The Question is above.

Answer:

The maximum acceleration over that interval is [tex]A(6) = 28[/tex].

Step-by-step explanation:

The acceleration of this car is modelled as a function of the variable [tex]t[/tex].

Notice that the interval of interest [tex]0 \le t \le 6[/tex] is closed on both ends. In other words, this interval includes both endpoints: [tex]t = 0[/tex] and [tex]t= 6[/tex]. Over this interval, the value of [tex]A(t)[/tex] might be maximized when [tex]t[/tex] is at the following:

Start by calculating the value of [tex]A(t)[/tex] at the two endpoints:

Apply the power rule to find the first and second derivatives of [tex]A(t)[/tex]:

[tex]\begin{aligned} A^{\prime}(t) &= 3\, t^{2} - 15\, t + 12 \\ &= 3\, (t - 1) \, (t + 4)\end{aligned}[/tex].

[tex]\displaystyle A^{\prime\prime}(t) = 6\, t - 15[/tex].

Notice that both [tex]t = 1[/tex] and [tex]t = 4[/tex] are first derivatives of [tex]A^{\prime}(t)[/tex] over the interval [tex]0 \le t \le 6[/tex].

However, among these two zeros, only [tex]t = 1\![/tex] ensures that the second derivative [tex]A^{\prime\prime}(t)[/tex] is smaller than zero (that is: [tex]A^{\prime\prime}(1) < 0[/tex].) If the second derivative [tex]A^{\prime\prime}(t)\![/tex] is non-negative, that zero of [tex]A^{\prime}(t)[/tex] would either be an inflection point (if[tex]A^{\prime\prime}(t) = 0[/tex]) or a local minimum (if [tex]A^{\prime\prime}(t) > 0[/tex].)

Therefore [tex]\! t = 1[/tex] would be the only local maximum over the interval [tex]0 \le t \le 6\![/tex].

Calculate the value of [tex]A(t)[/tex] at this local maximum:

Compare these three possible maximum values of [tex]A(t)[/tex] over the interval [tex]0 \le t \le 6[/tex]. Apparently, [tex]t = 6[/tex] would maximize the value of [tex]A(t)\![/tex]. That is: [tex]A(6) = 28[/tex] gives the maximum value of [tex]\! A(t)[/tex] over the interval [tex]0 \le t \le 6\![/tex].

However, note that the maximum over this interval exists because [tex]t = 6\![/tex] is indeed part of the [tex]0 \le t \le 6[/tex] interval. For example, the same [tex]A(t)[/tex] would have no maximum over the interval [tex]0 \le t < 6[/tex] (which does not include [tex]t = 6[/tex].)

Answer:

2/3

Step-by-step explanation:

slope =(y1-y2)/(x1-x2)

slope=(1-(-1))/(6-3)

slope =2/3

Answer:

II

Step-by-step explanation:

Quadrant I is +x + y

Quadrant II is -x + y

Quadrant III is -x - y

Quadrant IV is +x -y

Step-by-step explanation:

Let's use the number Zero as a placeholder.

7 in the hundredths place,

0.07

5 in the thousands place,

5000.07

4 in the hundreds place,

5400.07

7a. Write the number.

5400.07

7b. Write in word form.

Five thousand four hundred and seven hundredth

7c. Write in expanded form.

5000 + 400 + 0.07

7d. Write as a fraction.

540007 / 100

Answer: Charles

Step-by-step explanation:

Michael made 19 out of 30 free-throws. This gives 19/30 = 0.63

Larry's free throw average was 0.745.

Charles' was 0.81.

John made 47 out of 86 free-throws. This gives 47/86 = 0.55

The best free-throw shooter was Charles

Answer:

Charles

Step-by-step explanation:

The best free-throw shooter was Charles

Answer:

[tex]\huge\boxed{\sf Option \ 4}[/tex]

Step-by-step explanation:

y = The total cost

x = The number of movie tickets.

So, The equation that represents the function is:

y = 10.25 x

This shows that the total cost is equal to the cost of 1 ticket multiplied by the no. of tickets.

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

23.58

Step-by-step explanation:

Answer:

25 kilometers

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

The GCF of the two terms is the second term: 6k^2. When that is factored out, you have ...

  area = (6k^2)(5k +1)

According to the problem statement, this is interpreted as ...

  width: 6k^2

  length: 5k+1

9514 1404 393

Answer:

  5°

Step-by-step explanation:

The angle for 12 inches of ramp length and the angle for 12 inches of run are very similar. Both are near 4.8°, so are 5° when rounded.

If we say 12 inches of run, then the tangent relation applies.

  Tan = Opposite/Adjacent

  tan(α) = (1 in)/(12 in)

  α = arctan(1/12) ≈ 4.764°

The maximum angle is about 5°.

Answer:

ytviykgti

Step-by-step explanation:

Answer:  x = 2/3y + 4

Hope it helped u,

pls mark as the brainliest

^v^

Answer:

Yes, herbivores, carnivores, and omnivores are consumers.

Hope this helps :)

Answer:

yes it is yes here's your answer for the emanation use search hope it works

Answer:

Infinitely solution exists,

Required solution is, [tex](x_1,x_2,x_3)=(0, 4(1-t),t)[/tex]

Step-by-step explanation:

We have the given equations:

[tex]x_1+2x_2+8x_3=8[/tex]

[tex]x_1+x_2+4x_3=4[/tex]

Here, the augmented matrix is :

[tex]\left[\begin{matrix}1&2&8&8\\1&1&4&4\end{matrix}\right][/tex]

Now, find the echelon form of the augmented matrix.

[tex]=\left[\begin{matrix}1&2&8&8\\0&-1&-4&-4\end{matrix}\right]^{R_1\rightarrow R_2-R_1}[/tex]

[tex]=\left[\begin{matrix}1&0&0&0\\0&-1&-4&-4\end{matrix}\right]^{R_1\rightarrow R_1+2R_2}[/tex]

Therefore, [tex]x_1=0[/tex]

                [tex]-x_2-4x_3=-4[/tex]

             [tex]\Rightarrow x_2=4(1-x_3)[/tex]

Let [tex]x_3=t[/tex], then the required solution is

 [tex](x_1,x_2,x_3)=(0, 4(1-t),t)[/tex]

Answer:

4 + 2g

General Formulas and Concepts:

Pre-Algebra

Distributive Property

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

2(2 + g)

Step 2: Expand

Answer:

exterior: 90 degrees, interior: 360 degrees

Step-by-step explanation:

Answer:

its 6

Step-by-step explanation:

6

Answer:

In ΔECD

<E = <C = <D

using angle sum property of triangle

<E + <C + <D = 180°

<E + <E + <E = 180° ( As <E = <C = <D )

3<E = 180

<E = 60°

NOW

<BCA + <ACE + <ECD = 180 (L. P. A.)

50° + <ACE + 60° =180

110 + <ACE = 180

<ACE = 70°

NOW as

AC = AE

So using property of triangle that angle opposite to equal sides are equal we get

<ACE = <AEC = 70°

In triangle ΔAEC

Now using Angle sum property of triangle

<ACE + <AEC + <CAE = 180°

70° + 70° + x = 180

140 + x = 180

x = 40°

Now in ΔABC

AB = AC

using property of triangle that angle opposite to equal sides are equal

So <ACB = <ABC = 50°

Now using angle sum property of triangle in ΔABC

<ACB + <ABC + <CAB = 180

50 + 50 + y = 180

100 + y = 180

y = 80°

so x = 40° and y = 80°

Answer:

Sum :-    -76   Product :-    768

Step-by-step explanation:

Answer:

y= -2x + 9

Step-by-step explanation:

I got 2x because you use rise over run. As you can see in the image, the slope goes up two and to the left one ( 2x). It's plus 9 because that where it intersects the 9 on the y-intercept. The slope is negative because the line is going down from left to right ( always read it from left to right).

I hope this helps. I'm not that great at explaining so....:)

Answer:

2x+y-9=0

Step-by-step explanation:

let's take two co ordinates

(X1,y1)=(4,1)

(X2,y2)=(3,3)

Equation using two point :

(y-y1)/(y2-y1)=(x-x1)/(x2-x1)

plug in the values,(y-1)/(3-1)=(x-4)/(3-4)

(y-1)/2=(x-4)/-1

-1*(y-1)=(x-4)*2

-y+1=2x-8

0=2x+y-9

2x+y-9=0

Answer: {4, 14, 24, 34, 44}

Step-by-step explanation:

A general number can be written as:

aₙ*10ⁿ + ... + a₂*10² + a₁*10¹ + a₀*10⁰ + a₋₁*10⁻¹ ...

Where the a₁ coefficient is the "unit" of a number.

For example, the number 145.2 can be written in this form as:

1*10² + 4*10¹ + 5*10⁰ + 2*10⁻¹

Then the numbers having a 4 in the unit place, will be the numbers that have the digit 4 just at the left of the decimal point.

the set of natural numbers having 4 in the unit place, that also are between 1 and 50 are:

{4, 14, 24, 34, 44}

Answer:

y=4

Step-by-step explanation:

Step-by-step explanation: Input is the same as the x term.

If the input is -2, we substitute a -2 in for x.

So we have y = 2(-2) + 8 or y = -4 + 8 which is 4.

So the output or the y term is 4.

Answer:

The value of x = 24.4 units.

Step-by-step explanation:

Given

For a right-angled triangle with sides a and b, the hypotenuse  c is defined as

[tex]c=\sqrt{a^2+b^2}[/tex]

substituting c = x, a = 14 and b = 20

[tex]c=\sqrt{14^2+20^2}[/tex]

[tex]c=2\sqrt{149}[/tex]

[tex]c = 24.4[/tex] units

Therefore, the value of x = 24.4 units.

Answer:

Yes it can have the lengths 1, 5 and 5

Answer:

x=8

Step-by-step explanation:

∠B=∠A

Base Angle Thm/ Def. of Iso.

72=9x

x=8

Answer:

the median is 45

Step-by-step explanation:

The computation of the median is as follows:

First arrange in a sequential order

34, 50, 44, 45, 45, 60, 57, 75

Now as we can see that there are 8 numbers

= n ÷ 2

= 8 ÷ 2

= 4 number

= 45

Hence, the median is 45

The same is relevant and considered too

Answer:

8 29/42

Step-by-step explanation:

5/6 + 7 6/7 = 35/42 + 7 36/42 = 7 71/42 = 8 29/42

Answer:

The ball will be the 7 ft high at 2 different times.

Step-by-step explanation:

The height in meters of the ball is given by the following equation:

[tex]h(t) = -16t^2 + 25t[/tex]

7 feet high

The height, by the equation, is given in meters, so we have to work in meters. Since each feet has 0,3048 meters, 7 feet have have 2.1336 meters. So, we have to solve the following equation

[tex]2,1336 = -16t^2 + 25t[/tex]

[tex]16t^2 - 25t + 2,1336 = 0[/tex]

At how many different times will the ball be 7 ft. High?

We have to find the number of solutions for the equation above.

It is given according to the value of [tex]\Delta = b^2 - 4ac[/tex]. If it is positive, there are two solutions, zero one solution and negative no solutions.

In this equation [tex]a = 16, b = -25, c = 2.1336[/tex]. So

[tex]\Delta = b^2 - 4ac = (-25)^2 - 4*16*2.1336 = 488[/tex]

Since the coefficient is positive, the ball will be the 7 ft high at 2 different times.