A playground is being designed where children can interact with their friends in certain combinations.

Mathematics

1 answer:

levacccp [35]3 years ago

4 0

Answer:

Step-by-step explanation:

I think 17

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what is the y-intercept of the line perpendicular to the line y=-3/4x+5 that includes the point (-3,-3)?

Deffense [45]

Answer:

Step-by-step explanation:

For this question, your friend is the point-slope form.

Point-slope form = $y-y_1 = m(x-x_1)$

The only variables you replace are m = slope, y1 = y of a given point, and x1 = x of a given point.

First, we need to find the slope that is perpendicular to the equation $y=-\frac{3}{4}x+5$

An equation that is perpendicular to another equation have to be negative reciprocals (negative inverse) of each other.

If the slope is 3, then the negative reciprocal of 3 is $-\frac{1}{3}$ .

So, since the given slope is -3/4, the negative reciprocal is $\frac{4}{3}$ .

We will use the negative reciprocal as m since we are trying to find the equation of line that includes (-3, -3) and is perpendicular to the other equation.

We will use point slope form using the (-3, -3) points and negative reciprocal as m.

$y-y_1 = m(x-x_1)\\y-(-3) = \frac{4}{3} (x-(-3))\\y+3=\frac{4}{3}(x+3)$

Now, we need to convert this into slope-intercept form. The reason why we need to do this is because y = mx + b, where b is the y-intercept. To do this, solve for y - or in other words, isolate y..

$y+3=\frac{4}{3}(x+3)\\y+3=\frac{4x}{3}+4\\y+3-3=\frac{4x}{3}+4-3\\y=\frac{4}{3}x+1$

The y-intercept of the line is 1.

3 0

3 years ago

Evaluate the limit as x approaches 1 of the quotient of the square root of the quantity x squared plus 3 minus 2 and the quantit

IgorLugansk [536]

A graph shows the limit to be 1/2.
https://www.desmos.com/calculator/qrf6ay47tw

Since the value of the function is the indeterminate form 0/0, L'Hôpital's rule applies. The ratio of derivatives of numerator and denominator is
.. x/ $\sqrt{x^{2}+3 }$
Evaluated at x=1, this is
.. 1/ $\sqrt{1^{2}+3 }$ = 1/2