I need help on this qustion

Find the exact length of the curve. x=et+e−t, y=5−2t, 0≤t≤2 For a curve given by parametric equations x=f(t) and y=g(t), arc len

Rama09 [41]

The length of a curve C parameterized by a vector function r(t) = x(t) i + y(t) j over an interval a ≤ t ≤ b is

$\displaystyle\int_C\mathrm ds = \int_a^b \sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2} \,\mathrm dt$

In this case, we have

x(t) = exp(t ) + exp(-t ) ==> dx/dt = exp(t ) - exp(-t )

y(t) = 5 - 2t ==> dy/dt = -2

and [a, b] = [0, 2]. The length of the curve is then

$\displaystyle\int_0^2 \sqrt{\left(e^t-e^{-t}\right)^2+(-2)^2} \,\mathrm dt = \int_0^2 \sqrt{e^{2t}-2+e^{-2t}+4}\,\mathrm dt$

$=\displaystyle\int_0^2 \sqrt{e^{2t}+2+e^{-2t}} \,\mathrm dt$

$=\displaystyle\int_0^2\sqrt{\left(e^t+e^{-t}\right)^2} \,\mathrm dt$

$=\displaystyle\int_0^2\left(e^t+e^{-t}\right)\,\mathrm dt$

$=\left(e^t-e^{-t}\right)\bigg|_0^2 = \left(e^2-e^{-2}\right)-\left(e^0-e^{-0}\right) = \boxed{e^2-\frac1{e^2}}$

5 0

3 years ago

At a New Car Dealership, a particular model comes in 3 different trim levels (CX, DX,

xxMikexx [17]

Answer:

B. 48

Step-by-step explanation:

Multiply all the numbers of choices together.

trim levels: 3

colors: 4

interior: 4

number of combinations = 3 * 4 * 4 = 48

7 0

3 years ago

Read 2 more answers

Help! will give brainlist!

slega [8]

Answer:

117.5

Step-by-step explanation:

y= 3.5x + 30, where x = his number of toys sold

y= 3.5(25) + 30

y= 117.5

5 0

3 years ago

I round to 900 I have twice as many hundreds as ones and all my digits are different but their sums are 18 can someone answer th

stellarik [79]

Answer:

The number of once is 9.1

The number of hundreds is 8.9

Step-by-step explanation:

Given as :

The total of digits having ones and hundreds = 900

The sum of digits = 18

Let The number of ones digit = O

And The number of hundreds digit = H

So, According to question

H + O = 18 .........1

100 × H + 1 × O = 900 ........2

Solving the equation

( 100 × H - H ) + ( O - O ) = 900 - 18

Or, 99 H + 0 = 882

Or , 99 H = 882

∴ H = $\frac{882}{99}$

I.e H = 8.9

Put the value of H in eq 1

So, O = 18 - H

I.e O = 18 - 8.9

∴ O = 9.1

So, number of once = 9.1

number of hundreds = 8.9

Hence The number of once is 9.1 and The number of hundreds is 8.9

Answer

4 0

3 years ago

1.) Which domain restrictions apply to the rational expression? 14x-2x / x^2-7x

mezya [45]

Answer:

3. $\displaystyle 1\frac{1}{3} = x$

2C. $\displaystyle III.$

2B. $\displaystyle I.$

2A. $\displaystyle II.$

1. $\displaystyle Set-Builder\:Notation: [x|7, 0 ≠ x] \\ Interval\:Notation: (-∞, 0) ∪ (0, 7) ∪ (7, ∞)$

Step-by-step explanation:

3. See above.

2C. The keyword is ratio, which signifies division, so you would choose "III.".

2B. The keyword is percent, which signifies multiplication of a ratio by 100, so you would choose "I.".

2A. The keyword is total, which signifies addition, so you would choose "II.".

1. Base this off of the denominator. Knowing that the denominator CANNOT be zero, you will get this:

$\displaystyle x^2 - 7x \\ x[x - 7] = 0; 7, 0 = x \\ \\ Set-Builder\:Notation: [x|7, 0 ≠ x] \\ Interval\:Notation: (-∞, 0) ∪ (0, 7) ∪ (7, ∞)$

I am joyous to assist you anytime.

5 0

3 years ago