Question 1

Use the following to answer questions :
For a certain AC circuit, R = 35 $\Omega$, XS1U1B1LS1U1B0 = 20  $\Omega$ and XS1U1B1CS1U1B0 = 8  $\Omega$, with I = 2 A. 
-Find the total voltage across the circuit.

Accepted Answer

The total voltage across the circuit is the sum of the voltages across each resistor. The voltage across the 10 ohm resistor is 10 * 5 = 50V. The voltage across the 15 ohm resistor is 15 * 5 = 75V. The total voltage across the circuit is 50V + 75V = 125V.

Question 2

Use the following to answer questions :
A projectile is launched from a catapult with initial velocity 350 feet/sec at an angle of 65°.
-Find the position of the object after 4 seconds. Round to the nearest hundredth.

Accepted Answer

The answer of Use the following to answer questions :
A...

Question 3

Use the following to answer questions :
zS1U1B11S1U1B0 = 3 - 4i
zS1U1B12S1U1B0 = -1 - 3i
zS1U1B13S1U1B0 = 4 - i
-Express one complex number as the sum of the other two.

Accepted Answer

z₁ = z₂ + z₃ because (3 - 4i) = (-1 - 3i) + (4 - i).

Question 4

Use De Moivre's Theorem to compute  .

Accepted Answer

The answer of Use De Moivre's Theorem to compute ...

Question 5

Use the following to answer questions : -Compute the product z₁z₂ using the trigonometric form. Write your answer in exact rectangular form.

Accepted Answer

The answer of Use the following to answer questions :...

Question 6

Use the following to answer questions : zS1U1B11S1U1B0 = 3 - 4i zS1U1B12S1U1B0 = -1 - 3i zS1U1B13S1U1B0 = 4 - i -Graph the complex numbers z₁, z₂, and z₃ given.

Accepted Answer

The answer of Use the following to answer questions :
zS1U1B11S1U1B0...

Question 7

For the complex numbers z₁ = 1 - i and z₂ = -5 + 0i (a) Find the moduli r₁ and r₂ and the arguments $\theta$₁ and $\theta$₂. (b) Compute the quotient in rectangular form. (c) Find the modulus r and argument $\theta$ of the quotient. (d) Verify that = r and $\theta$₁ - $\theta$₂ = $\theta$.

Accepted Answer

The answer of For the complex numbers z₁ = 1...

Question 8

Write the complex number in trigonometric form. Answer in radians using both an exact form and an approximate form, rounding to four decimal places.
-4 + 6i

Accepted Answer

The answer of Write the complex number in trigonometric form....

Question 9

Write the complex number in trigonometric form using degrees. -4 + 4i

Accepted Answer

To convert the complex number -4 + 4i to trigonometric form, we need to find its magnitude (r) and angle in standard position (θ). Magnitude can be found using the Pythagorean theorem: r = √((-4)^2 + 4^2) = 4√2. The angle can be found using the inverse tangent function: θ = tan⁻¹(4/-4) = 135°. Therefore, the complex number can be expressed as 4√2(cos 135° + i sin 135°), which matches choice C.

Question 10

Use the following to answer questions : 
-Compute the quotient  using the trigonometric form. Write your answer in exact rectangular form.

Accepted Answer

The answer of Use the following to answer questions :...

Question 11

Use the following to answer questions :
For a certain AC circuit, R = 35 $\Omega$, XS1U1B1LS1U1B0 = 20  $\Omega$ and XS1U1B1CS1U1B0 = 8  $\Omega$, with I = 2 A. 
-Find the magnitude of Z, the phase angle between current and voltage, and write the result in trigonometric form.

Accepted Answer

The answer of Use the following to answer questions :
For...

Question 12

Graph the complex number using its trigonometric form, then convert it to rectangular form.

Accepted Answer

The answer of Graph the complex number using its trigonometric...

Question 13

Use the following to answer questions :
A projectile is launched from a catapult with initial velocity 350 feet/sec at an angle of 65°.
-Find the time(s) required to reach a height of 200 feet? Round to the nearest hundredth.

Accepted Answer

The time(s) to reach a height of 200 feet can be found by using the vertical component of the initial velocity and the formula for vertical motion under gravity. The vertical component of the velocity is $v_{0y} = v_0 \sin(\theta)$, where $v_0 = 350$ feet/sec and $\theta = 65^\circ$. The equation for the height $h$ at time $t$ is $h = v_{0y}t - \frac{1}{2}gt^2$, where $g$ is the acceleration due to gravity (approximately $32$ feet/sec$^2$ downward). Solving this quadratic equation for $t$ when $h = 200$ feet gives two possible times, one during the ascent and one during the descent of the projectile. The correct times, rounded to the nearest hundredth, are approximately 0.65 sec and 19.17 sec, which matches option C.

Question 14

Use the following to answer questions : u = ; v = -Find the projection of u along v (compute proj_vu). Round to the nearest hundredth as necessary.

Accepted Answer

Using the formula proj_vu = ((v · u)/(v · v)) * v, we get: ((11ea7f29_5006_c8ee_9ecd_d172e27464ca_TB3307_11_TB3307_11 · 11ea7f29_5006_a1dd_9ecd_6d6f1ae4772d_TB3307_11_TB3307_11)/(11ea7f29_5006_c8ee_9ecd_d172e27464ca_TB3307_11_TB3307_11 · 11ea7f29_5006_c8ee_9ecd_d172e27464ca_TB3307_11_TB3307_11)) * 11ea7f29_5006_c8ee_9ecd_d172e27464ca_TB3307_11_TB3307_11 Simplifying the numerator and the denominator, we get: ((c8ee - a1dd) + (9ecd - 6d6f) + (d172 - d172) + (e274 - 1ae4) + (64ca - 772d) + (TB3307_11 - TB3307_11) + (TB3307_11 - TB3307_11))/((c8ee - c8ee) + (9ecd - 9ecd) + (d172 - d172) + (e274 - e274) + (64ca - 64ca) + (TB3307_11 - TB3307_11) + (TB3307_11 - TB3307_11)) * 11ea7f29_5006_c8ee_9ecd_d172e27464ca_TB3307_11_TB3307_11 Simplifying further, we get: (f) * 11ea7f29_5006_c8ee_9ecd_d172e27464ca_TB3307_11_TB3307_11 Rounding f to the nearest hundredth, we get 0.84. Therefore, we get: 0.84 * 11ea7f29_5006_c8ee_9ecd_d172e27464ca_TB3307_11_TB3307_11 = 11ea7f29_5006_c8f1_9ecd_dfe9cab2f7ae_TB3307_11_TB3307_11 Therefore, the projection of u along v is 11ea7f29_5006_c8f1_9ecd_dfe9cab2f7ae_TB3307_11_TB3307_11, which is option C.

Question 15

Use De Moivre's Theorem to compute (4 + 4i)⁴.

Accepted Answer

The answer of Use De Moivre's Theorem to compute (4...

Question 16

Use De Moivre's Theorem to verify z = -1 + i is a solution to z⁴ - 2z³ - z² + 2z + 10 = 0.

Accepted Answer

The answer of Use De Moivre's Theorem to verify z...

Question 17

Convert the complex number to rectangular form.

Accepted Answer

The answer of Convert the complex number to rectangular form....

Question 18

For the complex numbers z₁ = 3 + 3i and z₂ = -2 - 2i (a) Find the moduli r₁ and r₂ and the arguments $\theta$₁ and $\theta$₂. (b) Compute their product in rectangular form. (c) Find the modulus r and argument $\theta$of the product. (d) Verify that r₁r₂ = r and$\theta$₁ + $\theta$₂ = $\theta$.

Accepted Answer

The answer of For the complex numbers z₁ = 3...

Question 19

Use the following to answer questions : 
-Compute the product  and the quotient  using the trigonometric form. Write your answer in rectangular form. Round to two decimal places as necessary.  = 15(cos 72° + i sin 72°),  = 2.5(cos 36° + i sin 36°)

Accepted Answer

The answer of Use the following to answer questions :...

Question 20

Use the following to answer questions : u = ; v = -Resolve u into vectors u₁ and u₂ where u₁ || v and u₂ $\bot$ v. Round to the nearest hundredth as necessary.

Accepted Answer

The answer of Use the following to answer questions :
u...

Quiz 7: Applications of Trigonometry

Use the following to answer questions : A projectile is launched from a catapult with initial velocity 350 feet/sec at an angle of 65°. -Find the position of the object after 4 seconds. Round to the nearest hundredth.

Use the following to answer questions : z₁ = 3 - 4i z₂ = -1 - 3i z₃ = 4 - i -Express one complex number as the sum of the other two.

Use De Moivre's Theorem to compute .

Use the following to answer questions : -Compute the product z₁z₂ using the trigonometric form. Write your answer in exact rectangular form.

Use the following to answer questions : z₁ = 3 - 4i z₂ = -1 - 3i z₃ = 4 - i -Graph the complex numbers z₁, z₂, and z₃ given.

Write the complex number in trigonometric form. Answer in radians using both an exact form and an approximate form, rounding to four decimal places. -4 + 6i

Write the complex number in trigonometric form using degrees. -4 + 4i

Use the following to answer questions : -Compute the quotient using the trigonometric form. Write your answer in exact rectangular form.

Graph the complex number using its trigonometric form, then convert it to rectangular form.

Use the following to answer questions : A projectile is launched from a catapult with initial velocity 350 feet/sec at an angle of 65°. -Find the time(s) required to reach a height of 200 feet? Round to the nearest hundredth.

Use the following to answer questions : u = ; v = -Find the projection of u along v (compute proj_vu) . Round to the nearest hundredth as necessary.

Use De Moivre's Theorem to compute (4 + 4i) ⁴.

Use De Moivre's Theorem to verify z = -1 + i is a solution to z⁴ - 2z³ - z² + 2z + 10 = 0.

Convert the complex number to rectangular form.

Use the following to answer questions : -Compute the product and the quotient using the trigonometric form. Write your answer in rectangular form. Round to two decimal places as necessary. = 15(cos 72° + i sin 72°), = 2.5(cos 36° + i sin 36°)

Quiz 7: Applications of Trigonometry

Use the following to answer questions : For a certain AC circuit, R = 35 Ω\OmegaΩ , XL = 20 Ω\OmegaΩ and XC = 8 Ω\OmegaΩ , with I = 2 A. -Find the total voltage across the circuit.

Use the following to answer questions : A projectile is launched from a catapult with initial velocity 350 feet/sec at an angle of 65°. -Find the position of the object after 4 seconds. Round to the nearest hundredth.

Use the following to answer questions : z1 = 3 - 4i z2 = -1 - 3i z3 = 4 - i -Express one complex number as the sum of the other two.

Use De Moivre's Theorem to compute .

Use the following to answer questions : -Compute the product z1z2 using the trigonometric form. Write your answer in exact rectangular form.

Use the following to answer questions : z1 = 3 - 4i z2 = -1 - 3i z3 = 4 - i -Graph the complex numbers z1, z2, and z3 given.

Write the complex number in trigonometric form. Answer in radians using both an exact form and an approximate form, rounding to four decimal places. -4 + 6i

Write the complex number in trigonometric form using degrees. -4 + 4i

Use the following to answer questions : -Compute the quotient using the trigonometric form. Write your answer in exact rectangular form.

Use the following to answer questions : For a certain AC circuit, R = 35 Ω\OmegaΩ , XL = 20 Ω\OmegaΩ and XC = 8 Ω\OmegaΩ , with I = 2 A. -Find the magnitude of Z, the phase angle between current and voltage, and write the result in trigonometric form.

Graph the complex number using its trigonometric form, then convert it to rectangular form.

Use the following to answer questions : A projectile is launched from a catapult with initial velocity 350 feet/sec at an angle of 65°. -Find the time(s) required to reach a height of 200 feet? Round to the nearest hundredth.

Use the following to answer questions : u = ; v = -Find the projection of u along v (compute projvu) . Round to the nearest hundredth as necessary.

Use De Moivre's Theorem to compute (4 + 4i) 4.

Use De Moivre's Theorem to verify z = -1 + i is a solution to z4 - 2z3 - z2 + 2z + 10 = 0.

Convert the complex number to rectangular form.

Use the following to answer questions : -Compute the product and the quotient using the trigonometric form. Write your answer in rectangular form. Round to two decimal places as necessary. = 15(cos 72° + i sin 72°), = 2.5(cos 36° + i sin 36°)

Use the following to answer questions : u = ; v = -Resolve u into vectors u1 and u2 where u1 || v and u2 ⊥\bot⊥ v. Round to the nearest hundredth as necessary.

Use the following to answer questions : z₁ = 3 - 4i z₂ = -1 - 3i z₃ = 4 - i -Express one complex number as the sum of the other two.

Use the following to answer questions : -Compute the product z₁z₂ using the trigonometric form. Write your answer in exact rectangular form.

Use the following to answer questions : z₁ = 3 - 4i z₂ = -1 - 3i z₃ = 4 - i -Graph the complex numbers z₁, z₂, and z₃ given.

Use the following to answer questions : u = ; v = -Find the projection of u along v (compute proj_vu) . Round to the nearest hundredth as necessary.

Use De Moivre's Theorem to compute (4 + 4i) ⁴.

Use De Moivre's Theorem to verify z = -1 + i is a solution to z⁴ - 2z³ - z² + 2z + 10 = 0.