Part A Assume the ball passes through the points ( 3 , 8 ) , ( 5 , 20 3 ) , and ( 6 , 5 ) . Use this data to set up a system of three equations and three unknowns (a, b, and c) that will allow you to find the equation of the parabola. Write the system in the space provided.

Step-by-step explanation:

the volume of a cylinder is as for any other regular 3D object :

ground area ×height

the ground area of a cylinder is a circle, so it is

pi×radius² × height

the radius is always half of the diameter (of the diameter is airways twice the radius).

radius = 6/2 = 3 ft.

the volume is then

pi × 3² × 9 = pi × 9 × 9 = pi × 81 ft³

so, the answer is 81pi ft³.

The rate of change of y with respect to x is given by dy/dx = xy - (3/2)x²y.

To find the rate of change of y with respect to x, we need to differentiate the given equation. The rate of change can be determined by taking the derivative of both sides of the equation with respect to x.

First, let's differentiate each term separately using the rules of differentiation.

Differentiating x²y with respect to x gives us 2xy using the product rule.

To differentiate 5, we know that a constant has a derivative of 0.

Differentiating 2ln(y) with respect to x requires the chain rule. The derivative of ln(y) with respect to y is 1/y, and then we multiply by dy/dx. So, the derivative of 2ln(y) is 2/y * dy/dx.

Differentiating x³ gives us 3x² using the power rule.

Now, we can rewrite the equation with its derivatives:

2xy - 2/y * dy/dx = 3x²

To solve for dy/dx, we can isolate it on one side of the equation. Rearranging the equation, we get:

2xy = 2/y * dy/dx + 3x²

To isolate dy/dx, we move the term 2/y * dy/dx to the other side:

2xy - 2/y * dy/dx = 3x²

2xy = 2/y * dy/dx + 3x²

2/y * dy/dx = 2xy - 3x²

Now, we can solve for dy/dx by multiplying both sides by y/2:

dy/dx = (2xy - 3x²) * (y/2)

Simplifying further, we have:

dy/dx = xy - (3/2)x²y

To know more about rate of change, refer here:

https://brainly.com/question/29181688#

#SPJ11

Answer:

four million, one hundred ninety three thousand, five hundred thirty eight

Step-by-step explanation:

Answer:

Four million, one hundred ninety-three thousand, five hundred thirty-eight

Step-by-step explanation:

Answer:

81:324

Step-by-step explanation:

3+12=15

405 div 15 =27

3 times 27 = 81

12 times 27 = 324

81:324

Answer:

c. 20%

Step-by-step explanation:

We need to write the equation for the expression "nine less than a number n":

Answer:

x ≥ 22/5

Step-by-step explanation:

I used a calculator called MathPapa

A diver who jumps off a pier at an angle of 25 degrees with an initial velocity of 3.2 m/s will land in the water approximately 2.7 meters away from the pier.

The horizontal and vertical motions of the diver are separate, with the initial velocity of 3.2 m/s at an angle of 25 degrees. We'll utilize the following equations to figure out how far from the pier the diver will land:

Yf = Yi + Viyt + 1/2gt²Xf = Xi + Vixt

Where X is the distance and Y is the height; the subscripts i and f indicate initial and final conditions; Viy and Vix represent the vertical and horizontal components of the velocity at time t; and g is the acceleration due to gravity (-9.8 m/s²).The initial vertical velocity can be calculated as follows:

Viy = Visin(θ)

Viy = 3.2m/s*sin(25) = 1.34 m/s

The final height is zero since the diver begins and ends at the same level (the water's surface).

Yf = Yi + Viyt + 1/2gt²0 = 0 + 1.34t - 4.9t²

We can solve this quadratic equation for t:

t = (1.34 ± √(1.34² - 4(-4.9)(0))) / (2(-4.9))

t = 0.28 s or 0.90 s

We can disregard the negative solution because time can't be negative, and the diver can't spend -0.28 seconds in the air! As a result, the diver spends approximately 0.90 seconds in the air before landing in the water. We can now use the horizontal velocity to determine how far the diver traveled during that time:

Xf = Xi + Vixt

Xf = 0 + 3.2cos(25) (0.90)

Xf ≈ 2.7 meters

To summarize, a diver who jumps off a pier at an angle of 25 degrees with an initial velocity of 3.2 m/s will land in the water approximately 2.7 meters away from the pier. This is calculated by using the initial velocity to find the vertical and horizontal components of the motion, calculating the time the diver spends in the air, and using the horizontal velocity to find the distance traveled during that time.

To know more about acceleration visit:

brainly.com/question/29583481

#SPJ11

Answer:

\(\frac{5}{16}\)

Answer:

You get 105

Step-by-step explanation:

50 divided by 1/2? = 100

100 + 15 = 115

115 - 10 = 105

You get 105.

Hope this helps - any questions put in the comments section.

Answer:

y= -1/3x-3

Step-by-step explanation:

The slope is -1/3 because the equation is rise/run. The rise is 1, and the run, or horizontal length, is 3. Because the line is slanting toward the left, the slope will be negative.

y=mx+b is the equation for a linear line.

y= -1/3x+b (substitute the slope in)

choose any point on the line, for example, (0,-3).

-3= -1/3(0)+b   (0 is the x, and -3 is the y)

b= -3

Your equation will be y= -1/3x-3

9514 1404 393

Answer:

  y = -1/4x -3

Step-by-step explanation:

The slope is found by counting grid squares between grid crossing points. The line crosses grid points at (0, -3) and again at (4, -4). That is, for 4 units to the right, it drops 1 unit, so the slope is ...

  m = rise/run = -1/4

The crossing at (0, -3) tells you the y-intercept is b = -3, so the slope-intercept equation is ...

  y = mx +b

  y = -1/4x -3

Hello!

Answer:

22-3= 19

Step-by-step explanation:

Hope this helps!

The notation "ER^2" represents the set of ordered pairs of real numbers. "x.y" is an ordered pair with "x" as the first component and "y" as the second. "x^2-1" specifies the condition for all ordered pairs (x,y) to be considered.

Let A be a set containing ordered pairs (x, y) belonging to the Euclidean plane ℝ², such that x² - 1 is a property related to these pairs. To explain this property, follow these steps:

1. Identify the property: x² - 1.
2. Recognize that A contains pairs (x, y) where x and y are real numbers (ℝ²).
3. Understand that for each pair in A, x must satisfy the property x² - 1.

Hence, The A = {x.y)ER^2: x^2-1 is set A is a collection of ordered pairs (x, y) from the Euclidean plane ℝ², where the x-coordinates of these pairs satisfy the equation x² - 1.

To learn more about the Euclidean plane click here: brainly.com/question/17304015

#SPJ11

Answer:

The answer is 47

Step-by-step explanation:

I'm pretty sure this is the answer :)

40 - 28 = 12

35 + 12 = 47

Proof: 35 - 28 = 7

          47 - 40 = 7

Answer:

m∠WZX = 41°

Step-by-step explanation:

diagonals bisect angles and opposite angles are congruent

therefore, ∠WXY ≅ ∠WZY

∠WZY must equal [360 - 2(68)] ÷ 2 which equals 112°

If ∠WXZ = 71° then so does ∠XZY

Which means that ∠WZX must equal 112-71 which is 41°

===================================================

Explanation:

Refer to the diagram below. I've marked up the figure with various angles to point out the angles we'll be working with.

To make things a bit simpler in terms of notation, and to match up colors with variable letters, I'm going to use the following

Notice how the two red angles I've marked up are alternate interior angles. This works because WX is parallel to ZY. Also notice that the red and blue angles combine to form the angle WZY, which is adjacent to angle XYZ in green.

For any parallelogram, the adjacent angles always add to 180.

(angle WZY) + (angle XYZ) = 180

(blueAngle+redAngle) + (greenAngle) = 180

(B+R) + (G) = 180

(B+71) + (68) = 180

B+139 = 180

B = 180-139

B = 41

The blue angle is 41 degrees, which means angle WZX is 41 degrees

Side note: Your steps and answer to problem 11 are correct. Nice work.

Answer:

Answers - d and e

Step-by-step explanation:

A surd is basically an irrational number, or a number that is not a whole number. (Surd examples - 1.2938, 5.3108)

The square root of 15 is between 3 and 4 (not a whole number) and the square root of 30 is between 5 and 6 (not a whole number)

hope this helps

Answer:

Claiming points again since all these answers are right, thank you yet again.

Step-by-step explanation:

⏁⊑⏃⋏☍ ⊬⍜⎍ ⎎⍜⍀ ⏁⊑⟒ ⌿⍜⟟⋏⏁⌇ ⎅⟒⏃⍀ ⎎⍀⟟⟒⋏⎅, ⟟ ⏃⋔ ⎎⍜⍀⟒⎐⟒⍀ ⟟⋏ ⊬⍜⎍⍀ ⎅⟒⏚⏁.

Answer:

17 hours

Step-by-step explanation:

We first want to figure out how much money shes making per hour.

We can simply divide 176 by 8 getting us 22

Since we know she makes 22 dollars an hour we can divide 374 by 22 getting us 17.

Now we know it would take 17 hours to make 374 dollars

If you want to double check you can simply multiply 17 by 22 which would get you 374

Answer: 17 hours

Step-by-step explanation

Answer:

The last one is the answer

Answer: For each hour that Michelle drove, she travelled an additional 50 miles.

Step-by-step explanation:

Test each option to see its accuracy

Calculate the slope:

\((x_{1}, y_{1}) = (7, 0)\\(x_{2}, y_{2}) = (0, 350)\\ \\\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{350-0}{0-7} =\frac{350}{-7} =-50\)

This means that Michelle drove 50 miles per hour.

The other three options are wrong because if you bring in:

into your function- y = -50x + 350, you would not get the stated miles.

the answer should be 35 songs in total

Answer:

3%

Step-by-step explanation:

Answer:

100%

Step-by-step explanation:

Markup % = ( Selling Price - Coast) / ( Coast) * 100

( $4 - $3) / ($3) * 100

1 * 100 = 100

Answer:\(56w^{7} y^{5}\\\)

if it doesn't work im sorry

Answer:

Step-by-step explanation:

Cost of bikes =  $500.00

If the sales tax is 7%, the amount paid as tax will be 7% of the total selling price of bike;

7% of $500.00

= \(\frac{7}{100} * 500\\\)

= $35

The final cost of bike = initial selling price + amount paid as tax

The final cost of bike  = $500.00 + $35.00

The final cost of bike = $535.00

Answer: 51

Step-by-step explanation:

a = first term = 156

d = common difference = 153 - 156 = -3

The nth term will be gotten using the formula:

= a + (n - 1)d

36th term = a + (36 - 1)d = a + 35d

= 156 + 35(-3)

= 156 - 105

= 51

Answer:

3.125 mg/ oz

Step-by-step explanation:

Amount of instant tea = 24 ounces

Amount of green tea = 12 ounces

Caffeine in instant tea = 24/8*30= 90 mg/oz

Also, caffeine in green tea = 12/8*15 =22.5 mg/oz.

Total amount of mixture= 24+12= 36 ounce

Total amount of caffeine in the mixture = 90+22.5 = 112.5 mg/oz

Caffeine per ounce in the final mixture = 112.5 / 36 = 3.125 mg/ oz

Answer:

180-(25x+5)=9x+5

180-25x-5=9x+5

-34x=-170

x=5

Answer:

Domain: 1, 6

Range: 4

Step-by-step explanation:

The Domain is the first coordinate which is x

The Range is the second coordinate which is y

The domain is the set of departure of a function into constrained to fall it is the sex X in the notation f:X-Y and is denoted as dom. The range is set of data is the diffrence between largest and smallest values so The domain is 1,6 and range is 4