Use the graph of y=-2(x-3)^2+2 to find the vertex. Decide whether the vertex is a maximum or a minimum point.

Use The Graph Of Y=-2(x-3)^2+2 To Find The Vertex. Decide Whether The Vertex Is A Maximum Or A Minimum

Answers

Answer 1

Answer: B. Vertex is a maximum point at (3, 2)

The vertex is the point at the peak of the graph: (3, 2)Since the graph opens downward, it's the maximum point

Related Questions

Find the solution of the differential equation that satisfies the given initial condition. (dP)/(dt)

Answers

Answer:

[tex]P = (\frac{1}{3}t^\frac{3}{2} + \sqrt 2 - \frac{1}{3})^2[/tex]

Step-by-step explanation:

Given

[tex]\frac{dP}{dt} = \sqrt{Pt[/tex]

[tex]P(1) = 2[/tex]

Required

The solution

We have:

[tex]\frac{dP}{dt} = \sqrt{Pt[/tex]

[tex]\frac{dP}{dt} = (Pt)^\frac{1}{2}[/tex]

Split

[tex]\frac{dP}{dt} = P^\frac{1}{2} * t^\frac{1}{2}[/tex]

Divide both sides by [tex]P^\frac{1}{2}[/tex]

[tex]\frac{dP}{ P^\frac{1}{2}*dt} = t^\frac{1}{2}[/tex]

Multiply both sides by dt

[tex]\frac{dP}{ P^\frac{1}{2}} = t^\frac{1}{2} \cdot dt[/tex]

Integrate

[tex]\int \frac{dP}{ P^\frac{1}{2}} = \int t^\frac{1}{2} \cdot dt[/tex]

Rewrite as:

[tex]\int dP \cdot P^\frac{-1}{2} = \int t^\frac{1}{2} \cdot dt[/tex]

Integrate the left hand side

[tex]\frac{P^{\frac{-1}{2}+1}}{\frac{-1}{2}+1} = \int t^\frac{1}{2} \cdot dt[/tex]

[tex]\frac{P^{\frac{-1}{2}+1}}{\frac{1}{2}} = \int t^\frac{1}{2} \cdot dt[/tex]

[tex]2P^{\frac{1}{2}} = \int t^\frac{1}{2} \cdot dt[/tex]

Integrate the right hand side

[tex]2P^{\frac{1}{2}} = \frac{t^{\frac{1}{2} +1 }}{\frac{1}{2} +1 } + c[/tex]

[tex]2P^{\frac{1}{2}} = \frac{t^{\frac{3}{2}}}{\frac{3}{2} } + c[/tex]

[tex]2P^{\frac{1}{2}} = \frac{2}{3}t^\frac{3}{2} + c[/tex] ---- (1)

To solve for c, we first make c the subject

[tex]c = 2P^{\frac{1}{2}} - \frac{2}{3}t^\frac{3}{2}[/tex]

[tex]P(1) = 2[/tex] means

[tex]t = 1; P =2[/tex]

So:

[tex]c = 2*2^{\frac{1}{2}} - \frac{2}{3}*1^\frac{3}{2}[/tex]

[tex]c = 2*2^{\frac{1}{2}} - \frac{2}{3}*1[/tex]

[tex]c = 2\sqrt 2 - \frac{2}{3}[/tex]

So, we have:

[tex]2P^{\frac{1}{2}} = \frac{2}{3}t^\frac{3}{2} + c[/tex]

[tex]2P^{\frac{1}{2}} = \frac{2}{3}t^\frac{3}{2} + 2\sqrt 2 - \frac{2}{3}[/tex]

Divide through by 2

[tex]P^{\frac{1}{2}} = \frac{1}{3}t^\frac{3}{2} + \sqrt 2 - \frac{1}{3}[/tex]

Square both sides

[tex]P = (\frac{1}{3}t^\frac{3}{2} + \sqrt 2 - \frac{1}{3})^2[/tex]

If f(1) =160 and f(n+1)=-2f(n),
What is f(4)?

Answers

Answer:

f(n+1=-2f(n)

f(x)=-2f(n)

f(4)

f(4)=-2f(4)

Answer:

f(4) = - 1280

Step-by-step explanation:

Using the recursive rule and f(1) = 60 , then

f(2) = - 2f(1) = - 2 × 160 = - 320

f(3) = - 2f(2) = - 2 × - 320 = 640

f(4) = - 2f(3) = - 2 × 640 = - 1280

Can anyone help me please? I've been trying for so long, but I can't figure out the answer to this problem. Picture attached. Thank you so much.

Answers

Answer:

C

Step-by-step explanation:

Start by simplifying what you can in each radicalfor example, the

∛(xy⁵)= y∛(xy²)

and

∛(x⁷y¹⁷)=x²y⁵∛(xy²)

So know our equation looks like

y∛(xy²)*x²y⁵∛(xy²)

Now because what's inside the radical is the same we can combine them

y⁶x²∛(xy²)²

distribute the square

so

∛(xy²)²=  ∛(x²y⁴)= y∛(x²y)

and finally,

y⁶x²*y∛(x²y)= y⁷x²∛(x²y)

this is equal to option C

Please help me i will give you brainlest

Answers

Answer:

a speaker receive credibility is a combination of competence trustworthiness and caring

A plane flying horizontally at an altitude of 2 miles and a speed of 410 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 5 miles away from the station.

Answers

Answer:

[tex]82\sqrt{21}\text{ or approximately 375.77 miles per hour}[/tex]

Step-by-step explanation:

Please refer to the diagram below. R is the radar station and x is the distance from the station to the plane.

We are given that the plane is flying horizontally at an altitude of two miles and at a speed of 410 mph. And we want to find the rate at which the distance from the plane to the station is increasing when it is five miles away from the station.

In other words, given da/dt = 410 and x = 5, find dx/dt.

From the Pythagorean Theorem:

[tex]a^2+4=x^2[/tex]

Implicitly differentiate both sides with respect to time t. Both a and x are functions of t. Hence:

[tex]\displaystyle 2a\frac{da}{dt}=2x\frac{dx}{dt}[/tex]

Simplify:

[tex]\displaystyle a\frac{da}{dt}=x\frac{dx}{dt}[/tex]

Find a when x = 5:

[tex]a=\sqrt{5^2-2^2}=\sqrt{21}[/tex]

Therefore, dx/dt when da/dt = 410, x = 5, and a = √(21) is:

[tex]\displaystyle \frac{dx}{dt}=\frac{(\sqrt{21})(410)}{5}=82\sqrt{21}\approx 375.77\text{ mph}[/tex]

The rate at which is distance from the plane to the radar station is increasing at a rate of approximately 375.77 miles per hour.

How do you graph this helppp and explain

Answers

Answer:

bottom graph

Step-by-step explanation:

f(x) = |3q-6|

because you have absolute value there are 2 possibilities

y= +(3q-6) and y= -(3q-6)

to find where the graph intersects the x-axis make y=0 because there the y coordinate is 0, so we have...

3q-6 =0 and -3q+6 =0

3q= 6 and -3q =-6

q=2 and q=2

the bottom graph has the intersection with x-axis only at 2, so is the correct one

9514 1404 393

Answer:

  bottom graph shown

Step-by-step explanation:

It can be helpful to rearrange the equation to either of the equivalent forms ...

  f(x) = |3(x -2)|

or ...

  f(x) = 3|x -2|

_____

The first of these forms represents a horizontal compression of the absolute value function by a factor of 3, then a right-shift by 2 units. This matches the bottom graph shown.

__

The second of these forms represents a horizontal right-shift by 2 units, and a vertical expansion by a factor of 3. This matches the bottom graph shown.

__

The attached graph shows the function given here along with the absolute value parent function.

_____

Additional comment

The transformations we're usually interested in are ...

g(x) = k·f(x) . . . . vertically scaled (stretched) by a factor of k

g(x) = f(kx) . . . . .horizontally compressed by a factor of k

g(x) = f(x) +k . . . shifted up by k units

g(x) = f(x -k) . . . . shifted right by k units

In many cases, as here, horizontal scaling and vertical scaling are indistinguishable as to which caused a given effect.

Where does the graph of f(x)=2√-x+2 start?

A. (−2,0)

B. (2,0)

C. (0,2)

D. (0,−2)

Answers

If Im doing my math right I think it’s B. (2,0)

Solve for x in the triangle. Round your answer to the nearest tenth.

Answers

Answer:

7.3 units

Step-by-step explanation:

Hi there!

We're given an angle and one leg of this right triangle and we must solve for the other leg. Given this circumstance, we can use the tangent ratio:

[tex]tan\theta=\frac{opposite}{adjacent}[/tex]

Plug in all values

[tex]tan39=\frac{x}{9}\\9*tan39=x\\7.3=x[/tex]

Therefore, the value of x when rounded to the nearest tenth is 7.3 units.

I hope this helps!

Does the expression represents a positive or negative 3(-2 1/3)

Answers

Answer:

Positive

Step-by-step explanation:

This is an equation, with distribution in it. The number on the outside is positive, and the one inside is negative. Furthermore, since the number on the outside is larger than the one inside, the outcome will be positive.

Answer:

positive

Step-by-step explanation:

when both positive and negative will multiply then will  makes negatives. so negative is correct option.

Calculate the difference and enter it below

-6 - 12

Answers

Answer:

-18

Step-by-step explanation:

Answer: -18 is the difference

Step-by-step explanation:

Evaluate = -18

Which law would you use to simplify the expression?

Answers

Answer:

A. quotient of Powers

Step-by-step explanation:

hope it helps

Answer:

A. Quotient of powers

Step-by-step explanation:

Hope it helps

With a.b.c=1 and a+b+c=1
Prove that:

Answers

Answer:

HOPE IT HELPS PLZ MARK ME BRAINLIEST

Step-by-step explanation:

abc=1

⟹c=1/ab

1/(1+a+1/b)+1/(1+b+1/c)+1/(1+c+1/a)

=1/(1+a+1/b)+1/(1+b+ab)+1/(1+1/ab+1/a)

=b/(1+b+ab)+1/(1+b+ab)+ab/(1+b+ab)

=1+b+ab/(1+b+ab)

=1

What angles can you construct using just a pair of compasses and a ruler?

Answers

Answer:

By using a pair of compasses and a ruler you can draw all angles

Put -3.0-3.45, -15, and -3.15 in order from least to greatest.

Answers

Answer:

-15 -3.45 -3.15 -3.0

Step-by-step explanation:

Drag the label to the correct location on the image

Answers

9514 1404 393

Answer:

  -∞ < y ≤ 12

Step-by-step explanation:

The range is the vertical extent of the graph of the function. Here the function values range from -∞ to a maximum of about 12. An appropriate description is ...

  -∞ < y ≤ 12

This Bar Chart shows the number of DVDs sold at a local music store during one week.

Which measure(s) of central tendency can be used to determine the average number of DVDs sold each day?

A. the median
B. the mean
C. the mean and the median
D. the mode

Answers

Answer:

B. the mean

Step-by-step explanation:

According to the Bar Chart shown, the number of DVDs sold at a local music store during one week are displayed.

Therefore, the measure(s) of central tendency that can be used to determine the average number of DVDs sold each day is the mean.

This is because the mean is the sum total of the number of DVDs sold, divided by the number, which gives the average.

Answer:

The Mean

Step-by-step explanation:

I took the test

What is the range of the given set of ordered pairs?
(9,-2) (4,3) ( 8, 10) (-4, 8)

Answers

Answer:

(-2,3,10,8)

Step-by-step explanation:

eg

(x,y)=(domain,range)

x components are domain and y components are range in the given set of ordered pairs

on the provided graph, plot the points where the following function crosses the x-axis and the y-axis g(x) = -5^x + 5, what does the graph look like?

Answers

Answer:

see image

Step-by-step explanation:

solve 5x^2-2=-12 by taking the square root

Answers

Answer:

[tex]x = \sqrt{-2} = 2i[/tex]

Step-by-step explanation:

[tex]5x^2-2=-12[/tex]

[tex]5x^2 =-10[/tex]

[tex]x^2 =-2[/tex]

[tex]x = \sqrt{-2} = 2i[/tex]

A banner ad created by Jonathan had CTR of 1.5% with 20,000 impression. How many people clicked on the banner ad

Answers

Answer:

300

Step-by-step explanation:

[tex] \frac{1.5}{100} = 20000 \\ 20000 \div 100 = 200 \\ 200 \times 1.5 = 300[/tex]

if A banner ad created by Jonathan had CTR of 1.5% with 20,000 impression then 300 people clicked on the banner ad

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity.

A banner ad created by Jonathan had CTR of 1.5% with 20,000 impression.

We need to find how many people clicked on the banner ad.

Let us find the value of  1.5%  of 20000

Convert 1.5 % to decimal

1.5/100=0.015

Now multiply 0.015 with 20000

0.015×20000

300

Hence, if A banner ad created by Jonathan had CTR of 1.5% with 20,000 impression then 300 people clicked on the banner ad

To learn more on Percentage click:

https://brainly.com/question/28269290

#SPJ5

Evaluate double integral of f(u,v)=∬dudv over region R where R is bounded by v^2-nu=0 , v^2-(n+1)u=0 and uv=n,uv=(n+1). Sketch neat graph and shade the bounded region. Clearly mention the points of intersection. Reverse the order of integration then evaluate. Where n is 100.

Answers

Answer:

5670272728262728227627

Solve the following inequality.
- 202-16
Which graph shows the correct solution?

Answers

Solve the following inequality.

– 202-16
VX
Which graph shows the correct solution?
27 28 29 30 31 32 33 34 35 36 37
27 28 29 30 31 32 33 34 35 36 37
3 4
++
10 11 12 13
5
6
7
9
O
3
4
5
6
7 8
9 10 11 12 13

HELP AGAIN sorry

What is the measure of ∠AOB?

Answers

180°

the question is asking for the measurement of AOB, meaning all three angles (A, O, and B) added together, which boils down to what is the total angle measurements of any given triangle? 180°
if i’m wrong i’m so sorry

The measure of angle ∠AOB is 180°. The correct option from the following is (A).

A turn's angle is quantified using degrees or °. A full turn encompasses 360°. A protractor can be used to determine the size of an angle. The term "acute" refers to an angle smaller than 90°. Obtuse refers to an angle between 90° and 180°. Reflex is an angle larger than 180 degrees. Right angles have an angle of exactly 90 degrees.

A quadrilateral is an enclosed form created by uniting four points, any three of which cannot be collinear. A quadrilateral is a polygon that has four sides, four angles, and four vertices. Let us study more about quadrilaterals' shapes, their characteristics, and the various kinds of quadrilaterals, as well as some examples of quadrilaterals.

For the given quadrilateral, the sum of angles is:

∠A + ∠O + ∠B = ∠AOB

60° + 60° + 60° = 180°

Hence, the correct option is (A).

To learn more about Angle, here:

https://brainly.com/question/17039091

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. a) In a group of 75 students, 20 liked football only, 30 liked cricket only and 18 did not like any of two games? (i) How many of them liked at least one game? (ii) Find the number of students who liked both the games. (iii) How many of them liked football? (iv) How many of them liked cricket? (v) Represent the result in a Venn diagram.​

Answers

i)50

Steps

30+20=50

ii)7

Steps

75-(30+20)-18

=75-(50)-18

=7

iii)20

Steps

From the available data from the question

iv)30

Steps

From the available data from the questionl

v)From the attcged image file

Which property is demonstrated by this expression? 142 x 1 = 142 One Associative Commutative​

Answers

Step-by-step explanation:

It is Associative property, I have seen this somewhere

Graph the solution set to this Inequality.
-2x + 9 < 51 12

Answers

Answer:

X<-2551.5

Step-by-step explanation:

-2x<5112-9

-2x/-2<5103/-2

x<-2551.5

HELPPPP ME ASAP

If f(x) = x2, g(x) = 5x, and h(x) = x +4, find each value.
Find g[h(-2)]

Answers

9514 1404 393

Answer:

  10

Step-by-step explanation:

Put the values where the arguments are and do the arithmetic.

  g(h(-2)) = g(-2+4) = g(2) = 5(2)

  g(h(-2)) = 10

What is 5.071 in words?

Answers

Answer:

Step-by-step explanation:

The number 5.071 written in english words is "five and seventy-one thousandths

Five point zero seventy one

A person is standing close to the edge on a 56 foot building and throws the ball vertically upward. The quadratic function h(t)=-16^2+104t+56 models the balls height above the ground,h(t),in feet, T seconds after it was thrown
what is the maximum height of ball.=
How many seconds did it take to hit the ground=
Please help!

Answers

Answer:

Part 1)

225 feet.

Part 2)

7 seconds.

Step-by-step explanation:

The height h(t) of the ball above the ground after t seconds is modeled by the function:

[tex]h(t)=-16t^2+104t+56[/tex]

Part 1)

We want to determine the maximum height of the ball.

Notice that the function is a quadratic with a negative leading coefficient, so its maximum will be at its vertex point.

The vertex of a parabola is given by:

[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]

In this case, a = -16, b = 104, and c = 56.

Find the x- (or rather t-) coordinate of the vertex. So:

[tex]\displaystyle t=-\frac{(104)}{2(-16)}=\frac{104}{32}=\frac{13}{4}=3.25\text{ seconds}[/tex]

In other words, the ball reaches its maximum height after 3.25 seconds.

To find the maximum height, substitute this value back into the function. Hence:

[tex]\displaystyle h(3.25)=-16(3.25)^2+104(3.25)+56=225\text{ feet}[/tex]

The maximum height of the ball is 225 feet in the air.

Part 2)

We want to find the amount of time it took for the ball to hit the ground.

When the ball hit the ground, its height above the ground is zero. Therefore, we can set h(t) to 0 and solve for t:

[tex]0=-16t^2+104t+56[/tex]

We can simplify a bit. Divide both sides by -8:

[tex]0=2t^2-13t-7[/tex]

We can factor. Find two numbers that multiply to 2(-7) = -14 and add to -13.

-14 and 1 works! Therefore, split the second term into -14 and 1:

[tex]\displaystyle 0=2t^2-14t+t-7[/tex]

Factor out a 2t from the first two terms and group the last two terms:

[tex]0=2t(t-7)+(t-7)[/tex]

Factor by grouping:

[tex]0=(2t+1)(t-7)[/tex]

Zero Product Property:

[tex]2t+1=0\text{ or } t-7=0[/tex]

Solve for each case:

[tex]\displaystyle t=-0.5\text{ or } t=7[/tex]

Since time cannot be negative, we can ignore the first case.

Therefore, it takes seven seconds for the ball to hit the ground.

An arch is in the form of a parabola given by the function h = -0.06d^2 + 120, where the origin is at ground level, d meters is the horizontal distance and h is the height of the arch in meters.
Graph this function on your graphing calculator then complete the following statements.
The height of the arch is: ------- m
The width to the nearest meter, at the base of the arch is ------ m

Answers

Answer:

See attachment for graph

The height of the arch is: 120 m

The width to the nearest meter, at the base of the arch is 22 m

Step-by-step explanation:

Given

[tex]h = -0.06d^2 + 120[/tex]

Solving (a): The graph

See attachment for graph

Variable h is plotted on the vertical axis while variable d is plotted on the horizontal axis.

Solving (b): The height

The curve of [tex]h = -0.06d^2 + 120[/tex] opens downward. So, the maximum point on the vertical axis represents the height of the arch,

Hence:

[tex]height = 120[/tex]

Solving (c): The width

The curve touches the horizontal axis at two different points.

[tex]x_1 = -11[/tex]

[tex]x_2 = 11[/tex]

The absolute difference of both points represents the width.

So:

[tex]Width = |x_2 - x_1|[/tex]

[tex]Width = |11 - -11|[/tex]

[tex]Width = |11 +11|[/tex]

[tex]Width = |22|[/tex]

Hence:

[tex]Width = 22[/tex]

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