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ss7ja [257]
3 years ago
7

what is the equation of a line parallel to the following line that passes through the points given. y=-4x+6 (2,-1)

Mathematics
1 answer:
Delvig [45]3 years ago
8 0

Answer:

Short Answer Type:

y = -4x + 6

Therefore slope = (-4)

Given:

Point = (2,-1)

Slope = -4

Therefore: -1 = -8 + c

=> c = 7

<h2><u>Therefore equation: y = -4x + 7</u></h2>

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Suppose r(t) = (et cos t)i + (et sin t)j. Show that the angle between r and a never changes. What is the angle?
tatyana61 [14]

Answer:

Angle = Ф = cos^{-1}(0) = 0

Hence, it is proved that angle between position vector r and acceleration vector a = 0 and is it never changes.

Step-by-step explanation:

Given vector r(t) = e^{t}cost i + e^{t}sint j

As we know that,

velocity vector = v = \frac{dr}{dt}

Implies that

velocity vector = (e^{t} cost - e^{t} sint)i + (e^{t} sint - e^{t}cost )j

As acceleration is velocity over time so:

acceleration vector = a = \frac{dv}{dt}

Implies that

vector a =

(e^{t}cost - e^{t}sint - e^{t}sint - e^{t}cost )i + ( e^{t}sint + e^{t}cost + e^{t}cost - e^{t}sint )j

vector a = (-2e^{t}sint) i + ( 2e^{t}cost)j

Now scalar product of position vector r and acceleration vector a:

r. a = . \\

r.a = -2e^{2t}sintcost + 2e^{2t}sintcost

r.a = 0

Now, for angle between position vector r and acceleration vector a is given by:

cosФ = \frac{r.a}{|r|.|a|} = \frac{0}{|r|.|a|} = 0

Ф = cos^{-1}(0) = 0

Hence, it is proved that angle between position vector r and acceleration vector a = 0 and is it never changes.

4 0
3 years ago
DESPERATELY NEED HELP!! TANGENT LINES; WHAT IS THE VALUE OF X? PLEASE EXPLAIN! BRAINLIEST GIVEN!!
ycow [4]
I believe x is 30 degrees.

The equilateral triangle has each angle equal to 60 degrees. So the small arc near x is also 60. The angle x is half the arc so would be 30.
This also makes sense because the triangle it forms with angle x and the center has center angle of 60 and angle formed by tangent and radius of 90. So it is a 30-60-90 triangle, making angle x 30.

4 0
3 years ago
The perimeter of a rectangle is 48 m. The width of the rectangle is 2 more than half the length. Find the length and the width
Ksivusya [100]

Answer:

Length = 14.6667

Width = 9.33333

Step-by-step explanation:

let the length be x

Width = (x/2)+2

Perimeter = 2(L+W)

Perimeter = 2(x+(x/2+2)) =48

2[(3/2)x + 2] =48

3x+4= 48

3x = 44

x =14.666667

width = (14.666667/2)+2

Width = 9.333333

<em>PLEASE RATE BRAINLIEST</em>


3 0
3 years ago
Please help me with this<br>no links
k0ka [10]

Step-by-step explanation:

  1. A(2,4)=A'(-4,-2)
  2. B(-3,-5)=B'(5,3)
  3. C(2,-3)=C'(3,-2)
  4. D(-4,9)=D'(-9,4)
  5. E(10,4)=E'(-4,-10)
  6. F(-1,-7)=F'(7,1)
  7. G(-4,8)=G'(-8,4)
  8. H(-4,-5)=H'(5,4)
  9. J(-7,-2)=J'(2,7)
  10. K(0,9)=K'(-9,0)
  11. L(0,-3)=L'(3,0)
  12. M(-5,0)=M'(0,5)
  13. l(1,-8)=l'(8,-1)
  14. N(2,0)=N'(0,-2)

<h2>stay safe healthy and happy.</h2>
6 0
3 years ago
Read 2 more answers
120% of what number is 36?
velikii [3]
The answer is 43.2 Hope this helps!
6 0
4 years ago
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