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faust18 [17]
4 years ago
6

If f(x) = 3x^2-10x+2 find the vertex of y=f(x+4)-5

Mathematics
1 answer:
allochka39001 [22]4 years ago
3 0

3 {(4 + x)}^{2}  - 10(x + 4) + 2 - 5
so
3( {x}^{2}  + 8x + 16) - 10x - 40 + 3
so
3 {x}^{2}  + 14x + 11
take differential calculus
6x + 14 = 0
you will find x then y
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Tcecarenko [31]
To put a slope-intercept into standard form, you have to first cancel out the fractions. So:
y = \frac{2}{5}x - \frac{5}{6}

Turns into:
(5)(6)y = (\frac{2}{5}x - \frac{5}{6})(5)(6)

Simplify:
30y =  (\frac{2}{5}x - \frac{5}{6})(30)

Distribute:
30y = 12x- 25

Since you want to get x and y on the same side, you subtract 12x from both sides to get:
-12x+30y = -25

So, your answer is C. Hope this all made sense! If it doesn't you know where to get a hold of me, so just dm me. Or if you more problems.
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4 years ago
6/7 divided by 12/14
S_A_V [24]

Answer:

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Step-by-step explanation:

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3 years ago
( !!!)<br><br> <br> 4 ÷ 1/2<br><br> ℍ :<br><br> :)
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6 0
3 years ago
Read 2 more answers
Please I need help with differential equation. Thank you
Inga [223]

1. I suppose the ODE is supposed to be

\mathrm dt\dfrac{y+y^{1/2}}{1-t}=\mathrm dy(t+1)

Solving for \dfrac{\mathrm dy}{\mathrm dt} gives

\dfrac{\mathrm dy}{\mathrm dt}=\dfrac{y+y^{1/2}}{1-t^2}

which is undefined when t=\pm1. The interval of validity depends on what your initial value is. In this case, it's t=-\dfrac12, so the largest interval on which a solution can exist is -1\le t\le1.

2. Separating the variables gives

\dfrac{\mathrm dy}{y+y^{1/2}}=\dfrac{\mathrm dt}{1-t^2}

Integrate both sides. On the left, we have

\displaystyle\int\frac{\mathrm dy}{y^{1/2}(y^{1/2}+1)}=2\int\frac{\mathrm dz}{z+1}

where we substituted z=y^{1/2} - or z^2=y - and 2z\,\mathrm dz=\mathrm dy - or \mathrm dz=\dfrac{\mathrm dy}{2y^{1/2}}.

\displaystyle\int\frac{\mathrm dy}{y^{1/2}(y^{1/2}+1)}=2\ln|z+1|=2\ln(y^{1/2}+1)

On the right, we have

\dfrac1{1-t^2}=\dfrac12\left(\dfrac1{1-t}+\dfrac1{1+t}\right)

\displaystyle\int\frac{\mathrm dt}{1-t^2}=\dfrac12(\ln|1-t|+\ln|1+t|)+C=\ln(1-t^2)^{1/2}+C

So

2\ln(y^{1/2}+1)=\ln(1-t^2)^{1/2}+C

\ln(y^{1/2}+1)=\dfrac12\ln(1-t^2)^{1/2}+C

y^{1/2}+1=e^{\ln(1-t^2)^{1/4}+C}

y^{1/2}=C(1-t^2)^{1/4}-1

I'll leave the solution in this form for now to make solving for C easier. Given that y\left(-\dfrac12\right)=1, we get

1^{1/2}=C\left(1-\left(-\dfrac12\right)^2\right))^{1/4}-1

2=C\left(\dfrac54\right)^{1/4}

C=2\left(\dfrac45\right)^{1/4}

and so our solution is

\boxed{y(t)=\left(2\left(\dfrac45-\dfrac45t^2\right)^{1/4}-1\right)^2}

3 0
3 years ago
(a)Find the commission on Rs65 000 if 4% commission is paid.
Neporo4naja [7]

Answer:

Step-by-step explanation:

commission amount = 4 % of Rs 65000

=4/100 * 65000

=260000/100

=2600

therefore commision amount is Rs 2600

SP od an article = Rs 2700

profit %=8%

let CP be x

SP=CP + profit% of CP

2700=x + 8/100 *x

2700=100x + 8x/100

2700*100 = 108x

270000=108x

270000/108=x

2500=x

therefore cost price (CP) of an article is Rs 2500.

5 0
3 years ago
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