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3 years ago

Solve the equation-8+6m= 1/2(4m+16) for m

Mathematics

2 answers:

Lena [83]3 years ago

6 0

Answer:

m = 4

Step-by-step explanation:

Given

- 8 + 6m = $\frac{1}{2}$ (4m + 16) ← distribute parenthesis

- 8 + 6m = 2m + 8 ( subtract 2m from both sides )

- 8 + 4m = 8 ( add 8 to both sides )

4m = 16 ( divide both sides by 4 )

m = 4

77julia77 [94]3 years ago

5 0

Answer:

6m - 8 = 2m + 8

4m = 16

m = 4

Step-by-step explanation:

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Find a numerical value of one trigonometric function of x for cscx = sinx tanx + cosx

Alex787 [66]

Answer:

Step-by-step explanation:

we have

$cscx = sinx tanx + cosx\\\\\frac{1}{sinx}=sinx.\frac{sinx}{cosx} +cosx\\\\\frac{1}{sinx}.sinx.cosx= sinx.\frac{sinx}{cosx}.sinx.cosx+cosx.sinx.cosx\\ cosx= (sinx)^{3} +sinx.(cosx)^{2} \\cosx= sinx[(sinx)^{2}+(cosx)^{2})\\ cosx=sinx.1\\cosx=sinx\\tanx=1\\x=\frac{\pi}{4} +k\pi,k-integer.$

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2 years ago

Problem 4: Solve the initial value problem

pishuonlain [190]

Separate the variables:

$y' = \dfrac{dy}{dx} = (y+1)(y-2) \implies \dfrac1{(y+1)(y-2)} \, dy = dx$

Separate the left side into partial fractions. We want coefficients a and b such that

$\dfrac1{(y+1)(y-2)} = \dfrac a{y+1} + \dfrac b{y-2}$

$\implies \dfrac1{(y+1)(y-2)} = \dfrac{a(y-2)+b(y+1)}{(y+1)(y-2)}$

$\implies 1 = a(y-2)+b(y+1)$

$\implies 1 = (a+b)y - 2a+b$

$\implies \begin{cases}a+b=0\\-2a+b=1\end{cases} \implies a = -\dfrac13 \text{ and } b = \dfrac13$

So we have

$\dfrac13 \left(\dfrac1{y-2} - \dfrac1{y+1}\right) \, dy = dx$

Integrating both sides yields

$\displaystyle \int \dfrac13 \left(\dfrac1{y-2} - \dfrac1{y+1}\right) \, dy = \int dx$

$\dfrac13 \left(\ln|y-2| - \ln|y+1|\right) = x + C$

$\dfrac13 \ln\left|\dfrac{y-2}{y+1}\right| = x + C$

$\ln\left|\dfrac{y-2}{y+1}\right| = 3x + C$

$\dfrac{y-2}{y+1} = e^{3x + C}$

$\dfrac{y-2}{y+1} = Ce^{3x}$

With the initial condition y(0) = 1, we find

$\dfrac{1-2}{1+1} = Ce^{0} \implies C = -\dfrac12$

so that the particular solution is

$\boxed{\dfrac{y-2}{y+1} = -\dfrac12 e^{3x}}$

It's not too hard to solve explicitly for y; notice that

$\dfrac{y-2}{y+1} = \dfrac{(y+1)-3}{y+1} = 1-\dfrac3{y+1}$

Then

$1 - \dfrac3{y+1} = -\dfrac12 e^{3x}$

$\dfrac3{y+1} = 1 + \dfrac12 e^{3x}$

$\dfrac{y+1}3 = \dfrac1{1+\frac12 e^{3x}} = \dfrac2{2+e^{3x}}$

$y+1 = \dfrac6{2+e^{3x}}$

$y = \dfrac6{2+e^{3x}} - 1$

$\boxed{y = \dfrac{4-e^{3x}}{2+e^{3x}}}$

7 0

2 years ago

In a drama classroom, 75% of the students are chosen to perform a play. Of those choosen, 15% have singing roles. What is the pr

Nikolay [14]

Answer:

1/5 or 0.2

Step-by-step explanation:

probability=No of students with singing roles/No of people in the play
15/75=1/5 or 0.2

4 0

3 years ago

a train is 12 feet tall. a model of the train was built with a scale of 1 inch : 3 feet. how tall is the model of the train

katrin2010 [14]

Answer:

3 inch

Step-by-step explanation:

1 inch = 3 feet

12 feet = x

x = 12/3

x = 3

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2 years ago

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MrRissso [65]

Answer:

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3 years ago

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