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3 years ago

14

write an equation of a line that passes through the point (5,-1) and is parallel to the line y = (-3/5)x -3

1 answer:

Rasek [7]3 years ago

6 0

Answer:

y = -3/5x + 2

Step-by-step explanation:

-1 = -3/5(5) + b

-1 = -3 + b

2 = b

y = -3/5x + 2

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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:

<u>Calculus</u>

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:

<u>Step 1: Define</u>

<em>Identify</em>

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

Interval [0, π]

<u>Step 2: Find Arc Length</u>

[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

3 years ago

What is the common ratio of 5,10,20,40...

Ratling [72]

The common ratio is the multiplication of 2 each time. 5x2= 10// 10x2=20// 20x2=40

5 0

3 years ago

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Calculate the future value (in dollars) of $1,550 deposited into an account earning an annual simple interest rate of 4% compoun

RUDIKE [14]

Answer: the future value is $1748.4

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = 1550

r = 4% = 4/100 = 0.04

n = 365 because it was compounded 365 times in a year.

t = 3 years

Therefore,.

A = 1550(1 + 0.04/365)^365 × 3

A = 1550(1+0.00011)^1095

A = 1550(1.00011)^1095

A = 1550 × 1.128

A = 1748.4

8 0

3 years ago

PLEASE HELPPP. What is the value of X? type the number TYPE ONLY THE NUMBER

masha68 [24]

Answer:

Value of X is 11

Step-by-step explanation:

hope it helps

7 0

3 years ago

Use the law of cosines to solve for the measure of the largest angle in triangle ABC.

marta [7]

AB is the longest side, so ∠C is the largest angle.
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6 0

4 years ago

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