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1 year ago

Prove the identities (sec^2-1)cot^2=1

Mathematics

1 answer:

In-s [12.5K]1 year ago

6 0

The trigonometric Identity proof (sec²θ - 1)cot²θ = 1 is as explained below.

<h3>How to prove trigonometric Identities?</h3>

We want to prove that;

(sec²θ - 1)cot²θ = 1

Now, we know from trigonometric identities that;

sec²θ - 1 = tan²θ

Thus, the left hand side of our original equation can be written as;

tan²θ * cot²θ

We also know in trigonometric identities that 1/tan θ = cot θ. Thus;

tan²θ * cot²θ can be written as;

tan²θ * (1/ tan²θ)

The above will cancel out to give us 1 which is also equal to the right hand side and as such our trigonometric proof is complete.

Read more about Trigonometric Identities at; brainly.com/question/7331447

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Akron Cinema sells an average of 500 tickets on Mondays, with a standard deviation of 50 tickets. If a simple random sample is t

Paha777 [63]

Answer:

Step-by-step explanation:

Assuming the number of tickets sales from Mondays is normally distributed. the formula for normal distribution would be applied. It is expressed as

z = (x - u)/s

Where

x = ticket sales from monday

u = mean amount of ticket

s = standard deviation

From the information given,

u = 500 tickets

s = 50 tickets

We want to find the probability that the mean will be greater than 510. It is expressed as

P(x greater than 510) = 1 - P(x lesser than or equal to 510)

For x = 510

z = (510 - 500)/50 = 0.2

Looking at the normal distribution table, the probability corresponding to the z score is 0.9773

P(x greater than 510) = 1 - 0.9773 = 0.0227

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2 years ago

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I need to know how to solve it and get the answer right to check my work

Ede4ka [16]

Solve it by finding out how many times 22 can be put into 22, which is once, so the answer is 1.

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3 years ago

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What is the slope of any line that is perpendicular to the line = y - 5 = 3/2 * (x + 1)

klio [65]

Answer:

-2/3

Step-by-step explanation:

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2 years ago

A small metal bar, whose initial temperature was 10° C, is dropped into a large container of boiling water. How long will it tak

IgorC [24]

Answer

According to newton law of cooling

$\dfrac{d T}{dt} = k (T - T_a)$

and

$T = Ce^{kt} + T_a$

now At Ta = 100

T₀ = 10 °C

T₁ = 12° C

$T(0) = Ce^{0} + T_a$

10 = C + 100

C = -90

now,

$12 = -90e^k + 100$

$e^k = \dfrac{88}{90}$

$k = ln{\dfrac{88}{90}}$

at time equal to t

T(t) = 70

$T(t) = -90 (\dfrac{88}{90})^t + 100$

$70 = -90(\dfrac{88}{90})^t + 100$

$(\dfrac{88}{90})^t = \dfrac{1}{3}$

$t\times ln(\dfrac{88}{90}) = ln(\dfrac{1}{3})$

t = 48.88 s

hence, after 48.88 s the temperature of the body will be 70°C

b) time taken to reach 98°C

$T(t) = -90 (\dfrac{88}{90})^t + 100$

$98 = -90(\dfrac{88}{90})^t + 100$

$(\dfrac{88}{90})^t = \dfrac{1}{45}$

$t\times ln(\dfrac{88}{90}) = ln(\dfrac{1}{45})$

t = 390 s

hence, after 390 s the temperature of the body will be 98°C

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2 years ago

The Dot plots below show the number of sales made by Jason and Shane at work over the past seven days. Which observation about t

IgorLugansk [536]

Jason's data distribution is symmetrical and shows no outliers; Shane's data distribution is uniform and shows no outliers also. Therefore, the correct observation about the data sets that is correct is:<em> Option B.</em>

<h3>Symmetrical and Uniform Data Distribution on a Dot Plot</h3>

If the data plotted on the dot plot shows a bell shape curve and can be divided into equal halves by a vertical line, the data distribution is symmetrical.

When the data is spread equally across the range with no clear peaks, the data distribution is uniform.

<h3>What are Outliers?</h3>

Outliers are values that are far from the middle and are entirely different from the rest of the data.

The dot plots for sales made by Jason and Shane are shown in the image attached below.

Learn more about data distribution on:

brainly.com/question/24309209

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