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tia_tia [17]
2 years ago
13

Carl is standing at the top of 35 Ft cliff looking down at a rock for motion in the sea. He estimates the angle of depression is

30' . What is the horizonal distance from Carl to the island?
Mathematics
1 answer:
Liula [17]2 years ago
7 0

The horizontal distance between Carl and the rock at sea is approximately 60.62ft.

Data;

  • Angle = 30 degree
  • Opposite = 35
  • Adjacent = x

<h3>Trigonometric Ratio</h3>

Given the angle of depression from his point to the sea, we can use trigonometric ratio to calculate for the horizontal distance from his location to the bottom of the sea.

SOHCAHTOA

Since we have the value of angle and opposite and we need to calculate the adjacent side of the right-angle triangle, we can use the tangent of the angle to this effect.

Tan\theta = \frac{opposite}{adjacent} \\tan 30 = \frac{35}{x}\\ x = \frac{35}{tan30}\\ x = 60.62ft

The horizontal distance between Carl and the rock at sea is approximately 60.62ft.

Learn more on trigonometric ratio here;

brainly.com/question/12172664

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explain the benefits of each of the three forms of quadratic equations, standard form, vertex form, and factored form. What do t
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Answer:

Summary:

Standard form allow us to quickly find the y-intercept.

Vertex form allow us to quickly locate the vertex.

And factored form allows us to quickly determine the roots/zeros.

Step-by-step explanation:

The three forms of quadratics are the standard form, vertex form, and the factored form. Each of them reveals a specific part about the quadratic.

Standard Form:

The standard form of a quadratic is:

ax^2+bx+c

There are only two details that can be conveyed by a quadratic in standard form immediately: (1) the leading coefficient a, and (2) the y-intercept.

The leading coefficient a will tell us if the parabola curves upwards or downwards.

And the constant c will give us the y-intercept.

Vertex Form:

The vertex form of a quadratic is:

a(x-h)^2+k

There are also two details that can be conveyed by a quadratic in vertex form:  (1) the vertex, and (2) the leading coefficient.

The leading coefficient is given by a. Again, this tells us the orientation of the parabola.

And the vertex is given by (h, k).

Hence, in my opinion, vertex form is the best form of a quadratic since it immediately reveals the vertex, the most important aspect of a quadratic.

Factored Form:

The factored form of a quadratic is:

a(x-p)(x-q)

Where p and q are the zeros/roots/solutions of the quadratic.

Again, factored form gives us two details about the quadratic: (1) the leading coefficient, and (2) the zeros.

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Summary:

Therefore, each form of a quadratic equation has its own benefits.

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Vertex form allow us to quickly locate the vertex.

And factored form allows us to quickly determine the roots/zeros.

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2 years ago
Easy Slider Inc. sold a 15-year $1,000 face value bond with a 10% coupon rate. Interest is paid annually. After flotation costs,
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Answer:

6.6%

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We find the cost of the bond. Yield to maturity is the yield for bond holder but cost for the  issuer like Easy Slider.

Formula is

P=CP(1-(1+x)^-n)/x + FV/(1+x)^n

where P is the price of bond in the market. So, the selling price of Easy Slider Inc bond is 928

CP= coupon payment. Here, CP is 10% of 1000. So, $100

FV= Face value. Here, FV is $1000

n= maturity of the bond. Here, n=15

x= cost of the bond before tax

putting the value in the equation

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solving for x, we get 0.1100

Now, if we find out after tax then

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0.1100(1-0.4)

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3 years ago
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Answer:

25.5 inches is the correct answer

8 0
3 years ago
Read 2 more answers
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