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Leni [432]
3 years ago
5

Add and write the result in the form a+bi. a. (4 + 2i) + (-6 - 7i)

Mathematics
1 answer:
lions [1.4K]3 years ago
7 0

Answer:

- 2 - 5i

Step-by-step explanation:

Given

(4 + 2i) + (- 6 - 7i) ← remove the parenthesis

= 4 + 2i - 6 - 7i ← collect like terms

= - 2 - 5i

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Fraction greater than 1​
Natali [406]

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Step-by-step explanation:

Any fraction where the numerator is bigger than the denominator is a fraction greater than 1. EX. 3/2

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What is the area of the base.(area=6 square in.x 5 in.
Murljashka [212]

Answer:

30 square inch

Step-by-step explanation:

area \: of \: base = 6 \times 5 = 30 \:  {inch}^{2}  \\

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3 years ago
The resquest of the y'+6y=e^4t, y(0)=2
kotegsom [21]
This is a linear differential equation of first order. Solve this by integrating the coefficient of the y term and then raising e to the integrated coefficient to find the integrating factor, i.e. the integrating factor for this problem is e^(6x). 
<span>Multiplying both sides of the equation by the integrating factor: </span>

<span>(y')e^(6x) + 6ye^(6x) = e^(12x) </span>

<span>The left side is the derivative of ye^(6x), hence </span>

<span>d/dx[ye^(6x)] = e^(12x) </span>

<span>Integrating </span>

<span>ye^(6x) = (1/12)e^(12x) + c where c is a constant </span>

<span>y = (1/12)e^(6x) + ce^(-6x) </span>

<span>Use the initial condition y(0)=-8 to find c: </span>

<span>-8 = (1/12) + c </span>
<span>c=-97/12 </span>

<span>Hence </span>

<span>y = (1/12)e^(6x) - (97/12)e^(-6x)</span>
7 0
3 years ago
A block of ice has a square top and bottom and rectangular sides. At a certain point in
Lilit [14]

Answer:

\frac{dV}{dt} = 360 \ cm^3/h

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

<u>Geometry</u>

  • Volume of a Rectangular Prism: V = lwh

<u>Calculus</u>

Derivatives

Derivative Notation

Differentiating with respect to time

Basic Power Rule:

  • f(x) = cxⁿ
  • f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

<u>Step 1: Define</u>

<u />l = 30 \ cm\\w = l\\\frac{dl}{dt} = 2 \ cm/h\\h = 20 \ cm\\\frac{dh}{dt} = 3 \ cm/h<u />

<u />

<u>Step 2: Differentiate</u>

  1. Rewrite [VRP]:                                                                                                 V = l^2h
  2. Differentiate [Basic Power Rule]:                                                                         \frac{dV}{dt} = 2l\frac{dl}{dt} \frac{dh}{dt}

<u>Step 3: Solve for Rate</u>

  1. Substitute:                                                                                                           \frac{dV}{dt} = 2(30 \ cm)(2 \ cm/h)(3 \ cm/h)
  2. Multiply:                                                                                                               \frac{dV}{dt} = 360 \ cm^3/h

Here this tells us that our volume is decreasing (ice melting) at a rate of 360 cm³ per hour.

3 0
3 years ago
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