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Harman [31]
3 years ago
14

Two cars are heading toward the same intersection. Car A travels due east at 20 miles per hour, and Car B travels due north at 5

0 miles per hour. At what rate, in miles per hour, is the distance between the two cars decreasing when Car A is 0.375 miles from the intersection and Car B is 0.5 miles from the intersection?
Mathematics
1 answer:
Genrish500 [490]3 years ago
3 0

Answer:

the distance between them is decreasing at a rate of 2 mph.

Step-by-step explanation:

List all given rates and the unknown rate.

Write the formula that relates the variables in the problem: x, y, and s.

There’s a right triangle in the diagram, so you use the Pythagorean Theorem:

For this problem, x and y are the legs of the right triangle, and s is the hypotenuse, so

Differentiate with respect to t.

Use the Pythagorean Theorem again to solve for s.

x = 0.4

y = 0.3

You can reject the negative answer because s obviously has a positive length. So s = 0.5.

Now you’ve got everything you need to substitute into the differentiation result and solve for ds/dt.

This negative answer means that the distance, s, is decreasing. Thus, when car A is 3 blocks north of the intersection and car B is 4 blocks east of the intersection, the distance between them is decreasing at a rate of 2 mph.

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If FGH QRS, find the measure of Q<br><br> A. 9<br> B.28<br> C.11<br> D.34
Ne4ueva [31]

Answer:

  • 28°

Step-by-step explanation:

<u>Since ΔFHG ≅ QRC, the corresponding angles are congruent:</u>

  • ∠F = ∠Q
  • (2x + 10)° = (3x + 1)°
  • 3x - 2x = (10 - 1)°
  • x = 9°

<u>Then, the angle Q measures:</u>

  • ∠Q = (3*9 + 1)° = 28°
6 0
3 years ago
A farmer finds there is a linear relationship between the number of bean stalks, n, she plants and the yield, y, each plant prod
-Dominant- [34]

Answer:

Step-by-step explanation:

Given that a farmer finds there is a linear relationship between the number of bean stalks, n, she plants and the yield, y, each plant produces

When we consider this graph as a straight line, the two points lying on the line would be

(30, 30) and (34, 28) taking n as horizontal and y vertical

Using two point equation we find that

the equation of the line is

\frac{y-y_1}{y_2-y_1} =\frac{x-x_1}{x_2-x_1}

Substitute the points as x =n

\frac{y-30}{28-30} =\frac{x-30}{34-30}\\y-30 = -0.5(x-30)\\y = -0.5x+45

is the linear relationship between n and y

7 0
3 years ago
Evaluate each expression if x = 6, y = 8, and z = 3. <br><br><br><br> y + xz2
Aleonysh [2.5K]

8+(6)(3)^2

8+(6)(9)

8+(54)

8+54

62

I hope it helps

if it's correct, say Thanks and mark Brainliest

If it's wrong, just rate 4 stars. Don't report or delete:)

5 0
2 years ago
Read 2 more answers
Name the polygon with seven sides_____
Andru [333]

a polygon with seven sides is called a heptagon

7 0
3 years ago
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Tell which set or sets of numbers below belongs to: natural numbers, whole numbers, integers, rational numbers, irrational numbe
Misha Larkins [42]

1/3 belongs to the rational set and to the real set.

<h3>To which sets does the number below belong?</h3>

Here we have the number 1/3.

First, remember that we define rational numbers as these numbers that can be written as a quotient between two integers.

Here 1 is an integer and 3 is an integer, then 1/3 is a rational number.

Also, the combination between the rational set and the irrational set is the set of the real numbers, then 1/3 is also a real number.

Then, concluding:

1/3 belongs to the rational set and to the real set.

If you want to learn more about rational numbers:

brainly.com/question/12088221

#SPJ1

6 0
2 years ago
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