For time t≥1
, the position of a particle moving along the x-axis is given by p(t)=t√−2. At what time t in the interval 1≤t≤16
is the instantaneous velocity of the particle equal to the average velocity of the particle over the interval 1≤t≤16

Answers

Answer 1

The time interval at which instantaneous velocity of the particle equal to the average velocity of the particle is t = 225

Given data ,

To find the instantaneous velocity of the particle, we need to take the derivative of the position function:

p'(t) = 1/(2√t)

To find the average velocity over the interval [1, 16], we need to find the displacement and divide by the time:

average velocity = [p(16) - p(1)] / (16 - 1)

= [√16 - 2 - (√1 - 2)] / 15

= (2 - 1) / 15

= 1/15

Now we need to find a time t in the interval [1, 16] such that p'(t) = 1/15

On simplifying the equation , we get

1/(2√t) = 1/15

Solving for t, we get:

t = 225

Hence , at time t = 225, the instantaneous velocity of the particle is equal to the average velocity over the interval [1, 16]

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Related Questions

The length, in inches, of a box is 3 inches less than twice its width, in inches. Which of the following gives the length, l inches, in terms of the width, w inches, of the box?


l = w + 3


l = w + 3


l = w – 3


l = 2w + 3


l = 2w – 3

Answers

Answer:

l = 2w – 3

Step-by-step explanation:

Answer:

l = 2w – 3

Step-by-step explanation:

Hope this helps!!!

What is the domain of the function graphed below?

Answers

Answer:

Positive infinite to negative infinite

Step-by-step explanation:

Last year, Diane opened an investment account with S6400. At the end of the year, the amount in the account had increased by 26%.
(a) Fill in the blank to write the year-end amount in terms of the original amount. Write
your answer as a decimal.
Year-end amount =. XOriginal amount
(1) Use your answer in part (ə) to determine the year-end amount in Diane's account
Year-end amount: $

Answers

Answer:

Your answer is.....

8064$

Mark it as brainlist answer . follow me for more answer.

Step-by-step explanation:

Jim is designing a seesaw for a children's park. The seesaw should make an angle of 30° with the ground, and the maximum height to which it should rise is 1 meter, as shown below: A seesaw is shown with one end on the ground and the other in the air. The seesaw makes an angle of 30 degrees with the ground. What is the maximum length of the seesaw? (6 points) Group of answer choices 1.4 meters 2 meters

Answers

The sine rule is the ratio of perpendicular to the hypotenuse, then the maximum length of the seesaw will be 2 meters.

What is a right-angle triangle?

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.

Jim is designing a seesaw for a children's park.

The seesaw should make an angle of 30° with the ground, and the maximum height to which it should rise is 1 meter.

Then the maximum length of the seesaw will be

We know that the sine rule is given as

[tex]L = \dfrac{1 }{ \sin 30} \\\\ L = \dfrac{1}{1/2} \\\\L = 2[/tex]

More about the right-angle triangle link is given below.

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Answer:

2 meters

Step-by-step explanation:

A survey was given to a random sample of the residents of a town to determine whether they support a new plan to raise taxes in order to increase education spending. The survey reported a confidence interval that between 16.5% and 25.5% of the residents supports the plan. What is the margin of error on the survey? Do not write \pm± on the margin of error.

Answers

Answer:

9

Step-by-step explanation:

The confidence interval is related to margin of error ; according to the relation :

Confidence interval = mean ± margin of error

Margin of Error = (upper boundary value - lower boundary value)

Confidence interval = 16.5% and 25.5%

Margin of Error = (25.5% - 16.5%)

Margin of Error = ±9

The margin of error on the survey is 9.

We know that

Confidence interval = mean ± margin of error

And,

Margin of Error = (upper boundary value - lower boundary value)

We have Confidence interval between 16.5% and 25.5%.

upper boundary value = 25.5%

lower boundary value = 16.5%

So, Margin of Error

= 25.5% - 16.5%

=9

Therefore, Margin of Error is 9.

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If the Federal Reserve buys $40,000 in Treasury bonds from a bank at 6%
interest, what is the immediate effect on the money supply?
A. It is decreased by $40,000
B. It is increased by $40,000
C. It is decreased by $2400
D.it is increased by $2400

Answers

Answer:

The answer would be it would increase by 40,000

The answer would be B it is increased by 40,000

Please help me with this

Answers

Answer:

1/5

Step-by-step explanation:

Hi there!

To find the answer, use inverse operations to solve.

Multiply 7/15 by 3/7 to isolate the unknown number.

7/15 * 3/7 is equal to 0.2, which can be simplified into fraction form as 1/5.

I hope this helps!

:)

Harold cut 18 1/2 noches of ropero that was 60 inches long how much is the length of the remaining rope un inches written un decimals f From

Answers

Answer:

41.5

Step-by-step explanation:

If you do 60- 18.5 (1/2 = 0.5), you get about 41.5 inches left of the rope

Expand and combine like terms.
(765 – 46)(765 + 46)

Answers

Answer:

587,341

Step-by-step explanation:

(I'm hoping this is what you mean by expand)

(765 – 46)(765 + 46)

First, multiply 765 by 765 = 585,225

Second, multiply 765 by 46 = 35,190

Third, multiply -46 by 765 = -35,190

Fourth, multiply -46 by 46 = -2,116

The second and third answers (35,190 and -35, 190) will cancel each other out. Then, just subtract -2,116 from 585,225.

585,225 - (-2,116) = 585,225 + 2,116 = 587,341

Evaluate the expression when a=3 and b=-6.
-a +6b

Answers

Answer:

Step-by-step explanation:

-a + 6b = -3 + 6 * (-6) = -3 - 36 = -39

Substitute the values in:

-a + 6b

-(3) + 6(-6)

-3 + (-36)

= -39

direction: find the quotiend​

Answers

Answer:

broo this is easy check the comments the on yo tail

Step-by-step explanation:

help me please will mark you brainliests ​

Answers

Answer:

tommorow what time exam you have you help me with answers iil help you back

Step-by-step explanation:

your answer is 180-2x hope it helps u

Add. (15w - 6x) and (6x + 20w)​

Answers

Answer:

35w

Step-by-step explanation:

15w-6x+6x+20w

collect like terms

15w+20w-6x+6x

=35w

I don’t really understand could you help

Answers

Answer:

M: (-7, -3)

A: (0, -3)

T: (0, -8)

Step-by-step explanation:

each of the points are associated with a letter. you can find the points by looking at the points it matches up with in the formatting of (x,y)

for example, for M, you can see that the dot on the x axis seems to be hovering below -7, on the y axis, it seems to be hovering next to -3. therefore, its (-7,-3)

If the temperature outside is 60 degrees at 6 pm and then drops by 15% at 10 pm, what is the temperature at 10 pm?

Answers

Answer:

51 degrees

Step-by-step explanation:=Given data

Temperature at 6pm = 60 degrees

percent drop= 15%

= 15/100*60

=0.15*60

=9 degrees

Hence the temperature at 10 pm is 60-9= 51 degrees

Find the product.
5
----
8

of

2
----
4

Answers

Answer:

5/16

Step-by-step explanation:

10/32=5/16

4. Consider the right triangle below.
If the perimeter is 1,013 units, find the value of x and the area of the
triangle.
16x + 27
14x - 45
25x
The value of x is
The area is
square units.

Answers

Answer:

16x+27+14x-45+25x=1013 units

X= 18.75

Area= b × h × (1/2)

A= 1/2 × 327 × 217.5 = 35561.25 units^2

Answers:

x = 1031/55 = 18.74545 approximatelyarea = 35,542.92 square units approximately

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

Explanation:

The perimeter is the sum of the exterior sides. We'll add up these three sides

16x+2714x-4525x

and set the sum equal to the perimeter 1013

The equation we need to solve is

(16x+27)+(14x-45)+(25x) = 1013

Solving for x leads to...

(16x+27)+(14x-45)+(25x) = 1013

16x+27+14x-45+25x = 1013

(16x+14x+25x)+(27-45) = 1013

55x-18 = 1013

55x = 1013+18

55x = 1031

x = 1031/55

x = 18.74545 approximately

-----------------------------

Use this x value to find the length of each side. I'll use the decimal form of x. We get the following side lengths:

16x+27 = 16*(18.74545) + 27 = 326.927214x - 45 = 14*(18.74545) - 45 = 217.436325x = 25*(18.74545) = 468.63625

Those values are approximate.

We can then find the area of the triangle

area = (1/2)*base*height

area = (1/2)*(326.9272)*(217.4363)

area = 35,542.92036868

area = 35,542.92

The area is approximate as well.

Find the slope when given (2,3) (3,5) plz

Answers

(y2-y1)/(x2-x1)
=(5-3)/(3-2)
=2/1
=2

so the slope is 2
hope this helps !
Answer:

The slope is 2.

Find the mean then the mean absolute deviation (MAD) of the following data set Round your answer to two decimal places if necessary
3, 1, 5, 4, 8,6

Answers

Rounded answers (are in parentheses )
Mean-4.5 (5)
Median-4.4 (5)
Mode-3,1,5,4,8,6
Range-7
(MAD)-1.83 (rounded 2)

find the value for x and y (no decimals

Answers

Answer:

x=6

y=3r3

Step-by-step explanation:

[tex]\frac{x}{sin90} =\frac{x}{sin60} =\frac{3}{sin3}\\x=6\\y=3\sqrt{3}=3r3[/tex]

Express as a trinomial. (x+3)(3x-1)

Answers

Answer:

3x^2+8x-3

Step-by-step explanation:

(x+3)(3x-1)

x*3x + x*(-1) + 3x*3 + 3*(-1)

x*3x = 3x^2

x*(-1) + 3x*3 = -x+9x = 8x

3*(-1) = -3

= 3x^2+8x-3

The expression for the trinomial ( x + 3 ) ( 3x - 1 ) is  [tex]3x^{2} + 8x - 3[/tex]

Given data:

The expression is represented as (x + 3)(3x - 1)

To express the product of (x + 3)(3x - 1) as a trinomial, perform the multiplication.

Using the FOIL method (First, Outer, Inner, Last), we multiply the terms:

(x + 3)(3x - 1) = x(3x) + x(-1) + 3(3x) + 3(-1)

Simplifying further:

[tex]3x^{2} - x + 9x - 3[/tex]

Combining like terms:

[tex]3x^{2} + 8x - 3[/tex]

Hence, the expression (x + 3)(3x - 1) can be expressed as the trinomial [tex]3x^{2} + 8x - 3[/tex] .

To learn more about polynomial equations, refer:

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Having trouble solving this:

Answers

Answer:

The answer is 24*(1/5)........

Answer:

the answer is D) 121/500

Step-by-step explanation:

The area of triangle ABC is?

Answers

Answer:

[tex] A(\triangle ABC) =17.5 \: {units}^{2} [/tex]

Step-by-step explanation:

AB = 4 - (-3) = 4 + 3 = 7 units

BC = 3 - (-2) = 3 + 2 = 5 units

[tex]A(\triangle ABC) = \frac{1}{2} \times AB\times BC \\ \\ A(\triangle ABC) = \frac{1}{2} \times 7\times 5 \\ \\ A(\triangle ABC) = \frac{1}{2} \times 35 \\ \\ A(\triangle ABC) =17.5 \: {units}^{2} [/tex]

El perímetro de un rombo es igual al de un pentagono regular más 9, y la medida del lado del rombo es el doble de lo que mide un lado del pentagono. ¿Cuánto miden los lados de cada figura?

Answers

Answer:

Rombo es 6

Pentágono es 3

Step-by-step explanation:

Formula del perímetro de un rhombus es 4a

Formula del perímetro de un pentágono es 5b

La pregunta dice

4a = 5b + 9

Otra vez, la pregunta dice la medida del lado del rombo es el doble de lo que mide un lado del pentagono. Entonces,

a = 2b

Si

4a = 5b + 9 y

a = 2b, entonces que

4(2b) = 5b + 9

8b = 5b + 9

8b - 5b = 9

3b = 9

b = 9/3

b = 3

si, b = 3, tan

a = 2(3)

a = 6

Entonces, la medida del lado del rombo es 6 y la medida del lado del pentágono es 3

What is the value of x?

Answers

Answer:

possibly 4 if not I'm sorry

HELP PELASE ASAPppppp

Answers

Answer:

(a)[tex]\frac{d}{a}=\frac{a}{f}[/tex]

(d)[tex]\frac{e}{c}=\frac{c}{f}[/tex]

(b)[tex]\frac{d}{b}=\frac{b}{e}[/tex]

Step-by-step explanation:

All right triangles are similar

When two triangles are similar then the ratio  of their corresponding sides are equal.

Using the property

[tex]\triangle ABC\sim \triangle DBA[/tex]

[tex]\frac{BC}{AB}=\frac{AB}{BD}[/tex]

[tex]\frac{e}{c}=\frac{c}{f}[/tex]

[tex]\triangle ACD\sim\triangle BAD[/tex]

[tex]\frac{CD}{AD}=\frac{AD}{BD}[/tex]

[tex]\frac{d}{a}=\frac{a}{f}[/tex]

[tex]\triangle ACD\sim \triangle BCA[/tex]

[tex]\frac{CD}{AC}=\frac{AC}{BC}[/tex]

[tex]\frac{d}{b}=\frac{b}{e}[/tex]

Correct options are

(a)[tex]\frac{d}{a}=\frac{a}{f}[/tex]

(d)[tex]\frac{e}{c}=\frac{c}{f}[/tex]

(b)[tex]\frac{d}{b}=\frac{b}{e}[/tex]

ANSWER ASAP GIVING BRAINLIEST FIVE STARS AND A HEART I ONLY NEED A FEW SENTENCES!
Please answer the following essay question:
An isosceles triangle has two congruent angles. Write an expression to represent the measure of the third angle of the triangle. Explain.

Answers

Answer:

third angle =180-two congruent angles. is expression.

There were 60 students enrolled in Grade 5 last year. If 66 students are enrolled in the same grade level this year, what is the percentage increase in the number of Students?

Answers

There is a 10% increase

There are 6 more students this year than there were last year.

If you find what 10% of 60 is and add that to 60, you'll find that it'll equal 66.

//

[tex]60 \times 0.10 = 6[/tex]

[tex]10\% \: of \: 60 \: is \: 6[/tex]

[tex]60 + 6 = 66[/tex]

Yep here we go again:

In the diagram below, the red angle angle YAK and the blue angle angle OAT are both right angles. If angle YAO=23 then what is the measure of angle KAT

If you don't know the answer or not sure, please don't answer it!
Whoever answers it correctly gets brainliest!!

Answers

Answer:

23 degrees

Step-by-step explanation:

90+23-90=23

9514 1404 393

Answer:

  23°

Step-by-step explanation:

Both angles YAO and KAT are complementary to angle OAK, so are congruent.

  ∠YAO = ∠KAT = 23°

A rectangular playground has an area of 3,394 square meters. If the width of the playground is 32 meters, find the length.

Answers

Answer:

106 square

Step-by-step explanation:

Area of rectangle = 3,394 square meters

Width = 32 meters

Length = ?

Area of rectangle = Length * Weight

3,394 = 32 * x

x = 3,394 /32

x = 106.0625

x = 106

The Length is 106 square

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