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MrRa [10]
2 years ago
14

A 13 ​-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 12 ft from the​ house, t

he base is moving away at the rate of 15 ​ft/sec.
a. What is the rate of change of the height of the top of the​ ladder?
b. At what rate is the area of the triangle formed by the​ ladder, wall, and ground changing​ then?
c. At what rate is the angle between the ladder and the ground changing​ then?
Mathematics
1 answer:
VARVARA [1.3K]2 years ago
8 0
I think the answer is B because all the air other answers are incorrect
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624 feet to 702 feet state whether the percent of the change is an increase or decrease
Ghella [55]

Answer:

The percent of change is an increase.

Step-by-step explanation:

624 has been changed to 702.

Percent change = [(Value after - Value before ) / Value before]*100

                          =\frac{702-624}{624}*100

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So we can clearly see that percentage change is a positive change. This means that the Value after change is higher than value before the change. So the percent of change is an increase.

8 0
3 years ago
Plot the following points on a xy-plane.<br> (5,2) , (-2, 1) , (-1,-3)
aliya0001 [1]

Answer: See below

Step-by-step explanation:

6 0
3 years ago
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1. What is an equation for the line with slope 2/3 and y-intercept 9?
Monica [59]
Question 1:

 The generic equation of the line is given by:
 y = mx + b&#10;
 Where,
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 b: cutting point with the y axis
 Substituting values ​​we have:
 y = \frac{2}3}x + 9&#10;
 Answer:
 an equation for the line with slope 2/3 and y-intercept is:
 y = \frac{2}3}x + 9

 Question 2:

 The standard equation of the line is given by:
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 (xo, yo): ordered pair that belongs to the line
 The slope of the line is:
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 Substituting values:
 m = \frac{1-(-3)}{3-1}
 m = \frac{1+3}{3-1}
 m = \frac{4}{2}
 m = 2&#10;
 We choose an ordered pair:
 (xo, yo) = (3, 1)&#10;
 Substituting values:
 y-1 = 2 (x-3)&#10;
 Rewriting:
 y = 2x - 6 + 1&#10;&#10;y = 2x - 5
 Answer:
 An equation in slope-intercept form for the line that passes through the points (1, -3) and (3,1) is:
 y = 2x - 5&#10;

 Question 3:

 For this case, since the variation is direct, then we have an equation of the form:
 y = kx&#10; Where,
 k: constant of variation.
 We then have the following equation:
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 y = \frac{8}{-4}x&#10;
 y = -2x&#10; Therefore, the constate of variation is given by:
 k = -2&#10;
 Answer:
 the constant of variation is:
 k = -2

 Question 4:

 For this case, since the variation is direct, then we have an equation of the form:
 y = kx&#10; Where,
 k: constant of variation.
 We must find the constant k, for this we use the following data:
 y = 24 when x = 8
 Substituting values:
 24 = k8&#10; Clearing k we have:
 k =  \frac{24}{8} &#10;
 k = 3&#10;
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 the value of y when x = 10 is:
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6 0
3 years ago
Read 2 more answers
PLS ANSWER ASAP 30 POINTS!!! CHECK PHOTO! WILL MARK BRAINLIEST TO WHO ANSWERS
Sveta_85 [38]

I'll do Problem 8 to get you started

a = 4 and c = 7 are the two given sides

Use these values in the pythagorean theorem to find side b

a^2 + b^2 = c^2\\\\4^2 + b^2 = 7^2\\\\16 + b^2 = 49\\\\b^2 = 49 - 16\\\\b^2 = 33\\\\b = \sqrt{33}\\\\

With respect to reference angle A, we have:

  • opposite side = a = 4
  • adjacent side = b = \sqrt{33}
  • hypotenuse = c = 7

Now let's compute the 6 trig ratios for the angle A.

We'll start with the sine ratio which is opposite over hypotenuse.

\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(A) = \frac{a}{c}\\\\\sin(A) = \frac{4}{7}\\\\

Then cosine which is adjacent over hypotenuse

\cos(\text{angle}) = \frac{\text{adjacent}}{\text{hypotenuse}}\\\\\cos(A) = \frac{b}{c}\\\\\cos(A) = \frac{\sqrt{33}}{7}\\\\

Tangent is the ratio of opposite over adjacent

\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(A) = \frac{a}{b}\\\\\tan(A) = \frac{4}{\sqrt{33}}\\\\\tan(A) = \frac{4\sqrt{33}}{\sqrt{33}*\sqrt{33}}\\\\\tan(A) = \frac{4\sqrt{33}}{(\sqrt{33})^2}\\\\\tan(A) = \frac{4\sqrt{33}}{33}\\\\

Rationalizing the denominator may be optional, so I would ask your teacher for clarification.

So far we've taken care of 3 trig functions. The remaining 3 are reciprocals of the ones mentioned so far.

  • cosecant, abbreviated as csc, is the reciprocal of sine
  • secant, abbreviated as sec, is the reciprocal of cosine
  • cotangent, abbreviated as cot, is the reciprocal of tangent

So we'll flip the fraction of each like so:

\csc(\text{angle}) = \frac{\text{hypotenuse}}{\text{opposite}} \ \text{ ... reciprocal of sine}\\\\\csc(A) = \frac{c}{a}\\\\\csc(A) = \frac{7}{4}\\\\\sec(\text{angle}) = \frac{\text{hypotenuse}}{\text{adjacent}} \ \text{ ... reciprocal of cosine}\\\\\sec(A) = \frac{c}{b}\\\\\sec(A) = \frac{7}{\sqrt{33}} = \frac{7\sqrt{33}}{33}\\\\\cot(\text{angle}) = \frac{\text{adjacent}}{\text{opposite}} \ \text{  ... reciprocal of tangent}\\\\\cot(A) = \frac{b}{a}\\\\\cot(A) = \frac{\sqrt{33}}{4}\\\\

------------------------------------------------------

Summary:

The missing side is b = \sqrt{33}

The 6 trig functions have these results

\sin(A) = \frac{4}{7}\\\\\cos(A) = \frac{\sqrt{33}}{7}\\\\\tan(A) = \frac{4}{\sqrt{33}} = \frac{4\sqrt{33}}{33}\\\\\csc(A) = \frac{7}{4}\\\\\sec(A) = \frac{7}{\sqrt{33}} = \frac{7\sqrt{33}}{33}\\\\\cot(A) = \frac{\sqrt{33}}{4}\\\\

Rationalizing the denominator may be optional, but I would ask your teacher to be sure.

7 0
1 year ago
Plzzzzzz help!! I will give brainliest to whoever answers
jarptica [38.1K]

Answer:

4 and -3 i think

Step-by-step explanation:

the dot is on 4 and -3

5 0
3 years ago
Read 2 more answers
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