Ask question

Ask question

All categories

2 years ago

6

The graph shows the function g(x) for a restricted domain. On a coordinate plane, a function starts at (negative 4, 0) and then

curves through the y-axis at (0, 1.5) and then goes through point (4, 2). Which is the function g(x) for a restricted domain?

1 answer:

Art [367]2 years ago

7 0

I can take it up to the house for you and you

You might be interested in

Amy and two of her friends eat lunch at a restaurant. Their bill, including tax, comes to $27.63. They decide to split the bill

Art [367]

Answer:

Step-by-step explanation:

$27.63 / 2 = $13.82

$13.82 * 0.20 = $2.76

$13.82 + $2.76 = $16.58

6 0

2 years ago

A barrel contains 56 litres of kerosene. It has two taps. One tap draws 500 ml every 6 minutes. After first 5 litres are drawn

tigry1 [53]

Answer:

The tank will empty in 4 hours.

Step-by-step explanation:

Since a barrel contains 56 liters of kerosene, and it has two taps, one tap that draws 500 ml every 6 minutes and after first 5 liters are drawn from the barrel, the second tap also starts, and it draws 1 liter in every 5 minutes, to determine how many hours will be taken in all to empty the tank, the following calculation must be performed:

0.5 x X = 5

X = 5 / 0.5

X = 10

10 x 6 = 60

1 hour = 51 liters

1 hour 30 minutes = 51 - (1 x 6) - (0.5 x 5) = 42.5

2 hours = 42.5 - (1 x 6) - (0.5 x 5) = 34

2 hours 30 minutes = 34 - (1 x 6) - (0.5 x 5) = 25.5

3 hours = 25.5 - (1 x 6) - (0.5 x 5) = 17

3 hours 30 minutes = 17 - (1 x 6) - (0.5 x 5) = 8.5

4 hours = 8.5 - (1 x 6) - (0.5 x 5) = 0

Therefore, the tank will empty in 4 hours.

3 0

2 years ago

Evaluate the line integral by the two following methods. xy dx + x2y3 dy C is counterclockwise around the triangle with vertices

nadezda [96]

Answer:

a)

$\frac{2}{3}$

b)

$\frac{2}{3}$

Step-by-step explanation:

a) The first part requires that we use line integral to evaluate directly.

The line integral is

$\int_C xydx + {x}^{2} {y}^{3} dy$

where C is counterclockwise around the triangle with vertices (0, 0), (1, 0), and (1, 2)

The boundary of integration is shown in the attachment.

Our first line integral is

$L_1 = \int_ {(0,0)}^{(1,0)} xydx + {x}^{2} {y}^{3} dy$

The equation of this line is y=0, x varies from 0 to 1.

When we substitute y=0 every becomes zero.

$\therefore \: L_1 =0$

Our second line integral is

$L_2 = \int_ {(1,0)}^{(1,2)} xydx + {x}^{2} {y}^{3} dy$

The equation of this line is:

$x = 0 \implies \: dx = 0$

y varies from 1 to 2.

We substitute the boundary and the values to get:

$L_2 = \int_ {1}^{2}1 \cdot y(0) + {1}^{2} \cdot \: {y}^{3} dy$

$L_2 = \int_ {1}^2 {y}^{3} dy = \frac{8}{3}$

The 3rd line integral is:

$L_3 = \int_ {(1,2)}^{(0,0)} xydx + {x}^{2} {y}^{3} dy$

The equation of this line is

$y = 2x \implies \: dy = 2dx$

x varies from 0 to 1.

We substitute to get:

$L_3 = \int_ {1}^{0} x \cdot \: 2xdx + {x}^{2} {(2x)}^{3}(2 dx)$

$L_3 = \int_ {1}^{0} 8 {x}^{5} + 2 {x}^{2} dx = - 2$

The value of the line integral is

$L = L_1 + L_2 + L_3$

$L = 0 + \frac{8}{3} + - 2 = \frac{2}{3}$

b) The second part requires the use of Green's Theorem to evaluate:

$\int_C xydx + {x}^{2} {y}^{3} dy$

Since C is a closed curve with counterclockwise orientation, we can apply the Green's Theorem.

This is given by:

$\int_C \: Pdx +Q \: dy = \int \int_ R \: Q_y - P_x \: dA$

$\int_C \: xydx + {x}^{2} {y}^{3} \: dy = \int \int_ R \: 3 {x}^{2} {y}^{2} - y \: dA$

We choose our region of integration parallel to the y-axis.

$\int_C \: xydx + {x}^{2} {y}^{3} \: dy = \int_ 0^{1} \int_ 0^{2x} \: 3 {x}^{2} {y}^{2} - y \: dydx$

$\int_C \: xydx + {x}^{2} {y}^{3} \: dy = \int_ 0^{1} \: {x}^{2} {y}^{3} - \frac{1}{2} {y}^{2} |_ 0^{2x} dx$

$\int_C \: xydx + {x}^{2} {y}^{3} \: dy = \int_ 0^{1} \: 8{x}^{5} - 2 {x}^{2} dx = \frac{2}{3}$

8 0

2 years ago

A repair bill for a car is $648.45. The parts cost $265.95. The labor cost is $85 per hour. Write and solve an equation to find

zysi [14]

Answer:

( t - p ) / 85x = h

( t - 265.95 ) / 85x = h

648.45 - 265.95 / 85x = 3.32h

h = 3.32

Therefore ( t - p ) / 85x = 3.32

Step-by-step explanation:

648.45 - 265.95

282.50 /85

= 3.32 hrs

Finding equation to find hours can be shown as

( t - p ) / 85x = 3.32

How we found equation to find total

Parts = 19 x 14 - 5/100 = 266- 0.05

648.45 - 265.95 = 282.5

282.5/85 = 3.323 near to 3,233529

Labour = 85x = 17 (5 + x)

Equation = 17(5+ x) + 14(19) - 5/100 = 648.45 where x = 85

Equation = ( 85x x 3 1/3) + 265 - 19/20 = t

3 0

1 year ago

Suppose that the height of the slide is 2 feet,

Lena [83]

$\bf \stackrel{\textit{average rate of change}}{slope = m\implies} \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{\stackrel{height}{2}}{\stackrel{width}{20}}\implies \cfrac{1}{10}$

5 0

2 years ago

Read 2 more answers