What is the next number? 2 7 8 3 12 9

Farmer Ed has 3,500 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not f

Alecsey [184]

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5 0

3 years ago

A line passes through the points (6,-6) and (9,-5). What is it’s equation in point slope form?

BARSIC [14]

Answer:

$y=\frac{1}{3}x-8$

Step-by-step explanation:

Slope-intercept form of an equation is written as $y=mx+b$ , where $m$ is the slope and $b$ is the y-intercept.

The slope of a line that passes through the points $(x_1,\: y_1)$ and $(x_2, \: y_2)$ is $m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$ . Using the coordinates $(6,-6)$ and $(9,-5)$ as given in the problem, we have slope of this line to be:

$m=\frac{-5-(-6)}{9-6}=\frac{1}{3}$ .

Now using this slope we've found and any point the line passes through, we can find the y-intercept of this equation:

$-6=\frac{1}{3}(6)+b, \\ b=-8$

Therefore, the equation of this line in slope-intercept form is $\fbox{$y=\frac{1}{3}x-8$}$ .

3 0

3 years ago

Given the data set (5, 9), (13, 12), (23, 16), which of the following equations best represents a line of best fit? A) y = 3/4x

alekssr [168]

The answer is c) y=2/5x+7
hope that helps

8 0

3 years ago

Read 2 more answers

Find the volume v of the described solid s. the base of s is an elliptical region with boundary curve 4x2 + 9y2 = 36. cross-sect

Tasya [4]

$4x^2+9y^2=36\iff\dfrac{x^2}9+\dfrac{y^2}4=1$

defines an ellipse centered at $(0,0)$ with semi-major axis length 3 and semi-minor axis length 2. The semi-major axis lies on the $x$ -axis. So if cross sections are taken perpendicular to the $x$ -axis, any such triangular section will have a base that is determined by the vertical distance between the lower and upper halves of the ellipse. That is, any cross section taken at $x=x_0$ will have a base of length

$\dfrac{x^2}9+\dfrac{y^2}4=1\implies y=\pm\dfrac23\sqrt{9-x^2}$
$\implies \text{base}=\dfrac23\sqrt{9-{x_0}^2}-\left(-\dfrac23\sqrt{9-{x_0}^2}\right)=\dfrac43\sqrt{9-{x_0}^2}$

I've attached a graphic of what a sample section would look like.

Any such isosceles triangle will have a hypotenuse that occurs in a $\sqrt2:1$ ratio with either of the remaining legs. So if the hypotenuse is $\dfrac43\sqrt{9-{x_0}^2}$ , then either leg will have length $\dfrac4{3\sqrt2}\sqrt{9-{x_0}^2}$ .

Now the legs form a similar triangle with the height of the triangle, where the legs of the larger triangle section are the hypotenuses and the height is one of the legs. This means the height of the triangular section is $\dfrac4{3(\sqrt2)^2}\sqrt{9-{x_0}^2}=\dfrac23\sqrt{9-{x_0}^2}$ .

Finally, $x_0$ can be chosen from any value in $-3\le x_0\le3$ . We're now ready to set up the integral to find the volume of the solid. The volume is the sum of the infinitely many triangular sections' areas, which are

$\dfrac12\left(\dfrac43\sqrt{9-{x_0}^2}\right)\left(\dfrac23\sqrt{9-{x_0}^2}\right)=\dfrac49(9-{x_0}^2)$

and so the volume would be

$\displaystyle\int_{x=-3}^{x=3}\frac49(9-x^2)\,\mathrm dx$
$=\left(4x-\dfrac4{27}x^3\right)\bigg|_{x=-3}^{x=3}$
$=16$

6 0

3 years ago

Trevor bought an antique desk. The net value of the desk is equal to the resale value of the desk minus what Trevor paid to buy

mel-nik [20]

Answer: 1st one

Step-by-step explanation:

6 0

4 years ago

Read 2 more answers