A proper, an improper, a mixed number or a decimal fraction?

a street light is at the top of a 18 ft tall pole. a woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a s

shutvik [7]

The most appropriate choice for similarity of triangles will be given by -

Speed of tip of the shadow of woman = 6 ft/s

What are similar triangles?

Two triangles are said to be similar, if the corrosponding angles of the triangles are same and the corrosponding sides of the triangles are in the same ratio.

Here,

The diagram has been attached here

Let the distance of woman from the pole be x ft and the distance of tip of the shadow to the pole be y ft.

Height of street light = 18 ft

Height of woman = 6ft

The two triangles are similar [As height of woman is parallel to the height of pole]

$\frac{y - x}{6}=\frac{y}{18}\\18y - 18x = 6y\\18y - 6y = 18x\\12y = 18x\\y = \frac{18}{12}x\\y = \frac{3}{2}x\\$

To find the speed, we have to differentiate both sides with respect to time 't'

$\frac{dy}{dt} =\frac{3}{2}\frac{dx}{dt}\\\frac{dy}{dt}=\frac{3}{2} \times 4\\\frac{dy}{dt} = 6$

Speed of tip of her shadow = 6 ft

To learn more about similarity of triangles, refer to the link-

brainly.com/question/14285697

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6 0

11 months ago

PLEASE HELP FOR A BRAINLIEST!!!! Create your own example and explain how to solve Quadratic Equation using Quadratic Formula. Wh

SVETLANKA909090 [29]

Step-by-step explanation:

1. Create your own example and explain how to solve Quadratic Equation using Quadratic Formula.

The quadratic formula is used to solve quadratic equations. It is shown as $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

A quadratic equation is generally shown in the form of $ax^{2} +bx + c = 0$

For example, if you saw the equation $7x^{2} + 3x + 20 = 0$

7 would be $a$ , 3 would be $b$ , and 20 would be $c$ .

To solve the equation above, you would fill in the quadratic formula as such, $x=\dfrac{-3\pm\sqrt{(3)^2-4(7)(20)}}{2(7)}$

Then you could solve for x.

2. What part in the Quadratic Formula is the discriminant?

The discriminant is the equation under the square root on the quadratic formula, $b^{2} - 4ac$

It is tells us whether there are two solutions, one solutions, or no solutions.

3. How do you know the number of solutions based on the value of the discriminant?

To know the number of solutions based off of the value of the discriminant, you need to plug in your values. Using the example quadratic equation, $7x^{2} + 3x + 20 = 0$

We will plug the values into the discriminant.

$3^{2} - 4(7)(20) = -551$

Now, if the discriminant is positive it has two real solutions. If the discriminant is zero the equation has no real-number solutions. And finally, if the discriminant is negative, the equation has one real solution. Because our discriminant is -551, the example equation has one real solution.

Hope this helps! (Please consider Brainliest)

8 0

3 years ago

Point m is the midpoint of kL. M(1,-1) and L(8,-7. What are the coordinates of point k?

Phoenix [80]

Answer: (-6, 5)

<u>Step-by-step explanation:</u>

Use the Midpoint Formula: $\dfrac{(x_k, y_k)+(x_L,y_L)}{2}=(x_m, y_m)$

Separate the x's and y's and solve them individually:

$\dfrac{x_k+x_L}{2}=x_m\qquad \qquad \qquad \qquad\dfrac{y_k+y_L}{2}=y_m\\\\\\\dfrac{x_k+8}{2}=1\qquad \qquad \qquad \qquad \qquad \dfrac{y_k-7}{2}=-1\\\\\\x_k+8=2\qquad \qquad \qquad \qquad \qquad y_k-7=-2\\\\\\x_k\quad =-6 \qquad \qquad \qquad \qquad \qquad y_k\qquad =5$