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3 years ago

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Alisa had some juice in a bottle. Then she drank 3/8 liter of juice. If this was 3/4 of the juice that was originally in the bot

tle, how much juice was there to start?

1 answer:

Inessa [10]3 years ago

8 0

3/4 x ? = 3/8

3/8 ÷ 3/4 = ?

3/8 x 4/3 = 12/24

12/24 = 1/2

1/2 of a liter was there to start.

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A sequence can be generated by using an = an-1 + 4, where a1 = 6 and n is a whole number greater than 1. What are the first four

Firlakuza [10]

<u>Answer:</u>

The first four terms are <u>4</u><u>,</u><u>8</u><u>,</u><u>1</u><u>2</u><u>,</u><u>1</u><u>6</u>

<u>Step-by-Step </u><u>Explanation</u><u>:</u>

The given relation between the nth term and it's previous term is given by:

$\boxed{an = an - 1 + 4}$

GiveN:

a1 = 4

Now finding the other three terms of the AP with the given relation.

$a2 = a1 + 4$

Putting a1 = 4,

$a2 = 4 + 4 = 8$

Now, Third term:

$a3 = a2 + 4$

Putting a2 = 8,

$a3 = 8 + 4 = 12$

Now, Fourth term:

$a4 = a3 + 4$

Putting a3 = 12,

$a4 = 12 + 4 = 16$

Hence, The first four terms of the AP is 4, 8, 12 & 16.

7 0

3 years ago

Find all the solutions for the equation:

Contact [7]

$2y^2\,\mathrm dx-(x+y)^2\,\mathrm dy=0$

Divide both sides by $x^2\,\mathrm dx$ to get

$2\left(\dfrac yx\right)^2-\left(1+\dfrac yx\right)^2\dfrac{\mathrm dy}{\mathrm dx}=0$

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2\left(\frac yx\right)^2}{\left(1+\frac yx\right)^2}$

Substitute $v(x)=\dfrac{y(x)}x$ , so that $\dfrac{\mathrm dv(x)}{\mathrm dx}=\dfrac{x\frac{\mathrm dy(x)}{\mathrm dx}-y(x)}{x^2}$ . Then

$x\dfrac{\mathrm dv}{\mathrm dx}+v=\dfrac{2v^2}{(1+v)^2}$

$x\dfrac{\mathrm dv}{\mathrm dx}=\dfrac{2v^2-v(1+v)^2}{(1+v)^2}$

$x\dfrac{\mathrm dv}{\mathrm dx}=-\dfrac{v(1+v^2)}{(1+v)^2}$

The remaining ODE is separable. Separating the variables gives

$\dfrac{(1+v)^2}{v(1+v^2)}\,\mathrm dv=-\dfrac{\mathrm dx}x$

Integrate both sides. On the left, split up the integrand into partial fractions.

$\dfrac{(1+v)^2}{v(1+v^2)}=\dfrac{v^2+2v+1}{v(v^2+1)}=\dfrac av+\dfrac{bv+c}{v^2+1}$

$\implies v^2+2v+1=a(v^2+1)+(bv+c)v$

$\implies v^2+2v+1=(a+b)v^2+cv+a$

$\implies a=1,b=0,c=2$

Then

$\displaystyle\int\frac{(1+v)^2}{v(1+v^2)}\,\mathrm dv=\int\left(\frac1v+\frac2{v^2+1}\right)\,\mathrm dv=\ln|v|+2\tan^{-1}v$

On the right, we have

$\displaystyle-\int\frac{\mathrm dx}x=-\ln|x|+C$

Solving for $v(x)$ explicitly is unlikely to succeed, so we leave the solution in implicit form,

$\ln|v(x)|+2\tan^{-1}v(x)=-\ln|x|+C$

and finally solve in terms of $y(x)$ by replacing $v(x)=\dfrac{y(x)}x$ :

$\ln\left|\frac{y(x)}x\right|+2\tan^{-1}\dfrac{y(x)}x=-\ln|x|+C$

$\ln|y(x)|-\ln|x|+2\tan^{-1}\dfrac{y(x)}x=-\ln|x|+C$

$\boxed{\ln|y(x)|+2\tan^{-1}\dfrac{y(x)}x=C}$

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3 years ago

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svetlana [45]

Answer:

122.67 average

Step-by-step explanation:

Mean = (every value added up)/(# of values)

Mean = (105 + 2(110) + 2(112) + 3(113) + 2(115) + 5(116) + 4(117) + 7(118) + 5(120) + 5(121) + 4(125) + 5(126) + 2(128) + 130 + 3(132) + 134 + 3(135) + 2(140) + 2(141) + 150)/60

= 7360/60

= 122.67

I had trouble understanding the data but I hope I did this right!

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3 years ago

X+2 = 7/8 mulltiplied by -15x

Marysya12 [62]

Answer:

x=16/113

Step-by-step explanation:

look at them in order

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3 years ago

2sin^2x - sinx - 3 = 0

e-lub [12.9K]

We have that
2sin²<span>x - sinx - 3 = 0
</span>
Let
A------> sin x
so
2A²-A-3=0

using a graph tool-----> to resolve the second order equation
see the attached figure

the solutions are
A=-1
A=1.5------> is not solution because sin x <span>can not be 1.5

the solution is
A=-1
therefore
sin x=-1
x=arc sin(-1)=-90</span>°

the answer is
sin x=-1
x=-90° or 270°

8 0

3 years ago