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2 years ago

7+(-14)+(-6)+13+4=-37

Mathematics

1 answer:

Kaylis [27]2 years ago

4 0

Answer:

Step-by-step explanation:

7+(-14)+(-6)+13+4

7+(-20)+13+4

(-13)+13+4

0+4

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What is the length of the curve with parametric equations x = t - cos(t), y = 1 - sin(t) from t = 0 to t = π? (5 points)

zzz [600]

Answer:

B) 4√2

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Parametric Differentiation

Integration

Integrals
Definite Integrals
Integration Constant C

Arc Length Formula [Parametric]: $\displaystyle AL = \int\limits^b_a {\sqrt{[x'(t)]^2 + [y(t)]^2}} \, dx$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \left \{ {{x = t - cos(t)} \atop {y = 1 - sin(t)}} \right.$

Interval [0, π]

Step 2: Find Arc Length

[Parametrics] Differentiate [Basic Power Rule, Trig Differentiation]: $\displaystyle \left \{ {{x' = 1 + sin(t)} \atop {y' = -cos(t)}} \right.$
Substitute in variables [Arc Length Formula - Parametric]: $\displaystyle AL = \int\limits^{\pi}_0 {\sqrt{[1 + sin(t)]^2 + [-cos(t)]^2}} \, dx$
[Integrand] Simplify: $\displaystyle AL = \int\limits^{\pi}_0 {\sqrt{2[sin(x) + 1]} \, dx$
[Integral] Evaluate: $\displaystyle AL = \int\limits^{\pi}_0 {\sqrt{2[sin(x) + 1]} \, dx = 4\sqrt{2}$

Topic: AP Calculus BC (Calculus I + II)

Unit: Parametric Integration

Book: College Calculus 10e

4 0

2 years ago

Write the equation of the line in slope-intercept that has passes through the points (2,-5) and (8, 13).

const2013 [10]

Answer:

The equation of the straight line in Slope- intercept form

y = 3 x - 11

Step-by-step explanation:

Explanation:-

Given points are (2,-5) and (8, 13)

The Slope of the line

$m = \frac{y_{2} -y_{1} }{x_{2} -x_{1} } = \frac{13-(-5)}{8-2} = \frac{18}{6} =3$

Equation of the line having slope 'm' and given point

$y - y_{1} = m (x - x_{1} )$

(x₁ , y₁) = ( 2, -5 )

$y - (-5) = 3 (x - 2 )$

y + 5 = 3x - 6

The equation of the straight line in slope intercept form

y = m x + c

y = 3 x - 6-5

y = 3 x - 11

Final answer:-

The equation of the straight line in Slope- intercept form

y = 3 x - 11

8 0

3 years ago

Must show all work for 15 points

andreyandreev [35.5K]

Answer:

Hey there!

10x-1=4x+2

6x-1=2

6x=3

x=1/2 cm.

10x-1=4 cm.

So the width of the rectangle is 10/4, or 2.5 cm.

l=3w

2l+2w=24

2(3w)+2w=24

6w+2w=24

8w=24

w=3

l=9

The are is 27 units squared.

Let me know if this helps :)

3 0

3 years ago

What’s the volume of the rectangular prism of 2cm, 7/3 cm and 2cm?

Eduardwww [97]

Answer:

9 1/3 cm³

Step-by-step explanation:

First multiply two numbers.

2x2=4

Then multiply the product by the third number.

4x7/3

4 x 7

1 x 3

= 28/3 or 9 1/3

hope it helps

3 0

2 years ago

What value of x makes this equation true? 12x-15= 6-3x

aleksley [76]

The answer is X is equal to 1.4

7 0

3 years ago

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7+(-14)+(-6)+13+4=-37​

7+(-14)+(-6)+13+4=-37