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
yan [13]
3 years ago
13

The altitude of a triangle is increasing at a rate of 1 cm/ min while the area of the triangle is increasing at a rate of 2 cm2

/ min. at what rate is the base of the triangle changing when the altitude is 10 cm and the area is 100 cm2 ?
Mathematics
1 answer:
serg [7]3 years ago
4 0
Ya, calculus and related rates, such fun!




everything is changing with respect to t

altitude rate will be dh/dt and that is 1cm/min
dh/dt=1cm/min

area will be da/dt which is increasing at 2cm²/min
da/dt=2cm²/min

base=db/dt

alright

area=1/2bh
take dervitivie of both sides
da/dt=1/2((db/dt)(h)+(dh/dt)(b))
solve for db/dt
distribute
da/dt=1/2(db/dt)(h)+1/2(dh/dt)(b)
move
da/dt-1/2(dh/dt)(b)=1/2(db/dt)(h)
times 2 both sides
2da/dt-(dh/dt)(b)=(db/dt)(h)
divide by h
(2da/dt-(dh/dt)(b))/h=db/dt

ok
we know
height=10
area=100
so
a=1/2bh
100=1/2b10
100=5b
20=b

so
h=10
b=20
da/dt=2cm²/min
dh/dt=1cm/min

therefor
(2(2cm²/min)-(1cm/min)(20cm))/10cm=db/dt
(4cm²/min-20cm²/min)/10cm=db/dt
(-16cm²/min)/10cm=db/dt
-1.6cm/min=db/dt

the base is decreasing at 1.6cm/min
You might be interested in
96cm2<br> 108cm2<br> 93cm2 <br> 120cm2<br><br> What is the area of the figure????
maksim [4K]
The answer to this question is 96cm2
3 0
3 years ago
Read 2 more answers
Cual es la respuesta de 5762÷34​
juin [17]

is is 169.47058823 yes this the anser

7 0
3 years ago
4000 / 19=<br>4000 / 19=​
katrin2010 [14]

Answer:

210.53

Step-by-step explanation:

here

hope it helps

7 0
2 years ago
How many counters would you place in the five frame to show the number
Leviafan [203]
Assuming the five frame is for the number five (5) then place 5 counters in the frame.
7 0
3 years ago
What is the solution set?<br><br> A.) (0, -2)<br> B.) (2, 0)<br> C.) (7, 0)<br> D.) (5, 3)
max2010maxim [7]

Answer:

D.) (5, 3)

Step-by-step explanation:

Solution is where two lines intersect

Both lines intersect at x = 5 and y = 3

Answer

D.) (5, 3)

8 0
3 years ago
Other questions:
  • Rate of change of y = –4.5x + 15
    6·1 answer
  • You are a loan officer trying to decide which clients deserve your best rates. The table below shows the credit scores of severa
    12·2 answers
  • Help I know is easy but I don't know ​
    8·2 answers
  • If the sumof two numbers,n and m,is rational,which statement is true?
    9·1 answer
  • Bulls records has the same sensor when is the area of the shaded region
    14·1 answer
  • The community center provides tutoring for students p. The cost of the tutoring is $18 per session. Write an equation to model t
    6·2 answers
  • -|-2r-1|=11 <br> HELP PLEASE
    14·1 answer
  • A train to New York city leaves a station every 7 minutes. Another train to Boston leaves the station every 6 minutes. Suppose i
    6·1 answer
  • What is the same as 15.39 ÷ 100?
    7·1 answer
  • The length of a rectangle is 13 centimeters less than four times its width. Its area is 35 square
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!