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yaroslaw [1]
3 years ago
8

What is the perimeter of the are. Please show work.​

Mathematics
1 answer:
Brilliant_brown [7]3 years ago
5 0

Answer:

p = 633.09 ft

Step-by-step explanation:

The distances of each leg are indicated

Add them to get the perimeter

p = 100 + 89.44 + 186.81 + 120.83 + 136.01

p = 633.09 ft

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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
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x = 8

Step-by-step explanation:

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16x-4 + 7x = 180, combine like terms

23x - 4 = 180, add 4 on both sides (isolate variable)

23x = 184, divide 23 on both sides

x = 8

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1 year ago
Solve this quadratic equation. x^2+2x-22=0
torisob [31]
X=⁻3 and x=1
because 
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A jewelry store is selling a set of 4 pairs of gemstone earrings for $58, including tax. Neva and three of her friends want to b
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Each member should pay $14.5, including tax.
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PLEASE SHOW YOUR WORK WITH YOUR ANSWER. Two bags had 50 kilograms of sugar each. After taking out 3 times as much sugar from bag
Svetllana [295]

Answer:

Bag 1: 20

Bag 2: 40

Step-by-step explanation:

Let x be the amount taken out of bag 2

Then the amount left in each bag can be written as:

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Bag 2: 50-x

Since we know that half of bag 2 is bag 1, that gives us:

50-3x = 1/2(50-x)

-> 50-3x = 25-x/2

Now lets isolate x and solve:

25 = 5x/2

-> 50 = 5x

-> x = 10

So plug x bag in for the original equations:

Bag 1: 50-3x = 50-3(10) = 20

Bag 2: 50-x = 50-10 = 40

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3 years ago
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