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rosijanka [135]
1 year ago
14

Find the coordinates of the vertex of the following parabola algebraically. Write your answer as and x,y point

Mathematics
1 answer:
Likurg_2 [28]1 year ago
8 0

The equation of the parabola in the vertex form is y =  (x - 3)^{2} - 5 with ( 3, -5) is the vertex of the parabola and 1 is the multiplier

In the above question, A parabolic equation is given as follows:

Y = x^2 - 6x + 4

The equation of the parabola in the vertex form is :

y = a (x - h)^{2} + k

Where a is a multiplier in the equation and (h,k) are the coordinates of the vertex

So, in order to obtain this form, we will use the method of completing square :

Y = x^2 - 6x + 4

y = x^{2} - 6x + (9 -9) + 4

y = (x - 3)^{2} + ( -9 + 4)

y =  (x - 3)^{2} - 5

where, ( 3, -5) is the vertex of the parabola and 1 is the multiplier

Hence, The equation of the parabola in the vertex form is y =  (x - 3)^{2} - 5 with ( 3, -5) is the vertex of the parabola and 1 is the multiplier

To learn more about, parabola, here

brainly.com/question/21685473

#SPJ1

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19.27 - (- 42.1)= subtract
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when you subtract twice you are essentially adding

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Which expression can be used to solve 3/5 ÷ 7/10​
marusya05 [52]

Answer:

Step-by-step explanation:

3/5 divided by 7/10

You use KCF

KCF stands for keep change flip

So it would be 3/5x10/7

3              10                    15

_      x       _        =            _

5               7                       7

you need to simplify it so the 5 in 3/5 would be a 1 and the 10 in 10/7 would be  5

5 0
3 years ago
For 15 hours of work, a plumber charges $435. If he charges the same amount for each hour of work, which table shows the correct
Volgvan

Answer:

29

Step-by-step explanation:

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7 0
2 years ago
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Integrate sin^-1(x) dx<br><br> please explain how to do it aswell ...?
Lynna [10]
If you're using the app, try seeing this answer through your browser:  brainly.com/question/2264253

_______________


Evaluate the indefinite integral:

\mathsf{\displaystyle\int\!sin^{-1}(x)\,dx\qquad\quad\checkmark}


Trigonometric substitution:

\mathsf{\theta=sin^{-1}(x)\qquad\qquad\dfrac{\pi}{2}\le \theta\le \dfrac{\pi}{2}}


then,

\begin{array}{lcl} \mathsf{x=sin\,\theta}&\quad\Rightarrow\quad&\mathsf{dx=cos\,\theta\,d\theta\qquad\checkmark}\\\\\\ &&\mathsf{x^2=sin^2\,\theta}\\\\ &&\mathsf{x^2=1-cos^2\,\theta}\\\\ &&\mathsf{cos^2\,\theta=1-x^2}\\\\ &&\mathsf{cos\,\theta=\sqrt{1-x^2}\qquad\checkmark}\\\\\\ &&\textsf{because }\mathsf{cos\,\theta}\textsf{ is positive for }\mathsf{\theta\in \left[\dfrac{\pi}{2},\,\dfrac{\pi}{2}\right].} \end{array}


So the integral \mathsf{(ii)} becomes

\mathsf{=\displaystyle\int\! \theta\,cos\,\theta\,d\theta\qquad\quad(ii)}


Integrate \mathsf{(ii)} by parts:

\begin{array}{lcl} \mathsf{u=\theta}&\quad\Rightarrow\quad&\mathsf{du=d\theta}\\\\ \mathsf{dv=cos\,\theta\,d\theta}&\quad\Leftarrow\quad&\mathsf{v=sin\,\theta} \end{array}\\\\\\\\ \mathsf{\displaystyle\int\!u\,dv=u\cdot v-\int\!v\,du}\\\\\\ \mathsf{\displaystyle\int\!\theta\,cos\,\theta\,d\theta=\theta\, sin\,\theta-\int\!sin\,\theta\,d\theta}\\\\\\ \mathsf{\displaystyle\int\!\theta\,cos\,\theta\,d\theta=\theta\, sin\,\theta-(-cos\,\theta)+C}

\mathsf{\displaystyle\int\!\theta\,cos\,\theta\,d\theta=\theta\, sin\,\theta+cos\,\theta+C}


Substitute back for the variable x, and you get

\mathsf{\displaystyle\int\!sin^{-1}(x)\,dx=sin^{-1}(x)\cdot x+\sqrt{1-x^2}+C}\\\\\\\\ \therefore~~\mathsf{\displaystyle\int\!sin^{-1}(x)\,dx=x\cdot\,sin^{-1}(x)+\sqrt{1-x^2}+C\qquad\quad\checkmark}


I hope this helps. =)


Tags:  <em>integral inverse sine function angle arcsin sine sin trigonometric trig substitution differential integral calculus</em>

6 0
3 years ago
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