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
Why is the opposite of a number also called the additive inverse
lana66690 [7]
<span>This </span>number<span> is </span>also<span> known as the </span>opposite<span> (</span>number<span>), sign change, and negation. For a real </span>number<span>, it reverses its sign: the </span>opposite<span> to a positive </span>number<span> is negative, and the </span>opposite<span> to a negative </span>number<span> is positive. Zero is the </span>additive inverse<span> of itself.</span>
7 0
2 years ago
Does any one know the answer please​
Fittoniya [83]

Answer:

Slope intercept form

Step-by-step explanation:

y = Mx + B

M = slope - 7/11

B = y intercept - 5

5 0
3 years ago
Question 3
MatroZZZ [7]

Answer:

x=3.5 glizzies with a but of ketchup and mustard which would round that up to about 6$ a glizzy

8 0
2 years ago
In the diagram, what is the value of x?
Ghella [55]

Answer:

x = 162

Step-by-step explanation:

the sum of the interior angles of a quadrilateral = 360°

sum the interior angles of the quadrilateral and equate to 360

90 + 60 + x + 48 = 360 , that is

198 + x = 360 ( subtract 198 from both sides )

x = 162

5 0
2 years ago
Help me, please......
denpristay [2]

Answer:

(x, y ) → (x - 4, y + 8 )

Step-by-step explanation:

4 units left in the x- direction means subtract 4 from the x- coordinate

8 units up in the y- direction means add 8 to the y- coordinate

Then the translation rule is

(x, y ) → (x - 4, y + 8 )

3 0
2 years ago
Other questions:
  • An analyst is creating a graph to show the salaries
    7·2 answers
  • In 2000 the population of a city was 588292 people. in 2002 the population of the city increased to 599656, what is the populati
    14·1 answer
  • Instructions:Type the correct answer in each box.
    7·1 answer
  • Select the correct answer. Which inequality is true? A. |-5| &gt; |-7| B. |-8| &lt; |-5| C. |9| &lt; |7| D. |-9| &gt; |8|
    13·1 answer
  • An experiment consists of 8 independent trials where the probability of success on each trial is 3 8 . Find the probability of o
    5·1 answer
  • Graph one period of the following functions with your graph showing the amplitude, period, five key points, and midline.
    15·1 answer
  • I'm so sorry for asking about this, I know I know how to solve this, but my mind keeps pulling a blank, please help!
    10·1 answer
  • I’m not sure how to solve this. help?
    13·1 answer
  • I need help pls! <br> this test is about angles, and i am having trouble with it.
    5·1 answer
  • Write the converse.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!