A ball was kicked into the air from a balcony 20 feet above the ground, and the ball’s height above the ground, in feet, t seconds after the ball was kicked was 2h(t) = 20 − 16t + 32t. What was the maximum height, in feet, of the ball above the ground after it was kicked?

Answers

Answer 1

Answer: 2h(t) = 20 - 16t + 32t

Not only is there something wrong with the way you've written the equation,
there's no way it could be true even after you fix the little mistake.

First let's divide each side by 2 :

h(t) = 10 - 8t + 16t

This is the equation of the height of a ball that starts from 10-ft above the ground, not 20, begins with 8 ft/sec of downward speed as soon as it's kicked, and what to do with that mysterious ' 16t ' at the end ? Well, if it were ' 16t-squared ', it very well could reflect the acceleration of gravity.

BUT ... since the '10' is positive, we know that the upward direction is the
positive direction for this problem, and then the sign of the acceleration term
can't be positive. That would mean that the ball is accelerating upward at the
rate of 32 ft/sec every second, and if we just wait a few minutes, that ball is on
its way to the moon !

-- If we accept the equation exactly as it's written in the question, then the ball
is kicked from an initial height of 10-ft, it has an upward speed of +8 ft/sec forever,
it never sinks lower than the initial 10-ft, and it has no maximum height.

-- If we make the last term ' 16t² ', then the ball is kicked from an initial height
of 10-ft, the kicker aims down and gives it an initial speed of 8 ft/sec DOWNward,
but it has an upward acceleration of 32 ft/sec every second, The lowest it ever gets
is 1-ft below the balcony, at exactly 0.25 second after the kick, then begins rising,
faster and faster. In this case also, the ball is headed for the moon, and has no
maximum height.

The question needs some serious work.

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Answers

Answer:

Step-by-step explanation:

When you count the units it's 3, but because the scale factor is 4, you have to multiply it by that. 3 times 4 is 12.

Ava graphs the function h(x) = x2 + 4. Victor graphs the function g(x) = (x + 4)2. Which statements are true regarding the two graphs? Check all that apply.Ava’s graph is a vertical translation of f(x) = x2.
Victor’s graph is a vertical translation of f(x) = x2.
Ava’s graph moved 4 units from f(x) = x2 in a positive direction.
Victor’s graph moved 4 units from f(x) = x2 in a positive direction.
Ava’s graph has a y-intercept of 4.
Victor’s graph has a y-intercept of 4.

Answers

Answers:

Ava’s graph is a vertical translation of f(x) = x^2.

Ava’s graph moved 4 units from f(x) = x^2 in a positive direction.

Ava’s graph has a y-intercept of 4.

Given:

Ava graphs the function $h(x) = x^2 + 4$ .

Victor graphs the function $g(x) = (x + 4)^2$

To find y intercept we plug in 0 for x

$h(x) = x^2 + 4$

$h(x) = 0 + 4$ = 4

So ,Ava’s graph has a y-intercept of 4.

Ava graphs the function $h(x) = x^2 + 4$

If any number is added at the end then the graph will be shifted up. 4 is added at the end so there will be vertical translation.

Hence , Ava’s graph is a vertical translation of f(x) = x^2. Also Ava moved 4 units up from f(x) = x^2 in a positive y- direction.

Victor graphs the function $g(x) = (x + 4)^2$

If any number added with x then the graph will be shifted left. the graph will be shifted in negative x direction.

Answer: 1, 3, 5

Step-by-step explanation:

Explain how to solve the equation. 49= x/7Part 1
Select the correct choice below and fill in the answer box within your choice.
(Type a whole number.)

A . Subtract _from both sides.

B . Multiply both sides by _

C . Add_ to both sides.

D . Divide both sides by _

Answers

$49 = (x)/(7)$

Multiply both sides of the equation by 7

$49 * 7 = (x)/( \cancel7) * \cancel7$

$343 = x$

$x = 343$

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OptionBisthecorrectchoiceandthenumberthatcomesintheblankis7...~

Rewrite $2x {}^(2) + 2y {}^(2) - 8x + 10y + 2 = 0$
in standard form find the center and radius of the circle.show all of your work for full credit

Answers

Final answer:

The given equation can be rewritten into the form of an equation for a circle with center (h,k) and radius r. After completing the squares for x and y coefficients, we determine the center as (2, -5/2) and radius as 1.

Explanation:

The provided equation is 2x2 + 2y2 - 8x + 10y + 2 = 0.Let's rewrite it in the form of an equation for a circle, which is (x-h)^2 + (y-k)^2 = r^2, where (h,k) represents the center of the circle and r represents the radius:

First, we group the terms related to x and y separately like this: 2(x2- 4x) + 2(y2 + 5y) +2 = 0.

Now, re-arrange the terms to complete the square: 2[(x-2)^2 - 4] + 2[(y+5/2)^2 - (5/2)^2] + 2 = 0.

Re-arrange again, this time to make it equate to zero: (x-2)^2 + (y+5/2)^2 = 1. Hence, the circle's center (h,k) is at (2, -5/2) and the radius (r) is the square root of 1, which is 1.

Learn more about Circle in Standard Form here:

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Answer:

first group x's with x's and y's with y's

then complete the squra with x's and y's

2x^2-8x+2y^2+10y+2=0

2(x^2-4x)+2(y^2+5y)+2=0

take 1/2 of linear coeficient and square

-4/2=-2, (-2)^2=4

5/2=2.5, 2.5^2=6.25

add that and negative inside

2(x^2-4x+4-4)+2(y^2+5y+6.25-6.25)+2=0

factor perfect squares

2((x-2)^2-4)+2((y+2.5)^2-6.25)+2=0

distribute

2(x-2)^2-8+2(y+2.5)^2-12.5+2=0

2(x-2)^2+2(y+2.5)^2-18.5=0

add 18.5 both sides

2(x-2)^2+2(y+2.5)^2=18.5

divide both sides by 2

(x-2)^2+(y+2.5)^2=9.25

that is a circle center (2,-2.5) with radius √9.25

A yoga studio sells monthly memberships. the function f(x) = −x2 50x − 264 models the profit in dollars, where x is the number of memberships sold. determine the zeros, and explain what these values mean in the context of the problem.

Answers

The zeros represent the number of monthly memberships where no profit is made; x = 6, x = 44.

To determine the zeroes, calculate:

The function we have is: $f(x) = -x^(2) +50x-264$

That models the profit in dollars, where $x$ is the number of memberships sold.

In order to get the zeros we'll use the quadratic formula:

$x_(1,2) =(-b+-(b^(2)-4ac) )/(2a) \n$

For,

$a=-1,b=50,c=-264: x^(1,2) =\frac{-50+-\sqrt[]{50^(2) -4(-1)(-264)} }{2(-1)} \nx_(1) =\frac{-50+\sqrt[]{50^(2) -4(-1)(-264)} }{2(-1)} =\frac{-50+\sqrt[]{50^(2) -4*1*264} }{2(-1)}=\frac{-50+\sqrt[]{1444} }{-2} =6\nx_(2) =\frac{-50+\sqrt[]{50^(2) -4(-1)(-264)} }{2(-1)} =\frac{-50-\sqrt[]{50^(2) -4*1*264} }{2(-1)}=\frac{-50-\sqrt[]{1444} }{-2} =44\n$

So, the zeroes are $x=6, x=44$ .

Therefore, the zeros represent the number of monthly memberships where no profit is made; x = 6, x = 44.

Know more about a function here:

brainly.com/question/25638609

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The complete question is given below:

A yoga studio sells monthly memberships. The function f(x) = −x2 + 50x − 264 models the profit in dollars, where x is the number of memberships sold.

Determine the zeros, and explain what these values mean in the context of the problem.

x = 6, x = 44; The zeros represent the number of monthly memberships that produce a maximum profit.

x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made.

x = 25, x = 361; The zeros represent the number of monthly memberships where no profit is made.

x = 25, x = 361; The zeros represent the number of monthly memberships that produce a maximum profit.

Answer:

The answer is: x = 6, x = 44; The zeros represent the number of monthly memberships when no profit is made.

Write the explicit rule.

-21, -51, -81, -111, -141

Answers

Answer:

aₙ = - 30n + 9

Step-by-step explanation:

You can tell this is an arithmetic sequence, as there is a difference of 30 between each value. Therefore the equation we will use here is aₙ = a₁ + (n - 1)d.

aₙ = a₁ + (n - 1)d

= - 21 + (n - 1) * - 30

= - 21 - 30n + 30

= - 30n + 9

Your solution would be option d. aₙ = - 30n + 9

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