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
creativ13 [48]
2 years ago
5

A triangle's base is increasing at the rate of 3 inches/sec, its height at 2 inches/sec. At what rate is the area of the rectang

le increasing when base is 10 inches and height is 14 inches
Mathematics
1 answer:
Triss [41]2 years ago
3 0

Answer:

dA/dt = 31  in²/ sec

Step-by-step explanation:

The area of the triangle is:

A(t)  = (1/2)*b*h     where  b is the base and h the height

Differentiation on both sides of the equation we obtain

dA/dt  =  (1/2)* db/dt * h + (1/2)* dh/dt * b   (1)

db/dt  = 3 in/sec

dh/dt =  2 n/sec

b =  10 in

h = 14 in

By substitution in (1)

dA/dt =  0,5* 3*14 +  0,5* 2*10

dA/dt =  21 in² /sec + 10 in²/sc

dA/dt = 31  in²/ sec

You might be interested in
Use a special right triangle to write sin 30° as a fraction.
borishaifa [10]

Answer:

1/2

Step-by-step explanation:

So do this, think of an equilateral triangle. A 30-60-90 triangle is just half of an equilateral triangle. If the original side length was x, then the hypotenuse is x, one leg is x/2, and the third, by Pythagorean theorem, is x sqrt3

Sin is opposite over hypotenuse, so we have (x/2)/x = 1/2

6 0
3 years ago
Thomas bought 9 1/3 feet of of wood to fix his fence. When he finished, he had 3 2/3 feet of of wood left. How much wood did Tho
qwelly [4]

Answer:

He used 17/3 feet = 5 and 2/3 feet

Step-by-step explanation:

∵ He bought 9 and 1/3 feet = 28/3 feet

∵ He had 3 and 2/3 feet left = 11/3 feet

∴ He used = 28/3 - 11/3 = 17/3 feet = 5 and 2/3 feet

8 0
3 years ago
Sometimes, Cindy's little brother interrupts her during homework time. So, she made a triangular "Do Not Disturb" sign to hang o
Marta_Voda [28]

Answer:

A = 1/2(b×h)

Step-by-step explanation:

Area = 1/2(base×height)

6 0
3 years ago
Identify the values of a, b, and c that would be used in the quadratic formula to solve the equation 3x2− 5x + 5 = 0. A. a = 3,
stepan [7]
<span>3x2− 5x + 5 = 0.
a=3 b=-5 c=5

A. a = 3, b = 5, c = 5
B. a = 3, b = −5, c = 5
C. a = 5, b = −5, c = 0
D. a = −3, b = 5, c = −5

answer is B


</span>
6 0
3 years ago
The random variable X is exponentially distributed, where X represents the time it takes for a person to choose a birthday gift.
garik1379 [7]

Answer:

The probability that X is less than 32 minutes is 0.736.

Step-by-step explanation:

Given : The random variable X is exponentially distributed, where X represents the time it takes for a person to choose a birthday gift. If X has an average value of 24 minutes.

To find : What is the probability that X is less than 32 minutes?

Solution :

If X has an average value of 24 minutes.

i.e. \lambda=24

The random variable X is exponentially distributed, where X represents the time it takes for a person to choose a birthday gift.

The exponentially function is \frac{1}{\lambda}e^{-\frac{x}{\lambda}}

The function form according to question is

f(x)=\{\frac{1}{24}e^{-\frac{x}{24}}, x>0\}

The probability that X is less than 32 minutes is

P[x

P[x

P[x

Therefore, the probability that X is less than 32 minutes is 0.736.

7 0
3 years ago
Other questions:
  • A school typically sells 500 yearbooks each year for $50. The economics class does a project and discovers that they can sell 10
    9·1 answer
  • Jacob mixes the letters J K L J K M N and P thoroughly.Without looking, Terry draws one letter. Expressed as a fraction, decimal
    15·1 answer
  • The town of Manchester (population 50,000) has the shape of a rectangle that is 5 miles wide and 7 miles long.
    14·1 answer
  • Ashby ate a lot for thanksgiving dinner.he decided to go on a long run. He ran 6 miles in 57 minutes.how long did it take him to
    9·1 answer
  • The sales tax in Sandra's town is 6.5%. If she buys 2 shirts for $23.99 each and a pair of shoes for $41.99, how much sales tax
    15·1 answer
  • Can someone give me the answers please
    14·1 answer
  • What is the Pythagorean theorm
    7·2 answers
  • I need help ASAP!!
    6·1 answer
  • 121.4 divided by 19 round to the nearest tenths​
    12·1 answer
  • Rafe and Sebastian both rode in a 5 mile bike race. There were so many riders that they started groups at different times. Rafe
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!