Find the exact value of sec theta if csc theta = -4/3 and the terminal side of theta lies in quadrant III

Answers

Answer 1

Answer:

-4 sqrt(7)/7

Step-by-step explanation:

csc theta = -4/3

csc theta = hypotenuse / opposite side

hypotenuse = 4  

opposite  = 3

Using the pythagorean theorem

a^2 + b^2 = c^2

3^2 + b^2 = 4^2

9+b^2 = 16

b^2 = 16-9

b^2 = 7

Taking the square root

sqrt(b^2) = sqrt(7)

b = sqrt(7)

We are in the third quadrant so only tan  and cot are positive

that means the x and y values are "negative"  so a = -3 and b = - sqrt(7)

sec theta = hypotenuse / adjacent

                = 4/ - sqrt(7)

rationalizing  

                   -4 sqrt(7)/ sqrt(7)* sqrt(7)

                = -4 sqrt(7)/7

           


Related Questions

In the table, Pattern A uses the rule "add 5" and Pattern B uses the rule "add 10." Pattern A 10 15 20 25 30 Pattern B 20 30 40 50 60 Which statement is true? Every term in Pattern B is 10 more than the corresponding term in Pattern A. Every term in Pattern B is 2 times the corresponding term in Pattern A. Every term in Pattern B is 12 the corresponding term in Pattern A. Every term in Pattern B is 10 times the corresponding term in Pattern A.

Answers

Step-by-step explanation:

the true statement is:

every term in pattern B is 2 times the corresponding term in pattern A

Answer:

Every term in Pattern B is 2 times the corresponding term in Pattern A.

Step-by-step explanation:

Pattern A

10 15 20 25 30

Pattern B

20 30 40 50 60

Statements:

Every term in Pattern B is 10 more than the corresponding term in Pattern A.

False

Every term in Pattern B is 2 times the corresponding term in Pattern A.

True

Every term in Pattern B is 12 the corresponding term in Pattern A.

False

Every term in Pattern B is 10 times the corresponding term in Pattern A.

False

Consider the following function. x6 1 + x2 dx (a) Determine an appropriate trigonometric substitution. Use x = sin(θ), where − π 2 ≤ θ ≤ π 2 , since the integrand contains the expression 1 + x2 . Use x = tan(θ), where − π 2 < θ < π 2 , since the integrand contains the expression 1 + x2 . Use x = sec(θ), where 0 ≤ θ < π 2 or π ≤ θ < 3π 2 , since the integrand contains the expression 1 + x2 . (b) Apply the substitution to transform the integral into a trigonometric integral. Do not evaluate the integral. x6 1 + x2 dx = dθ

Answers

Answer:

Step-by-step explanation:

In the first part, we are given the function:

[tex]\int \dfrac{x^6}{\sqrt{1+x}^2} \ dx[/tex]

Suppose we make x = tan θ

Then dx = sec² θ.dθ

[tex]= \int \dfrac{tan^6 (\theta)}{\sqrt{1+ tan ^2 \theta }}* dx[/tex]

[tex]= \int \dfrac{tan^6 (\theta)}{\sqrt{1+ tan ^2 \theta }}* sec ^2 (\theta) * d\theta[/tex]

Since; sec² θ - tan² θ = 1

sec² θ = 1+ tan² θ

[tex]sec \ \theta = \sqrt{1 + tan^2 \ \theta}[/tex]

[tex]= \int \dfrac{tan^6 (\theta)}{sec \ \theta}* sec ^2 (\theta) * d\theta[/tex]

[tex]= \int tan^6 (\theta)* sec (\theta) * d\theta[/tex]

Thus; In the first part, Use x = tan θ, where  [tex]- \dfrac{\pi}{2} < \theta <\dfrac{\pi}{2}[/tex], since the integrand comprise the expression [tex]\sqrt{1+x^2}[/tex]

From the second part by using substitution method;

[tex]\int \dfrac{x^6}{\sqrt{1+x^2}} \ dx = \int \mathbf{tan^6(\theta) * sec ( \theta) } \ d \theta[/tex]

Complete the assignment on a separate sheet of paper

Please attach pictures of your work.

Answers

Answer:

Value of x =  15.1 unit (Approx.)

Step-by-step explanation:

Given:

For angle 54°

Base of triangle = 11 unit

Perpendicular of triangle = x unit

Find:

Value of x

Computation:

Using trigonometry function;

Tanθ = Perpendicular / Base

Tan 54 = Perpendicular of triangle / Base of triangle

Tan 54 = x / 11

1.376 = x / 11

Value of x = 1.376 × 11

Value of x = 15.136

Value of x =  15.1 unit (Approx.)

If z = -1.3, mu=80, sigma=30 What is the actual data value? Round to 2 decimal places.

Answers

Step-by-step explanation: This simple confidence interval calculator uses a Z statistic and sample mean (M) to generate an interval estimate of a population mean (μ).

Note: You should only use this calculator if (a) your sample size is 30 or greater; and/or (b) you know the population standard deviation (σ), and use this instead of your sample's standard deviation (an unusual situation). If your data does not meet these requirements, consider using the t statistic to generate a confidence interval.

where:

M = sample mean

Z = Z statistic determined by confidence level

sM = standard error = √(s2/n)

As you can see, to perform this calculation you need to know your sample mean, the number of items in your sample, and your sample's standard deviation (or population's standard deviation if your sample size is smaller than 30). (If you need to calculate mean and standard deviation from a set of raw scores, you can do so using our descriptive statistics tools.)

Which postulate describes that AABC – ADEF?
A)
AA
B)
ASA
C)
SAS
D)
SSS

Answers

it’s a) AA

because there isn’t Congruency lines that AC &DF are congruent so we can’t assume. that leaves us with the correct answer being AA (2 angles that are congruent)

How many gallons of water does the shower
stream in 6 minuets (need lots of help lol) thanks ❤️❤️

Answers

Answer: The answer is 15 gallons. Hope this helped!

Step-by-step explanation:

Write and solve the equation that represents the sentence below. The product of 18 and a number is 109.8. Which statements are correct? Check all that apply. It can be solved by using the division property of equality. It can be solved by using the multiplication property of equality. The equation should be StartFraction x Over 18 EndFraction = 109.8. The equation should be 18 x = 109.8. The answer is 6.1. The answer is 1,976.4.

Answers

Answer:

the answer is a, d, e

Step-by-step explanation:

the product of 18 and a number is 109.8=

18n=109.8

to find n, you need to divided by 109.8 by 18. You will get 6.1

To check, replace c with 6.1.

18x6.1=109.8

Answer:

ade

Step-by-step explanation:

I need help with this

Answers

Answer:

C. 16 inch 3

Step-by-step explanation:

82.6% into lowest form

Answers

Answer:

0.825

Step-by-step explanation:

To convert to lowest form, you have to shift the decimal place 2 places to the left.

Please help me and use laws of exponents​

Answers

Answer:

5^2x ÷ 5^-3 = 5⁵(5×5×5×5×5)

5^2x ÷ 1/5³(5×5×5) = 3125

5^2x ÷ 1/125 = 3125

5^2 × 4 = 3125

125

5⁸(5×5×5×5×5×5×5×5) = 3125

125

390625 = 3125

125

so the value X is = 4

For which equation is a = 4 not the solution?

9 a = 36
5 a = 54
8 a = 32

Answers

The correct answer is 5a = 54

Answer:

nAnI

Step-by-step explanation:

Match the base to the corresponding height.

Answers

Answer:

See picture

Step-by-step explanation:

A study by Consumer Reports showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name brands. the manager of the Publix in Clemson believes 64% is too low for his own store, to investigate whether this result applies to its own store, SC asked a random sample of 100 shoppers whether they believed that supermarket brands were as good as the national brands, 52 believe the supermarket brands were as good as the national brands.

Required:
At the 10% significance level test the managers claim.

Answers

Answer:

The calculated value  |Z| = |-2.5| >2.326 at 0.05 level of significance

The alternative hypothesis is accepted at a 0.05 level of significance

The manager of  Publix in Clemson believes 64% is too high for his own store

Step-by-step explanation:

Step:-1

Given that the consumer Reports showed that 64% of supermarket shoppers.

Given that the population proportion

                                 P = 0.64

Given that random sample size 'n' = 100

Given that 52 believe the supermarket brands were as good as the national brands.

sample proportion

                          [tex]p^{-} = \frac{x}{n} = \frac{52}{100} = 0.52[/tex]

Step:-2

Null hypothesis: The manager of the Publix in Clemson believes 64% is too low for his own store

μ < 0.64

Alternative Hypothesis:H₁:μ > 0.64

Test statistic

               [tex]Z = \frac{p-P}{\sqrt{\frac{PQ}{n} } }[/tex]

               [tex]Z = \frac{0.52-0.64}{\sqrt{\frac{0.64 X 0.36}{100} } }[/tex]

              Z =  -2.5

Level of significance = 0.05

Z₀.₀₅ = 2.326

The calculated value  |Z| = |-2.5| >2.326 at 0.05 level of significance

Final answer:-

The null hypothesis is rejected at a 0.05 level of significance

The alternative hypothesis is accepted at a 0.05 level of significance

HELPPP
Saul decides to use the IQR to measure the spread of the data. Saul calculates the IQR of the data set to be 17.
Saul asks Jasmine to check his work. Saul copies the data in numerical order from least to greatest for Jasmine.
15, 18, 30, 30, 30, 30, 34, n, 150
What is the value of n that will make the IQR of the data set equal to 172

Answers

Answer:

n = 78

Step-by-step explanation:

hope that helped!

Can you help I’m really stuck on this question.?.?.
No links. Pleas

Answers

Answer:

We can't see it all that well sorry.

Step-by-step explanation:

The average monthly cell phone bill was reported to be $50.07 by the U.S. Wireless Industry. Random sampling of a large cell phone company found the following monthly cell phone charges: 55.83 49.88 62.98 70.42 60.47 52.45 49.20 50.02 58.60 51.29 At the 0.05 level of significance can it be concluded that the average phone bill has increased?

Answers

Answer:

www.numerade.com/questions/the-average-monthly-cell-phone-bill-was-reported-to-be-5007-by-the-us-wireless-industry-random-sampl/

Step-by-step explanation:

In order to justify this claim for the Ferengi a sample of 16 coils is taken. For this sample set, the mean warp phase flux is found to be 73.7 cochranes with a sample measured standard deviation of 12 cochranes. Is this claim justified at the two-sided 95% or 90% levels? (Derive and define the appropriate values to show true or false for each of the levels. Eg. Is the found mean within the allowed range?)

Answers

Answer:

The responses to these question can be defined as follows:

Step-by-step explanation:

[tex]n = 16\\\\ \bar{x}= 73.7\\\\\sigma = 12\\\\a = 0.05\ or\ a = 0.10\\\\H_{o} \ : \mu = 68\\\\H_{a} \ : \mu \neq 68\\\\a = 0.05\\\\[/tex]

critical values [tex]=\pm t0.025,15 = \pm 2.131\\\\[/tex]

[tex](n-1) = 15^{\circ}\\\\a = 0.10\\\\[/tex]

critical values[tex]= \pm t0.05,15 = \pm 1.753\\\\[/tex]

[tex](n-1) = 15^{\circ}\\\\[/tex]

Testing the statistic values:

[tex]t = \frac{x-\mu_{0}}{ \frac{s}{\sqrt{n}}}\\\\[/tex]

  [tex]= \frac{73.7-68}{(\frac{12}{\sqrt{16}})}\\\\\ = \frac{5.7}{(\frac{12}{4})}\\\\ = \frac{5.7}{(3)}\\\\ = 1.9\\[/tex]

Test statistic ta [tex]= -1.90\ lies[/tex]

The critical values[tex]\pm t_{0.05,15} =\pm 1.753[/tex]

It is in the region of dismissal. We dismiss the 10% significant null hypothesis.

[tex]t_a = 1.90 \\\\df = 15\\\\a = 0.05\\\\p-value = 076831\\\\[/tex]

P - value is greater than the level of significance a= 0.05  

Null hypothesis we don't reject. At a 95% level, the claim is justified.

[tex]t_a = 1.90\\\\ df = 15\\\\ a = 0.10\\\\p-value = 076831\\\\[/tex]

P - value below the meaning level a = 0.10, we reject the hypothesis null. At a level of 90% the claim is not justified.

anyone wanna to study math subject?? as a free coaching??​

Answers

Step-by-step explanation:

Math is hard.....

and I don't like it anymore

Question

If Johnathon has work 16 hours a day from 8am to 12pm, and he has to drive from point a to b, which the distance is 3600 miles. His car can drive for 700 miles on a full tank of gas, which 1 gallon is 28 miles. What is the amount of stops and gallons of gas to get to point a and b?

Step-by-step explanation:

tan C-
I need help with this pleases help

Answers

Answer:

is 40/41 because is de answerv

Test the hypothesis that the average content of containers of a particular lubricant is 15 liters if the contents of a random sample of 15 containers are 10.2, 9.7, 10.1, 10.3, 10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.3, 10.5,11.2,11.3 and 9.8 liters. Use a 0.01 level of significance and assume that the distribution of contents is normal.
Also find 95% confidence interval for the population mean. Interpret your results

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Given The samples:

X = 10.2, 9.7, 10.1, 10.3, 10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.3, 10.5,11.2,11.3, 9.8

Using a calculator ;

Sample mean, xbar = 10.27

Sample standard deviation, s = 0.462

H0 : μ = 15

H1 : μ < 15

The test statistic :

(xbar - μ) ÷ (s/sqrt(n))

(10.27 - 15) / (0.462/sqrt(15))

-4.73 / 0.1192878

= - 39.65

Using the Pvalue form Tscore, calculator, df = 14

Pvalue = 0.000001,

Since, Pvalue < α ; then we reject the Null

Confidence interval :

Xbar ± Margin of error

Margin of Error = Tcritical * s/√n

TCritical at 95%, df = 14

Margin of Error = 2.145 * 0.462/sqrt(15) = 0.2559

Lower boundary :

10.27 - 0.2559 = 10.0141

Upper boundary :

10.27 + 0.2559 = 10.5259

(10.0141 ; 10.5259)

The true population means should reside within the interval

Helllllllllppppppppppppppppppppppppp

Answers

37.68 is the answer ........................
It’s 12.00 or the first answer choice.

The graph of f(x) = 3x2 – 5x – 22 passes through the point (0, –22) and one of its zeros is (–2, 0). What is the other zero of the function?

Answers

Step-by-step explanation:

this is your answer....

The other zero of the given function is [tex](\frac{11}{3}, 0)[/tex] .

How to find the x-intercept of a quadratic function ?

Let us assume f(x) [tex]=ax^{2} +bx+c[/tex], then to find the x-intercepts of this quadratic equation, let y = 0, i.e. [tex]ax^{2} +bx+c=0[/tex]

How to find zeros of the given function ?

Given, f(x)= [tex]3x^{2} -5x-22[/tex], whose one zero is (-2,0)

Now, to find the x-intercepts of the given quadratic equation, we have to take y = 0.

∴ [tex]3x^{2} -5x-22=0[/tex]

Now we have to solve this equation to find it's another zero.

[tex]3x^{2} -5x-22=0[/tex]

⇒ [tex]3x^{2} -(11-6)x-22=0[/tex]

⇒ [tex]3x^{2} -11x+6x-22=0[/tex]

⇒ [tex]x(3x-11)+2(3x-11)=0[/tex]

⇒ [tex](3x-11)(x+2)=0[/tex]

We know that, if multiplication of two terms is zero, then each of this term is seperately zero.

∴ [tex]3x-11=0[/tex]   or [tex]x+2=0[/tex]

⇒ [tex]3x=11[/tex]    or [tex]x=-2[/tex]

⇒ [tex]x=\frac{11}{3}[/tex]  or [tex]x=-2[/tex]

So, another zero of the function is [tex](\frac{11}{3}, 0)[/tex].

Learn more about zeros of a quadratic equation here :

https://brainly.com/question/1498156

#SPJ2

Can you please help me solve this problem using the Pythagorean theorem I’m so lost!!! (I Will give a brainliest if you help)

Answers

the answer here is 3.

basically for the pythagorean theorem you use the formula a^2 + b^2 = c^2

it works for right triangles, with a and being being sides of the triangles and c being the hypotenuse

therefore for this specific example, you plug in the side 4 and the hypotenuse 5:

a^2 + 4^2 = 5^2

a^2 + 16 = 25

a^2 = 9

a = 3

Madison has 3 quarts of juice she gave each of her friends 2 1/2 cups of juice how many cups does Madison have left​

Answers

Answer:

0

Step-by-step explanation:

It is zero because Madison friends were not specified(number)

You flip a fair coin 32 times. About how many times would you expect heads to appear?

Answers

Its a 50/50 chance so about 16

Answer:15 heads out of 30 is the most likely outcome when flipping 30 coins, if you run the same calculation with 14 or 16 heads you will get two equal, but smaller probabilities, same with 13 and 17 heads, and so on.

Step-by-step explanation:

What are the dimensions of this matrix?

2 x 1


2 x 2


1 x 1


1 x 2

Answers

Answer:

el primero es 2

el segundo es 4

el trersero es 1

y la última es 2

si multiplicas 2 x 1 y los otros el resultado sería

9

What is the difference? complete the equation.

Answers

Answer:

-3/5

Step-by-step explanation:

Not sure.....................

If 2(x+1)+8(x-1)=5x then x=

Answers

Answer:

x= 1.2  or  6/5

Step-by-step explanation:

Answer:

6/5 or 1.2 or 1 1/5

Step-by-step explanation:

but 6/5 is the exact answer

Solve the following system of equations x-2y=14
X+3y=9

Answers

9514 1404 393

Answer:

  (x, y) = (12, -1)

Step-by-step explanation:

I find the simplest solution is often found using a graphing calculator.

  (x, y) = (12, -1)

__

We notice that the coefficients of x are identical, so we can eliminate x by subtracting the first equation from the second.

  (x +3y) -(x -2y) = (9) -(14)

  5y = -5 . . . . simplify

  y = -1 . . . . . divide by 5

  x = 14 +2y = 14 +2(-1) . . . . using the first equation to find x

  x = 12

Will Identify the outlier in the data set. 77, 73, 78, 78, 71, 75, 120, 75, 77, 72, 75, 70 The outlier is​

Answers

Answer:

120

Step-by-step explanation:

120

every other number is in the 70s

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