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Gnesinka [82]
2 years ago
15

Find the lowest natural number which when divided by 12, 45, 15 and 10 leaves the remainder of

Mathematics
1 answer:
Levart [38]2 years ago
5 0
12=2*2*3
45=3*3*5
15=3*5
10=2*5
L.C.M=2*2*3*3*5=180
required number 180+2=182
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Pls look at the picture and answer
melisa1 [442]

Answer:

-0.5 goes between -2 and 1

0.5 goes between -2 and 1

-4.5 goes below -2

-2.5 goes below -2

1.5 goes above 1

4 goes above 1

5 0
2 years ago
Read 2 more answers
Solution for dy/dx+xsin 2 y=x^3 cos^2y
vichka [17]
Rearrange the ODE as

\dfrac{\mathrm dy}{\mathrm dx}+x\sin2y=x^3\cos^2y
\sec^2y\dfrac{\mathrm dy}{\mathrm dx}+x\sin2y\sec^2y=x^3

Take u=\tan y, so that \dfrac{\mathrm du}{\mathrm dx}=\sec^2y\dfrac{\mathrm dy}{\mathrm dx}.

Supposing that |y|, we have \tan^{-1}u=y, from which it follows that

\sin2y=2\sin y\cos y=2\dfrac u{\sqrt{u^2+1}}\dfrac1{\sqrt{u^2+1}}=\dfrac{2u}{u^2+1}
\sec^2y=1+\tan^2y=1+u^2

So we can write the ODE as

\dfrac{\mathrm du}{\mathrm dx}+2xu=x^3

which is linear in u. Multiplying both sides by e^{x^2}, we have

e^{x^2}\dfrac{\mathrm du}{\mathrm dx}+2xe^{x^2}u=x^3e^{x^2}
\dfrac{\mathrm d}{\mathrm dx}\bigg[e^{x^2}u\bigg]=x^3e^{x^2}

Integrate both sides with respect to x:

\displaystyle\int\frac{\mathrm d}{\mathrm dx}\bigg[e^{x^2}u\bigg]\,\mathrm dx=\int x^3e^{x^2}\,\mathrm dx
e^{x^2}u=\displaystyle\int x^3e^{x^2}\,\mathrm dx

Substitute t=x^2, so that \mathrm dt=2x\,\mathrm dx. Then

\displaystyle\int x^3e^{x^2}\,\mathrm dx=\frac12\int 2xx^2e^{x^2}\,\mathrm dx=\frac12\int te^t\,\mathrm dt

Integrate the right hand side by parts using

f=t\implies\mathrm df=\mathrm dt
\mathrm dg=e^t\,\mathrm dt\implies g=e^t
\displaystyle\frac12\int te^t\,\mathrm dt=\frac12\left(te^t-\int e^t\,\mathrm dt\right)

You should end up with

e^{x^2}u=\dfrac12e^{x^2}(x^2-1)+C
u=\dfrac{x^2-1}2+Ce^{-x^2}
\tan y=\dfrac{x^2-1}2+Ce^{-x^2}

and provided that we restrict |y|, we can write

y=\tan^{-1}\left(\dfrac{x^2-1}2+Ce^{-x^2}\right)
5 0
3 years ago
Estimate the solution to the system of equations. asap, please!! I will mark for brain list
Darya [45]

Answer:

(1 \frac{1}{3}, 2 \frac{1}{3} )

Step-by-step explanation:

Given the 2 equations

7x - y = 7 → (1)

x + 2y = 6 → (2)

Multiplying (1) by 2 and adding to (2) will eliminate the y- term

14x - 2y = 14 → (3)

Add (2) and (3) term by term to eliminate y

15x = 20 ( divide both sides by 15 )

x = \frac{20}{15} = \frac{4}{3} = 1 \frac{1}{3}

Substitute this value of x into either of the 2 equations and solve for y

Substituting in (2)

\frac{4}{3} + 2y = 6

2y = 6 - \frac{4}{3} = \frac{14}{3} ( divide both sides by 2 )

y = \frac{7}{3} = 2 \frac{1}{3}

7 0
3 years ago
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katrin [286]

Answer:

27 years

Step-by-step explanation:

Given that :

Adrian's age = 3

Father's age = 34

In how many years will Adrian be twice as young as his father?

Let the number of years = x

2(3 + x) = 34 + x

6 + 2x = 34 + x

2x - x = 34 - 6

x = 28

3 0
3 years ago
On a map the Browns are using 2
Alona [7]

Answer: 337.5 km

Step-by-step explanation:

Use proportion:

2:75=9:x

2x=675

x=675/2

X=337.5

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3 years ago
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