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dangina [55]
3 years ago
6

PLEASE HELP ME SOLVE

Mathematics
1 answer:
jasenka [17]3 years ago
8 0

Two lines are perpendicular if their slope m and m' satisfy the equation

mm'=-1

The slope of the given line is 4, because the line is written in the slope-intercept y=mx+q, where m is the slope.

So, the perpendicular slope is

4m'=-1 \iff m'=-\dfrac{1}{4}

So, we want a line with slope -1/4 and passing through (-1,3). We can use the formula

y-b=m(x-a)

for the line passing trough (a,b) with slope m:

y-3=-\dfrac{1}{4}(x+1) \iff y=-\dfrac{1}{4}x-\dfrac{1}{4}+3\iff y=-\dfrac{1}{4}x+\dfrac{11}{4}

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(a) Find a vector parallel to the line of intersection of the planes −4x+2y−z=1 and 3x−2y+2z=1.
valentinak56 [21]

Find the intersection of the two planes. Do this by solving for <em>z</em> in terms of <em>x</em> and <em>y </em>; then solve for <em>y</em> in terms of <em>x</em> ; then again for <em>z</em> but only in terms of <em>x</em>.

-4<em>x</em> + 2<em>y</em> - <em>z</em> = 1   ==>   <em>z</em> = -4<em>x</em> + 2<em>y</em> - 1

3<em>x</em> - 2<em>y</em> + 2<em>z</em> = 1   ==>   <em>z</em> = (1 - 3<em>x</em> + 2<em>y</em>)/2

==>   -4<em>x</em> + 2<em>y</em> - 1 = (1 - 3<em>x</em> + 2<em>y</em>)/2

==>   -8<em>x</em> + 4<em>y</em> - 2 = 1 - 3<em>x</em> + 2<em>y</em>

==>   -5<em>x</em> + 2<em>y</em> = 3

==>   <em>y</em> = (3 + 5<em>x</em>)/2

==>   <em>z</em> = -4<em>x</em> + 2 (3 + 5<em>x</em>)/2 - 1 = <em>x</em> + 2

So if we take <em>x</em> = <em>t</em>, the line of intersection is parameterized by

<em>r</em><em>(t)</em> = ⟨<em>t</em>, (3 + 5<em>t</em> )/2, 2 + <em>t</em>⟩

Just to not have to work with fractions, scale this by a factor of 2, so that

<em>r</em><em>(t)</em> = ⟨2<em>t</em>, 3 + 5<em>t</em>, 4 + 2<em>t</em>⟩

(a) The tangent vector to <em>r</em><em>(t)</em> is parallel to this line, so you can use

<em>v</em> = d<em>r</em>/d<em>t</em> = d/d<em>t</em> ⟨2<em>t</em>, 3 + 5<em>t</em>, 4 + 2<em>t</em>⟩ = ⟨2, 5, 2⟩

or any scalar multiple of this.

(b) (-1, -1, 1) indeed lies in both planes. Plug in <em>x</em> = -1, <em>y</em> = 1, and <em>z</em> = 1 to both plane equations to see this for yourself. We already found the parameterization for the intersection,

<em>r</em><em>(t)</em> = ⟨2<em>t</em>, 3 + 5<em>t</em>, 4 + 2<em>t</em>⟩

3 0
2 years ago
What is 12% of 1350?
antoniya [11.8K]
162 is the answer to your question siskjsskjajanajajajsjskskaiw
3 0
3 years ago
Read 2 more answers
Angel borrowed $141 to buy a stereo. He pays backs $14 each week. How much does he still owes after each week? Use a graph if yo
Harrizon [31]

Logically, he would owe 14 less each week

Let x = # of weeks passed

Algebraic Expression: 141 - 14x =

Week 1: 141 - 14 = 127

Week 2: 141 - 14(2) = 113

Week 3: 141 - 14(3) = 99

etc.....

Hope this helps


3 0
3 years ago
Plz help this is urgent
Alex777 [14]

Answer:

A. 13 + t = 17

Step-by-step explanation:

The top rectangle shows 13 and t, the 13 and t rectangle is the same size as the 17 rectangle so 13 + t = 17. It's not multiplication as there's no multiple's of 13 or t on the diagram.

6 0
2 years ago
Please help mee. don’t troll neitha.
labwork [276]

Answer: 60 units²

Step-by-step explanation:

The total area of the rectangle is equal:

(4+4)*(9+3)=

8*12=

96 units²

The area of the unpainted part of the rectangle is equal:

4*9=

36 units²

The area of the shaded region is equal:

96-36=

60 units²

4 0
1 year ago
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