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ANTONII
3 months ago
9

An ant arrives at the snail’s starting position at time minutes and follows the snail’s path. During the interval minutes, the a

nt 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 minutes. The ant’s velocity at time is B inches per minute. Find the value of B.
Mathematics
1 answer:
babunello [11.8K]3 months ago
5 0

QUESTION INTRODUCTION

A snail is moving in a straight line. Its speed can be represented by v(t)=1.4ln(1+t^2) inches per minute for the duration of 0 ≤ t ≤ 15 minutes.

Response:

B=22.35 inches per minute

Detailed Explanation:

Assuming the snail moves at v(t)=1.4ln(1+t^2) inches per minute, its displacement from 0 to 15 minutes is determined by the integral:

\int v(t) dt=\int (1.4ln(1+t^2))dt=76.04307

The ant's acceleration remains constant at 2 inches per minute squared.

This results in the ant's velocity as:

\int 2 dt=2t+K, $where K is a constant of integration$

During the period of 12≤t≤15, the ant’s displacement is:

\int_{12}^{15}(2t+K) dt=81+3K

Given that the displacement of the snail matches that of the ant during 12≤t≤15.

81+3K=76.04307

3K=76.04307-81

3K=-4.95693

K=-1.65231

At t=12, the ant’s speed becomes:

2t+K=2(12)-1.65231=22.348 inches per minute

B=22.348 inches per minute

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100 point!!!
Leona [12618]

Answer:

45 grams

Step-by-step explanation:

1st order: 27 people

15 people:

100 g

Ginger: 20 g

Turmeric: 25 g

Coriander: 35 g

Cumin Seeds: 20 g

20+25+35+20=60+40=100

For 1 person:

Ginger: 1 1/3 g

Turmeric: 1 2/3 g

Coriander: 2 1/3 g

Cumin Seeds: 1 1/3 g

Multiply the total by 27

For 27 people:

Ginger: 36 g

Turmeric: 45 g

Coriander: 63 g

Cumin Seeds: 36 g

45 g for Turmeric

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1 month ago
The graph shows the altitude of a helicopter over time. A graph measuring altitude and time. A line runs through coordinates (0,
Zina [12379]
To determine the slope, subtract the y coordinates from each other and the x coordinates as well. That gives us: 10000 - 4000 over 0 - 15, which simplifies to 6000 over -15. When divided, it results in -400. So, the slope amounts to -400. I hope this aids you!:D
6 0
2 months ago
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In the diagram below BD is parallel to XY. What is the value of x
Svet_ta [12734]

The value of x equals 60 degrees.

This is because alternate interior angles are equal by definition :)

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5 0
3 months ago
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A coordinate grid with 2 lines. The first line is labeled y equals negative StartFraction 7 over 4 EndFraction x plus StartFract
AnnZ [12381]

Answer:

1) (2.2, -1.4)

2) (1.33, 1)

Detailed solution:

Question 1)

We are provided with two linear equations representing lines, and we need to find the intersection point that solves the system.

The lines given are:

Line 1 equation:

y=\frac{-7}{4}x+\frac{5}{2}

This line passes through points (0, 2.5) and (2.2, -1.4).

Line 2 equation:

y=\frac{3}{4}x-3

The second line goes through (0, -3) and (2.2, -1.4).

According to the graph and data, the solution to the system is the coordinate where both lines intersect.

The solution to a system of linear equations is the coordinate pair common to both lines, i.e., the intersection point.

Here, both lines share the point (2.2, -1.4), indicating it is their intersection and the solution.

Therefore, the solution for question 1 is (2.2, -1.4).

Question 2)

The equations given are:

y = 1.5x - 1               Equation 1

y = 1                           Equation 2

The method of substitution can be used to find the solution.

Replacing y from Equation 2 into Equation 1 gives:

1 = 1.5x - 1

Add 1 to both sides:

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3 months ago
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