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3 years ago

Find the point slope equation for the line that passes through the points (7,-21) (-4,23)

1 answer:

5 0

$\bf (\stackrel{x_1}{7}~,~\stackrel{y_1}{-21})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{23}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{23-(-21)}{-4-7}\implies \cfrac{23+21}{-11}\\\\\\ \cfrac{44}{-11}\implies -4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-21)=-4(x-7)\implies y+21=-4(x-7)$

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Estimate and classify the critical points for the graph of the function<br> Please show work

ikadub [295]

The critical points of the function graphed are given as follows:

x = -1.5: Local maximum.

x = -1: Local minimum.

<h3>What are the critical points of a function?</h3>

The critical points of a function are the values of x for which:

$f^{\prime}(x) = 0$

In a graph, they are turning points, and are classified as follows:

Local maximum, if the functions changes from increasing to decreasing.

Local minimum, if the functions changes from decreasing to increasing.

Looking at the graph, the turning points are approximately:

x = -1.5: Local maximum.

x = -1: Local minimum.

More can be learned about critical points at brainly.com/question/2256078

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2 years ago

the angle of depression from an airplane at an altitude of 8000 feet to the airport is 7 degrees. Find the direct distance from

Aleks [24]

Answer:

direct distance = 65,644.07 feet

horizontal distance = 65,154.77 feet

Step-by-step explanation:

The angle of depression is the angle that the airplane does with the horizontal plane.

So, if this angle is 7° and the airplane is at an altitude if 8000 feet, we can find the direct distance and the horizontal distance using the tangent and the sine relations of the angle.

In the tangent of the angle, the opposite side will be the height of the airplane, and the adjacent side will be the horizontal distance (hd), so:

tangent(7) = 8000 / hd

hd = 8000 / tangent(7) = 65,154.77 feet

In the sine of the angle, the opposite side will be the height of the airplane, and the hypotenusa will be the direct distance (d), so:

sine(7) = 8000 / d

d = 8000 / sine(7) = 65,644.07 feet

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3 years ago

Which of the following points is collinear with (1, 1), and (2, 2)? (4, 1) (3, 2) (5, 6) (3, 3)

aleksandrvk [35]

<span>Points (1, 1), and (2, 2) are on a line which has a slope of 1

ok?

The only point that lies on this line is (3,3).
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4 years ago

2. Jessica's grandparents gave her $2000 for college to put in a savings account until she starts

rodikova [14]

Answer:

<em>I </em>=2000(0.075)4= $600

Step-by-step explanation:

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3 years ago

What is the distance between the origin and the point (2,-5) on a graph? The options are: square root of 7. Square root of 29. 7

Sunny_sXe [5.5K]

Answer:

Square root of 29.

Step-by-step explanation:

Distance = sqrt(2^2 + (-5)^2)

= sqrt 29.

3 0

3 years ago