4x-4y=-2 -9x-4y=-3

The deck of a bridge is suspended 275 feet above a river. If a pebble falls off the side of the bridge, the height, in feet, of

Ivenika [448]

Answer:

Our equation for the height is:

y(t) = 275 - 16*t^2.

a) To find the average velocity between two times, t1 and t2, (where t2 > t1) the equation is:

$AV = \frac{y(t2) - y(t1)}{t2 - t1}$

Then:

i) t1 = 4s, t2 = 4s + 0.1s = 4.1s

The average velocity is:

$AV = \frac{(275 - 16*4.1^2) - (275 - 16*4^2)}{4.1 - 4} = \frac{16(4^2 - 4.1^2)}{0.1} = -129.6$

And the units will be ft/s, so the average speed is:

-129.6 ft/s

The minus sign is because te pebble is falling down.

ii) t1 = 4s, t2 = 4s + 0.05s = 4.05s

The average velocity is:

$AV = \frac{(275 - 16*4.05^2) - (275 - 16*4^2)}{4.05 - 4} = \frac{16(4^2 - 4.05^2)}{0.05} = -128.8$

So the average speed is -128.9 ft/s

iii) t1 = 4s, t2 = 4s + 0.01s = 4.01s

The average speed is:

$AV = \frac{(275 - 16*4.01^2) - (275 - 16*4^2)}{4.01 - 4} = \frac{16(4^2 - 4.01^2)}{0.01} = -128.16$

The average speed is -128.16 ft/s.

b) The instantaneous velocity of the pebble after 4 seconds can be obtained by looking at the velocity equation, that is the derivative of the height equation.

v(t) = dy(t)/dt.

v(t) = -2*16*t + 0

Then the velocity at t = 4s is:

v(4s) = -32*4 = -128

The instantaneous velocity at t = 4s is -128 ft/s.

3 0

3 years ago

A family has an annual income of $30,600 Of this, 1/4 is spent for food, 1/5 for housing, 1/10 for clothing, 1/9 for savin

Ksenya-84 [330]

Answer:

$6,120

Step-by-step explanation:

1/5 (one-fifth) of the family's annual income ($30,600) is spent on housing- as the word problem states.

You have to find 1/5 (one-fifth) of* $30,600.

Write it out as an equation.

$\frac{1}{5} \times 30600$

*The of in the word equation (1/5 of 30600) simply means multiplication.

4 0

2 years ago

Riley has a farm on a rectangular piece of land that is 200200200 meters wide. This area is divided into two parts: A square are

777dan777 [17]

Answer:

The inequality that models the situation for her to have money to save is

7L² > 3(200L - L²)

On simplifying and solving,

L > 60 meters

Step-by-step explanation:

The length of her farm = L meters

The farm where she grows avocados is of square dimension

Area of the farm = L × L = L²

The piece of land is 200 m wide.

Total area of the piece of land = 200 × L = (200L) m²

If the area of her farm = L²

Area of the side where she lives will be

(Total area of the land) - (Area of the farm)

= (200L - L²)

= L(200 - L)

Every week, Riley spends $3 per square meter on the area where she lives, and earns $7 per square meter from the area where she grows avocados.

Total amount she earns from the side she grows the avocados = 7 × L² = 7L²

Total amount she spends on the side where she lives = 3 × (200L - L²) = 3(200L - L²)

For her to save money, the amount she earns must be greater than the amount she spends, hence the inequality had to be

(Amount she earns) > (Amount she spends)

7L² > 3(200L - L²)

To simplify,

7L² > 3L(200 - L)

Since L is always positive, we can divide both sides by L

7L > 3(200 - L)

7L > 600 - 3L

10L > 600

L > 60 meters

Hope this Helps!!!

7 0

3 years ago

Austin is on the swim team. Each week he swims a total of 3000 meters. How many kilometers does he swim each week?

marishachu [46]

Answer:

3 km

Step-by-step explanation:

(NOTE: One kilometer is 1000 meters)

Divide 3000 by 1000 to get 3

8 0

2 years ago

A new hospital tracked the number of births during its first 6 months of operation, as shown in the table. Find a quadratic func

UNO [17]

Let x refers to the Month numbers
And y refers to Number of births

There is 5 steps to find the quadratic function that models the data.

First step ⇒ Plot the data pairs (x, y) in a coordinate plane.
 which are the blue circles in the attached figure

Second step ⇒ Draw the parabola you think best fits the data.
 Which is the red function in the attached figure.

Third step ⇒ Estimate the coordinates of three points on the
 parabola, which are (2, 108), (4, 68), and (6, 75).
 which are the black squares in the attached figure

Fourth step ⇒ Substitute the coordinates of the points into the model 
 y = ax2 + bx + c
 to obtain a system of three linear equations.

 4a + 2 b + c = 108 ---------(1)
 16a + 4 b + c = 68 ---------(2)
36a + 6 b + c = 75 ---------(3)

Fifth step ⇒ Solve the linear system.
 By using the calculator
 a = 5.875 , b = -55.25 , c = 195

So, the quadratic model for the data is ⇒ y = 5.875 x²- 55.25 x + 195
============================================
To predict the number of births for month 8
substitute with x = 8 ⇒ y = 5.875 * 8²- 55.25 * 8 + 195 = 129

3 0

3 years ago

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4x-4y=-2 -9x-4y=-3 ​

4x-4y=-2 -9x-4y=-3