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4 years ago

9

The sum of two complex numbers, where the real numbers do not equal zero, results in a sum of 34i. Which statement must be true

about the complex numbers?

1 answer:

Ipatiy [6.2K]4 years ago

8 0

Answer:

The complex numbers have opposite real numbers.

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If anyone could help that would be great! The topic is calculus, and substitution + integrals. I need help with the ones circled

Alex_Xolod [135]

Answer:

$\displaystyle \int\limits^{\frac{-\pi}{2}}_{\frac{-2 \pi}{3}} {\frac{sin \ x}{1 + cos \ x}} \, dx = -ln(2)$

General Formulas and Concepts:

<u>Calculus</u>

Differentiation

Derivatives
Derivative Notation

Trig Derivatives

Integration

Integrals
Definite Integrals
Integration Constant C

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Trig Integration

Logarithmic Integration

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

$\displaystyle \int\limits^{\frac{-\pi}{2}}_{\frac{-2 \pi}{3}} {\frac{sin \ x}{1 + cos \ x}} \, dx$

<u>Step 2: Integrate Pt. 1</u>

<em>Identify variables for u-substitution.</em>

Set <em>u</em>: $\displaystyle u = 1 + cos(x)$
[<em>u</em>] Differentiate [Trig Derivative]: $\displaystyle du = -sin(x) \ dx$
[Bounds of Integration] Change: $\displaystyle [\frac{1}{2}, 1]$

<u>Step 3: Integrate Pt. 2</u>

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^{\frac{-\pi}{2}}_{\frac{-2 \pi}{3}} {\frac{sin \ x}{1 + cos \ x}} \, dx = -\int\limits^{\frac{-\pi}{2}}_{\frac{-2 \pi}{3}} {\frac{-sin \ x}{1 + cos \ x}} \, dx$
[Integral] U-Substitution: $\displaystyle \int\limits^{\frac{-\pi}{2}}_{\frac{-2 \pi}{3}} {\frac{sin \ x}{1 + cos \ x}} \, dx = -\int\limits^{1}_{\frac{1}{2}} {\frac{1}{u}} \, du$
[Integral] Logarithmic Integration: $\displaystyle \int\limits^{\frac{-\pi}{2}}_{\frac{-2 \pi}{3}} {\frac{sin \ x}{1 + cos \ x}} \, dx = -(ln|u|) \bigg| \limits^{1}_{\frac{1}{2}}$
Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^{\frac{-\pi}{2}}_{\frac{-2 \pi}{3}} {\frac{sin \ x}{1 + cos \ x}} \, dx = -ln(2)$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

8 0

3 years ago

What place value is the 4 in 246?

faltersainse [42]

2 is in the hundreds place
4 is in the tens place
6 is in the ones place

6 0

3 years ago

Jonathon paid $237 for 15 pizzas, which included the $12 delivery charge. How much will he pay for 22 pizzas

RUDIKE [14]

237-12=225=cost of 15 pizzas without delivery charge
225/15=15=cost per pizza
15*22=$330=cost of 22 pizzas

8 0

4 years ago

Please help. I’ll mark you as brainliest if correct!

tatyana61 [14]

Answer:

Dave worked 60 hours.

Step-by-step explanation:

Let's assume that Dave worked a total of $x$ hours.

Since Kate worked 5 hours less than Dave: $x-5$

And Sarah worked 10 more hours than Dave: $x+10$

Combined, the three siblings worked 185 hours.

$(x)+(x+10)+(x-5) = 185\\x+x+10+x-5 = 185\\3x + 5 =185\\3x = 185 - 5\\3x = 180\\x = 180 \div 3\\x = 60$

Dave worked 60 hours,

Kate worked 55 hours and Sarah worked 70 hours.

To check:

55 + 60 + 70 = 185 hours

6 0

3 years ago

Enter <, >, or = to make the<br> statement true.<br> .320 [?] .051

koban [17]

Answer: .320 is greater than .051 (use the > sign)

Step-by-step explanation:

too lazy to explain, but yes

3 0

3 years ago