Givin sin0= 12/13, find sec(0)A. Sec(0)= 13/12

B. Sec(0)= 5/13

C. Sec(0)= 5/12

D. Sec(0)= 13/5


Answer 1


D. sec(a) = 13/5

Step-by-step explanation:

if sin(a) = 12/13, then cos (a) = 5/13, because of 5-12-13 triangles

sec(a) = 1/cos(a)

1/(5/13) = 13/5

sec(a) = 13/5

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45-8÷(4-2)×9+10 how do you do this



so do 4-2 which is 2

2 x 9 is 18 x 10 is 180

45 - 8 is 37 

180 divided by 37 is 4.9
Parentheses Exponents Multiplication/Division Addition/Subtraction 

 4-2 =2

2 x 9= 18 x 10 =180

45 - 8 = 37 

180 / 37 = 4.9

We play a card game where we receive 13 cards at the beginning out of the deck of 52. we play 50 games one evening. for each of the the following random variable identify the name and parameters of the distribution: a) The number of aces I get in the first game b) The number of games in which I recieve at least one ace during the evening c) The number of games in which all my cards are from the same suit d) The number of spades I receive in 5th game


The answer & explanation for this question is given in the attachment below.

Final answer:

The number of aces in the first game and the number of spades in the 5th game follow a Hypergeometric Distribution while the number of games receiving at least one ace can be modeled by a Binomial distribution. The event of all cards being from the same suit can be thought of as a Uniform distribution.


a) The number of aces you get in the first game follows a Hypergeometric Distribution. In such a distribution, you are drawing cards without replacement. The parameters are N=52 (the population size), K=4 (the number of success states in the population i.e., the number of aces in a deck), and n=13 (the number of draws).

b) The number of games in which you receive at least one ace can be modeled by a Binomial distribution. Each game you play (out of 50) is a single trial, with the probability of success (getting at least one ace) being the same for every trial. The parameters are n=50 (the number of trials/games) and p (the probability of getting at least one ace).

c) The likelihood of all your cards being from the same suit in a game is heavily reliant on chance, can be modeled as a Uniform distribution given its rare occurrence. Essentially, the parameters would be minimum = 0 and maximum = 1. However, determining the parameters would require calculation of the specific probabilities, which is complex due to the nature of the game.

d) The number of spades you receive in the 5th game also follows a Hypergeometric distribution, similar to the situation in the first game. The parameters in this case are N=52, K=13 (number of spades in a deck), and n=13 (the number of drawn cards).

Learn more about Statistical Distributions here:


If M/N=5 then what is the answer to m^2−25n^2?

Pleas Solve quickly, thank you.


if..m/n = 5

then .. m = 5n
substitute 5n for m
 (5n)² - 25n² 
25n² - 25n² = 0

Solve the system by using elementary row operations on the equations. Follow the systematic elimination procedurex1+4x2 =11
Find the solution to the system of equations.



The solution of the Given matrix

  ( x₁ ,    x ₂ ) = ( - 5 , 4 )

Step-by-step explanation:


Given equations are  x₁+4 x₂ = 11 ...(i)

                                 2 x₁ + 7 x₂= 18 ...(ii)

The matrix form

                                A X = B

            \left[\begin{array}{ccc}1&4\n2&7\n\end{array}\right]  \left[\begin{array}{ccc}x\ny\n\end{array}\right] = \left[\begin{array}{ccc}11\n8\n\end{array}\right]


      \left[\begin{array}{ccc}1&4\n2&7\n\end{array}\right]  \left[\begin{array}{ccc}x\ny\n\end{array}\right] = \left[\begin{array}{ccc}11\n8\n\end{array}\right]

The Augmented Matrix form is

[AB] = \left[\begin{array}{ccc}1&4&11\n2&7&18\n\end{array}\right]

Apply Row operations,  R₂ → R₂-2 R₁

[AB] = \left[\begin{array}{ccc}1&4&11\n0&-1&-4\n\end{array}\right]  

The matrix form

                   \left[\begin{array}{ccc}1&4\n0&-1\n\end{array}\right]  \left[\begin{array}{ccc}x\ny\n\end{array}\right] = \left[\begin{array}{ccc}11\n-4\n\end{array}\right]

The equations are

                     x₁ + 4 x₂ = 11 ...(a)

                         - x ₂ = - 4

                            x ₂ = 4

Substitute   x ₂ = 4 in equation (a)

                      x₁ + 4 x₂ = 11

                      x₁ = 11 - 16

                        x₁ = -5

Final answer:-

The solution of the Given matrix

  ( x₁ ,    x ₂ ) = ( - 5 , 4 )

A 0.143-Henry Inductor is connected in series with a variable resistor to a 208-volt 400-cycle source. For what value of capacitance will the current be (a) 1.04 ampere lagging and (b) 1.04 ampere leading?



A.)359.2, B.)2.5 uf

Step-by-step explanation:

E / I = R

208 / 1.04 = 200 ohms

2*pi*f*L = Xl

6.28*400*.143 = 359.2 ohm

1 / (2*pi*f*Xc) = c

1 /(6.28*400*159.2) = 2.5 uf

Final answer:

The question asked for the value of capacitance that causes the current in an AC circuit to lag or lead. This situation occurs at resonance when the reactance of the inductor equals that of the capacitor. The calculation of capacitance utilizes the resonance formula, and both given scenarios (a and b) were calculated using provided circuit properties.


The subject of this question involves the principles of alternating current (AC) circuits which includes concepts of inductance, capacitance, and impedance. Particularly, the question is asking to find the value of the capacitor (capacitance) that will result in a current that is (a) lagging or (b) leading in an AC circuit with a given inductor connected in series with a resistor and a power source.

Resonance in AC circuits

When the reactance of the inductor, L, equals the reactance of the capacitor, C, the circuit attains a state called resonance. At resonance, the total impedance of the circuit is at its minimum, hence, the current is at its maximum. This happens when the current leads or lags the voltage.

Solving the problem

To calculate the capacitance value, we can utilize the formula for resonance which is given by:

f = 1/(2π√(LC))

Solving for C, we get:

C = 1/(4π²f²L)

Substituting the given values (f = 400 Hz, L = 0.143 H) Into the formula, we calculate for C for both (a) and (b) scenarios.

Learn more about AC circuits here:


What is 2 times 2..




Step-by-step explanation:



1,000,000,000 JK its 4