x_1}[/tex]

[tex]=\frac {-2+1}{0+1}\\\\=-1[/tex]

Equation, y =mx + c

y=-x+2

x + y=2

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The number of solutions of the system of equations 10x - 12 = 10x + 4 is given as follows:

Zero.

The system of equations 10x - 12 = ax + b would have an infinite number of solutions when:

The systems in this problem are defined by linear functions, which have the following format:

y = mx + b.

In which:

The slope and the y-intercept are used to determine the number of solutions of the system, as follows:

The system of equations 10x - 12 = 10x + 4 falls in the second case, while for a system to have an infinity number of solutions, it must fall on the third case.

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By evaluating the given formula, we will see that the fifth term of the sequence is 32.

Here we have a sequence defined by the formula below:

aₙ = 2ⁿ

So that formula gives the n-th term of the sequence. To find the fifth term, we just need to replace the value of n by the value 5 in the formula above.

We will get.

a₅ = 2⁵  

a₅ = 32

The fifth term of the sequence is 32.

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