Complex numbers Questions and Answers

Expressed in a + bi form, 5/3-4i is equivalent to

Evaluate the following expressions. (a) log3 3^8 = (b) log3 243 = (c) log5 625 = (d) log4 4³ =

A person standing close to the edge on top of a 56-foot building throws a ball vertically upward. The quadratic function h = 16t² + 104t + 56 models the ball's height above the ground, h, in feet, t seconds after it was thrown. a) What is the maximum height of the ball? ______ feet b) How many seconds does it take until the ball hits the ground?

For a class project, students in Health class ask every tenth student entering the school if they eat breakfast in the morning.

solve the following LP using M-method. Maximize z = x₁ + 5x₂ 3x₁+ 4x₂ ≤ 6 X₁ + 3x₂ ≥ 2, X₁, X₂ ≥ 0.

Let S be the part of the sphere x² + y² + z² = 25 that lies above the plane z = 4. Let S have constant density k. (a) Find the center of mass. (x, y, z) = __ (b) Find the moment of inertia about the z-axis. I₂ =

Simplify leaving your answer with positive exponents (5m²/³/n²/³)‾³

In the figure a semi circumference is shown with diameter being the segment AB and center O, also, the ray AD is bisector of the angle (CAB). If AC=12 and AB=14, What is the value of the segment BE?

An investment is projected to generate a continuous revenue stream at the rate of R(t) = 40,000 e⁰.⁰²ᵗ dollars/year for the next 3 years. If the income stream is invested in a bank that pays interest at the rate of 5.5%/year compounded continuously, find the total accumulated value (in dollars) of this income stream at the end of 3 years. (Round your answer to the nearest dollar.)

(1)Using the graph, determine any relative maxima or minima of the function and the intervals on which the function is increasing or decreasing. f(x) = -x² +9x - 14 (2)Using the graph, determine any relative maxima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (A) The relative maximum value(s). . .occur(s) at x =. . . (Use a comma to separate answers as needed. Type integers or decimals.) (B) The function has no relative maximum.

For f(x) = 7x³, construct and simplify the difference quotient f(x+h)-f(x)/h f(x+h)-f(x)/h =

Given the functions f (x) = x- 3x- 10 and g(x) = x-5, graph the function h (x) where, h(x) = f(x)÷g(x)

In the diagram, ∆ABC has a right angle at B and M is the midpoint of BC. A circle is drawn using BC as its diameter. P is the point of intersection of the circle with AC. The tangent to the circle at P cuts AB at Q. Prove that QM is parallel to AC.

The functions q and r are defined as follows. Find the following. Simplify your answers. Do not use decimals. (1)q(x)=2x-2 (2)r(x) = -2x²-2 (3)q (r (-5))= (4) r(r(3))

In the diagram, two circles are tangent to each other at point B. A straight line is drawn through B cutting the two circles at A and C, as shown. Tangent lines are drawn to the circles at A and C. Prove that these two tangent lines are parallel. In the diagram, AB and BC are chords of the circle with AB < BC. If D is the point on the circle such that AD is perpendicular to BC and E is the point on the circle such that DE is parallel to BC, prove that LEAC+ ZABC = 90°.

Let f(x) = -x² + 6x. Find the difference quotient for f(4+h) f(4)/h (Simplify your answer completely.) What steps or reasoning did you use? Your work counts towards your score You can submit show my work an unlimited number of times

Solve the equation for the interval [0, 2π). 11) 2 sin²x = sin x A) x = 0, π, π/6, 5π/6 B) x = π/3 , 2π/3 C) x = π/6 , 5π/6 D) x = π/2 , 3π/2 , π/3 , 2π/3

Find the equation with following roots: a) -2 ± 5√√7

Rewrite √(-20) in terms of the imaginary unit, i. Simplify your answer as much as possible.

Identify the graph of the polar equation r = 3 - 2 sin θ a) Cardioid with hole b) Cardioid pointing up c) Strawberry pointing up d) Strawberry pointing down

Perform the operation. Write your answer in terms of i. (3/8-i/3)-(1/2-1/2i)

Simplify your answer as much as possible. i (1 + i)

Use Euler's method with h = 0.2 to approximate y(0.6) of the IVP: 1.127 1:171 1.042 1.422

Simplify the following expression. Write your answer in terms of i. (-8-3i) + (5 + 2i) Provide your answer below: _________________

Solve the system by elimination . y = -3x² + x + 2 y = x+4 (A) ( 5 , 3) (B) ( 2 , -9) (C) ( -4 , 29) (D) ( 1 , 1) (E) ( 4 , -11) (F) ( -6 , 22) (G) ( 0 , 2) (H) ( -7 , -8) (I) no solutions

Write as a radical and then simplify. (-1024)¹/⁵ Provide your answer below:

Find the function value. Round to four decimal places. tan 22 ° 24°

Find all complex fourth roots in the rectangular form of w=81cos(4π/3)+ i sin (4π/3)

Write the complex number in standard form a + bi. (3 - √-24) / 6 Select the correct answer below: (a) 2/3 - (√6)/3i (b) 1/2 + (√6)/3i (c) 1/2 - (√6)/3i (d) 1/2 + (√6)/6i

Write the standard equation for the circle whose center is at (1,10) and whose radius is 2. Choose the correct answer below. A). (x+1)² + (y+10)² = 2 B). (x-1)²-(y+10)² = 2 C). (x-1)² + (y-10)² = 4 D). (x + 1)² + (y+10)² = 4

Simplify the following expression. √(-2){√(-2) - √6} Select the correct answer below: A) -2 - 2i√3 B) -2 - 4i√3 C) −2 + 2i√3 D) 2i + 2i√3

20.Which of the following is NOT coterminal to an angle measuring 2π/3? a) 14π/3 b) -4π/3 c) 32π/3 d) -20π/3 21.sinθ=-9/41 and π ≤ θ ≤ 3π/2 , what is cosθ? a) 41/40 b)-41/40 c) 40/41 d) -40/41

Rewrite √-81 in terms of the imaginary unit, i. Provide your answer below:

Simplify the following expression . 3-i /2i

Simplify the following expression, and write in terms of i. -i√3/3+√2i

Simplify the following expression{15/1-2i}

If the Babylonian numeral V stands for one and the Babylonian numeral < stands for ten, then write the Babylonian numeral as a Hindu-Arabic numeral. VVV <VV VVV (A) 11,523 (B) 1083 (C) 18 (D) 903

Rewrite √(-48) in terms of imaginary unit, i. Simplify your answer as much as possible. Provide your answer below:

A total of 464 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was three times the number of adult tickets sold. How many adult tickets were sold?

For the following structure, which is proper symmetry or antisymmetry boundary condition can be used on the dashed line for simplifying the FE model using only its potion instead of the whole model. 1. Ux=0; Uy=0 2. Ux=0; Uy is free 3.Ux is free; Uy=0 4.Ux is free; Uy is free

Simplify the following expression, and write in terms of i (-√-6 /( √18 +√-4) )

Solve the following differential equation using Laplace transforms: y" – 5y' + 6y = sinh(t), y(0) =y'(0) = 0

Which function has an amplitude of 3 and a period of pi/2 ? (a)f(x) = 3 cos(4x) (b)f(x) = 4 cos(3x) (c)f(x) = 3 cos(1/2x) (d)f(x) = 1/2cos(3x)

(6) Find the magnitude and the direction angle for: a) v =< 2, -2√3> b) v =< -3, -3 > c) v =< -5√3, 5> (7) Find the quotient or product and write the result in standard complex form: (a) 6(cos 225° + i sin 225°) / (3cos135° + i sin135°) b) 2 (cos120° +i sin120°) * 4 (cos 90° +i sin 90°)

Convert each point to exact polar coordinates using positive values for r and θ. (a) (-5,0) (b) (4,-4√3)

Simplify the following expression. (4+3i)² Provide your answer below:

Select the correct answer. Which absolute value function corresponds to the graph with these characteristics? • The vertex is at (2,4). • As x approaches negative infinity, fx) approaches positive infinity. • The domain is all real numbers. • It is decreasing on the interval (-∞, 2). A. f(x) = |x+2|-4 B. f(x)= |x-2|+4 C. f(x)= |x+2|+4 D. f(x)= |x+2|-4

Solve the triangle. a = 4.24 ft , b = 3.72 ft , c = 5.82 ft A = B = C =

Enter the correct answer in the box. Rewrite this logarithmic equation as an exponential equation. log2 18 = x

For the function given below, (a) use the product-to-sum formulas to express the product as a sum, and (b) use the method of adding y-coordinates to grach the function on (a) G(x)= (b) Choose the correct graph below G(x) = cos(4x) cos(2x)