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
zimovet [89]
3 years ago
6

A road perpendicular to a highway leads to a farmhouse located d miles away. An automobile traveling on this highway passes thro

ugh this intersection and continues at a constant speed of r mph. Compute how fast the distance betwen the automobile and the farmhouse is increasing when the automobile is 30 miles past the intersection of the highway and the road, in terms of d, and r.

Mathematics
1 answer:
pshichka [43]3 years ago
3 0

Answer:

\frac{dh}{dt}=\frac{30r}{\sqrt{d^{2}+900}}

Step-by-step explanation:

A road is perpendicular to a highway leading to a farmhouse d miles away.

An automobile passes through the point of intersection with a constant speed \frac{dx}{dt} = r mph

Let x be the distance of automobile from the point of intersection and distance between the automobile and farmhouse is 'h' miles.

Then by Pythagoras theorem,

h² = d² + x²

By taking derivative on both the sides of the equation,

(2h)\frac{dh}{dt}=(2x)\frac{dx}{dt}

(h)\frac{dh}{dt}=(x)\frac{dx}{dt}

(h)\frac{dh}{dt}=rx

\frac{dh}{dt}=\frac{rx}{h}

When automobile is 30 miles past the intersection,

For x = 30

\frac{dh}{dt}=\frac{30r}{h}

Since h=\sqrt{d^{2}+(30)^{2}}

Therefore,

\frac{dh}{dt}=\frac{30r}{\sqrt{d^{2}+(30)^{2}}}

\frac{dh}{dt}=\frac{30r}{\sqrt{d^{2}+900}}

You might be interested in
The vertex of f(x) = 3x ^2+ 5x + 2 is a:<br> minimum<br> maximum<br> none of these
timama [110]

Answer:

minimum

Step-by-step explanation:

Given a quadratic in standard form f(x) = ax² + bx + c ( a ≠ 0 )

• If a > 0 then vertex is a minimum

• If a < 0 then vertex is a maximum

f(x) = 3x² + 5x + 2 ← is in standard form

with a = 3

Since a > 0 then vertex is a minimum

6 0
3 years ago
Prove that 5^7+5^6 is divisible by 6.
Valentin [98]

Answer:

5^7+5^6 = 93750

93750/6 = 15625

Hence 5^7+5^6 is divisible by 6.

Step-by-step explanation:

3 0
3 years ago
5. g(x) = 7x, find g(-7)
kompoz [17]

Answer:

just plug in

g(x)=7x

g(-7)=7*(-7)

7*(-7)=-49

Step-by-step explanation:

3 0
2 years ago
On Monday, the temperature at 10 a.m. at Sam’s house was –6° Fahrenheit. The
Alika [10]

Answer:

8

Step-by-step explanation:

to find the answer, subtract the second amount (2) from the first amount (-6), -6 - 2 = -8, the temperat decreased by 8

6 0
2 years ago
Read 2 more answers
In 32 days, a person saved $56. What was the person's average daily savings?
ss7ja [257]

Answer: $ 1792

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Other questions:
  • 4-[(x+3)/ ((x^2 +5x +6)/(x-2))]
    6·1 answer
  • PLEASE ANSWER The length of a rectangle is 4 centimeters (cm) less than three times the width. The perimeter is 64 cm. Find the
    5·2 answers
  • 8 9/10 into an improper fraction in lowest terms
    8·1 answer
  • You roll a die and flip three coins. find the number of possible outcomes.
    12·2 answers
  • An exponential function is written as F(x) = a • bx, where the coefficient a is a constant, the base b is _____ but not equal to
    6·2 answers
  • How often should you study
    14·1 answer
  • Calculate the size of angle x. the sides are 8cm, 11cm and 15cm
    15·2 answers
  • Plzzzzz can any one help me I don’t understand :(
    7·1 answer
  • Find the fraction with a product between 1 and 2
    12·1 answer
  • −6x+8=2x−24<br> Please help me
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!