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3 years ago

3. A line goes through the points (3,4) and (-3,6).

Mathematics

1 answer:

Galina-37 [17]3 years ago

7 0

Answer:

Part a) The slope is $m=-\frac{1}{3}$

Part b) The equation in point slope form is $y-4=-\frac{1}{3}(x-3)$

Part c) The equation in slope-intercept form is $y=-\frac{1}{3}x+5$

Step-by-step explanation:

we have the points (3,4) and (-3,6)

Part a) What is the slope of the line?

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the given points

$m=\frac{6-4}{-3-3}$

$m=\frac{2}{-6}$

$m=-\frac{1}{3}$

Part b) Write the equation of the line in point-slope form

$y-y1=m(x-x1)$

we have

$m=-\frac{1}{3}$

$point\ (3,4)$

substitute

$y-4=-\frac{1}{3}(x-3)$ ---> equation in point slope form

Part c) Write the equation of the line in slope-intercept form

$y=mx+b$

we have

$y-4=-\frac{1}{3}(x-3)$

Isolate the variable y

distribute right side

$y-4=-\frac{1}{3}x+1$

Adds 4 both sides

$y=-\frac{1}{3}x+1+4$

$y=-\frac{1}{3}x+5$ ---> equation in slope intercept form

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Solve for x. Thank you.

Bas_tet [7]

Answer:

D) 50/3

Step-by-step explanation:

6/10 = 10/(6+x-6)

6/10 = 10/x

6x = 100

x = 100/6

x = 50/3

4 0

3 years ago

The sale is for $30 this is 75 % of the original price find the original price

Sauron [17]

1. $52.80

2. 80

3. 46 people

4. 15 minutes

5. 2%

6. 147.03

I think these answers are correct but I am not 100% sure

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3 years ago

PLZ ANSWER IT HARD FOR ME

creativ13 [48]

First you have to find a common denominator between all the fractions which would be 12 for the first week it would be reduced to 6 3/12 and the second 4 8/12 both added together would be 10 and 11/12 so the equation would be 15 4/12 - 10 11/12 which would be 4 5/12.

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3 years ago

Hey Bestie! 50 pts Pls help! Real answers only pls <3

frosja888 [35]

Answer:

$1. \: 3i$

2. option D

3. option C

4. option D

5. option C

6. option B

7. option C

8. option D

9. option C

10. option C

Step-by-step explanation:

$\sqrt{ - 1(9)}$

$\sqrt{ - 1} \times \sqrt{ 9}$

$i \times \sqrt{9}$

$i \times \sqrt{ {3}^{2} }$

$i \times 3$

$3i$

$\sqrt{ - 1(8)}$

$\sqrt{ - 1} \times \sqrt{8}$

$i \times \sqrt{8}$

$i \times \sqrt{ {2}^{2} \times 2 }$

$2i \sqrt{2}$

$\sqrt{ - 1} \times \sqrt{80}$

$i \times \sqrt{80}$

$4i \: \sqrt{5}$

$\sqrt{ - 1} \times \sqrt{75}$

$i \times \sqrt{75}$

$i \times \sqrt{ {5}^{2} \times 3 }$

$5i \sqrt{3}$

$\sqrt{ - 1} \times \sqrt{72}$

$i \times \sqrt{72}$

$i \times ( {6}^{2} \times 2)$

$6i \sqrt{2}$

$\sqrt{ - 1} \times \sqrt{20}$

$i \times \sqrt{20}$

$i \times \sqrt{ {2}^{2} \times 5}$

$2i \sqrt{5}$

$\sqrt{ - 1} \times \sqrt{27}$

$i \times \sqrt{27}$

$i \times \sqrt{ {3}^{2} \times 3}$

$3i \sqrt{3}$

$\sqrt{ - 1 \times 12}$

$i \times \sqrt{12}$

$i \times \sqrt{4(3)}$

$2i \sqrt{3}$

$\sqrt{ - 1} \times \sqrt{125}$

$i \times \sqrt{ {5}^{2} \times 5 }$

$5i \sqrt{5}$

$\sqrt{ - 1} \times \sqrt{180}$

$i \times \sqrt{ {6}^{2} \times 5 }$

$6i \sqrt{5}$

<h3>Hope it is helpful...</h3>

5 0

2 years ago

Find the absolute extrema for f(x,y)=4-x^2-y^4+1/2y^2 over the closed disk D:x^2+y^2 is less than or equal to 1

algol [13]

Find the critical points of $f(x,y)$ :

$\dfrac{\partial f}{\partial x}=-2x=0\implies x=0$

$\dfrac{\partial f}{\partial y}=y-4y^3=y(1-4y^2)=0\implies y=0\text{ or }y=\pm\dfrac12$

All three points lie within $D$ , and $f$ takes on values of

$\begin{cases}f(0,0)=4\\f\left(0,-\frac12\right)=\frac{65}{16}\\f\left(0,\frac12\right)=\frac{65}{16}\end{cases}$

Now check for extrema on the boundary of $D$ . Convert to polar coordinates:

$f(x,y)=f(\cos t,\sin t)=g(t)=4-\cos^2-\sin^4t+\dfrac12\sin^2t=3+\dfrac32\sin^2t-\sin^4t$

Find the critical points of $g(t)$ :

$\dfrac{\mathrm dg}{\mathrm dt}=3\sin t\cos t-4\sin^3t\cos t=\sin t\cos t(3-4\sin^2t)=0$

$\implies\sin t=0\text{ or }\cos t=0\text{ or }\sin t=\pm\dfrac{\sqrt3}2$

$\implies t=n\pi\text{ or }t=\dfrac{(2n+1)\pi}2\text{ or }\pm\dfrac\pi3+2n\pi$

where $n$ is any integer. There are some redundant critical points, so we'll just consider $0\le t< 2\pi$ , which gives

$t=0\text{ or }t=\dfrac\pi3\text{ or }t=\dfrac\pi2\text{ or }t=\pi\text{ or }t=\dfrac{3\pi}2\text{ or }t=\dfrac{5\pi}3$

which gives values of

$\begin{cases}g(0)=3\\g\left(\frac\pi3\right)=\frac{57}{16}\\g\left(\frac\pi2\right)=\frac72\\g(\pi)=3\\g\left(\frac{3\pi}2\right)=\frac72\\g\left(\frac{5\pi}3\right)=\frac{57}{16}\end{cases}$

So altogether, $f(x,y)$ has an absolute maximum of 65/16 at the points (0, -1/2) and (0, 1/2), and an absolute minimum of 3 at (-1, 0).

5 0

2 years ago