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
jeyben [28]
3 years ago
15

the height h(t) of a trianle is increasing at 2.5 cm/min, while it's area A(t) is also increasing at 4.7 cm2/min. at what rate i

s the base b(t) chaging when the height h=15cm and the area A= 130cm2
Mathematics
1 answer:
nekit [7.7K]3 years ago
6 0

Answer:

The base of the triangle decreases at a rate of 2.262 centimeters per minute.

Step-by-step explanation:

From Geometry we understand that area of triangle is determined by the following expression:

A = \frac{1}{2}\cdot b\cdot h (Eq. 1)

Where:

A - Area of the triangle, measured in square centimeters.

b - Base of the triangle, measured in centimeters.

h - Height of the triangle, measured in centimeters.

By Differential Calculus we deduce an expression for the rate of change of the area in time:

\frac{dA}{dt} = \frac{1}{2}\cdot \frac{db}{dt}\cdot h + \frac{1}{2}\cdot b \cdot \frac{dh}{dt} (Eq. 2)

Where:

\frac{dA}{dt} - Rate of change of area in time, measured in square centimeters per minute.

\frac{db}{dt} - Rate of change of base in time, measured in centimeters per minute.

\frac{dh}{dt} - Rate of change of height in time, measured in centimeters per minute.

Now we clear the rate of change of base in time within (Eq, 2):

\frac{1}{2}\cdot\frac{db}{dt}\cdot h =  \frac{dA}{dt}-\frac{1}{2}\cdot b\cdot \frac{dh}{dt}

\frac{db}{dt} = \frac{2}{h}\cdot \frac{dA}{dt} -\frac{b}{h}\cdot \frac{dh}{dt} (Eq. 3)

The base of the triangle can be found clearing respective variable within (Eq. 1):

b = \frac{2\cdot A}{h}

If we know that A = 130\,cm^{2}, h = 15\,cm, \frac{dh}{dt} = 2.5\,\frac{cm}{min} and \frac{dA}{dt} = 4.7\,\frac{cm^{2}}{min}, the rate of change of the base of the triangle in time is:

b = \frac{2\cdot (130\,cm^{2})}{15\,cm}

b = 17.333\,cm

\frac{db}{dt} = \left(\frac{2}{15\,cm}\right)\cdot \left(4.7\,\frac{cm^{2}}{min} \right) -\left(\frac{17.333\,cm}{15\,cm} \right)\cdot \left(2.5\,\frac{cm}{min} \right)

\frac{db}{dt} = -2.262\,\frac{cm}{min}

The base of the triangle decreases at a rate of 2.262 centimeters per minute.

You might be interested in
Find the square root of 784 using prime factorization.
WINSTONCH [101]

Answer:

first check the smallest number that divide 784

i.e 2

784/2 = 392/2= 196/2 =98/2 =49/7=7

we get

748= 2*2*2*2*7*7

for square root take one out of 2 same number

square root of 784= 2*2*7 = 28

7 0
3 years ago
Read 2 more answers
I just need to find the value of b
WITCHER [35]

Answer:

straight line add up to 180 so subtract 42 from 180 thts ur answer

8 0
2 years ago
Please help I'm a little confused!
zaharov [31]

I will have "x" represent the unknown number, or you could use a "?", doesn't matter.

8\leq \frac{x}{-4}     [8 is less than or equal to (≤) the quotient (÷) of a number and -4, so the number is being divided by -4]

If you need to solve this, you need to isolate/get the variable "x" by itself in the inequality:

8\leq \frac{x}{-4}   Multiply -4 on both sides to get rid of the fraction and get "x" by itself

(-4)8\geq \frac{x}{-4} (-4)    When you multiply/divide by a negative number, you flip the sign (< >)

-32 ≥ x          [-32 is greater than or equal to x, or x is less than or equal to -32]

8 0
3 years ago
Multiply or divide as indicated.<br><br> X^5<br> ____<br> X^-3
Sophie [7]
<span>x^5        
____   = x^8
x^-3

[x^5 - (-3) = x^8

i hope this helps</span>
3 0
3 years ago
2(2ax-y)= 3ax-4y; for y <br><br>explain please
marta [7]
2(2ax-y)=3ax-4y
4ax-2y=3ax-4y

Move 3ax from the right to the left. You do so by subtracting 3ax from both sides. Once doing so, you should have:
ax-2y=-4y

Isolate ax. You do so by adding (-2y) to both sides. After doing so, you should have:
ax=-2y

To isolate y by itself, you divide everything by -2, thus, equaling y= ax/-2


8 0
3 years ago
Other questions:
  • Today there is a 60 % of rain. What is the chance that they win their game today?
    5·2 answers
  • Answer choices for A : 6, 5 , 5.5
    9·1 answer
  • If y varies directly as x, and y is 48 when x is 6, which expression can be used to find the value of y when c is 2?
    7·1 answer
  • A jar has 15 pink gumballs, 21 blue gumballs, 19 red gumballs, and 19 yellow gumballs. Which colored gumball has the greatest pr
    10·2 answers
  • Below are two parallel lines with a third line intersecting them.
    11·1 answer
  • Which answer is correct? Please hurry &lt;3
    6·1 answer
  • Judy built a rectangular patio that is 9 units wide and has a perimeter of 40 units.
    15·1 answer
  • Marcelo had $22.17 in his bank account . He paid two fees of $17.50 each, and then he made two deposits of 92.75 each. What is t
    7·1 answer
  • 1+w=3<br> what is the answer to this equation
    5·1 answer
  • The letters of the words "possible outcomes" are put in a bag. Find the probability of picking the letter o.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!