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tatuchka [14]
2 years ago
8

A hot air balloon descends from an altitude of 2,000 feet at a constant rate of 90 feet per minute. The graph shows the altitude

of the balloon over time. Write a linear function in the form y = mx + b to represent the situation.

Mathematics
1 answer:
SSSSS [86.1K]2 years ago
3 0
Y=90x+2,000

90 is the rate of change because the hot air balloon descends 90 feet per minute.
And 2,000 is the starting point because the hot air balloon started the descent at 2,000 feet.
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Jeremiah plans on building a 5 meter long garden walkway that is paved with square stones that measure LaTeX: \frac{5}{6}5 6 met
yan [13]

Answer:

Example 1

A backyard farmer wants to enclose a rectangular space for a new garden. She has purchased 80 feet of wire fencing to enclose 3 sides, and will put the 4th side against the backyard fence. Find a formula for the area enclosed by the fence if the sides of fencing perpendicular to the existing fence have length

L.

In a scenario like this involving geometry, it is often helpful to draw a picture. It might also be helpful to introduce a temporary variable,

W, to represent the side of fencing parallel to the 4th side or backyard fence.

Since we know we only have 80 feet of fence available, we know that

L + W + L = 80, or more simply, 2L + W = 80. This allows us to represent the width, W, in terms of L: W = 80 – 2L

Now we are ready to write an equation for the area the fence encloses. We know the area of a rectangle is length multiplied by width, so

A = LW = L(80 – 2L)

A(L) = 80L – 2L2

This formula represents the area of the fence in terms of the variable length

L.

Example 2

Returning to our backyard farmer from the beginning of the section, what dimensions should she make her garden to maximize the enclosed area?

Earlier we determined the area she could enclose with 80 feet of fencing on three sides was given by the equation

A(L) = 80L – 2L2. Notice that quadratic has been vertically reflected, since the coefficient on the squared term is negative, so the graph will open downwards, and the vertex will be a maximum value for the area.

In finding the vertex, we take care since the equation is not written in standard polynomial form with decreasing powers. But we know that

a is the coefficient on the squared term, so a = -2, b = 80, and c = 0.

Finding the vertex:

h

=

−

80

2

(

−

2

)

=

20

,

k

=

A

(

20

)

=

80

(

20

)

−

2

(

20

)

2

=

800

The maximum value of the function is an area of 800 square feet, which occurs when

L = 20 feet. When the shorter sides are 20 feet, that leaves 40 feet of fencing for the longer side. To maximize the area, she should enclose the garden so the two shorter sides have length 20 feet, and the longer side parallel to the existing fence has length 40 feet.

Example 3

A ball is thrown upwards from the top of a 40 foot high building at a speed of 80 feet per second. The ball’s height above ground can be modeled by the equation

H(t) = –16t2 + 80t + 40.

What is the maximum height of the ball?

When does the ball hit the ground?

To find the maximum height of the ball, we would need to know the vertex of the quadratic.

h

=

−

80

2

(

−

16

)

=

80

32

=

5

2

,

k

=

H

(

5

2

)

=

−

16

(

5

2

)

2

+

80

(

5

2

)

+

40

=

140

The ball reaches a maximum height of 140 feet after 2.5 seconds.

To find when the ball hits the ground, we need to determine when the height is zero—when

H(t) = 0. While we could do this using the transformation form of the quadratic, we can also use the quadratic formula:

t

=

−

80

±

√

80

2

−

4

(

−

16

)

(

40

)

2

(

−

16

)

=

−

80

s

q

r

t

8960

−

32

Since the square root does not simplify nicely, we can use a calculator to approximate the values of the solutions:

t

=

−

80

−

s

q

r

t

8960

−

32

a

p

p

r

o

x

5.458

The second answer is outside the reasonable domain of our model, so we conclude the ball will hit the ground after about 5.458 seconds.Step-by-step explanation:

8 0
3 years ago
Anyone get this?? I really appreciated if you’ed help me :)
notsponge [240]

Answer:

V =5292 in ^3

Step-by-step explanation:

To find the volume for a rectangular prism

V = l*w*h

V = 6 * 36 * 24.5

V =5292 in ^3

6 0
3 years ago
With a slope of m = -2 and a point being (5,-2) what’s the Y-intercept?
almond37 [142]

Answer:

c = 8

Step-by-step explanation:

Given the following data;

Slope, m = -2

Points (x, y) = (5, -2)

To find the intercept, c;

Equation of a straight line is given by the formula: y = mx + c

Where;

m is the slope.

x and y are the points

c is the intercept.

Substituting the values in order to find the intercept, we have;

-2 = -2(5) + c

-2 = -10 + c

c = 10 - 2

c = 8

Therefore, the y-intercept is 8.

3 0
3 years ago
Help me on Algebra it may look easy but to me it is hard
Zina [86]
It’s a 90 degree clockwise rotation as coordinates become (y,-x).
8 0
2 years ago
The line 3x+4y=24 cuts the x axis at point A and y axis at point B<br><br> Find the lenght if AB
sweet [91]
Length A is (8,0) and the length of B is (0,6)
4 0
3 years ago
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