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3 years ago

13

Simplify the following expression: Sqrt (-16) + sqrt(-25+5)

1 answer:

Studentka2010 [4]3 years ago

7 0

Answer:

(4 + 2√5) i

Step-by-step explanation:

√(-16) + √(-25 + 5)

√(-16) + √(-20)

4i + 2i√5

(4 + 2√5) i

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Mapoela walks 2 km 30 minutes. At that rate, how far could she walk in 1 ½ hours

kogti [31]

Answer:

5

Step-by-step explanation:

2=30 so 30= 1/2 or an hour so 2+2=4 witch makes an gour half of 2 is 1 so it would make 5

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2 years ago

How do u write the problem

mr Goodwill [35]

I don’t know ‍♀️ I am very sorry

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3 years ago

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

The function in Exercise represents the rate of flow of money in dollars per year. Assume a 10-year period at 8% compounded cont

anzhelika [568]

Answer:

a) The present value is 688.64 $

b) The accumulated amount is 1532.60 $

Step-by-step explanation:

<u>a)</u><u> The preset value equation is given by this formula:</u>

$P=\int^{T}_{0}f(t)e^{-rt}dt$

where:

T is the period in years (T = 10 years)
r is the annual interest rate (r=0.08)

So we have:

$P=\int^{T}_{0}(0.01t+100)e^{-rt}dt$

Now we just need to solve this integral.

$P=\int^{T}_{0}0.01te^{-rt}dt+\int^{T}_{0}100e^{-rt}dt$

$P=e^{-0.08t}(-1.56-0.13t)|^{10}_{0}+1250e^{-0.08t}|^{10}_{0}$

$P=0.30+688.34=688.64 $$

The present value is 688.64 $

<u>b)</u><u> The accumulated amount of money flow formula is:</u>

$A=e^{r\tau}\int^{T}_{0}f(t)e^{-rt}dt$

We have the same equation but whit a term that depends of τ, in our case it is 10.

So we have:

$A=e^{r\tau}\int^{T}_{0}(0.01t+100)e^{-rt}dt=e^{0.08\cdot 10}P$

$A=e^{0.08\cdot 10}688.64=1532.60 $$

The accumulated amount is 1532.60 $

Have a nice day!

6 0

3 years ago

What is the line of the slope shown below

andrezito [222]

Answer:

3

Step-by-step explanation:

$\frac{-3-6}{2--1}=\frac{-9}{3}=3$

4 0

2 years ago

Read 2 more answers