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3 years ago

Test Review that I cannot understand

Mathematics

1 answer:

maria [59]3 years ago

7 0

Answer:

I will help you with the first one

Step-by-step explanation:

x= -3 -2 -1

y= -4 -3 -2.59

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Find point P that divides segment AB into a 2:3 ratio. The point should be closer to A. A(-3,1) and B(3,5). p=

cestrela7 [59]

To find the point that divides the segment into a 2:3 partition, a formula can be used. The formula is:

[ x1 + (ratio)*(x2 - x1) , y1 + (ratio)*(y2 - y1) ]

Substituting the given values:

[ -3 + (2/5)*(3 + 3) , 1 + (2/5)*(5 - 1) <span>]
</span>(-0.6 , 2.6)

Therefore, the point P that divides segment AB into a 2:3 ratio is found at (-0.6 , 2.6).

8 0

3 years ago

Hello can you help om really struggling

gulaghasi [49]

Answer:

its b, decreasing

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Find the exact area of the surface obtained by rotating the curve about the x-axis.

padilas [110]

$\bf \begin{cases}
y=sin\left( \frac{\pi x}{6} \right)\\
0\le x\le 6\\
\textit{about the x-axis, or }y=0
\end{cases}\\\\
-----------------------------\\\\
\textit{using the disc method}
\\\\
V=\int\limits_{0}^{6}\pi \left[ sin\left( \frac{\pi x}{6} \right) \right]^2\cdot dx\implies \pi\int\limits_{0}^{6} \left[ sin\left( \frac{\pi x}{6} \right) \right]^2\cdot dx
\\\\\\
 \pi\int\limits_{0}^{6} sin^2\left( \frac{\pi x}{6} \right) \cdot dx\\\\
-----------------------------\\\\$

$\bf \textit{now, let us check the double angle identities}
\\\\
cos(2\theta)=
\begin{cases}
cos^2(\theta)-sin^2(\theta)\\
\boxed{1-2sin^2(\theta)}\\
2cos^2(\theta)-1
\end{cases}
\\\\\\
thus\implies cos(2\theta)=1-2sin^2(\theta)\implies 2sin^2(\theta)=1-cos(2\theta)
\\\\\\
sin^2(\theta)=\cfrac{1-cos(2\theta)}{2}\qquad thus\\\\
-----------------------------$

$\bf \pi\int\limits_{0}^{6} \left[ sin\left( \frac{\pi x}{6} \right) \right]^2\cdot dx\implies 
\pi\int\limits_{0}^{6} \cfrac{1-cos\left(2\cdot \frac{\pi x}{6} \right)}{2}\cdot dx
\\\\\\
\pi\int\limits_{0}^{6}\cfrac{1}{2}dx-\pi \cdot \cfrac{1}{2}\pi\int\limits_{0}^{6}cos\left(\frac{\pi x}{3} \right)dx
\\\\\\
\left[\cfrac{\pi x}{2}-\cfrac{\pi }{2}\cdot \cfrac{sin\left(\frac{\pi x}{3} \right)}{\frac{\pi x}{3} } \right]\implies \left[ \cfrac{\pi }{2}x-\cfrac{3sin\left(\frac{\pi x}{3} \right)}{2x} \right]_0^6$

and surely, you'd know how to get the values for the bounds there

5 0

3 years ago

The slope of the line below is 3. Use the coordinates of the labeled point to

Makovka662 [10]

The point-slope equation of the line is y - 8 = 3(x - 6)

<h3>How to determine the equation?</h3>

The points are given as:

(x1, y1) = (6, 8)

The slope is given as:

m= 3

The equation is then calculated as:

y - y1 = m(x - x1)

This gives

y - 8 = 3(x - 6)

Hence, the point-slope equation of the line is y - 8 = 3(x - 6)

Read more about linear equations at:

brainly.com/question/11365604

#SPJ1

5 0

1 year ago

The diversity of algal species in a lake is calculated for a coastal area before and after an oil spill.

Svetradugi [14.3K]

I think it’s A.Indpendent Variable

5 0

3 years ago