1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Kamila [148]
3 years ago
8

1. (a). A police car, approaching right-angled intersection from the north, is chasing a speedmg

Mathematics
1 answer:
tamaranim1 [39]3 years ago
7 0

Answer:

<em>The SUV is running at 70 km/h</em>

Step-by-step explanation:

<u>Speed As Rate Of Change </u>

The speed can be understood as the rate of change of the distance in time. When the distance increases with time, the speed is positive and vice-versa. The instantaneous rate of change of the distance allows us to find the speed as a function of time.

This is the situation. A police car is 0.6 Km above the intersection and is approaching it at 60 km/h. Since the distance is decreasing, this speed is negative. On the other side, the SUV is 0.8 km east of intersection running from the police. The distance is increasing, so the speed should be positive. The distance traveled by the police car (y) and the distance traveled by the SUV (x) form a right triangle whose hypotenuse is the distance between them (d). We have:

d=\sqrt{x^2+y^2}

To find the instant speeds, we need to compute the derivative of d respect to the time (t). Since d,x, and y depend on time, we apply the chain rule as follows:

\displaystyle d\ '=\frac{x.x'+y.y'}{\sqrt{x^2+y^2}}

Where x' is the speed of the SUV and y' is the speed of the police car (y'=-60 km/h)

We'll compute  :

d=\sqrt{(0.8)^2+(0.6)^2}=\sqrt{0.64+0.36}

d=1\ km

We know d'=20 km/h, so we can solve for x' and find the speed of the SUV

\displaystyle \frac{x.x'+y.y'}{\sqrt{x^2+y^2}}=20

Thus we have

x.x'+y.y'=20

Solving for x'

\displaystyle x'=\frac{20-y.y'}{x}

Since y'=-60

\displaystyle x'=\frac{20+0.6(60)}{0.8}

x'=70\ km/h

The SUV is running at 70 km/h

You might be interested in
Compare 6x10 to the 10 power to 3x10 to the 6 power
Serhud [2]
6*10^10 would equal 60000000000 and 3*10^6 would equal 3000000





hope this helps
6 0
3 years ago
Read 2 more answers
On the blueprint of a house, 38 millimeters represents 6 meters. the length of the living room is 57 millimeters on the blueprin
Pie
For this case we can make the following rule of three:
 38 milimeters ---------> 6 meters
 57 milimeters ---------> x
 Clearing x we have:
 x = (57/38) * (6)
 x = 9 meters
 Answer:
 
the current length of the living room is:
 
x = 9 meters
3 0
3 years ago
If g(x) = 3x − 4, what is the value of g−1(g(13))?
Vsevolod [243]
The function g(x) = 3x-4 is a linear function. Therefore the inverse does exist (which is also linear)

Because we have an inverse, this means we can use the rule 
g^{-1}(g(x)) = x

Replace x with 13
g^{-1}(g(x)) = x
g^{-1}(g(13)) = 13

The answer is choice D

7 0
3 years ago
Read 2 more answers
What makes a pair linear?
zavuch27 [327]

Answer:

A linear pair of angles is formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.

6 0
3 years ago
Read 2 more answers
At a restaurant mike and his three friends decide to divide the bill evening. If each person paid 13 then what was the total bil
Hatshy [7]
At a restaurant Mike and his three friends that means that there was four people splitting the bill. If each of them paid $13 then the bill was $52

4 * 13 = $52
8 0
3 years ago
Other questions:
  • In triangle A B C, angle C is a right angle and BC = 11. If lower m angle B equals 30 degrees, find AC.
    9·2 answers
  • Why would negative numbers not make sense for the values of variables
    12·1 answer
  • PLSSS HURRY THANKS
    9·2 answers
  • How do i solve y=4-1/(3+x)
    7·1 answer
  • The radius of a circle is 7m. Find the circumference to the nearest tenth(urgent)
    11·2 answers
  • How can 934,200,000,000 be written in words?
    10·1 answer
  • A teaspoon of common table salt contains about 2,000 mg of sodium. how many grams of sodium is this?
    12·1 answer
  • What is the image point of ( -8,3) after a translation right 2 units and up 3 units? Submit Answer attempt out of 2 N​
    11·1 answer
  • An example on how to solve age problems in consecutive integers
    8·1 answer
  • Select the correct answer.
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!