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VLD [36.1K]
3 years ago
6

Let y = 4t + 2 be a linear function representing the distance from home for an ant t minutes after starting out from a location

near its home. What does the number 2 represent in this function?. . A. The ant is moving 4 feet every 2 minutes.. B. The ant is moving at 2 feet per minute.. C. The ant is 2 feet from its home after t minutes.. D. The ant started out 2 feet from its home.. . is it D?
Mathematics
2 answers:
Whitepunk [10]3 years ago
8 0

Let

t-------> the time in minutes

y------> the distance from home for an ant in feet

we know that

y=4t+2

In this linear equation

the slope m is equal to

m=4\frac{feet}{minute}

The y-intercept is equal to--------> 2

in this problem the y-intercept is the value of the distance in feet when the value of the time in minutes is zero

so

The y-intercept is equal to--------> 2\ feet

therefore

<u>the answer is the option</u>

D. The ant started out 2 feet from its home

dlinn [17]3 years ago
8 0
"The ant started out 2 feet from its home" is the one among the following choices given in the question that number 2 represent in this function. The correct option among all the options that are given in the question is the fourth option or option "D". I hope that this is the answer that has actually come to your desired help.
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Integral of 17/(x^3-125)
daser333 [38]

Answer:

17/75 ln│x − 5│− 17/150 ln(x² + 5x + 25) − 17/(5√75) tan⁻¹((2x + 5) / √75) + C

Step-by-step explanation:

∫ 17 / (x³ − 125) dx

= 17 ∫ 1 / (x³ − 125) dx

= 17 ∫ 1 / ((x − 5) (x² + 5x + 25)) dx

Use partial fraction decomposition:

= 17 ∫ [ A / (x − 5) + (Bx + C) / (x² + 5x + 25) ] dx

Use common denominator to find the missing coefficients.

A (x² + 5x + 25) + (Bx + C) (x − 5) = 1

Ax² + 5Ax + 25A + Bx² − 5Bx + Cx − 5C = 1

(A + B) x² + (5A − 5B + C) x + 25A − 5C = 1

Match the coefficients and solve the system of equations.

A + B = 0

5A − 5B + C = 0

25A − 5C = 1

A = 1/75

B = -1/75

C = -2/15

So the integral is:

= 17 ∫ [ 1/75 / (x − 5) + (-1/75 x − 2/15) / (x² + 5x + 25) ] dx

Simplify:

= 17/75 ∫ [ 1 / (x − 5) − (x + 10) / (x² + 5x + 25) ] dx

Factor ½ from the numerator of the second fraction:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 20) / (x² + 5x + 25) ] dx

Split the fraction:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 5) / (x² + 5x + 25) − ½ (15) / (x² + 5x + 25) ] dx

Multiply the last fraction by 4/4:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 5) / (x² + 5x + 25) − 30 / (4x² + 20x + 100) ] dx

Complete the square:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 5) / (x² + 5x + 25) − 15 / ((2x + 5)² + 75) ] dx

Split the integral:

= 17/75 ∫ 1 / (x − 5) dx − 17/150 ∫ (2x + 5) / (x² + 5x + 25) dx − 17/5 ∫ 1 / ((2x + 5)² + 75) dx

The first integral is:

∫ 1 / (x − 5) dx = ln│x − 5│

The second integral is:

∫ (2x + 5) / (x² + 5x + 25) dx = ln(x² + 5x + 25)

The third integral is:

∫ 1 / ((2x + 5)² + 75) dx = 1/√75 tan⁻¹((2x + 5) / √75)

Plug in:

= 17/75 ln│x − 5│− 17/150 ln(x² + 5x + 25) − 17/(5√75) tan⁻¹((2x + 5) / √75) + C

4 0
3 years ago
Pleas help it’s due tomrrow
katovenus [111]

Answer:

Step-by-step explanation:

K is located at -25

L is located at -15

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hope this helps <3

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The pair of angles are adjacent angles and supplementary and their measure =180
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Julie multiplies 6.27 by 7 and claims the product is 438.9. Explain without multiplying how you know Julie’s answer is not corre
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Answer:

SHe put the decimal point in the wrong spot, it's suppose to be 43.89

Step-by-step explanation:

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