(3+\sqrt(2))^(2)-(3-\sqrt(2))^(2)

Step-by-step explanation:

Given the expression for the position of a body moving along the s-axis expressed as;

[tex]s = t^3-27t^2+200t[/tex]

The acceleration of the body function will be gotten by finding the second derivative of the displacement function as shown;

[tex]\frac{ds}{dt} = 3t^2-2(27)t+200\\ \frac{ds}{dt} = 3t^2-54t+200\\\\\\a = \frac{d^2s}{dt^2} = 2(3)t-54\\a = \frac{d^2s}{dt^2} = 6t-54\\[/tex]

First we need to get the time taken when the velocity is zero.

[tex]Given \ v(t) = \frac{ds}{dt} = 3t^2-53t+200\\at \ v(t) = 0\\0 = 3t^2-54t+200\\[/tex]

factorize;

t = 54±√54²-4(3)(200)/2(3)

t = 54±√2916-2400/2(3)

t = 54±√516/6

t = 54±22.72/6

t = 54+22.72/6 and 54-22.72/6

t = 12.79s and t = 5.21s

Get the acceleration;

at t = 12.79

a = 6t-54

a = 6(12.79)-54

a = 76.74-54

a = 22.74m/s²

at t = 5.21

a = 6t-54

a = 6(5.21)-54

a = 31.26-54

a = -22.74m/s²

Hence the body's acceleration each time the velocity is zero are 22.74m/s² and -22.74m/s²

Answer:

36

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Answer:

(3+x)+24

Step-by-step explanation:

24+(3+x)

Since addition is communitive, you could take out the parenthesis.

24+3+x

Hope this helps. Have an AWESOME night!!! :)

Answer:

y=13.50x

Explanation:

Answer:

Step-by-step explanation:

stop the cappppppppppp

Answer:

the sum of 7/8 and -7/8 is zero

Step-by-step explanation:

this is because they cancel each other out

Answer:

Step-by-step explanation:

Answer:

D. 81

Step-by-step explanation:

This answer was confirmed by two people in the comments.

What I did to get this answer was subtract 162 by 81 so the math that I did was to make sure I got the same number as the answers.

[tex]162-81=81[/tex] ☑

[tex]162-72=90[/tex] ☒

[tex]162-162=0[/tex] ☒

[tex]162-324=-162[/tex] ☒

So, therefore the answer is [tex]81[/tex].

I hope this helped you. :)

Answer:

$1.20 per candy bar

Step-by-step explanation:

7.2 ÷ 6 = 1.2

Answer:

So you pretty much just solved your math by yourself :)

Step-by-step explanation:

Answer:

Angle STR = 78°

Step-by-step explanation:

So, since line QS is a straight line, we know that it's 180°. We also know that angles QTR and STR both add up to 180°. That gives us an equation:

20x + 12 + 10x + 33 = 180

Combine like terms

30x + 45 = 180

Subtract 45 from both sides

30x = 135

Divide both sides by 30

x = 4.5

Now we know the value of x. We just need to plug it into angle STR's given value:

10(4.5) + 33 = angle STR

45 + 33 = angle STR

78° = angle STR

Answer:

1

Step-by-step explanation:

i did this in 8th grade so last year. trust me

can i get brainlest

Answer: 2.4 x 10^8

Step-by-step explanation:

Answer: 2.4x10^8

Step-by-step explanation:start from the end and move the decimal point all the time way up to the middle of 2 and 4 and u move 8 times to get there which is how we got the exponent 8

Answer:

The rate of change of the diver's elevation was 10 53/89 ft./min

Step-by-step explanation:

The given parameters are;

The initial elevation of the diver = 0 feet (Ocean surface level)

The depth to which the diver dove = -59 9/10 feet

The rate at which the diver descended = -18.4 feet/minute

The duration the diver spends at the elevation, t₁ = 12 minutes

The depth to which the diver ascended to = -18 9/10 feet

The total time the diver takes so far in the ocean, [tex]t_{(tot)}[/tex] = 19 1/8 minutes

Therefore, we have;

The time it takes the diver to descend to -59 9/10 feet t₂ = -59 9/10/(-18.4) = 3 47/184 minutes

The duration of the divers ascent = [tex]t_{(tot)}[/tex] - t₁ - t₂ = 19 1/8 - 12 - 3 47/184 = 3 20/23 minutes

The rate of change of the divers elevation in ascent = Distance of elevation/Time

The rate of elevation of the divers elevation in ascent = (-18 9/10 - (-59 9/10))/(3 20/23) = 41/(3 20/23) = 943/89 feet/minute = 10 53/89 feet/minute

The rate of change of the diver's elevation = 10 53/89 ft./min ≈ 10.6 ft./min.

2.73

For each pound of walnuts, it costs $2.73.

All you have to do is divide 10.92 by 4.

Answer:

-10

Step-by-step explanation:

Answer:

Slope= − 1.500/2.000

= -0.750

x intercept= 102/3

= 34

y−intercept= 102/4

= 51/2

= 25.50000

Step-by-step explanation:

sorry if this is wrong, I tried!

Answer:

1,820 trout

Step-by-step explanation:

Set up a proportion where x is the number of trout in the lake:

[tex]\frac{7}{25}[/tex] = [tex]\frac{x}{6,500}[/tex]

Cross multiply and solve for x:

25x = 45,500

x = 1820

So, you could expect 1,820 trout to be in the lake.

Answer:

b=80-8t

Step-by-step explanation:

"b" represents the charge remaining

"t" represents the number of hrs that have passed.

"80" is the reference we will be subtracting the hours from.

"8" is the percentage per hour we will be subtracting

therefore, the equation b=80-8t would solve for the remaining battery after "t" number of hours.  

Answer:

4.47, 121/25, 4 17/20, 4.859

More details: U could just change them into decimals bc it’s easier that way but people have different ways so it’s ok that’s just my opinion.

9514 1404 393

Answer:

  the scale drawing is larger

Step-by-step explanation:

The scale tells you that ...

  17 cm on the scale drawing represent 1 mm on the actual object.

17 cm is larger than 1 mm, so the scale drawing is larger.

Answer:

y=3x+8

Step-by-step explanation:

Answer:

The perimeter is 100 feet. This means that all the sides of the shape must add up to equal 100.

x + x + 5 + x - 3 + x + 4 = 100

4x + 5 - 3 + 4 = 100

4x + 6 = 100

4x = 94

x = 94/4

x = 23.5 feet

Answer:

A

Step-by-step explanation:

Answer:

m∠4 = m∠3 = 74° (vertically opposite angles are equal)

m∠8 + m∠3 = 180° (linear pair)

m∠8 + 74° = 180°

m∠8 = 180° - 74°

m∠8 = 106°

m∠7 = m∠8 = 106° (vertically opposite angles are equal)

m∠2 = m∠3 = 74° (alternate interior angles are equal)

m∠1 = m∠2 = 74° (vertically opposite angles are equal)

m∠6 + m∠1 = 180° (linear pair)

m∠6 + 74° = 180°

m∠6 = 180° - 74°

m∠6 = 106°

m∠5 = m∠6 = 106° (vertically opposite angles are equal)

hope it helps you❤

Answer:

x=-144

Step-by-step explanation:

[tex]\frac{x}{6} +12=-12[/tex] subtract 12 on both sides

[tex]\frac{x}{6}=-24[/tex] multiply by six

x=-144

Answer:

16 ft^2

Step-by-step explanation:

If it is a perfect square, all you have to do is find the square root of the area, which in this case, is 16.

Answer:

2

Step-by-step explanation:

This question is incomplete

Complete Question

An arts academy requires there to be 5 teachers for every 90 students and 3 tutors for every 30 students.

How many students does the academy have per​ teacher?Per​ tutor?

How many tutors does the academy need if it has 80 students

Answer:

a) 18 students per teacher

b) 10 students per tutor

c) 8 tutors

Step-by-step explanation:

a) How many students does the academy have per teacher?

5 teachers for every 90 students

Hence,

5 teachers = 90 students

1 teacher = x students

Cross Multiply

5 × x = 1 × 90

5x= 90

x = 90/5

x = 18 students

We have 18 students per teacher

b) How many students Per​ tutor?

3 tutors = 30 students.

1 tutor = x students

3 × x = 30 × 1

x = 30/3

x = 10 students

We have 10 students per tutor

c) How many tutors does the academy need if it has 80 students

3 tutors = 30 students.

30 students = 3 tutors

80 students = x tutors

Cross Multiply

30 × x = 80 × 3

x = 80 × 3/30

x = 8 tutors

The school needs 8 tutors for 80 students.

Answer:

x=3

hope this answers is ok na

Step-by-step explanation:

I am answering blanks left to right and top to bottom.

3x

30 30

-9

-3 -3

x = 3

Answer: 360 degrees

Step-by-step explanation: There are 4 sides in an angle. Substitute that value in for n and u have: (4-2) x180. After doing that, subtract inside the parenthesis and multiply your difference by 180. You should get 360 degrees. I hoped this helped.

Answer:

360!!!!!!!!!!!!!!!!!!!! ;)

Step-by-step explanation: