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Svetradugi [14.3K]
3 years ago
8

CAN SOMEONE HELP ME FIND THE DISTANCE..​

Mathematics
1 answer:
kirill115 [55]3 years ago
5 0

The angle of elevation from point C to point A is 32^{\circ}

<em><u>Solution:</u></em>

Given that we have to find the angle of elevation from point C to Point A

Given in figure that, angle A = 58^{\circ}

Given is a right angled triangle ABC where angle B = 90^{\circ}

We have to find angle C

The angle sum property of a triangle states that the angles of a triangle always add up to 180°

Therefore, in given triangle ABC

angle A + angle B + angle C = 180

58^{\circ} + 90^{\circ} + C = 180^{\circ}

148^{\circ} + C = 180^{\circ}\\\\C = 180^{\circ} - 148^{\circ}\\\\C = 32^{\circ}

Therefore angle C = 32^{\circ}

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zavuch27 [327]

Answer:

The equation contains exact roots at x = -4 and x = -1.

See attached image for the graph.

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We start by noticing that the expression on the left of the equal sign is a quadratic with leading term x^2, which means that its graph shows branches going up. Therefore:

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Since in our case a=1 and b=5, we get that the x-position of the vertex is: x_v=\frac{-b}{2a} \\x_v=\frac{-5}{2(1)}\\x_v=-\frac{5}{2}

Now we can find the y-value of the vertex by evaluating this quadratic expression for x = -5/2:

y_v=f(-\frac{5}{2})\\y_v=(-\frac{5}{2} )^2+5(-\frac{5}{2} )+4\\y_v=\frac{25}{4} -\frac{25}{2} +4\\\\y_v=\frac{25}{4} -\frac{50}{4}+\frac{16}{4} \\y_v=-\frac{9}{4}

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We can now continue plotting different parabola's points, by selecting x-values to the right and to the left of the x_v=-\frac{5}{2}. Like for example x = -2 and x = -1 (moving towards the right) , and x = -3 and x = -4 (moving towards the left.

When evaluating the function at these points, we notice that two of them render zero (which indicates they are the actual roots of the equation):

f(-1) = (-1)^2+5(-1)+4= 1-5+4 = 0\\f(-4)=(-4)^2+5(-4)_4=16-20+4=0

The actual graph we can complete with this info is shown in the image attached, where the actual roots (x-axis crossings) are pictured in red.

Then, the two roots are: x = -1 and x = -4.

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