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1 year ago

Find the slope of line

Mathematics

2 answers:

tamaranim1 [39]1 year ago

8 0

Just take the coordinates of both those red dots and use the slope formula: y2-y1 all divided by x2-x1. that should give you slope

zheka24 [161]1 year ago

3 0

The formula to find the slope of a line is $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ , in other words <em>the y coordinate of the second point minus the y coordinate of the first point over the x coordinate of the second point minus the x coordinate of the first point</em>.

On this graph, the two points given are (-3,4) and (1,-2). With this, we can determine $x_{1} , x_{2} , y_{1} , and y_{2}$

$x_{1}=-3 \\ x_{2}=1\\ y_{1}=4\\ y_{2}=-2$

Plug these values correctly into the slope formula, and you can find your answer.

$\frac{-2-4}{1--3} =\frac{-6}{4} =\frac{-3}{2}$

The slope of the line is-3/2.

Hope this helps!

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Kevin is buying water for his camping trip. He knows he needs at least 20 gallons of water for the trip. He already has five and

s2008m [1.1K]

Answer:

$5.5+0.25x\geq 20$

Step-by-step explanation:

Kevin already has five and a half gallons of water for the trip

He knows he needs at least 20 gallons of water for the trip.

The water comes in 32-fluid ounce (quarter-gallon) containers.

1 fluid ounce =0.0078125 gallons

32-fluid ounce $=32 \times 0.0078125 =0.25$

Let x be the number 32-fluid ounce (quarter-gallon) containers required to have at least 20 gallons of water for the trip.

1 container contains 0.25 gallons of water

So, x container contains 0.25x gallons of water

So, Kelvin has total gallons of water = $5.5+0.25x$

Since we are given that He knows he needs at least 20 gallons of water for the trip.

So, $5.5+0.25x\geq 20$

Hence the algebraic inequality represents this situation is $5.5+0.25x\geq 20$

5 0

1 year ago

Read 2 more answers

Trong một lớp học có $35$ sinh viên nói được tiếng Anh, $25$ sinh viên nói được tiếng Nhật trong đó có $10$ sinh viên nói được c

Reil [10]

Answer:

please write this question in English then I give answer

8 0

1 year ago

Use green's theorem to compute the area inside the ellipse x252+y2172=1. use the fact that the area can be written as ∬ddxdy=12∫

Pavel [41]

The area of the ellipse $E$ is given by

$\displaystyle\iint_E\mathrm dA=\iint_E\mathrm dx\,\mathrm dy$

To use Green's theorem, which says

$\displaystyle\int_{\partial E}L\,\mathrm dx+M\,\mathrm dy=\iint_E\left(\frac{\partial M}{\partial x}-\frac{\partial L}{\partial y}\right)\,\mathrm dx\,\mathrm dy$

( $\partial E$ denotes the boundary of $E$ ), we want to find $M(x,y)$ and $L(x,y)$ such that

$\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1$

and then we would simply compute the line integral. As the hint suggests, we can pick

$\begin{cases}M(x,y)=\dfrac x2\\\\L(x,y)=-\dfrac y2\end{cases}\implies\begin{cases}\dfrac{\partial M}{\partial x}=\dfrac12\\\\\dfrac{\partial L}{\partial y}=-\dfrac12\end{cases}\implies\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1$

The line integral is then

$\displaystyle\frac12\int_{\partial E}-y\,\mathrm dx+x\,\mathrm dy$

We parameterize the boundary by

$\begin{cases}x(t)=5\cos t\\y(t)=17\sin t\end{cases}$

with $0\le t\le2\pi$ . Then the integral is

$\displaystyle\frac12\int_0^{2\pi}(-17\sin t(-5\sin t)+5\cos t(17\cos t))\,\mathrm dt$

$=\displaystyle\frac{85}2\int_0^{2\pi}\sin^2t+\cos^2t\,\mathrm dt=\frac{85}2\int_0^{2\pi}\mathrm dt=85\pi$

###

Notice that $x^{2/3}+y^{2/3}=4^{2/3}$ kind of resembles the equation for a circle with radius 4, $x^2+y^2=4^2$ . We can change coordinates to what you might call "pseudo-polar":

$\begin{cases}x(t)=4\cos^3t\\y(t)=4\sin^3t\end{cases}$

which gives

$x(t)^{2/3}+y(t)^{2/3}=(4\cos^3t)^{2/3}+(4\sin^3t)^{2/3}=4^{2/3}(\cos^2t+\sin^2t)=4^{2/3}$

as needed. Then with $0\le t\le2\pi$ , we compute the area via Green's theorem using the same setup as before:

$\displaystyle\iint_E\mathrm dx\,\mathrm dy=\frac12\int_0^{2\pi}(-4\sin^3t(12\cos^2t(-\sin t))+4\cos^3t(12\sin^2t\cos t))\,\mathrm dt$

$=\displaystyle24\int_0^{2\pi}(\sin^4t\cos^2t+\cos^4t\sin^2t)\,\mathrm dt$

$=\displaystyle24\int_0^{2\pi}\sin^2t\cos^2t\,\mathrm dt$

$=\displaystyle6\int_0^{2\pi}(1-\cos2t)(1+\cos2t)\,\mathrm dt$

$=\displaystyle6\int_0^{2\pi}(1-\cos^22t)\,\mathrm dt$

$=\displaystyle3\int_0^{2\pi}(1-\cos4t)\,\mathrm dt=6\pi$

3 0

1 year ago

Frans filing cabinet is 6 feet tall 1 1/3 feet wide and 3 feet deep. She plans to paint all sides except the bottom of the cabin

aleksley [76]

Well you are look at a 3d image here
so if area is length times width then we need to find the area of every side of the cabinet and add it up
11/3 on the calculator is 3.66666667 sooooo....
top: 3 x 11/3 = 11
side 1: 3 x 6 = 18
side 2: 3 x 6 = 18
front: 6 x 11/3 = 22
back: 6 x 11/3 = 22
so we have all of our measurements:)
now we just add them up together.
11+18+18+22+22= 91!!
so Frans would have to paint 91 square inches of that cabinet:) hope i helped

6 0

2 years ago

The line 3y+x=25 is a normal to the curve y=x2-5x+k.find the value of constant k.

ladessa [460]

Answer:

k = 11.

Step-by-step explanation:

y = x^2 - 5x + k

dy/dx = 2x - 5 = the slope of the tangent to the curve

The slope of the normal = -1/(2x - 5)

The line 3y + x =25 is normal to the curve so finding its slope:

3y = 25 - x

y = -1/3 x + 25/3 <------- Slope is -1/3

So at the point of intersection with the curve, if the line is normal to the curve:

-1/3 = -1 / (2x - 5)

2x - 5 = 3 giving x = 4.

Substituting for x in y = x^2 - 5x + k:

When x = 4, y = (4)^2 - 5*4 + k

y = 16 - 20 + k

so y = k - 4.

From the equation y = -1/3 x + 25/3, at x = 4

y = (-1/3)*4 + 25/3 = 21/3 = 7.

So y = k - 4 = 7

k = 7 + 4 = 11.

6 0

2 years ago