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
anygoal [31]
3 years ago
5

A police car is located 40 feet on a small straight road perpendicular to main highway. A red car is driving along a highway in

the direction of an intersection with that small road and is 180 feet away from the intersection. The police radar reads that the distance between the police car and the red car (this distance is straight between them - not on either road) is decreasing at a rate of 100 feet per second. How fast is the red car actually traveling along the road
Mathematics
1 answer:
xeze [42]3 years ago
4 0

Answer:

the red car is traveling at 102.44 ft/s along the road

Step-by-step explanation:

From the given information:

Let consider p be how far the car is up the road and  q be how far the police is off the road.

Also, suppose that r is the distance between the police and the car.

Then, we can have a right triangle in which  we can use the Pythagorean Theorem to calculate the r (distance between the cop and the car)

NOW,

p² + q² = r²

r² = 40² + 180²

r² = 1600 + 32400

r² = 34000

r = \sqrt{34000}

r = 184.39

If we consider q'  to be how fast the car is traveling down the road.

And, p' be how fast the police is traveling toward the road.

r' be how fast the distance between the police and the car is changing.

then , the derivative of our equation, p² + q² = r² with respect to time can now be:

2p(p') +2q(q') = 2r(r')

p(p') +q(q') = r(r')

By replacing our values; we have:

40(0) +180(y') = \sqrt{34000} \times 100    (given that the police is not moving p' =0)

180(y') = \sqrt{34000} \times 100

(y') = \dfrac{\sqrt{34000} \times 100}{180}

(y') = \dfrac{184.39 \times 100}{180}

\mathbf{(y') = 102.44 \ ft/s}

the red car is traveling at 102.44 ft/s along the road

You might be interested in
14 2/3 divided by 3/4
pentagon [3]
I think the answer is 19.46
6 0
3 years ago
Which of the following is in the solution set to 3x - y = 12? (hint: what
expeople1 [14]
3(8)-12=12
24-12=12
The fourth choice.
Yeah I think you already got it
5 0
3 years ago
Write a two-column proof. Given: line BD bisects angle CBE. Prove: angle ABD approximately equal to angle FBD.
ale4655 [162]

Answer:

The proof is derived from the summarily following equations;

∠FBE + ∠EBD = ∠CBA + ∠CBD

∠FBE + ∠EBD = ∠FBD

∠CBA + ∠CBD = ∠ABD

Therefore;

∠ABD ≅ ∠FBD

Step-by-step explanation:

The two column proof is given as follows;

Statement {}                                       Reason          

\underset{BD}{\rightarrow} bisects ∠CBE {}                            Given

Therefore;

∠EBD ≅ ∠CBD  {}                              Definition of angle bisector

∠FBE ≅ ∠CBA {}                                Vertically opposite angles are congruent

Therefore, we have;

∠FBE + ∠EBD = ∠CBA + ∠CBD {}     Transitive property

∠FBE + ∠EBD = ∠FBD {}                    Angle addition postulate

∠CBA + ∠CBD = ∠ABD {}                   Angle addition postulate

Therefore;

∠ABD ≅ ∠FBD        {}                          Transitive property.

3 0
3 years ago
What is the estimate answer and the exact answer of 17/10 ÷2 4/5
OLEGan [10]
Both 17/10 and 2 4/5 should be rounded up in preparation for this estimation.

17/10 is close to 2 and 2 4/5 is close to 3.  Thus, your estimated answer should be
                     2/3, or approx. 0.6666....

Exact answer:    divide 17/10 by 14/5.  LCD is 10, so convert 14/5 to 28/10.

Now divide 17/10 by 28/10.  Answer:  17/28 = approx.   =  0.607 approx.

These two results are comparable:   0.6666....  and 0.6071 ....
8 0
3 years ago
Se necesitan conductores voluntarios para llevar a 80 estudiantes al juego de béisbol de campeonato. Los conductores tienen auto
NemiM [27]

Esta pregunta esta incompleta

Pregunta completa

Se necesitan conductores voluntarios para llevar a 80 estudiantes al juego de béisbol del campeonato. Los conductores cuentan con automóviles, con capacidad para 4 estudiantes, o camionetas, con capacidad para 6 estudiantes. La ecuación describe la relación entre la cantidad de automóviles y la cantidad de camiones que pueden transportar exactamente 80 estudiantes.

Seleccione todas las afirmaciones que sean verdaderas sobre la situación.

a) Si van 12 coches, se necesitan 2 furgonetas.

b) c = 14 y v = 4 son un par de soluciones de la ecuación.

c) Si van 6 coches y van 11 furgonetas, habrá espacio adicional.

d) 10 coches y 8 furgonetas no son suficientes para transportar a todos los estudiantes.

e) Si pasan 20 autos, no se necesitan camionetas.

f) 8 furgonetas y 8 coches son números que cumplen con las limitaciones en esta situación.

Answer:

La opción b, e y f.

Step-by-step explanation:

Pasando por las opciones dadas:

c = coches que pueden llevar a 4 estudiantes

v = furgonetas con capacidad para 6 estudiantes

a) Si van 12 coches, se necesitan 2 furgonetas.

= 12 (4) + 2 (6)

= 48 + 12

= 60

60 ≠ 80

La opción a es incorrecta

b) c = 14 y v = 4 son un par de soluciones de la ecuación.

14 (4) + 4 (6)

56 + 24 = 80 estudiantes

La opción b es correcta

c) Si van 6 coches y van 11 furgonetas, habrá espacio adicional.

Por lo tanto:

5 (4) + 11 (6)

= 20 + 66

= 86.

86 es mayor que 80, la opción c es correcta, habría un espacio adicional para 6 estudiantes.

d) 10 coches y 8 furgonetas no son suficientes para transportar a todos los estudiantes.

Por lo tanto:

10 (4) + 8 (6)

40 + 48

= 88

e) Si pasan 20 autos, no se necesitan camionetas.

20 (4) = 80 estudiantes

La opción e es correcta

f) 8 furgonetas y 8 coches son números que cumplen con las limitaciones en esta situación.

8 (6) + 8 (4)

= 48 + 32

= 80 estudiantes.

La opción b es correcta

Por lo tanto, la ecuacióna que describe la relación entre la cantidad de automóviles y la cantidad de camiones que pueden transportar exactamente 80 estudiantes es la opción b, e y f.

7 0
2 years ago
Other questions:
  • 10 times 10 times 10 <br> exponent form:<br> word form:
    9·2 answers
  • Can someone help me I’m just trynna pass algebra
    14·1 answer
  • Biologists have observed that the chirping rate of crickets is linearly related to temperature. A cricket produces 120 chirps pe
    13·1 answer
  • What digit 0-9 does not appear in the first 30 digits of pi
    11·1 answer
  • Michelle receives 32K per year as an assistant fast food manager. Her benefits include health insurance, paid holidays, retireme
    10·1 answer
  • Find the exact solutions of the equation x2 +3x + 1=0.
    7·2 answers
  • Cds are packaged in boxes of 90. every 28 boxes are loaded onto a crate. how many crates would be needed if you had 260000 cdsto
    13·1 answer
  • Two six sided dice are rolled. Find the probability to get the same digits on the top faces
    6·1 answer
  • Remove the brackets and simplify
    7·2 answers
  • First to type something random in the answer box gets 100 points!
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!