In a time of t seconds, a particle moves a distance of s meters from its starting point, where s = 6t^2 + 4.
(a) Find the average velocity between t = 1 and t = 1 + k if (i) h = 0.1 (ii) h = 0.01 (iii) h = 0.001 Enter the exact answers.
(i) When h = 0.1, the average velocity between t = 1 and t = 1 + h is m/sec.
(ii) When h = 0.01, the average velocity between t = 1 and t = 1 + h is m/sec.
(iii) When h = 0.001, the average velocity between t = 1 and t = 1 + h is m/sec.
(b) Use your answers to part (a) to estimate the instantaneous velocity of the particle at time t = 1. Round your estimate to the nearest integer. The instantaneous velocity appears to be m/sec.

Answers

Answer 1

Answer:

(a)

i) [tex]V=12.6m/s[/tex]

ii) [tex]V=12.06m/s[/tex]

iii) [tex]V=12.006m/s[/tex]

(b)

[tex]V = 10m/s[/tex]

Step-by-step explanation:

Given

[tex]s = 6t^2 + 4[/tex]

Solving (a): Average velocity between t = 1 and t = 1 + h

When t = 1

[tex]t_1 = 1[/tex]

[tex]s_1 = 6t^2 + 4 = 6 * 1^2 + 4 = 6 + 4 =10[/tex]

i) h = 0.1

When t = 1 + h

[tex]t_2 = 1 + 0.1 = 1.1[/tex]

[tex]s_2= 6t^2 + 4 = 6 * (1.1)^2 + 4 = 11.26[/tex]

Average velocity is then calculated as:

[tex]V = \frac{s_2 - s_1}{t_2 - t_1}[/tex]

[tex]V = \frac{11.26 - 10}{1.1- 1} = \frac{1.26}{0.1} = 12.6[/tex]

[tex]V=12.6m/s[/tex]

ii) h = 0.01

When t = 1 + h

[tex]t_2 = 1 + 0.01 = 1.01[/tex]

[tex]s_2= 6t^2 + 4 = 6 * (1.01)^2 + 4 = 10.1206[/tex]

Average velocity is then calculated as:

[tex]V = \frac{s_2 - s_1}{t_2 - t_1}[/tex]

[tex]V = \frac{10.1206 - 10}{1.01- 1} = \frac{0.1206}{0.01} = 12.06[/tex]

[tex]V=12.06m/s[/tex]

ii) h = 0.001

When t = 1 + h

[tex]t_2 = 1 + 0.001 = 1.001[/tex]

[tex]s_2= 6t^2 + 4 = 6 * (1.001)^2 + 4 = 10.012006[/tex]

Average velocity is then calculated as:

[tex]V = \frac{s_2 - s_1}{t_2 - t_1}[/tex]

[tex]V = \frac{10.012006 - 10}{1.001- 1} = \frac{0.012006 }{0.001} = 12.006[/tex]

[tex]V=12.006m/s[/tex]

Solving (b): Instantaneous velocity at t = 1

When t = 1

[tex]t = 1[/tex]

[tex]s = 6t^2 + 4 = 6 * 1^2 + 4 = 6 + 4 =10[/tex]

Velocity is:

[tex]V = \frac{s}{t}[/tex]

[tex]V = \frac{10}{1}[/tex]

[tex]V = 10m/s[/tex]


Related Questions

A mathematician simplifies the expression mentally.
17.2 (20+45) - (4.75)
What is the best estimate of the value of the expression?
0 381
O 1,114
O 1,844
O 5,521

Answers

Answer:

1,114

Step-by-step explanation:

17.2(65)- (4.75)

1118 - 4.75

1113.25

Answer:

Step-by-step explanation:

1114

Which of the following equations has no solution?
3x + 1 = 2x + 1
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3x + 1 = 3x + 2

Answers

Answer:

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..

Which expression is equivalent to 1/4(2 – 5x + 6)?


Answers

Answer: the answer is CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

C

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A model rocket is launched directly upward at a speed of 28 meters per second from a height of 12 meters. The function f(t) = - 4.9t ^ 2 + 28t + 12, mo models the relationship between the height of the rocket and the time after launch. in seconds When seconds after launch will the rocket hit the ground? Do not round until the final answer. Then round your answer to two decimal places. Provide your answer below:

Answers

Answer:

6.11 seconds

Step-by-step explanation:

Given

[tex]f(t) = -4.9t^2 + 28t + 12[/tex]

Required

When will it hit the ground?

When it hits the ground, f(t) = 0.

So, we have:

[tex]0 = -4.9t^2 + 28t + 12[/tex]

Solve quadratic equation using formula

[tex]t = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]

[tex]t = \frac{-28 \± \sqrt{28^2 - 4*-4.9*12}}{2*-4.9}[/tex]

[tex]t = \frac{-28 \± \sqrt{1019.2}}{-9.8}[/tex]

[tex]t = \frac{-28 \± 31.92}{-9.8}[/tex]

Split

[tex]t = \frac{-28 + 31.92}{-9.8}[/tex] or [tex]t = \frac{-28 - 31.92}{-9.8}[/tex]

[tex]t = \frac{3.92}{-9.8}[/tex] or [tex]t = \frac{-59.92}{-9.8}[/tex]

[tex]t = -0.4[/tex] or [tex]t = 6.11[/tex]

Time can not be negative. So:

[tex]t = 6.11[/tex]

50 POINTS AND BRAINLIEST!

Determine if the graphed function is linear or nonlinear.
Select from the drop down menu to correctly complete the sentence.
The graphed function is

A. Linear
B. Non-linear

Answers

Answer:

its A linear

Step-by-step explanation:

its going upwards and that means its linear and when the end point is going downwards that means its non linear  

Answer:

my answer was incorrect my mistake

HELPP! I"LL GIVE THE FIRST RIGHT ANSWER BRAINLIEST!!!

Answers

Answer:

61

Step-by-step explanation:

Heights of Smith's Adult grandchildren median: 339

Heights of Thompsons' Adult Grandchildren median: 400

400 - 339 = 61

SYSTEM OF EQUATIONS

The sum of three times Sophia's age and twice Nick's age is 73. Twice Sophia's age plus four times Nick's age is 86. How old is Sophia?

Answers

3s+2n=73
2s+4n=86


Multiply top equation by 2 and then subtract second equation

4s=60
Sophia is 15
Nick is 14

A local ice cream shop sells root beer floats for $2.75 and milkshakes for $6. One day the shop sold 10 more root beer floats than milkshakes and made $290. How many root beer floats were sold on this day? How many milkshakes?

Answers

Answer:

30 milkshakes and 40 root beer floats

Step-by-step explanation:

Set up a system of equation (r is root beer and m is milkshake)

2.75r+6m=290

m+10=r

Substitute

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m=30

Now plug in 30 and solve for r

30+10=40

Determine if the equation y = 15(1.35)* represents exponential growth or decay and justify. Hint: Think about the growth and decay equations.​

Answers

Answer:sdfghgfdfghnhgfdfgh

Step-by-step explanatsdfghjhgfghjk

Answer: Exponential growth

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

Explanation:

The equation is in the form y = a*(b)^x

The 'a' is the initial or starting value. In this case, a = 15.

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Since b = 1.35, and 1.35 > 1, this means b > 1 and the given equation represents exponential growth.

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Simplify: -6(x + 5) show work plz

Answers

Answer:

The answer is -6x - 30

Step-by-step explanation:

1) Expand by distributing terms.

[tex] - 6x - 6 \times 5[/tex]

2) Simplify 6 × 5 to 30.

[tex] - 6x - 30[/tex]

Thus, the answer is -6x - 30.

Answer:

-6x - 30

Step-by-step explanation:

Multiply using the distributive property.

-6x - 30

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Use the given area of the base and the height to find the volume of the right rectangular prism, in cubic units.

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Answers

Answer:

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Step-by-step explanation:

I hope this helps! I am sorry if I am wrong!

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

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Answers

Answer:

K = - 6

Step-by-step explanation:

Let's solve your equation step-by-step.

2(4k+5)+3(3−3k)=25

Step 1: Simplify both sides of the equation.

2(4k+5)+3(3−3k)=25

(2)(4k)+(2)(5)+(3)(3)+(3)(−3k)=25(Distribute)

8k+10+9+−9k=25

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−k+19=25

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An item costs $410 before tax, and the sales tax is $24.60.
Find the sales tax rate. Write your answer as a percentage.

Answers

Answer:

$434.60

Step-by-step explanation:

$410.60 added to $24.60 equals $434.60

Solve triangle ABC if a = 19, b = 16, and the m∠A = 61°.


c =

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Answers

Answer:

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Step-by-step explanation:

A=absinγ

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Answers

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Answers

9 x (24 / 12)^2 + 5

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Use the order of operations to know what to simplify first in an expression. P = parenthesis so you simplify what is in parenthesis first. 24/12 = 2, so your first box is 2. The expression now looks like this:
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The next letter is E, which stands for exponents. You square two next. 2^2 = 4 so your next box is 4. The equation now looks like this:

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The next two letters of PEMDAS or MD, which stand for multiplication/division. If you have either or both of these to do in your expression, you do them now. That means you now calculate 9 x 4, which is 36. This leaves you with 36 + 5. Your 3rd box is 36.

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Manuel and Peter are standing 12 ft. apart from each other and looking up at a kite that is flying between them. Manuel is flying the kite on a 65 ft. string at an angle of 70(degrees) with the ground. How far is Peter from the kite?

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Answers

Answer:

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Step-by-step explanation:

Hope this helps

Answer:

Trigonometric Identities and Applications Test Part 1

1. a,c,e

2. B sinx

3.b,d

4. D sec thea

5. b,c

6. A. 0.67

7. A sqrt 6- sqrt2/4

8. A cos^2 47=....

9. B 2+sqrt3/4

10. c,e

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14 D 86.2

15 61.9 ft

16 writen

17. a,d

18. b,c

19 a,d

20 writen

Step-by-step explanation:

took part one and I missed some but it's to help others in need :)

Nick is splitting 4 quarts of ice cream with 9 members of the team. If the ice cream is split​ evenly, how many will each person​ get? Explain.

Answers

Answer:

Each member will get 3 and 1/2 cups or 3.5 cups of ice cream.

A video game store is selling video games 3 for $37.50. How much would they earn if they sold 2?​

Answers

Answer:

25

Step-by-step explanation:

ok so you need to find out how much each game is sold for

First 37.50 divided by 3 and that will equal 12.5

second, you need to find out how much 2 games cost so you  eithermultiply

12.5 by 2 or add 12.5 two times and you will get 25

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Mean = 25


Standard Deviation = 3.8


P(X

Find the value of k.


Round to 2 decimal values.

Answers

Answer:

The normal distribution is explained for the solution of this question.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Mean = 25, Standard Deviation = 3.8

This means that [tex]\mu = 25, \sigma = 3.8[/tex]

So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{X - 25}{3.8}[/tex]

If P(X > k) = a

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If P(X < k) = a

We have to find [tex]X = k[/tex] when Z has a pvalue of a.

Two angles are complementary. The measure of the first is (3x+14) and the measure of the second one is (5x-20). What are the measures of the two angles?

Answers

Answer:

x=17

Step-by-step explanation:Isolate the variable by dividing each side by factors that don't contain the variable. x=17. I hope this helps

Which expression is equivalent to f(x)=6x^2-13x+5

Answers

Answer:

(3x - 5)(2x - 1)

Step-by-step explanation:

6x² - 13x + 5

6x² - (10 + 3)x + 5

6x² - 10x - 3x + 5

2x(3x - 5) - (3x - 5)

(3x - 5)(2x - 1)

Which means, 6x² - 13x + 5 is equivalent to (3x - 5)(2x - 1) or vice versa

Tai has 1/2 gallon of milk left in his
refrigerator. He pours the milk into
glasses that can each hold a 5/64 gallon.
How many glasses can Tai fill
completely with milk?

Answers

Answer:

He can completely fill six glasses, and there will be one glass 2/5 of the way full.

Step-by-step explanation:

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