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Ymorist [56]
3 years ago
10

A yacht is anchored 90 feet offshore from the base of a lighthouse. The angle of elevation from the boat to the top of the light

house is 26 degrees . The distance between the yacht and the top of the lighthouse is about 100 feet. Which of these is nearest to the height of the lighthouse ?
Mathematics
1 answer:
Morgarella [4.7K]3 years ago
7 0
≈ 43.8 , lmk if u need like an explanation or something
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How many real solutions does this system of equations have? x^2 + y^2 = 36
Vinvika [58]

Answer:

C:  there are two real solutions

Step-by-step explanation:

x^2 + y^2 = 36 is the equation of a circle centered at the origin and with radius √36, or 6.  Even a rough sketch of this circle would enable you to visualize what is happening here.  

3x – y + 1 = 0 may be solved for y:  y = 3x + 1.  The y-intercept of this straight line is (0, 1).  Plot this point inside the circle of radius 6 mentioned above and then draw a straight line with slope m = 3 through it.  This line will intersect the circle in two places; they represent real solutions.

Alternatively, substitute 3x + 1 for y in x^2 + y^2 = 36:

x^2 + (3x + 1)^2 = 36, or

x^2 + 9x^2 + 6x + 1 = 36, or

10 x^2 + 6x + 1 - 36 = 0, or

10 x^2 + 6x - 35 = 0.  This is a quadratic equation.  We'll use the quadratic formula to find solutions which represent the intersections of this line with this circle:

The coefficients are a = 10, b = 6 and c = -35.  Thus, the discriminant is

b^2 - 4ac, or 6^2 - 4(10)(-35), or 1436.  

Because the discriminant is positive, we can safely conclude that there are two real solutions, that is, two different, real x-values, each representing the x-coordinate of a point of intersection of the circle and the line.

The correct answer to this prolem is C:  there are two real solutions.

4 0
3 years ago
Please help me quick please i don't understand
Shtirlitz [24]
Square root of 15 is an irrational number.
7 0
3 years ago
Can you help me <br> If y= -4 when x = 10, find y when x = 5
Dafna1 [17]

Answer:

-2

I think it's -2 because you're dividing x by 2 so you'd divide -4 by 2.

7 0
3 years ago
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How to find each angle indicated
Natalija [7]
The answer is 80 because all triangles equal 180
8 0
3 years ago
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Which two complex numbers that could have been added together to make -11+3i
irina [24]

Answer:

Step-by-step explanation:

There are an infinite number of possible solutions.

here's a few

(1 - 4i) + (-12 + 4i)

(-5.5 + 2i) + (-5.5 + i)

(-24 - 27i) + (13 + 30i)

3 0
3 years ago
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