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labwork [276]
3 years ago
5

Show that the given curve c(t) is a flow line of the given velocity vector field F(x, y, z).

Mathematics
1 answer:
liq [111]3 years ago
6 0

Answer:

a) c'(t) = (2 Cos(t), -2 Sin(t), 9e^t)

b) c'(t) = (2 Cos(t), -2 Sin(t), 9e^t)

Step-by-step explanation:

We are given in the question:

c(t) = (2 Sin(t), 2 Cos(t), 9e^t)

F(x,y,z) = (y, -x, z)  

a) c'(t)

We differentiate with respect to t.

c'(t) = (2 Cos(t), -2 Sin(t), 9e^t)

b) F(c(t))

This is a composite function.

F(c(t)) = F(2 Sin(t), 2 Cos(t), 9e^t)

= (2 Cos(t), -2 Sin(t), 9e^t)

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Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2 and the profit
coldgirl [10]
Changing the equation into slope form: y = mx + c, where m is the slope [gradient] and c is the y-intercept.

2x+3y=1470
3y = -2x+1470
y= - \frac{2}{3}x+ \frac{1470}{3}
y=- \frac{2}{3}x+490

The gradient is - \frac{2}{3} and y-intercept is at y=490

Graphing y=- \frac{2}{3}x+490 using slope-intercept method:
a) The slope is a negative slope. The line will go 'down hill'
b) The line must pass the point (0, 490)
c) The line will intercept the x-axis at y = 0
    0 = - \frac{2}{3}x+490
    \frac{2}{3}x = 490
    2x = 1470
    x = \frac{1470}{2}
    x = 735
    So, x-intercept is at (735, 0)

The graph of this function is shown below. The intercepts are labelled at:
y = 490
x = 735

-----------------------------------------------------------------------------------------------------------

Next month's profit equation

2x+3y=1593

Rewriting this into slope-equation form

3y = -2x+1593
y=- \frac{2}{3}+ \frac{1593}{3}
y= - \frac{2}{3}+531

The gradient, m, equals to - \frac{2}{3}
The y-intercept, c, equals to 531

The equation still has the same gradient with last month's profit equation but different y-intercept. 

-------------------------------------------------------------------------------------------------------------

A linear graph show points of (0, 300) and (450, 0)

We work out the slope: 
\frac{300-0}{0-450} = \frac{300}{-450}=- \frac{20}{30}  =- \frac{2}{3}


Y-intercept at x = 0, so it's at y = 300

Equation y = - \frac{2}{3}+300

6 0
3 years ago
Find the vertex of the graph of the function.
lapo4ka [179]

Answer: The correct options are  (1) (5,10), (2) (3,-3), (3) x = -1, (4) y=(x+2)^2+3, (5) 21s and (6) 0, -1, and 5.

Explanation:

Te standard form of the parabola is,

f(x)=a(x-h)^2+k        .....(1)

Where,  (h,k) is the vertex of the parabola.

(1)

The given equation is,

f(x)=(x-5)^2+10

Comparing this equation with equation (1),we get,

h=5 and k=10

Therefore, the vertex of the graph is (5,10) and the fourth option is correct.

(2)

The given equation is,

f(x)=3x^2-18x+24

f(x)=3(x^2-6x)+24

To make perfect square add (\frac{b}{2a})^2, i.e., 9. Since there is factor 3 outside the parentheses, so subtract three times of 9.

f(x)=3(x^2-6x+9)+24-3\times 9

f(x)=3(x-3)^2-3

Comparing this equation with equation (1),we get,

h=3 and k=-3

Therefore, the vertex of the graph is (3,-3) and the fourth option is correct.

(3)

The given equation is

f(x)=4x^2+8x+7

f(x)=4(x^2+2x)+7

To make perfect square add (\frac{b}{2a})^2, i.e., 1. Since there is factor 4 outside the parentheses, so subtract three times of 1.

f(x)=4(x^2+2x+1)+7-4

f(x)=4(x+1)^2+3

Comparing this equation with equation (1),we get,

h=-1 and k=3

The vertex of the equation is (-1,3) so the axis is x=-1 and the correct option is 2.

(4)

The given equation is,

y=x^2+4x+7

To make perfect square add (\frac{b}{2a})^2, i.e., 2^2.

f(x)=x^2+4x+4+7-4

f(x)=x^2+4x+4+7-4

f(x)=(x+2)^2+3

Therefore, the correct option is  4.

(5)

The given equation is,

h=-16t^2+672t

It can be written as,

h=-16(t^2-42t)

It is a downward parabola. so the maximum height of the function is on its vertex.

The x coordinate of the vertex is,

x=\frac{b}{2a}

x=\frac{42}{2}

x=21

Therefore,  after 21 seconds the projectile reach its maximum height and the correct option is first.

(6)

The given equation is,

f(x)=3x^3-12x^2-15x

f(x)=3x(x^2-4x-5)

Use factoring method to find the factors of the equation.

f(x)=3x(x^2-5x+x-5)

f(x)=3x(x(x-5)+1(x-5))

f(x)=3x(x-5)(x+1)

Equate each factor equal to 0.

x=0,-1,5

Therefore, the zeros of the given equation is 0, -1, 5 and the correct option is 2.

3 0
3 years ago
4 ten thousands 4 thousands time 10
damaskus [11]
44,000 *10
440,000

when multiplying by ten, add one more zero to the end of the number
5 0
2 years ago
Whats the decimal equivalent of 16%
masha68 [24]

Answer:

0.16

Step-by-step explanation:

Percent means 'per 100'. So, 16% means 16 per 100 or simply 16/100.

The answer is 0.16

8 0
2 years ago
Read 2 more answers
14. Point P has the coordinates (-2,-4). Point P is dilated with a center at the origin and
DedPeter [7]

Answer:

Step-by-step explanation:

The answer is b (1,-1)

3 0
2 years ago
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