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3 years ago

1/6 divided by x = 1/2

Mathematics

2 answers:

8090 [49]3 years ago

6 0

We want to solve for x

(1/6)/x = 1/2

We multiply both sides by x to get the x in the numerator

1/6 = x*(1/2)

We can divide both sides by 1/2 to get the x alone on the right side

(1/6)/(1/2) = x

When simplified...

x = 1/3

bonufazy [111]3 years ago

3 0

$\frac{\frac{1}{6}}{x}=\frac{1}{2}$

$\frac{1}{6}=\frac{1}{2}.x$

$\frac{\frac{1}{6}}{\frac{1}{2}}=x$

$\frac{1}{6}.\frac{2}{1}=x$

$\frac{2}{6}=x$

$\frac{1}{3}=x$

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June drinks 2.5 ounces of water every 20 minutes. How much water does she drink per hour?

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Answer:

7.5 ounces

Step-by-step explanation:

$\frac{2.5}{20} =\frac{x}{60} \\\\20x=150\\x= 7.5$

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3 years ago

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a sports store sells three different packs of tennis balls. which pack is the best to buy? 4 sleeves for 11.49, 6 sleeves for 16

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Answer:

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Step-by-step explanation

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3 years ago

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Answer:

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Step-by-step explanation:

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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 c)

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

This becomes the solution m=α±βi where α=0 and β=2

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

Where A and B 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

4 years ago

Let A = {3, 4, 5, 6, 7, 9, 10, 11}

Troyanec [42]

Answer:

a. 256

b. 255

Step-by-step explanation:

If a set has “n” elements, then the number of subset of the given set is $2^n$ and number of proper subset is $2^n-1$

A = {3, 4, 5, 6, 7, 9, 10, 11}

Here, n = 8

No of subsets

$= {2}^{n} = {2}^{8} = 256$

No of proper subsets

= $2^n-1 = 256-1=255$

5 0

2 years ago