what is the answer to this?

The voltage of the circuit is 8 + i .  Option C

From the information given, we have that;

E = IZ

Where;

We have that;

I = 3 + 2i

Z = 2 - i

Substitute into the formula

E = IZ

E = ( 3 + 2i) ( 2 - i)

Making the product of complex numbers we have:

E = ( 3 × 2 - i ) + ( 4i - 2i²)

E = ( 6 - 3i ) + ( 4i - 2 ( -1) )

E = ( 6 + 2) + ( 4 - 3 ) i

E = 8 + i

Thus, the voltage of the circuit is 8 + i .  Option C

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Answer:

It's C

Step-by-step explanation:

a. Recall that in polar coordinates, we can parameterize [tex]x=r\cos(\theta)[/tex] and [tex]y=r\sin(\theta)[/tex]. So, doing as the hint suggests, we have

[tex]r = 6\cos(\theta) + 8 \sin(\theta)[/tex]

[tex]\implies r^2 = 6r\cos(\theta) + 8r\sin(\theta)[/tex]

[tex]\implies \boxed{x^2 + y^2 = 6x + 8y}[/tex]

b. By completing the square, we get

[tex]x^2 + y^2 = 6x + 8y[/tex]

[tex]x^2 - 6x + y^2 - 8y = 0[/tex]

[tex]x^2 - 6x + 9 + y^2 - 8y + 16 = 25[/tex]

[tex](x-3)^2 + (y-4)^2 = 5^2[/tex]

which is the equation of the circle centered at (3, 4) with radius 5. Thus the area bounded by [tex]C[/tex] is [tex]\pi\cdot5^2 = \boxed{25\pi}[/tex].

c. This is made easier if you can consult a plot (attached). In the first quadrant, we have [tex]0\le\theta\le\frac\pi2[/tex], while the radial coordinate [tex]r[/tex] runs uninterrupted from the origin [tex]r=0[/tex] to the circle [tex]r=6\cos(\theta)+8\sin(\theta)[/tex]. So the area is

[tex]\displaystyle \int_0^{\pi/2} \int_0^{6\cos(\theta) + 8\sin(\theta)} r\,dr\,d\theta = \boxed{\frac12 \int_0^{\pi/2} \left(6\cos(\theta) + 8\sin(\theta)\right)^2 \, d\theta}[/tex]

d. Evaluate the integral.

[tex]\displaystyle \frac12 \int_0^{\pi/2} \left(36\cos^2(\theta) + 96\sin(\theta)\cos(\theta) + 64 \sin^2(\theta)\right) \, d\theta[/tex]

Simplify the integrand with the help of the identities

[tex]\cos^2(x) + \sin^2(x) = 1[/tex]

[tex]\sin(x)\cos(x) = \dfrac12 \sin(2x)[/tex]

[tex]\sin^2(x) = \dfrac{1 - \cos(2x)}2[/tex]

[tex]\displaystyle \frac12 \int_0^{\pi/2} \left(50 + 48\sin(2\theta) - 14 \cos(2\theta)\right) \, d\theta[/tex]

The rest is easy. You should end up with

[tex]\displaystyle \frac12 \int_0^{\pi/2} \left(6\cos(\theta) + 8\sin(\theta)\right)^2 \, d\theta = \boxed{24 + \frac{25\pi}2}[/tex]

a) The Cartesian equation that described curve C is x² + y² = 6 · x + 8 · y.

b) The area inside C is A = π · 5² = 25π square units.

c) The integral that computed the area inside curve C within the first quadrant is A = (1 / 2)∫ (6 · cos θ + 8 · sin θ)² dθ, for θ ∈ [0, 0.5π].

d) The integral evaluated at the given limits is equal to an area of 20.139π square units.

In this question we find a polar equation in explicit form. a) To find the equivalent form in rectangular coordinates, we must apply the following substitutions x = r · cos θ, y = r · sin θ:

r = 6 · cos θ + 8 · sin θ

r² = 6 · r · cos θ + 8 · r · sin θ

x² + y² = 6 · x + 8 · y       (1)

The Cartesian equation that described curve C is x² + y² = 6 · x + 8 · y.

b) Perhaps the equation represents a conic section, possibly a circunference. To prove this assumption, we must apply algebraic handling until standard form is obtained:

x² - 6 · x + y² - 8 · y = 0

x² - 6 · x + 9 + y² - 8 · y + 16 = 25

(x - 3)² + (y - 4)² = 5²          (1b)

Which indicates a circumference centered at point (h, k) = (3, 4) and with a radius of 5 units. By the area formula for a circle we find that the area inside C is A = π · 5² = 25π square units.

c) The polar form of the area integral is presented herein:

A = ∫ ∫ r dr dθ, for r ∈ [0, r(θ)] and θ ∈ [0, 0.5π]  

A = (1 / 2)∫ [r(θ)]² dθ, for θ ∈ [0, 0.5π]  

A = (1 / 2)∫ (6 · cos θ + 8 · sin θ)² dθ, for θ ∈ [0, 0.5π]  

The integral that computed the area inside curve C within the first quadrant is A = (1 / 2)∫ (6 · cos θ + 8 · sin θ)² dθ, for θ ∈ [0, 0.5π].

d) By algebraic handling, trigonometric formulas and integral properties:

A = 25 ∫ dθ  + 24 ∫ sin 2θ dθ - 14 ∫ cos 2θ dθ, for θ ∈ [0, 0.5π]  

A = 25 · θ - 12 · cos 2θ - 7 · sin 2θ, for θ ∈ [0, 0.5π]  

A = 20.139π

The integral evaluated at the given limits is equal to an area of 20.139π square units.  

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Answer:

Your answer is - 28

Step-by-step explanation:

Given,

          a = 2

          b = - 3

          c = - 1

          d = 4

Now,

       - 2 ( b²  -  5 c )

= - 2 ( -3²  -  5 ( - 1 ) )

= - 2 ( 9 + 5 )

= - 2 × 14

= - 28   ans….

Hope its helpful :-)

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The equation for the horizontal asymptote will be y = -2.

Since the degree of the numerator and denominator of f(x) is the same both being 1, therefore horizontal asymptote exists and is given by:

y = Leading coefficient of numerator of f(x) / Leading coefficient of denominator of f(x)

= y = -2/1

= y = -2

The vertical asymptote will be f(x) = -2x / (x + 3). To find the vertical asymptote we will equate the denominator of f(x) = 0

= x + 3 = 0

= x = -3

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The equation for the trajectories orthogonal to the family of functions of the form 5 · x² - 2 · y² = C is equal to (1 / 5) · ㏑ x + (1 / 2) · ㏑ y = C.

In this problem we have a family of functions in implicit form, that is, a function of the form f(x, y, c) = 0. The equation of a orthogonal trajectory is always perpendicular to a particular form of a equation. First, we determine the first derivative of the given expression:

5 · x² - 2 · y² = C

10 · x - 4 · y · y' = 0

4 · y · y' = 10 · x

y' = (10 · x) / (4 · y)

y' = (5 · x) / (2 · y)

If f(x, y) = (5 · x) / (2 · y), then the differential equation for the orthogonal trajectories related to the family of functions is:

y' = - 1 / f(x, y)

y' = - (2 · y) / (5 · x)

dy / (2 · y) = - dx / (5 · x)

By indefinite integration we get the following solution to the ordinary differential equation:

(1 / 2) · ㏑ y = - (1 / 5) · ㏑ x + C

(1 / 5) · ㏑ x + (1 / 2) · ㏑ y = C

The equation for the trajectories orthogonal to the family of functions of the form 5 · x² - 2 · y² = C is equal to (1 / 5) · ㏑ x + (1 / 2) · ㏑ y = C.

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Answer:

Joey needs 9 boxes.

Step-by-step explanation:

You will use the fact that a dozen is 12 cookies. You're trying to find how many dozen are in 100.

Something like:

12b = 100

or if you're studying inequalities:

12b >= 100

Divide by 12 to solve. See image. Interpret the results. See image.

Answer:

Yes

Step-by-step explanation:

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side or largest side. So, 7+6 = 13 which is greater than 9

Answer:

Yes, triangle with sides 6, 7 ,9 can be formed.

Step-by-step explanation:

The sum of any two sides of the triangle should be greater than the third side. If so, triangle can be formed.

6 + 7 = 13  >  9

7+ 9 = 16    > 6

6 +9 = 15   > 7

Answer:

[tex]2 {x}^{2} + 7xy - 15 {y}^{2} [/tex]

Step-by-step explanation:

We can use the rainbow expansion method to find the expression.

[tex](2x - 3y)(x + 5y) \\ = 2 {x}^{2} + 10xy - 3xy - 15 {y}^{2} \\ = 2 {x}^{2} + 7xy - 15 {y}^{2} [/tex]

The solution to 1 - cos(6x) is 2sin²(x).

Hence, option B) 2sin²(x) is the correct answer.

Given that; 1 - cos(6x) = ?

First, we rewrite using trig identity

1 - cos(2 × 3x)

Using the double angle identity, { cos2(x) = 1 - 2sin²(x) }

1 - ( 1 - 2sin²(x) )

Eliminate the parentheses

1 - 1 + 2sin²(x)

2sin²(x)

The solution to 1 - cos(6x) is 2sin²(x).

Hence, option B) 2sin²(x) is the correct answer.

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Answer: 55.2 in

Step-by-step explanation:

1ft = 12 in

41.4/9 = 4.6 ft

4.6 x 12 = 55.2 in

Answer:

2 1/8

Step-by-step explanation:

I counted from 29 to 31 and then saw that for 29 it was 3/8 and for 31 it was 2/8 so i knew that the answer would be 2 1/8

Step-by-step explanation:

1 kilogram (kg) = 1000 grams (g)

as "kilo" means 1000.

b = a × c / 1000

it is simple : we have "c" square meters. as we need to apply "a" grams per square meter, we need to multiply both numbers to know how many grams we need for that many square meters. hence a × c.

and to get kg, we need to divide this number of grams by 1000.

that's it.

-0.81 has negative direction and o.81 is the magnitude, 0.40 has  positive direction and 0.40 is the magnitude, 0.15 positive direction and 0.15 is the magnitude, -0.08 has negative direction and 0.08 is the magnitude and 0.29 has positive direction and 0.29 is the magnitude

A quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another.

-0.81

Minus zero point eight one has negative direction and o.81 is the magnitude

0.40

zero point four zero has positive direction and 0.40 is the magnitude

0.15

Zero point one five has positive direction and 0.15 is the magnitude

-0.08

Minus zero point zero eight has negative direction and 0.08 is the magnitude

0.29

Zero point two nine has positive direction and 0.29 is the magnitude

Hence -0.81 has negative negative direction and o.81 is the magnitude, 0.40 has  positive direction and 0.40 is the magnitude, 0.15 positive direction and 0.15 is the magnitude, -0.08 has negative direction and 0.08 is the magnitude and 0.29 has positive direction and 0.29 is the magnitude

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Answer: [tex]x=-5[/tex]

Step-by-step explanation:

[tex]x+5=0 \implies x=-5[/tex]

Answer:

x-1 gave ggs is it correct

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

To prove two lines parallel, we need to check if the two angles involving the lines acts as some angle pair with defininte property.

In the given figure,

( by Alternate Exterior angle pair )

Hence, the two lines are parallel.

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer: $51156

Step-by-step explanation:

a = b x p%

how much will the price increase

a = 49,000 x 4.4%

= 49,000 x 0.044

= $2156

price of next model

49,000 + 2156 = $51156

Answer: 22.5 inches

Step-by-step explanation:

[tex]p=s+s+s+s+s[/tex]

[tex]5(4.5 in)=p[/tex]

∴ 22.5 inches = perimeter of the pentagon

Answer:

160 cm × 120 cm

Step-by-step explanation:

this means 1 cm turns into 20 cm.

so, 8 cm × 6 cm becomes

8×20 = 160 cm × 6×20 = 120 cm

Answer:

ummm the answer is very simple

The answer is 0/6

Step-by-step explanation:

[tex] \frac{1}{2 \times 3} - \frac{1}{6} [/tex]

[tex] \frac{1}{6} - \frac{1}{6} [/tex]

[tex]1 - 1 = \frac{0}{6} [/tex]

Answer: 3 loops

Step-by-step explanation: The loop is 1.2 miles, and the total walk is 3.6 miles. You want to find out how many laps are in the 3.6 miles. This can be found using division. 3.6/1.2= the number of 1.2 mile laps inside the 3.6 mile walk, which is 3 laps. hope this helped!

Answer:

[tex]-3(x-2)^2+5[/tex]

Step-by-step explanation:

First we can factor a -3 from the [tex]x^2[/tex] term and the [tex]x[/tex] term to get [tex]-3(x^2-4x)-7[/tex].

Then we want the stuff in the parentheses to have the form of [tex](x+b)^2[/tex], or equivalently, [tex](x^2+2b+b^2)[/tex] . So we can let [tex]2b = -4[/tex]. By solving it, we get [tex]b = -4/2 = -2[/tex]. Then our [tex]b^2[/tex] term should be [tex]b^2 = (-2)^2 = 4[/tex].

In order to make our [tex]b^2[/tex] term appear in the parentheses, we need to add and subtract our [tex]b^2[/tex] term, so we get [tex]-3(x^2 - 4x + 4 - 4) -7[/tex].

What we to keep inside our parentheses is [tex](x^2 - 4x + 4)[/tex] , so we can factor the [tex]-4[/tex] out of parentheses to get [tex]-3(x^2-4x+4-4)-7 = -3(x^2-4x+4)+(-3)(-4) - 7 = -3(x^2 - 4x + 4) + 12 - 7 = -3(x^2 - 4x + 4) + 5[/tex]

Finally, plugging  [tex]b = -2[/tex]  that we computed earlier into the equation [tex](x^2+2b+b^2) = (x+b)^2[/tex], we get  [tex](x^2 - 4x + 4) = (x-2)^2[/tex].

So we have [tex]-3(x^2-4x+4)+5 = -3(x-2)^2+5[/tex].

In summary, the procedure is

[tex]-3x^2+12x-7 \\= &-3(x^2-4x) -7 \\= &-3(x^2-4x+4-4)-7 \\= -3(x^2-4x+4) + (-3)(-4)-7\\=-3(x^2-4x+4)+12-7\\= -3(x^2-4x+4)+5 \\= -3(x-2)^2+5[/tex]

Answer:

Step-by-step explanation:

2^0 is less than or equal to 1!, because 1<= 1

if 2^n <= (n+1)!, we wish to show that 2^(n+1) <= (n+2)!, since

(n+2)! = (n+1)! * (n+2), and (n+1)!>= 2^n, then we want to prove that n+2<=2, which is always true for n>=0

The answer is |-4 - 1|.

If you solve this absolute value, the answer would be 5 and if you look at the number line, the distance between the two dots is 5 units.

|-4 - 1| --> |-5| --> 5

in an absolute value, there are no negative numbers so the -5 becomes 5.

The Lateral area of the cube = 900 in.²

The Surface area of the cube = 1,350 in.².

A cube's lateral area is the area covered by the lateral surfaces of the cube shape. The formula for the lateral area of a cube is given as: LA = 4a², where:

a = edge length of cube.

The surface area of a cube is the total area of all its 6 surfaces. The formula for finding the surface area of a cube is: 6a², where:

a = edge length of cube.

Edge length of cube (a) = 15 in.

Lateral area = 4a² = 4(15²)

Lateral area = 4(225)

Lateral area of the cube = 900 in.²

Surface area = 6a² = 6(15²)

Surface area = 6(225)

Surface area of the cube = 1,350 in.².

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Answer:

t = 21

Step-by-step explanation:

The ball strikes the groujd when h = 0.

[tex]-3.2t^2 + 54.4t+268.8=0 \\ \\ 32t^2 - 544t-2688=0 \\ \\ t^2 - 17t-84=0 \\ \\ (t-21)(t+4)=0 \\ \\ t=-4, 21[/tex]

Since time must be positive, t = 21.

The addition of the polynomials x⁴ - 3x + 1, 4x² - 2x + 8, x³ - 9 in descending powers of x is x⁴ + x³ + 4x² - 5x.

Adding the polynomial

(x⁴ - 3x + 1) + (4x² - 2x + 8) + (x³ - 9)

= x⁴ - 3x + 1 + 4x² - 2x + 8 + x³ - 9

= x⁴ + x³ + 4x² - 3x - 2x + 1 + 8 - 9

= x⁴ + x³ + 4x² - 5x

Therefore, the addition of the polynomials x⁴ - 3x + 1, 4x² - 2x + 8, x³ - 9 in descending powers of x is x⁴ + x³ + 4x² - 5x.

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Answer:

$824.56

Step-by-step explanation:

Use the compound interest formula which is A = P(1+r/n)^nt

1st using the given information we are going to find out values:
P is our initial amount of $500
r is the annual rate of interest (expressed as a decimal) 8% becomes 0.08.
n is how many times interest is compounded per year, in this case since its not stated we are going to assume its annually, so n is 1
t is how long the money is deposited (in years) so t is 6.5
A is our final amount

2nd plug in our values into the equation

Plugging all these values we get A = 500 (1 +0.08/1)^(0.08)(6.5)

A = $824.56