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2 years ago

Evaluate the function rule for the given value. y = 6 ∙ 2x for x = –2

Mathematics

2 answers:

Aleks04 [339]2 years ago

4 0

6×4=24 is the right answer hope this helps

dybincka [34]2 years ago

3 0

Y = 6 times -4
y = -24

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A tunnel is in the shape of a parabola. The maximum height is 50 m and it is 10 m wide at the base as shown below. What is the v

LiRa [457]

Refer to the figure shown below.

Because the maximum height of the parabola is 50 m, its equation is of the form
y = ax² + 50

This equation places the vertex at (0,50). The constant a should be negative for the vertex to be the maximum of y.

The base of the parabola is 10 m wide. Therefore the x-intercepts are (5,0) and (-5,0).
Set x=5 and y=0 to obtain
a(5²) + 50 = 0
25a = -50
a = -2

The equation of the parabola is
y = - 2x² + 50

At 2 m from the edge of the tunnel, x = 5 - 2 = 3 m.
Therefore the height of the tunnel (vertical clearance) at x = 3 m is
h = y(3)
= -2(3²) + 50
= - 18 + 50
= 32 m

Answer: 32 m

3 0

2 years ago

How many tens are there in 342

Svet_ta [14]

The answer is there are 34 tens in 342

4 0

2 years ago

Read 2 more answers

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

nadezda [96]

Answer:

$\frac{2}{3}$

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

There are 135 people in a sport centre. 77 people use the gym. 62 people use the swimming pool. 65 people use the track. 27 peop

umka21 [38]

Answer:

The correct answer is $\frac{2}{9}$ .

Step-by-step explanation:

There are 135 people in a sport centre.

Let the experiment be to pick a person from the sport centre who only uses exactly one of the facilities.

Total number of possible outcomes = 135

For the gym:

77 people use the gym.

27 people use the gym and the pool.

31 people use the gym and the track.

4 people use all three facilities.

Total number of people using only the gym are 77 - ( 27 + 31 + 4) = 15

For the swimming pool:

62 people use the swimming pool.

27 people use the gym and the pool.

23 people use the pool and the track.

4 people use all three facilities.

Total number of people using only the swimming pool are 62 - ( 27 + 23 + 4) = 8

For the tracks:

65 people use the track.

23 people use the pool and the track.

31 people use the gym and the track.

4 people use all three facilities.

Total number of people using only the tracks are 65 - ( 23 + 31 + 4) = 7

A person is selected at random.

Favorable outcomes = 7 + 8 + 15 = 30

Probability that the person uses exactly one of the facilities = $\frac{Favorable}{Total}$ = $\frac{30}{135} = \frac{2}{9}$ .

5 0

2 years ago

Veronique and Lily compare their investment accounts to see how much they will have in the accounts after seven years. They subs

ch4aika [34]

Answer:

Veronique: A = 1,000 (1 + 0.05) superscript 7, Lily: A = 1,800 (1 + 0.09) Superscript 7

Step-by-step explanation:

the equation used to calculate future value of an investment (or bank deposit) using compound interest is:

future value = present value x (1 + interest rate)ⁿ

Veronique: future value = $1,000 x (1 + 5%)⁷ = $1,057
Lily: future value = $1,800 x (1 + 9%)⁷ = $3,290.47

6 0

2 years ago