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Mathematics

1 answer:

Licemer1 [7]3 years ago

4 0

Answer:

Started hang gliding at a height of 700 ft and descends 15 feet every seconds

Started hang gliding at a height of 575 ft and descends 10 feet every seconds

Step-by-step explanation:

The function that models Fred's hang gliding is $f(x)=-15x+700$

The initial value is 700 feet. This Fred was 700 feet above see level before he starts descending.

The rate of descent is -15 ft/s. This means Fred descends 15 feet in one second.

From the table the initial height is 575 ft. This means Gene was 575 feet above sea-level at the beginning of the hang gliding.

The rate of descent is $\frac{565-575}{1-0} =-10$ ft/s.

This means that in every seconds, Gene descends 10 feet.

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Miriam has 62 feet of fencing to make a rectangular vegetable garden. Which dimensions will give Miriam the garden with greatest

lidiya [134]

Perimeter: P=62 feet
P=2(b+h)
62=2(b+h)
Dividing both sides of the equation by 2:
62/2=2(b+h)/2
31=b+h
b+h=31 (1)

Area: A=bh (2)

Isolating h in equation (1)
(1) b+h=31→b+h-b=31-b→h=31-b (3)

Replacing h by 31-b in equation (2)
(2) A=bh
A=b(31-b)
A=31b-b^2

To maximize the area:
A'=0

A'=(A)'=(31b-b^2)'=(31b)'-(b^2)'=31-2b^(2-1)→A'=31-2b

A'=0→31-2b=0
Solving for b:
31-2b+2b=0+2b
31=2b
Dividing both sides by 2:
31/2=2b/2
31/2=b
b=31/2=15.5

Replacing b by 31/2 in equation (3)
h=31-b
h=31-31/2
h=(2*31-31)/2
h=(62-31)/2
h=31/2

The dimensions are 31/2 ft x 31/2 ft = 15.5 ft x 15.5 ft
The area with these dimensions is: A=(15.5 ft)(15.5 ft)→A=240.25 ft^2

These dimensions are not in the options

1) The first option has an area of: A=(18 ft)(13 ft)→A=234 ft^2
2) The second option has an area of: A=(19 ft)(12 ft)→A=228 ft^2
3) The third option has an area of: A=(17 ft)(14 ft)→A=238 ft^2

The third option has the largest area.

Answer: Third option

4 0

3 years ago

Read 2 more answers

X^2 =1 how many solutions are there

HACTEHA [7]

Answer:

Answer:

x=1 or x=−1

Step-by-step explanation:

I think just 2

5 0

3 years ago