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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.

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Triangle A'B'C' is the image of triangle ABC under a rotation about point Q.<br><br>​
yan [13]

9514 1404 393

Answer:

  True; about 120° CCW rotation about Q

Step-by-step explanation:

Triangle A'B'C' appears to be congruent to triangle ABC and about the same distance from point Q. The angle of rotation from ABC to A'B'C' appears to be about 120° counterclockwise when measured using a geometry program.

Triangle A'B'C' is the image of triangle ABC under rotation about 120° CCW about point Q.

_____

<em>Additional comment</em>

If choices of rotation angle are ±135° or ±165°, the best choice would be ...

  135°

3 0
2 years ago
Which equation represents "the product of a number and 24 is 72"?
Nataly [62]

Answer:

Step-by-step explanation:

24 p=72

5 0
3 years ago
Read 2 more answers
a father is twice as old as his son. 20 yrs ago the father was four times as old as his son. find their present ages
Roman55 [17]

Answer:

son's present age = 30

father's present age=60

Step-by-step explanation:

his son's present age = x years

his father's present age = 2x years

before 20 years his son's age=(x-20) years

before 20 years father's age=(2x-20) years4(x-20)=(2x-20)

4x-80=2x-20

4x-2x=80-20

2x=60

x=30

5 0
2 years ago
28.Neethi had 8
Ludmilka [50]

Answer:

2 1/3 cupcakes

Step-by-step explanation:

A cupcake can make 3 four cups of flour

In 8 fourteen cups of flour, require (14 X 4)/(3 X 8) of cupcakes

  = 56/24 = 2 1/3 cupcakes

5 0
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Bob purchase a bus pass card with 320 points,each weeks costs 20 points for unlimited bus rides
blagie [28]
It would be 20 points bcuz it says each week it costs 20 points for unlimited bus rides
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