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Maru [420]
3 years ago
13

I don’t understand this one

Mathematics
1 answer:
Masja [62]3 years ago
5 0

Answer:

  see below

Step-by-step explanation:

Put -1 where x is in each expression and evaluate it.

__

You will find that the expression is zero when the numerator is zero. And you will find the numerator is zero when it has a factor that is equivalent to ...

  (x +1)

Substituting x=-1 into this factor makes it be ...

  (-1 +1) = 0

__

Evaluating the first expression, we have ...

\dfrac{4(x+1)}{(4x+5)}=\dfrac{4(-1+1)}{4(-1)+5}=\dfrac{4\cdot 0}{1}=0

This first expression is one you want to "check."

You can see that the reason the expression is zero is that x+1 has a sum of zero. You can look for that same sum in the other expressions. (The tricky one is the one with the factor (x -(-1)). You know, of course, that -(-1) = +1.)

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Mary makes f dollars the first day of her new job. She makes $25 ¾ the second day of her job. In total, Mary made $60.00. Solve
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All you have to do is: 60-25.75 = 34.25.

f = 34.25
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May someone please help me, please? This is about exponents by the way. About 5 questions I need help with.
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16=16^1

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#1. Graph the following equation.<br> Y=6/5x + 1
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A box contains 20 miniature golf putt-putt balls; 10 are
stellarik [79]

Answer: The answer is provided below

Step-by-step explanation:

From the question, a box contains 20 miniature golf putt-putt balls out of which 10 are yellow, 6 are red, and the remaining 4 are pink.

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5 0
3 years ago
Write down the explicit solution for each of the following: a) x’=t–sin(t); x(0)=1
Kay [80]

Answer:

a) x=(t^2)/2+cos(t), b) x=2+3e^(-2t), c) x=(1/2)sin(2t)

Step-by-step explanation:

Let's solve by separating variables:

x'=\frac{dx}{dt}

a)  x’=t–sin(t),  x(0)=1

dx=(t-sint)dt

Apply integral both sides:

\int {} \, dx=\int {(t-sint)} \, dt\\\\x=\frac{t^2}{2}+cost +k

where k is a constant due to integration. With x(0)=1, substitute:

1=0+cos0+k\\\\1=1+k\\k=0

Finally:

x=\frac{t^2}{2} +cos(t)

b) x’+2x=4; x(0)=5

dx=(4-2x)dt\\\\\frac{dx}{4-2x}=dt \\\\\int {\frac{dx}{4-2x}}= \int {dt}\\

Completing the integral:

-\frac{1}{2} \int{\frac{(-2)dx}{4-2x}}= \int {dt}

Solving the operator:

-\frac{1}{2}ln(4-2x)=t+k

Using algebra, it becomes explicit:

x=2+ke^{-2t}

With x(0)=5, substitute:

5=2+ke^{-2(0)}=2+k(1)\\\\k=3

Finally:

x=2+3e^{-2t}

c) x’’+4x=0; x(0)=0; x’(0)=1

Let x=e^{mt} be the solution for the equation, then:

x'=me^{mt}\\x''=m^{2}e^{mt}

Substituting these equations in <em>c)</em>

m^{2}e^{mt}+4(e^{mt})=0\\\\m^{2}+4=0\\\\m^{2}=-4\\\\m=2i

This becomes the solution <em>m=α±βi</em> where <em>α=0</em> and <em>β=2</em>

x=e^{\alpha t}[Asin\beta t+Bcos\beta t]\\\\x=e^{0}[Asin((2)t)+Bcos((2)t)]\\\\x=Asin((2)t)+Bcos((2)t)

Where <em>A</em> and <em>B</em> are constants. With x(0)=0; x’(0)=1:

x=Asin(2t)+Bcos(2t)\\\\x'=2Acos(2t)-2Bsin(2t)\\\\0=Asin(2(0))+Bcos(2(0))\\\\0=0+B(1)\\\\B=0\\\\1=2Acos(2(0))\\\\1=2A\\\\A=\frac{1}{2}

Finally:

x=\frac{1}{2} sin(2t)

7 0
3 years ago
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