A snail is traveling along a straight path. The snail's velocity can be modeled by v(t) = 1.4 In 1 +r?) inches per minute for 0 Sis 15 minutes. (a) Find the acceleration of the snail at time t = 5 minutes. (b) What is the displacement of the snail over the interval 0 Sis 15 minutes? (c) At what time 1, OSIS 15, is the snail's instantaneous velocity equal to its average velocity over the interval OSIS 15 ? (d) An ant arrives at the snail's starting position at time i = 12 minutes and follows the snail's path. During the interval 12 s1 s 15 minutes, the ant travels in the same direction as the snail with a constant acceleration of 2 inches per minute per minute. The ant catches up to the snail at time t = 15 minutes. The ant's velocity at time 1 = 12 is B inches per minute. Find the value of B.

Answers

Answer 1

The acceleration of the snail at time t=5 minutes can be found by taking the derivative of the velocity function v(t) with respect to time t.  When the ant catches up to the snail at time t = 15, their displacements are equal, so we have s(15) - s(12) = v_ant(12)(15-12).

(a) The acceleration of the snail at time t=5 minutes can be found by taking the derivative of the velocity function v(t) with respect to time t. Thus, we have a(t) = v'(t) = 1.4/(1+e^(1.4t))^2 * 1.4 = 1.96/(1+e^(1.4t))^2 evaluated at t=5. Plugging in t=5, we get a(5) = 0.0935 inches per minute per minute.

(b) The displacement of the snail over the interval 0 <= t <= 15 minutes can be found by integrating the velocity function v(t) with respect to time t. Thus, we have s(t) = ∫v(t)dt = 1.4ln(1+e^(1.4t)) evaluated from t=0 to t=15. Plugging in these values, we get s(15) - s(0) = 9.335 inches.

(c) To find the time t when the snail's instantaneous velocity equals its average velocity over the interval 0 <= t <= 15 minutes, we need to solve the equation v(t) = (s(15)-s(0))/15. Substituting the expressions for v(t) and s(t), we get 1.4ln(1+e^(1.4t)) = 0.6223t + 0.6223. This equation cannot be solved analytically, so we can use numerical methods to approximate the solution.

(d) Since the snail and ant are traveling in the same direction, the displacement of the ant over the interval 12 <= t <= 15 minutes is equal to the displacement of the snail over the same interval. Thus, we can use the same formula for s(t) as in part (b). We know that the ant has a constant acceleration of 2 inches per minute per minute, so its velocity at time t = 12 is given by v_ant(12) = B + 2(12-12) = B. When the ant catches up to the snail at time t = 15, their displacements are equal, so we have s(15) - s(12) = v_ant(12)(15-12). Substituting the expressions for s(t) and v_ant(12), we get 1.4ln(1+e^(1.415)) - 1.4ln(1+e^(1.412)) = 3B. Solving for B, we get B = (1.4ln(1+e^(21))-1.4ln(1+e^(16)))/3.

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Related Questions

Calculate the amount of work done if you use a 150N force to push a 50kg box 5m across the kitchen floor.

Answers

Answer:

750 J

Step-by-step explanation:

Find the maeasure of the exterior angle in the figure

Answers

Answer:

the answer would be 5b as the exterior angle is subdivided with the co efficient

Step-by-step explanation:

PLZZZZZ HELP ME!
It’s math btw

Answers

Answer:

1. 9/10

2. 15/16

4. 3/5

5. 3/5

Step-by-step explanation:

1. 7/10 + 2/10 = 9/10

2. 13/16 + 2/16 = 15/16

4. 7/15 + 2/15 = 9/15 = 3/5

5. 9/20 + 3/20 = 12/20 = 3/5

Answer: 1 r1 for second

Step-by-step explanation: 13/16+2/16=15/16 divide 15/16 gets 1 r1

The product of two numbers is 4 2/9, if one of the number is 38, find the number

Answers

Answer:

let x and y be the two number then according to question ,

xy=4 2/9

or, xy= 38/9

if one of the number is 38 then,

38x=38/9

or, x= 1/9 is the correct ans.

The Hiking Club is on a trip to hike up a mountain. The members increased their elevation 290 feet during their hike
this morning. Now they are at an elevation of 450 feet.

a. Explain how to find their elevation before the hike.

b. Han says the equation e + 290 = 450 describes the situation.
What does the variable e represent?

C. Han says that he can rewrite his equation as
e = 450 + -290 to solve for e. Compare Han's strategy to your
strategy for finding the beginning elevation.

Answers

Answer:

Step-by-step explanation:

A. Subtract 290 from 450, 450-290= 160

B. The variable e represents the elevation before they started the hike

C. 450+-290= 450-290

The requried elevation before the hike is given as 160 feet and the required equation model of the situation is e + 290 = 450 where e represents the elevation before the hike.

What are equation models?

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

a. To find the members' elevation before the hike, we can subtract the increase in elevation from their current elevation. So, their elevation before the hike would be 450 - 290 = 160 feet.

b. In the equation e + 290 = 450, the variable "e" represents the members' elevation before the hike.

c. Han's strategy for finding the beginning elevation involves adding -290 to both sides of the equation e + 290 = 450 to get e = 450 + -290. This is equivalent to subtracting 290 from both sides of the equation e + 290 = 450. Both strategies result in the same equation, e = 160, which tells us that the members' elevation before the hike was 160 feet.

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ANSWER QUICKKK
HELP !!!!! i

Answers

Answer:

its B

Step-by-step explanation:

find the value and add them together

Huey is reading a book that is 697 pages long.
He tells a friend that he is about 3/4 of the way done.

About how many more pages must Huey read before he finishes the book?

Answers

Answer:

700 books huey finish he your answer

Answer:

175 pages

Step-by-step explanation:

Answer:

. 175

Step-by-step explanation:

There are 2 ways that we can find the answer to this question:

1. Take 1/4 of 697

2. Take 3/4 of 697 and minus the product from 697.

Let's do it both ways:

If we are doing it the first way it would look like this:

(1/4)(697) = 175

Note that we get 1/4 because Huey already read 3/4 of the book so he has 1/4 left.

The second way would look like this:

(3/4)(697) = 523

679 - 523 = 174 (roughly 175)

Therefore, the answer to your question would be . 175. pls mark brainliest

How many LaTeX: \frac{1}{3}1 3 inch cubes does it take to fill a box with width LaTeX: 2\frac{2}{3}2 2 3 inches, length LaTeX: 3\frac{1}{3}3 1 3 inches, and height LaTeX: 2\frac{1}{3}2 1 3 inches?

Answers

Answer:

186.7 cubes

Step-by-step explanation:

How many LaTeX: \frac{1}{3}1 3 inch cubes does it take to fill a box with width LaTeX: 2\frac{2}{3}2 2 3 inches, length LaTeX: 3\frac{1}{3}3 1 3 inches, and height LaTeX: 2\frac{1}{3}2 1 3 inches?

Step 1

We find the volume of the box

= Length × Width × Height

Length = 3 1/3 inches = 10/3 inches

Width = 2 2/3 inches = 8/3 inches

Height = 2 1/3 inches = 7/3 inches

The volume of the box =

10/3 inches × 8/3 inches × 7/3 inches

= 560/9 cubic Inches

= 62 2/9 cubic inches

Step 2

How many 1/3 inch cubes would fill the box.

This is calculated as:= 62 2/9 cubic inches/ 1/3 inches

= 560/9 ÷ 1/3

= 560/9 × 3/1

= 186.66666667 cubes

Approximately = 186.7 cubes

Write an explicit and recursive rule for the geometric sequence -5, 10, -20, 40… and use it to find the 12th

Answers

Answer:

See solutions below

Step-by-step explanation:

Given the sequence -5, 10, -20, 40...

The nth term of the GP is expressed as;

Tn = ar^n-1

a is the first term

r is the common ratio

n is the number of terms

From the sequence, a = -5

r = 10/-5 = -20/10 = -2

Substitute

Tn = -5(-2)^n-1

This gives the explicit formula

For recursive;

a1 = -5

a2 = 10 = -2(-5) = -2a1

a3 = -20 = -2(10) = -2a2

From the shown sequence, we can see that;

an = -2an-1

This gives the recursive formula

Get the 12th term;

Using the explicit formula

T12 = -5(-2)^12-1

T12 = -5(-2)^11

T12 = -5(-2048)

T12 = 10240

Hence the 12th term is 10240

hellppp fast plzzzzzz​

Answers

i cant see it that much

Answer:

49? I think

Step-by-step explanation:

what is the center of the circle?
(-5,-9)
(-4,-7)
(-6,-5)
(-5,-6)

Answers

Answer:

1000000066756355688777

Work out, giving your answer in its simplest form:
4/7 divided by 2 1 / 3

Answers

Step-by-step explanation:

4/7÷21/3

=4/7*3/21

=12/147

Answer:

[tex]\frac{12}{49}[/tex]

Step-by-step explanation:

Given

[tex]\frac{4}{7}[/tex] ÷ 2 [tex]\frac{1}{3}[/tex] ← change mixed number to improper fraction

= [tex]\frac{4}{7}[/tex] ÷ [tex]\frac{7}{3}[/tex]

To perform the division

Leave the first fraction. change division to multiplication and turn the second fraction upside down.

= [tex]\frac{4}{7}[/tex] × [tex]\frac{3}{7}[/tex] ← multiply numerators/ denominators together

= [tex]\frac{4(3)}{7(7)}[/tex]

= [tex]\frac{12}{49}[/tex]

A object falls at 16t^2 feet in t seconds you drop a rock from a bridge that is 906 what is the hight in feet after the rock is droped

Answers

Answer:

824 feet

Step-by-step explanation:

Given

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

[tex]H = 906[/tex] -- Initial Height

Required

Calculate the height after 2 seconds --- missing from the question

First, we calculate the distance moved in 2 seconds

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

[tex]h(2) = 16*2^2[/tex]

[tex]h(2) = 16*4[/tex]

[tex]h(2) = 64[/tex]

This means that the object covered 64feet

The object current height is then calculated as:

[tex]Height = H - h(t)[/tex]

t = 2. So, the equation becomes

[tex]Height = H - h(2)[/tex]

Substitute values for H and h(2)

[tex]Height = 906- 64[/tex]

[tex]Height = 824[/tex]

Cual es el 5% de 80?

Answers

4 porque...
.05*80=4

in estimating the body temperature of a person, what difficulties did you encounter?Explain​

Answers

Answer:

In general , While estimating a bodies temperature that temperature is not the same for long, the temperature of the body is not at homeostasis, the temperature constantly has bumps and drops in the temperature this causes in accuracy thats why the thermometer takes 10-20 seconds because it takes the average of all the temperature's so it is accurate, that is a difficulty when estimating temperature because estimates are not good and the temperature keeps having ups and downs.

Factor completely
x^2 - 8x + 16

Answers

Answer:

(x - 4)^2

Step-by-step explanation:

someone help me with this answer please !!

Answers

Answer:

-27

Step-by-step explanation:

I dont really understand this question, can anyone help me out?

Answers

[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the Angles.

Complementary angles sum up together to become 90°.

Supplementary Angles sum up together to become 180°.

hence,

1.) Ans ==>Angle ABC and Angle NMP

2.) Ans ==> angle ABC and angle EFG

Complementary angles add up to 90 degrees while supplementary angles will add up to 180 degrees.

1) ABC & NMP
2) EFG & RST

Find the distance between (2, 8) and (−6, 2).

The distance is ( ) units.

Answers

Answer:

✓100 = 10

Step-by-step explanation:

2= x1

8= x2

-6= y1

2= y2

Then you apply your distance formula to solve.

Hope it helps

the original pattern for dress is 33 3/4 inches long. kimmy needs her dress to be 32 1/2 inches long how much shorter than the pattern does kimmy need to make her dress​

Answers

Answer: 1 1/4

Step-by-step explanation: 32 1/2 is the same as 32 2/4 so all you have to do is subtract 32 2/4 from 33 3/4 which leaves you with 1 1/4

what iis the answer to this question
1/5x40

Answers

Answer:

8

Step-by-step explanation:

Answer:

1/5 x 40 = 8

(Hope this helps! Btw, I am the first to answer.)

PLEASE HELP 50 POINTS Which terms can be combined in the expression below? Select three options.

StartFraction 5 over 6 EndFraction a minus 2 b minus 16.3 + StartFraction b over 12 EndFraction + c minus 0.9 b
StartFraction 5 over 6 EndFraction a
–2b
–16.3
StartFraction b over 12 EndFraction
–0.9b

Answers

Answer:

it -16.3

Step-by-step explanation:

Answer:

Answer:

Option 2nd , 4th and 6th correct

2,4 and 6

Step-by-step explanation:

Like terms are those terms which have same variable to the same power.

Combine like terms

Simplify:

Therefore, the  term can be combined in the given expression is,

2, 4 and 6Barinliest?

Find the slope of the line passing through the points (-7, 4) & (-7, -8)

Answers

Answer:

Undefined

Step-by-step explanation:

The equation for finding the slope is:

y2 - y1

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

x2 - x1

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

4 - (-8)

----------

-7 - (-7)

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

4 + 8

--------

-7 +7

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

12

----

0

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

The slope is Undefined, so there is no answer

1. Um prêmio em dinheiro foi dividido entre 3
pessoas: a primeira recebeu 1/4 do valor do
prêmio a segunda recebeu 1/3 e a terceira
ganhou R$ 1000,00. Então, o valor desse prêmio,
em reais, era de:
a) 2400,00
b) 2200,00
c) 2100,00
d) 1800,00​

Answers

I think the answer is b

Find the slope of the line

Answers

Answer:

-1

Step-by-step explanation:

Using rise over run for the two points

4 - 0/ -1 - 3 = -1

Answer:

We found 2 coordinates

1. ( 0 ,3)

2.(3,0)

Now slope = tan theta = 3/3 = 1

Answer is 1

Mark it as brainlist answer

Step-by-step explanation:

The square table top has an area of 369 square
inches. The length of one side of the table top is
between which two measurements?

Answers

Answer:

19 in. and 20 in.

Step-by-step explanation:

18^2 = 18 * 18 = 324

19^2 = 19 * 19 = 361

20^2 = 20 * 20 = 400

369 is between 361 and 400, so the side of the table is between 19 in. and 20 in.

Answer:

19 in. and 20 in.

Step-by-step explanation:

18^2 = 18 * 18 = 324

19^2 = 19 * 19 = 361

20^2 = 20 * 20 = 400

369 is between 361 and 400, so the side of the table is between 19 in. and 20 in.

I didn't mean to click an answer but please help me out

Answers

Answer:

135

Step-by-step explanation:

135+45=180, and supplementary angles always equal 180

Answer:

The answer is 135

Step-by-step explanation:

Definition of supplementary angles: either of two angles whose sum is 180°, so 180 - 45 = 135!

Please mark as brainliest.

f(x)= 10x find the inverse of the function

Answers

This is the answer I got.

Write a system of linear inequalities so the points,(1,2) and (4,-3) are solutions of the system, but the point (-2,8) is not a solution of the system.

Answers

Answer:

The sample system is:

y < 5y > x - 8

see the attached

The points (1, 2) and (4, -3) are in the intersected region but the point (-2, 8) is outside

There are 20 animals in the barn. There are chickens and sheep in the barn. If there are
a total of 62 legs, how many of each animal are there? *

Answers

Answer: Nope I was wrong

There are 11 sheep, and nine chickens.
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