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juin [17]
3 years ago
7

We want to change .8333 to a fraction

Mathematics
1 answer:
OleMash [197]3 years ago
4 0
Let x =0.8333.... Then 10x=8.3333-----(1) 100x=83.333..----(2) So (2)-(1) ,90x=75 x=75/90 =7.5/9 Hope it helps !!!!
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Luisa recieved $108 for a necklace she sold on an online auction. The auction site took a fe of 10% of selling price. What was t
Vera_Pavlovna [14]
I believe it might be 107.9 after if that’s what your asking-like taking off 10% of $108.
3 0
2 years ago
An equilateral triangle has side length 10 centimeters. Find its area in square centimeters. HINT: The altitude of an equilatera
dmitriy555 [2]
30cmsquared hope this helps!!!!!
3 0
3 years ago
Solve the system by graphing. Y=2x-9 y=-2x-1
sattari [20]

Answer:

(2,-5)

Step-by-step explanation:

See attachment

One can also solve this by calculation:

y=2x-9

y=-2x-1

-

Rearrange either equation to find x.  I'll use the first:

y=2x-9

2x = y+9

x = (y+9)/2

Now use this value of x in the second equation:

y =  -2x-1

y =-2((y+9)/2)-1

y = (-2y-18)/2)-1

y = -y -9 - 1

2y = -10

y = -5

Now use -5 for y in the rearranged equation:

y =  -2x-1

-5 =  -2x-1

-2x = -4

x = 2

Solution is (2,-5)

But the question wants a graph solution, which is also fun when you use DESMOS.

4 0
2 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
How do I solve this problem?
Morgarella [4.7K]
Next time use the desmos calculator online and input the numbers.

The answer to this equation is:

y = (x - 3)^2 - 2
5 0
3 years ago
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