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tatiyna
2 years ago
14

1 Line AB passes through the points A(-1, -2) and B(3,8). Would AB be parallel to a line whose slope is equal to 3?

Mathematics
1 answer:
enyata [817]2 years ago
7 0

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the line above

(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-1)}}}\implies \cfrac{8+2}{3+1}\implies \cfrac{10}{4}\implies \cfrac{5}{2}~\hfill \stackrel{\textit{\large nope}}{\cfrac{5}{2}\ne 3}

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dsp73

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Step-by-step explanation:

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Find the vectors T, N, and B at the given point. r(t) = < t^2, 2/3t^3, t >, (1, 2/3 ,1)
maxonik [38]

Answer with Step-by-step explanation:

We are given that

r(t)=< t^2,\frac{2}{3}t^3,t >

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r'(t)=

\mid r'(t) \mid=\sqrt{(2t)^2+(2t^2)^2+1}=\sqrt{(2t^2+1)^2}=2t^2+1

T(t)=\frac{r'(t)}{\mid r'(t)\mid}=\frac{}{2t^2+1}

Now, substitute t=1

T(1)=\frac{}{2+1}=\frac{1}{3}

T'(t)=\frac{-4t}{(2t^2+1)^2} +\frac{1}{2t^2+1}

T'(1)=-\frac{4}{9}+\frac{1}{3}

T'(1)=\frac{1}{9}=

\mid T'(1)\mid=\sqrt{(\frac{-2}{9})^2+(\frac{4}{9})^2+(\frac{-4}{9})^2}=\sqrt{\frac{36}{81}}=\frac{2}{3}

N(1)=\frac{T'(1)}{\mid T'(1)\mid}

N(1)=\frac{}{\frac{2}{3}}=

N(1)=

B(1)=T(1)\times N(1)

B(1)=\begin{vmatrix}i&j&k\\\frac{2}{3}&\frac{2}{3}&\frac{1}{3}\\\frac{-1}{3}&\frac{2}{3}&\frac{-2}{3}\end{vmatrix}

B(1)=i(\frac{-4}{9}-\frac{2}{9})-j(\frac{-4}{9}+\frac{1}{3})+k(\frac{4}{9}+\frac{2}{9})

B(1)=-\frac{2}{3}i+\frac{1}{3}j+\frac{2}{3}k

B(1)=\frac{1}{3}

5 0
3 years ago
Rearrange the equation so u is the independent variable,<br> 4u + 8w = -3u + 2w<br><br> W=
Katyanochek1 [597]

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w=-1.16u

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first you want to put the W's on one side and the U's on the other. we can do this by subtracting 4u from the left side and the right side making the equations 8w=-7u+2w.

next we want to subtract 2w from both sides making the equation 6w=-7u then we divide by 6 to get w=-1.16u

3 0
2 years ago
I only need number 11 in the picture please help and show work ​
IgorLugansk [536]

Answer:

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2 years ago
Read 2 more answers
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