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posledela
2 years ago
14

Help please . . . .

Mathematics
1 answer:
Travka [436]2 years ago
3 0

Answer:

Your answer is A.

Step-by-step explanation:

Looking at the graphing two-equation: y = x^3 -3 and y = x^2+6 are up there, it can help us determine the limit of domain.

The dot is the x<=2 for equation y=x^3-3.

The circle is x>2 for equation y=x^2+6

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Find an equation of the tangent to the curve x =5+lnt, y=t2+5 at the point (5,6) by both eliminating the parameter and without e
svet-max [94.6K]

ANSWER

y = 2x -4

EXPLANATION

Part a)

Eliminating the parameter:

The parametric equation is

x = 5 +  ln(t)

y =  {t}^{2}  + 5

From the first equation we make t the subject to get;

x - 5 =  ln(t)

t =  {e}^{x - 5}

We put it into the second equation.

y =  { ({e}^{x - 5}) }^{2}  + 5

y =  { ({e}^{2(x - 5)}) }  + 5

We differentiate to get;

\frac{dy}{dx}  = 2 {e}^{2(x - 5)}

At x=5,

\frac{dy}{dx}  = 2 {e}^{2(5 - 5)}

\frac{dy}{dx}  = 2 {e}^{0}  = 2

The slope of the tangent is 2.

The equation of the tangent through

(5,6) is given by

y-y_1=m(x-x_1)

y - 6 = 2(x - 5)

y = 2x - 10 + 6

y = 2x -4

Without eliminating the parameter,

\frac{dy}{dx}  =  \frac{ \frac{dy}{dt} }{ \frac{dx}{dt} }

\frac{dy}{dx}  =  \frac{ 2t}{  \frac{1}{t} }

\frac{dy}{dx}  =  2 {t}^{2}

At x=5,

5 = 5 +  ln(t)

ln(t)  = 0

t =  {e}^{0}  = 1

This implies that,

\frac{dy}{dx}  =  2 {(1)}^{2}  = 2

The slope of the tangent is 2.

The equation of the tangent through

(5,6) is given by

y-y_1=m(x-x_1)

y - 6 = 2(x - 5) =

y = 2x -4

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3 years ago
Natasha wants to find out if the neighborhood supports lowering the speed limit on the street in front of her school. Which is a
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The answer is
Thirty residents who live within a 2 mile radius of natashas school.
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2 years ago
two circles are externally tangent to each other. One circle has a diameter of 62 yards and the distance between the centers of
maksim [4K]

Answer:

108 yards

Step-by-step explanation:

Let circle A be the circle with the 62 yard diameter

Let circle B be the circle whose diameter we are trying to solve for.

  • Externally tangent circles are circles which touch each other and share a common external tangent.
  • Circle A has a tangent of 62 yards and thus a radius ( half the diameter) of 31 yards.
  • The distance between the centers of the 2 circles is 85 yards. If you subtract the radius ( distance from the center of the circle to its circumference) of circle A then we'll only be left with the radius of circle B.
  • 85 - 31= 54 yards which is the radius of circle B
  • To get the diameter: 54 x 2 = 108 yards

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Answer:

Step-by-step explanation:

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