Eliminate the parameter t. Find a rectangular equation for the plane curve defined by the parametric equations.
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• (1) x= sqrt t, y=4t+3; 0 ≤ t ≤ 4

A) y = - 3x ^ 2 + 19; 0 ≤ x ≤ 2
B ) y = - 3x + 19; 0 ≤ x ≤ 2
C) y=4x^ 2 +3; 0 ≤ x ≤ 2
D ) y=3x^ 2 +4; -1 ≤ x ≤ 2

• (2) x=2t, y=t+2; -2 ≤ t ≤ 3

A ) y=x ^2 + 1; - 2 ≤ x ≤ 2
B) y= 1/2x -2; -∞ C) y= 1/2x +2; -4 ≤ x ≤ 6
D ) y=-2x+2; -∞

Answer:

The rate of change of the height is approximately [tex]-6.577\times 10^{-3}\,\frac{in}{min}[/tex].

Step-by-step explanation:

From Geometry we know that volume of cylinder ([tex]V[/tex]), measured in cubic inches, is expressed by:

[tex]V = \pi\cdot r^{2}\cdot h[/tex] (1)

Where:

[tex]r[/tex] - Radius, measured in inches.

[tex]h[/tex] - Height, measured in inches.

Given that volume remains constant, the expression for the rate of change of the height ([tex]\dot h[/tex]), measured in inches per minute, is:

[tex]2\pi\cdot r \cdot h \cdot \dot r + \pi \cdot r^{2}\cdot \dot h = 0[/tex]

[tex]2\cdot h\cdot \dot r + r\cdot \dot h = 0[/tex]

[tex]r\cdot \dot h = -2\cdot h \cdot \dot r[/tex]

[tex]\dot h = -\frac{2\cdot h\cdot \dot r}{r}[/tex]

[tex]\dot h = - \left(\frac{2\cdot \dot r}{r}\right)\cdot \left(\frac{V}{\pi\cdot r^{2}} \right)[/tex]

[tex]\dot h = -\frac{2\cdot \dot r \cdot V}{\pi\cdot r^{3}}[/tex] (2)

Where [tex]\dot r[/tex] is the rate of change of the radius, measured in inches per minute.

If we know that [tex]r = 44\,in[/tex], [tex]\dot r = 2\,\frac{in}{min}[/tex] and [tex]V = 440\,in^{3}[/tex], then the rate of change of the height is:

[tex]\dot h = - \frac{2\cdot \left(2\,\frac{in}{min} \right)\cdot \left(440\,in^{3}\right)}{\pi\cdot (44\,in)^{3}}[/tex]

[tex]\dot h \approx -6.577\times 10^{-3}\,\frac{in}{min}[/tex]

The rate of change of the height is approximately [tex]-6.577\times 10^{-3}\,\frac{in}{min}[/tex].

9514 1404 393

Answer:

  x can be any value (infinite number of solutions)

Step-by-step explanation:

The equation simplifies to ...

  2(x -2) +3 = 2x -1

  2x -4 +3 = 2x -1

  2x -1 = 2x -1

This is true for every value of x. There are an infinite number of solutions.

Answer:

The answer is H.

Step-by-step explanation:

There is no "b" in this y = mx + b, so it has to go through zero, eliminating the bottom two. If we insert y = 2(1), the point should be at (1, 2), and if when looking at the possible answers, we can go with letter H.

Answer:

3

Step-by-step explanation:

subtract 3y from both sides

add 9 to both sides

3y=12x+9

divide everything by 3

y=4x+3

y-intercept is 3

Answer:

215.00

Step-by-step explanation:

Answer:

0.625

Step-by-step explanation:

5/6 x 3/4 = 0.625 in decimal form.

Answer:

The concession stand sold  46  hot dogs and  32  hamburgers.

Step-by-step explanation:

Answer:

24 13/34

Step-by-step explanation:

The distance covered by Dennis will be 9.23 miles.

Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance. Speed is a scalar quantity and does not require any direction to represent it.

Given that Dennis can walk about 2(5/6) miles each hour. The distance covered by Dennis in 3 hours 15 minutes will be calculated as:-

Distance = 2 ( 5 /  6)  x  3 hour 15 minute

Distance = 2.84 x 3 ( 1 / 4)

Distance = 2.84 x 3.25

Distance = 9.23 miles.

Therefore, the distance covered by Dennis will be 9.23 miles.

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Answer:

i think it's 13/16

Step-by-step explanation:

1/8 times 2 is 2/16 and 3/8 times 2 is 6/16 so add all up to get 13/16

Answer:

2i - (-3 + i)

Step-by-step explanation:

I think this is it. Sorry if it's wrong

Answer:

7 -3i

Step-by-step explanation:

Simplify by combining the real and imaginary parts of each expression

Answer: A

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

its 6

Answer:

here is a simple version

lets make A equal the exponent so (A=^2 or 3 or whatever)

the exponent will be the amount of times you want to repeat the process.

Now lets make x = the first array, so x=3

and lets make y = the second array, y=7

now a simple equation would be (3x)(7y)^A or for this you could say

(3x)(7y)^6

Answer:

diameter = 28 cm

Step-by-step explanation:

circumference = 2πr

88 cm = 2 * 3.14.*r. ( π = 3.14 )

r = ( 88)/(3.14*2)

r = 14 cm

diameter = 2 * radius

diameter = 2 * 14 cm

diameter = 28 cm

Answer:

Step-by-step explanation:

Circumference formula:

Substitute values of circumference and the π to find the diameter:

Answer:

Good for her

Step-by-step explanation:

Answer:

x=  16 /20420505

Step-by-step explanation:

Let's solve your equation step-by-step.

5(215)x=16

Step 1: Simplify both sides of the equation.

20420505x=16

Step 2: Divide both sides by 20420505.

20420505x /20420505  =  16 /20420505

x=  16 /20420505

Answer:

y=-1/2x-2

Step-by-step explanation:

I dont think any of those options are the right one so thats the correct answer

Answer:    y = -1/2x - 2

Step-by-step explanation:

To first write the equation, we need to find the slope and the y intercept and write it in the form  y=mx +b

To find the slope, we will find the difference between the y coordinates and divide it by the difference between the x coordinates.

The y coordinates of the points are , 0 and -2

The x coordinates of the points are -4 and 0

0 - (-2) = 2

-4 -0 = -4

Slope:  2/-4 = -1/2

Now using the formula y=mx+b, you will input the slope and use one of the given point's coordinates to solve for b the y intercept.

We will use the point (0,-2)

  -2 = -1/2(0) + b

-2 = b

  This means the equation will be  y = -1/2x - 2

Answer:

I do!

Step-by-step explanation:

Answer:

no sorry but i do know some friends that play..

Answer:

1.75

Step-by-step explanation:

To do this you would have to do

105/60=1.75

so that would be the answer

Answer:

2.73

Step-by-step explanation:

Bc I did this

Answer:

See below

Step-by-step explanation:

R is the midpoint of SQ

R is the midpoint of PT

SQ and PT intersect at point R ⇒

Triangles PQR and TSR have two sides and the included angle congruent, therefore:

as per SAS congruence postulate

Answer: 47

we have:

41° + 3x - 2 = 180°

⇔ 3x - 2 = 180 - 41

⇔ 3x - 2 = 139

⇔ 3x = 139 + 2

⇔ 3x = 141

⇔ x = 141/3

⇔ x = 47

Step-by-step explanation:

Answer:

The formula for slope is sometimes referred to as "rise over run", because the fraction onsists of the "rise" (being the change in y, going up or down) divided by the "run" (being the change in x, going from left to the right).

Step-by-step explanation:

Answer:

IS there a picture?

Step-by-step explanation:

Answer:

Step-by-step explanation:

there is no choices to choose from only a question so I'm not sure what the answer choices are.