A volleyball is an example of a____a0.

Answer:

The answer is x=5.

Step-by-step explanation:

11x + 7x + 90 = 180

18x + 90 = 180

       -90    -90

= 18x = 90

 x = 5

x is 5!

Value of x is 10°.

Correct option is B.

A figure which is formed by two rays or lines that shares a common endpoint is called an angle. The word “angle” is derived from the Latin word “angulus”, which means “corner”.

Given,

a || b

cut by transversal s and t

lines b and t have angle = 90°

The first top left angle between a, s, t = 7x

The last bottom angle between s and b = 11x

a || b, so a and t will also have angle = 90°

by the figure,

180° - 11x + 90° - 7x + 90° = 180°

360° - 18x = 180°

18x = 180°

x = 10°

Hence, 10° is value of x.

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Answer:

t = pn

Step-by-step explanation:

We are to find the relationship between total cost and the number of items.

First we would represent the relationship between total cost and number of items with variables

Let the total cost = t

and the number of items = n

Total cost t is proportional to the number n of items:

t ∝ n

t = kn

where k is constant

Since it is purchased at a constant price p, the constant of proportionality would be p. the k would be replaced with p

t = pn

Answer:

0.75 = 75% probability that exactly one tag is lost, given that at least one tag is lost

Step-by-step explanation:

Independent events:

If two events, A and B, are independent, then:

[tex]P(A \cap B) = P(A)*P(B)[/tex]

Conditional probability:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: At least one tag is lost

Event B: Exactly one tag is lost.

Each tag has a 40% = 0.4 probability of being lost.

Probability of at least one tag is lost:

Either no tags are lost, or at least one is. The sum of the probabilities of these events is 1. Then

[tex]p + P(A) = 1[/tex]

p is the probability none are lost. Each one has a 60% = 0.6 probability of not being lost, and they are independent. So

p = 0.6*0.6 = 0.36

Then

[tex]P(A) = 1 - p = 1 - 0.36 = 0.64[/tex]

Intersection:

The intersection between at least one lost(A) and exactly one lost(B) is exactly one lost.

Then

Probability at least one lost:

First lost(0.4 probability) and second not lost(0.6 probability)

Or

First not lost(0.6 probability) and second lost(0.4 probability)

So

[tex]P(A \cap B) = 0.4*0.6 + 0.6*0.4 = 0.48[/tex]

Find the probability that exactly one tag is lost, given that at least one tag is lost (write it up to second decimal place).

[tex]P(B|A) = \frac{0.48}{0.64} = 0.75[/tex]

0.75 = 75% probability that exactly one tag is lost, given that at least one tag is lost

Answer:

4

Step-by-step explanation:

A função em questão, f(x), é:

[tex]f(x)=4x-9[/tex]

Primeiramente calcule os valores das funções para x=5 e x=6:

[tex]f(5)=4*5-9\\f(5)=11\\f(6)=4*6-9\\f(6)=15[/tex]

Em seguida, subtraia f(5) de f(6):

[tex]f(6)-f(5) = 15-11\\f(6)-f(5) = 4[/tex]

A resposta para o problema é 4

Answer:

Step-by-step explanation:

Given that,

μ = 25.1

σ = 0.26

a) since standard deviation is ideal measure of dispersion , a combination of control chart for mean x and standard deviation known as

[tex]\bar x \\\text {and}\\\mu[/tex]

Chart is more appropriate than [tex]\bar x[/tex] and R - chart for controlling process average and variability

so we use

[tex]\bar x \\\text {and}\\\mu[/tex]charts

b)

n = 11

we have use 2 σ confidence

so, control unit for [tex]\bar x[/tex] chart are

upper control limit  = [tex]\mu +2\times\frac{ \sigma}{\sqrt{n} }[/tex]

lower control limit = [tex]\mu -2\times\frac{ \sigma}{\sqrt{n} }[/tex]

control limit = μ

μ = 25.1

upper control limit  =

[tex]25.1+2\times \frac{0.26}{\sqrt{11} } \\\\=25.2567[/tex]

lower control limit =

[tex]25.1-2\times \frac{0.26}{\sqrt{11} } \\\\=24.9432[/tex]

Upper control limit and lower control limit are in between the specification limits , that is in between 24.9 and 25.6

so, process is in control

c) if we use 3 sigma limit with n = 11

then

upper control limit  = [tex]\mu +3\times\frac{ \sigma}{\sqrt{n} }[/tex]

[tex]25.1+3\times\frac{0.26}{\sqrt{11} } \\\\=25.3351[/tex]

lower control limit  = [tex]\mu -2\times\frac{ \sigma}{\sqrt{n} }[/tex]

[tex]25.1-3\times\frac{0.26}{\sqrt{11} } \\\\=24.8648[/tex]

control limit is 25.1

Then, process is in control since upper control limit and lower control limit lies between specification limit

So, process is in control

Answer: About 14.14 in^3

Step-by-step explanation:

We know that the circumference of a sphere is C=2πr. We are given that the circumference is 9.42 in. We can find the radius to get our volume.

[tex]9.42=2\pi r[/tex]

[tex]4.71=\pi r[/tex]

[tex]r=1.5\\[/tex]

Now that we know radius, we can find our volume.

[tex]V=\frac{4}{3} \pi r^3[/tex]

[tex]V=\frac{4}{3} \pi (1.5)^3[/tex]

[tex]V=14.14in^3[/tex]

Complete Question

1. Waiting times​ (in minutes) of customers at a bank where all customers enter a single waiting line and a bank where customers wait in individual lines at three different teller windows are listed below. Find the coefficient of variation for each of the two sets of​ data, then compare the variation.

Bank A (single lines): 6.5, 6.6, 6.7, 6.8, 7.2, 7.3, 7.4, 7.6, 7.6, 7.7

Bank B (individual lines): 4.1, 5.4, 5.8, 6.3, 6.8, 7.8, 7.8, 8.6, 9.3, 9.7

- The coefficient of variation for the waiting times at Bank A is ----- %?

- The coefficient of variation for the waiting times at the Bank B is ----- ​%?

- Is there a difference in variation between the two data​ sets?

Answer:

a

The coefficient of variation for the waiting times at Bank A is [tex]l =[/tex]6.3%

b

The coefficient of variation for the waiting times at Bank B is [tex]l_1 =[/tex]25.116%

c

The waiting time of Bank B has a considerable higher variation than that of Bank A

Step-by-step explanation:

From the question we are told that

  For Bank A  : 6.5, 6.6, 6.7, 6.8, 7.2, 7.3, 7.4, 7.6, 7.6, 7.7

 For  Bank B : 4.1, 5.4, 5.8, 6.3, 6.8, 7.8, 7.8, 8.6, 9.3, 9.7

The sample size is  n =10

The mean for Bank A is

          [tex]\mu_A = \frac{6.5+ 6.6+ 6.7+ 6.8+ 7.2+ 7.3+ 7.4+ 7.6+ 7.6+ 7.7}{10}[/tex]

          [tex]\mu_A = 7.14[/tex]

The standard deviation is mathematically represented as

      [tex]\sigma = \sqrt{\frac{\sum|x- \mu|}{n} }[/tex]

        [tex]k = \sum |x- \mu | ^2 = 6.5 -7.14|^2 + |6.6-7.14|^2+ |6.7-7.14|^2+ |6.8-7.14|^2 + |7.2-7.14|^2+ |7.3-7.14|^2, |7.4-7.14|^2+ |7.6-7.14|^2+|7.6-7.14|^2+|7.7-7.14|^2[/tex]

[tex]k = 2.42655[/tex]

    [tex]\sigma = \sqrt{\frac{2.42655}{10} }[/tex]

    [tex]\sigma = 0.493[/tex]

The coefficient of variation for the waiting times at Bank A is  mathematically represented as  

        [tex]l = \frac{\sigma}{\mu} *100[/tex]

        [tex]l = \frac{0.493}{7.14} *100[/tex]

       [tex]l =[/tex]6.3%

Considering Bank B

     The mean for Bank B is

               [tex]\mu_1 = \frac{4.1+ 5.4+ 5.8+ 6.3+6.8+ 7.8+ 7.8+ 8.6+ 9.3+ 9.7}{10}[/tex]

              [tex]\mu_1 = 7.16[/tex]

The standard deviation is mathematically represented as      

       [tex]\sigma_1 = \sqrt{\frac{\sum|x- \mu_1|}{n} }[/tex]

    [tex]\sum |x- \mu_1 | ^2 =4.1-7.16|^2 +| 5.4-7.16|^2+ |5.8-7.16|^2 + | 6.3-7.16|^2 + |6.8-7.16|^2 + | 7.8-7.16|^2 +|7.8-7.16|^2 +|8.6-7.16|^2 + |9.3-7.16|^2 +|9.7-7.16|^2[/tex]

[tex]\sum |x- \mu_1 | ^2 =32.34[/tex]

    [tex]\sigma_1 = \sqrt{\frac{32.34}{10} }[/tex]

     [tex]\sigma_1 = 1.7983[/tex]

The coefficient of variation for the waiting times at Bank B is  mathematically represented as  

        [tex]l_1 = \frac{\sigma }{\mu} *100[/tex]

        [tex]l_1 = \frac{1.7983 }{7.16} *100[/tex]

        [tex]l_1 =[/tex]25.116%

Answer:

One mask=$4

One pack of glove=$2

Step-by-step explanation:

Let mask=m

Let glove=g

4m+g=18 (1)

4m+3g=22 (2)

From (1)

g=18-4m

Substitute g=18-4m into equation (2)

4m+3g=22

4m+3(18-4m)=22

4m+54-12m=22

4m-12m=22-54

-8m=-32

Divide both sides by -8

m=4

Substitute m=4 into equation (1)

4m+g=18

4(4)+g=18

16+g=18

g=18-16

g=2

One mask=$4

One pack of glove=$2

Answer:

[tex]w>48[/tex] pounds

Step-by-step explanation:

The customer will be charged extra if the weight of their suitcase is above 48 pounds.

Let the weight of the suitcase = w (in pounds)

Therefore, w above (greater than) 48 pounds is written mathematically as:

[tex]w>48[/tex] pounds

This is the inequality that represents w, the weight of the suitcase in pounds, that will have an extra charge.

Answer:

5   : 4

Step-by-step explanation:

4:  3.2

Multiply by 10 to get rid of the decimal

4*10 : 3.2* 10

40 : 32

Divide each side by 8 to simplify

40/8   : 32/ 8

5   : 4

We have been given that Mr. Collins and Ms. LaPointe are saving money to buy a new motorcycle. The total amount of money Mr. Collins will save is given by the function [tex]p(x) = 62+5x[/tex]. The total amount of money Ms. LaPointe will save is given by the function [tex]a(x) = x^2+38[/tex]. We are asked to find number of months when they have the same amount of money saved.

To solve our given problem, we will equate both equations as:

[tex]x^2+38=62+5x[/tex]

[tex]x^2-5x+38=62+5x-5x[/tex]

[tex]x^2-5x+38=62[/tex]

[tex]x^2-5x+38-62=62-62[/tex]

[tex]x^2-5x-24=0[/tex]

[tex]x^2-8x+3x-24=0[/tex]

[tex]x(x-8)+3(x-8)=0[/tex]

[tex](x-8)(x+3)=0[/tex]

[tex](x-8)=0,(x+3)=0[/tex]

[tex]x=8,x=-3[/tex]

Since time cannot be negative, therefore, after 8 months they will have the same amount of money saved.

Answer:

Reject [tex]H_o[/tex] if [tex]t < -2.306[/tex]

Step-by-step explanation:

The decision rule for rejecting the null hypothesis is shown below:-

The machine is thought to be underfilling so that the test is left tailed.

Now the Degrees of freedom is

= 9 - 1

= 8

Critical left tailed value t for meaning level [tex]8 \ df[/tex] and 0.025 = -2.306

Therefore Decision rule will be in the following way:

Reject [tex]H_o[/tex] if [tex]t < -2.306[/tex]

Answer: A

Step-by-step explanation:

Formula for inverse of a matrix is:

[tex]A=\left[\begin{array}{cc}a&b\\c&d\end{array}\right]\qquad \rightarrow \qquad A^{-1}=\dfrac{1}{ad-bc}\left[\begin{array}{cc}d&-b\\-c&a\end{array}\right][/tex]

[tex]A=\left[\begin{array}{cc}2&5\\3&8\end{array}\right] \qquad \rightarrow \qquad A^{-1}=\dfrac{1}{2(8)-5(3)}\left[\begin{array}{cc}8&-5\\-3&2\end{array}\right]\\\\\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \quad =\dfrac{1}{1}\left[\begin{array}{cc}8&-5\\-3&2\end{array}\right]\\\\\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \quad =\left[\begin{array}{cc}8&-5\\-3&2\end{array}\right][/tex]

We have that  Option A is the correct option as its the correct in verse of the Matrix A

From the question we are told that:

[tex]A= \begin{vmatrix}2 & 5 \\3 & 8\end{vmatrix}[/tex]

Inverse of a Matrix

The inverse of matrix is another matrix, which on multiplication with the given matrix gives the multiplicative identity. For a matrix A, its inverse is A^{-1}, and A.A^{-1} = I.

Therefore the inverse of the Matrix A is

[tex]A= \begin{vmatrix}2 & 5 \\3 & 8\end{vmatrix}[/tex]

Giving

[tex]A^{-1}= \begin{vmatrix}8 & -5 \\-3 & -2\end{vmatrix}[/tex]

In conclusion

The correct Option is Option A as its the correct in verse of the Matrix A

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In conclusion

Answer:

441

Step-by-step explanation:

84 / 4 = 21

21 x 21 = 441

Answer:

441

Step-by-step explanation:

84/2=42

Answer:

Scalene triangle

Step-by-step explanation:

Step-by-step explanation:

The temperature outside when Colin went to bed was -4°F. When he woke up the next  morning, it was -11°F outside

To find the change in the temperature , find the difference in temperature

Change in temperature = temperature in morning - temperature at night

change in temperature = [tex]-11 -(-4)= -7[/tex]

temperature changed by -7 °F

So the temperature is dropped by 7°F

Answer:

the temperature is dropped by 7°F

The temperature change when he woke up the next morning given the data was –7 °F.

From the question given above , the following data were obtained:

The temperature change when Colin woke up can be obtained by taking the difference in the temperature at night and morning. This is illustrated as follow:

ΔT = T₂ – T₁

ΔT = –11 – (–4)

ΔT = –11 + 4

ΔT = –7 °F

Thus, from the calculation made above, we can conclude that there was a temperature drop of –7 °F when he woke up the next morning

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Answer:

P(X ≥ 125) = 0.9812

Step-by-step explanation:

To solve this question, we need to understand the Poisson distribution and the normal distribution.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\lambda[/tex] is the mean in the given interval, which is the same as the variance.

Normal distribution:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The Poisson can be approximated to the normal, with [tex]\mu = \lambda, \sigma = \sqrt{\lambda}[/tex]

Let μ = 2.5 every minute

This is the mean of the Poisson, so [tex]\lambda = 2.5n[/tex], in which n is the number of minutes.

P(X ≥ 125) over an hour

An hour has 60 minutes, so [tex]n = 60, \lambda = 2.5*60 = 150, \sigma = \sqrt{150} = 12.25[/tex]

Using continuity correction, this is [tex]P(X \geq 125 - 0.5) = P(X \geq 124.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 124.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{124.5 - 150}{12.25}[/tex]

[tex]Z = -2.08[/tex]

[tex]Z = -2.08[/tex] has a pvalue of 0.0188

1 - 0.0188 = 0.9812

So

P(X ≥ 125) = 0.9812

Answer:

18/35

Step-by-step explanation:

1 1/5 ÷ 2  1/3

Change from mixed numbers to improper fractions

1 1/5 = (5*1+1)/5 = 6/5

2 1/3 = (3*2+1)/3 = 7/3

6/5÷ 7/3

Copy dot flip

6/5* 3/7

18/35

Answer:

Step-by-step explanation:

I don't say you must have to mark my ans as brainliest but if it has really helped u plz don't forget to thank me my friend...

Answer:

  1707

Step-by-step explanation:

Let's designate the three sets of collinear points, A, B, C, having 4, 6, 7 points, respectively.

Since there are 3 sets of collinear points, exactly two of the vertices must come from the same set.

For two vertices from set A, the remaining two must come from the 13 members of sets B and C. There are a total of (4C2)(13C2) = 468 such quadrilaterals.

For two vertices from set B, we have already counted the quadrilaterals that result when the remaining two are from set A. There are 4·7 = 28 ways to have one each from sets A and C, and 7C2 = 21 ways to have two from set C. Thus, the additional number of quadrilaterals having 2 vertices in set B is ...

  (6C2)(28 +21) = 735

For two vertices from set C, we have already counted the cases where two are from A or two are from B. There are 4·6 = 24 ways to have one each of the remaining vertices from sets A and B. Then the number of additional quadrilaterals having two points from set C is ...

  (7C2)(4)(6) = 504

So, the total number of unique quadrilaterals is ...

  468 +735 +504 = 1707

__

nCk means "the number of ways to choose k from n"

nCk = n!/(k!(n-k)!)

Answer:

Step-by-step explanation:

Answer:

98.57

Step-by-step explanation:

3.5% over 100% X 102=3.43

102-3.43= 98.57

Answer:

1a) (i) 0.0537

(ii) 0.0250

(iii) 0.6188

1b) The probability that neither Kofi nor Mensah solves the problem correctly = (9/20) = 0.45

Step-by-step explanation:

The complete Question is presented in the attached image to this answer.

1a) This is a normal distribution problem with

Mean lifetime of bulbs = μ = 210 hours

Standard deviation = σ = 56 hours

(i) at least 300 hours, P(x ≥ 300)

We first standardize 300 hours

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (300 - 210)/56 = 1.61

To determine the required probability

P(x ≥ 300) = P(z ≥ 1.61)

We'll use data from the normal probability table for these probabilities

P(x ≥ 300) = P(z ≥ 1.61) = 1 - P(z < 1.61)

= 1 - 0.94630 = 0.0537

(ii) at most 100 hours, P(x ≤ 100)

We first standardize 100 hours

z = (x - μ)/σ = (100 - 210)/56 = -1.96

To determine the required probability

P(x ≤ 100) = P(z ≤ -1.96)

We'll use data from the normal probability table for these probabilities

P(x ≤ 100) = P(z ≤ -1.96) = 0.0250

(iii) between 150 and 250 hours.

P(150 < x < 250)

We first standardize 150 and 250 hours

For 150 hours

z = (x - μ)/σ = (150 - 210)/56 = -1.07

For 250 hours

z = (x - μ)/σ = (250 - 210)/56 = 0.71

To determined the required probability

P(150 < x < 250) = P(-1.07 < z < 0.71)

We'll use data from the normal probability table for these probabilities

P(150 < x < 250) = P(-1.07 < z < 0.71)

= P(z < 0.71) - P(z < -1.07)

= 0.76115 - 0.14231

= 0.61884 = 0.6188 to 4 d.p.

1b) Probability that Kofi solves the problem correctly = P(K) = (1/4)

Probability that Mensah solves the problem correctly = P(M) = (2/5)

Probability that Kofi does NOT solve the problem correctly = P(K') = 1 - P(K) = 1 - (1/4) = (3/4)

Probability that Mensah does NOT solve the problem correctly = P(M') = 1 - P(M) = 1 - (2/5) = (3/5)

To find the probability that neither of them solves the problem correctly, we first make the logical assumption that the probabilities of either of them solving the problem are independent of each other.

Hence, the probability that neither of them solves the problem correctly = P(K' n M')

P(K' n M') = P(K') × P(M') = (3/4) × (3/5) = (9/20) = 0.45

Hope this Helps!!!

Answer:

$6.03

Step-by-step explanation:

Let's begin by listing out the given variables:

height (h) = 12 cm, diameter (d) = 8 cm, r = d ÷ 2  ⇒ r = 4 cm, cost of coconut oil (c) = $0.01 /cm³

The formula of cylinder is given by:

V = πr²h = π * 4² * 12 = 603.1858 cm³

cost of filling the tin can with coconut oil = cost of coconut oil * Volume of cylinder

Cost = c * V = 0.01 * 603.1858

Cost = $6.03

Answer:

C. No, the program is not statistically significant because the results are likely to occur by chance.

Step-by-step explanation:

At a significance level that is smaller than 0.2, the effect is not significant.

We have a P-value of 20%, which means that we have 20% chances of getting this sample given that the method has no effect.

We then can conclude that there is not enough evidence to support the claim that the method is effective.

Answer:it’s ZERO

Step-by-step explanation:

The discriminant of the function is zero

A relation is a function if it has only One y-value for each x-value.

The discriminant tells you where the graph of the parabola goes through the x-axis, if at all.

If the discriminant is negative there are no real zeros and the parabola does not cross or touch the x-axis;

if the discriminant is positive the parabola will go through the x axis in 2 places;

if the discriminant is 0 the parabola will touch the x-axis in 1 place.

Our discriminant is 0 since the parabola only touches the x-axis but does not go through.

Hence, the discriminant of the function is zero

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Answer:

A = 36pi in^2

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

A = pi 6^2

A = 36pi in^2

Radius(r)=6 inches

Area of circle=?

Now,

Area of circle=pi r ^2

=pi (6)^2

36 pi inches^2

So the right answer is 36 pi inches^2

Hope it helps

Answer:

(1)Equivalence Relation

(2)Not Transitive, (0,3) is missing

(3)Equivalence Relation

(4)Not symmetric and Not Transitive, (2,1) is not in the set

Step-by-step explanation:

A set is said to be an equivalence relation if it satisfies the following conditions:

(1) {(0,0), (1,1), (2,2), (3,3)}

(3) {(0,0), (1,1), (1,2), (2,1), (2,2), (3,3)}

The relations in 1 and 3 are Reflexive, Symmetric and Transitive. Therefore (1) and (3) are equivalence relation.

(2) {(0,0), (0,2), (2,0), (2,2), (2,3), (3,2), (3,3)}

In (2), (0,2) and (2,3) are in the set but (0,3) is not in the set.

Therefore, It is not transitive.

As a result, the set (2) is not an equivalence relation.

(4) {(0,0), (0,1), (0,2), (1,0), (1,1), (1,2), (2,0), (2,2), (3,3)}

(1,2) is in the set but (2,1) is not in the set, therefore it is not symmetric

Also, (2,0) and (0,1) is in the set, but (2,1) is not, rendering the condition for transitivity invalid.

Answer:

A cup of water can hold a cup of water (or about 250 mL)

Step-by-step explanation:

anything between 1 and 4 cups should be an acceptable answer

If this helps, please consider giving me brainliest

Answer:

I'm gonna go with 250 ML

Step-by-step explanation:

One liter is a little more than 1 quart.

250 mL = 0.25 L

Answer:

0 = 3x -2y -6

Step-by-step explanation:

The general form of the equation of a line is 0 = Ax + By + C

y = 3/2x -3

Subtract y from each side

0 = 3/2x -y -3

Multiply each side by 2

0 = 3x -2y -6

Answer:

answer is in exaplation

Step-by-step explanation:

cosA

+

cosA

1+sinA

=2secA

Step-by-step explanation:

\begin{lgathered}LHS = \frac{cosA}{1+sinA}+\frac{1+sinA}{cosA}\\=\frac{cos^{2}A+(1+sinA)^{2}}{(1+sinA)cosA}\\=\frac{cos^{2}A+1^{2}+sin^{2}A+2sinA}{(1+sinA)cosA}\\=\frac{(cos^{2}A+sin^{2}A)+1+2sinA}{(1+sinA)cosA}\\=\frac{1+1+2sinA}{(1+sinA)cosA}\end{lgathered}

LHS=

1+sinA

cosA

+

cosA

1+sinA

=

(1+sinA)cosA

cos

2

A+(1+sinA)

2

=

(1+sinA)cosA

cos

2

A+1

2

+sin

2

A+2sinA

=

(1+sinA)cosA

(cos

2

A+sin

2

A)+1+2sinA

=

(1+sinA)cosA

1+1+2sinA

/* By Trigonometric identity:

cos² A+ sin² A = 1 */

\begin{lgathered}=\frac{2+2sinA}{(1+sinA)cosA}\\=\frac{2(1+sinA)}{(1+sinA)cosA}\\\end{lgathered}

=

(1+sinA)cosA

2+2sinA

=

(1+sinA)cosA

2(1+sinA)

After cancellation,we get

\begin{lgathered}= \frac{2}{cosA}\\=2secA\\=RHS\end{lgathered}

=

cosA

2

=2secA

=RHS

Therefore,

\begin{lgathered}\frac{cosA}{1+sinA}+\frac{1+sinA}{cosA}\\=2secA\end{lgathered}

1+sinA

cosA

+

cosA

1+sinA

=2secA