Choose the function that shows the correct transformation of the quadratic function shifted two units to the right one

Two children, Ferdinand and Isabella, are playing with a water hose on a sunny summer day. Isabella is holding the hose in her h

wolverine [178]

Answer:

f = 0.84 or 84%

Step-by-step explanation:

Given:

- Original constant velocity of water v_o = 3.5 m/s

- The original diameter of the hose opening d_o = 1.5 cm

- The total vertical distance y(f) = 1.0 m

- The total range x(f) = 10.0 m

Find:

What fraction of the original area does Isabella has to reduce or pinch so the water can cover the entire range.

Solution:

- We will assume the flow of water as a stream of particles that follow a path of single point.

- Using second kinematic equation in the vertical direction and compute the time it takes the water to reach the ground:

y(t) = y(0) + v_y*t + 0.5*gt^2

Where, y(0) = v_y = 0,

1.0 = 0.5*g*t^2

t = sqrt ( 2*1 / 9.81 )

t = 0.4515 s

- Now we will use the second equation of motion for the x- direction motion:

x(t) = x(0) + v_x*t

Where, x(0) = 0,

10 = 0 + v_x*(0.4515)

v_x = 10 / 0.4515 = 22.1 m/s

- We have calculated the minimum velocity required to reach the range from isabella and ferdinand.

- We will use the continuity equation to compute the area required for the velocity calculated v_x = 22.1 m/s:

A_f*v_x = A_o*v_o

A_f = A_o*v_o / v_x

A_f = pi*0.015^2*3.5 / 4*22.1

A_f = 1.12 * 10^-4 m^2

- The fraction f of the reduction of area is:

f = (A_o - A_f) / A_o

f = (7.068*10^-8 - 1.12*10^-4) / (7.068*10^-8)

f = 0.84 or 84%

4 0

3 years ago

Amy is helping plan her school's new basketball court. The west edge of the basketball court is located on the line y = 2x + 5.

ipn [44]

Answer:

Line of east wedge is: 2x - y = 96

So, Option 1 is correct.

Step-by-step explanation:

The east edge cannot intersect with the west edge means that two lines are parallel.

If the two lines are parallel then they have same slope. We need to find the slopes of given lines and check which line has slope same as slope of west edge.

Slope of west edge.

y = 2x + 5

The standard equation for slope intercept form is:

y = mx+b

where m is the slope. So, m= 2

Now finding line for east edge.

Option 1.

Convert each given equation to standard slope intercept form and find the slope.

2x -y =96

-y = -2x +96

Multiply with -1

y = 2x -96

m = 2

Option 2.

-2x -y = 96

-y = 2x +96

y = -2x-96

m = -2

Option 3

-y-2x =48

-y = 2x +48

y = -2x -48

m = -2

Option 4.

y+2x = 48

y = -2x+48

m = -2

So, only line of Option 1 has slope = 2 which is equal to the slope of west edge.

Line of east wedge is: 2x - y = 96

So, Option 1 is correct.

7 0

3 years ago

Rectangle A measures 10 inches by 8 inches. Rectangle B is an enlarged copy of Rectangle A. Select all of the measurement pairs

Fudgin [204]

Answer:

See Explanation

Step-by-step explanation:

Given

Rectangle A:

$Length: 10\ in$

$Width: 8\ in$

Required

Determine the possible dimensions of Rectangle B

The question has missing options; however, the question can still be solved.

Rectangle B being an enlarged copy of A implies that the dimension of A A is enlarged in equal proportion to form B

Take for instance, the measurements of Rectangle B are

$Length: 15 in$

$Width: 12 in$

Divide the corresponding lengths of B by A to get the enlargement ratio

$Ratio = \frac{B}{A}$

For length:

$Ratio = \frac{15}{10}$

$Ratio = 1.5$

For width

$Ratio = \frac{12}{8}$

$Ratio = 1.5$

Notice that both ratios are the same.

For this measurement of B, we can conclude that B is an enlargement of A

Assume another measurements for B

$Length: 20\ in$

$Width: 10\ in$

Calculate Ratios

$Ratio = \frac{B}{A}$

For length:

$Ratio = \frac{20}{10}$

$Ratio = 2$

For width

$Ratio = \frac{10}{8}$

$Ratio = 1.25$

Notice that, both ratios are not equal.

For this measurement of B, we can conclude that B is not an enlargement of A

Conclusively, all you have to do is: determine the ratios of the dimensions of B to A, if the result are equal then B is an enlarged copy of A; if otherwise, then B is not an enlarged copy

5 0

3 years ago

X + 98 x + 98 Solve for x

disa [49]

Answer:

I believe your answer is commutative property

4 0

3 years ago

Please help asap What is the least common denominator of the fractions?

Reil [10]

The answer is B. 6m^3n^5. Hope I actually helped!

6 0

3 years ago