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
Afina-wow [57]
2 years ago
12

The hypotenuse of a right triangle is 25 feet long The height of the right triangle is shrinking at a rate of 1 ft/week. What is

the rate of change of the base of the triangle when the height is 7 feet?
Mathematics
1 answer:
Lesechka [4]2 years ago
8 0

9514 1404 393

Answer:

  increasing 7/24 ft per week

Step-by-step explanation:

An expression for the length of the base can be written from the Pythagorean theorem relation between the sides of the triangle.

If the height is 7-x, where x is the number of weeks after the height is 7 feet, then the base length is ...

  b = √(25^2 -(7-x)^2) = √(625 -(49 -14x +x^2)) = √(-x^2 +14x +576)

Then the rate of change of b with respect to x is ...

  b' = (-2x +14)/(2√(-x^2 +14x +576))

When x=0, the rate of change of the base is ...

  b' = 14/(2√576) = 7/24

The base is increasing 7/24 ft per week when the height is 7 ft.

You might be interested in
When x = -3 on the graph of y = 2|x| + 3 what will be the y-coordinate?
SCORPION-xisa [38]
Substitute -3 into the equation

y = 2|x| + 3
y = 2 (3) + 3
y = 6 + 3
y = 9

Answer D
5 0
3 years ago
A simple dart target has two concentric circles. The larger circle has a radius of 4. The smaller circle has a radius of 2. The
Natali5045456 [20]

Answer:

3 times more.

Step-by-step explanation:

The odds of landing a dart in any of the circles correspond to the surface area of the circle.

Calculate the surface area of both circles:

The formula for the area of a circle is \pi r^{2}.

  • inner circle: A=\pi 2^{2}=12.566
  • for the outer circle, use the formula then subtract the value of the inner circle, to find the remaining area: A=(\pi 4^{2} )-12.566=37.699

Calculating greater chance:

Divide the larger area by the smaller area:

37.699/12.566 = 3

That means that the area of the outer circle is 3 times larger, making it 3 times more likely to hit the outer circle. Therefore the points for hitting the inner circle should be 3 times more.

7 0
3 years ago
If Samantha can pay off her loan in 36 months at a 10% interest rate rather than in 48 months at a 12% interest rate, how much m
Ymorist [56]
Hi there
The simple interest formula is
I=prt
I interest changes
P amount of the loan 6000
R interest rate
T time( number of months/12 months)

The interest in 36 months at a 10%
I=6,000×0.1×(36÷12)=1,800
The interest in 48 months at a 12%
6,000×0.12×(48÷12)=2,880
she will save
2,880−1,800=1,080

Good luck!
7 0
3 years ago
Write an equation of the line passing through point P(0, −1)P(0, −1) that is parallel to the line y = −2x+3y = −2x+3.
Feliz [49]
This is the answer y= -2x-1
5 0
3 years ago
How do I get blood off my shoes
s344n2d4d5 [400]

find the best angle to wipe the blood and calculate how many times you need to wipe the blood off.

4 0
2 years ago
Other questions:
  • A bag of marbles had 18 green marbles and the rest were blue. For a game, 5/6 of the 18
    12·1 answer
  • Which graph represents a linear function?
    8·2 answers
  • which of the following is NOT equal to 50 millimeters?a. 5,000,000 nanometersb. 0.05 metersc. 5 centimetersd. 50,000 micrometers
    11·1 answer
  • Use the elimination method to solve the system of equations. Choose the
    8·1 answer
  • Will give you brainlyist pls help​
    13·1 answer
  • Simplify the expression. -2(x + 5) - x + 4
    10·1 answer
  • HELP ME PLEASE ILL GIVE BRAINLIEST
    8·1 answer
  • Write an equation in slope-intercept form for the line with slope -2/5 and y-intercept 6 .
    9·1 answer
  • Please help asap!<br> have a great day!
    15·2 answers
  • 4x-12=24<br> how would this be solved
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!