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Harlamova29_29 [7]

2 years ago

7

A 15 foot ladder is leaning against a wall of a house. The base of the ladder is pulled away from the wall at a rate of 2ft/sec.

Find the rate at which the area of the triangle is changing when the base of the ladder is 9ft from the wall

1 answer:

valina [46]2 years ago

3 0

The rate at which the area of the triangle is changing when the base of the ladder is 9 ft from the wall will be the negative 8/3.

<h3>What is differentiation?</h3>

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.

A 15-foot ladder is leaning against a wall of a house.

The base of the ladder is pulled away from the wall at a rate of 2ft/sec.

Then the equation will be

x² + y² = 15²

x² + y² = 225

Differentiate with respect to time. Then we have

2x (2) + 2yy' = 0

y' = -2x / y

Then the rate at which the area of the triangle is changing when the base of the ladder is 9 ft from the wall will be

Then the value of x will be

x² + 9² = 15²

x² + 81 = 225

x² = 144

x = 12 ft

Then the rate will be

y' = -2x / y

y' = – 2 × 12 / 9

y' = – 8/3

More about the differentiation link is given below.

brainly.com/question/24062595

#SPJ1

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3 0

3 years ago

Find an equation for the line below. Thanks !

daser333 [38]

Answer:

$\huge\boxed{y=\frac{1}{4}x + \frac{13}{4}}$

Step-by-step explanation:

In order to find the equation to this line, we need to note that we see two points on this graph. Using these two points, we can use them to find the slope of the graph and use one to find the y-intercept.

We know that the slope of a line is defined by $\frac{\Delta y}{\Delta x}$ (change in y / change in x). Therefore, we can use our two points that we know - (-5, 2) and (3, 4) to find the slope.

The change in y is $4 - 2 = 2$ , and the change in x is $3 - (-5) = 3+5= 8$ . Therefore, our slope is $\frac{2}{8} = \frac{1}{4}$ .

Now that we know our slope, our equation in slope-intercept form looks something like this.

$y = \frac{1}{4}x + b$

However, we still have b to solve for. We can solve for this by substituting a point we already know into the equation. Let's substitute (3, 4) inside.

$4 = \frac{1}{4} \cdot 3+b$
$4 = \frac{3}{4} + b$
$b = \frac{16}{4}- \frac{3}{4}$
$b = \frac{13}{4}$

So now we know that the y-intercept is $\frac{13}{4}$ . Plugging that into our equation finishes it off, leaving our final equation to be $y = \frac{1}{4}x + \frac{13}{4}$ .

Hope this helped!

4 0

3 years ago

Read 2 more answers

Find the possible values of k if one of the roots of the quadratic equation x^2 - kx + 8 = 0 is twice the other.

kondor19780726 [428]

Answer:

$k=\pm 6$

Step-by-step explanation:

The given quadratic equation is :

$x^2 - kx + 8 = 0$

One of the roots of this equation is twice that of the other. Let the roots are $\alpha \ and\ \beta$ , $\alpha =2\beta$

Sum of roots, $\alpha +\beta =\dfrac{-b}{a}$

$\alpha +\beta =\dfrac{-(-k)}{1}\\\\\alpha +\beta =k\\\\3\beta =k\ .......(1)$

Product of roots,

$\alpha \beta =\dfrac{c}{a}\\\\2\beta ^2=\dfrac{8}{1}\\\\\beta =\pm 2$

If $\beta =\pm2$ ,

$k=3(2)\\\\=\pm 6$

So, the value of k is equal to $\pm 6$ .

8 0

2 years ago