if sec2a is 3 find the value of sina.​

Answers

Answer 1

By using trigonometry, it can be calculated that

The value of sina is [tex]\pm \frac{1}{\sqrt{3}}[/tex]

What is Trigonometry?

Trigonometry shows the relationship between sides and angles of a right angled triangle.

There are six trigonometrical functions. They are

[tex]sin \theta, \ cos\theta, \ tan \theta, \ cot\theta, \ sec\theta, \ cosec\theta[/tex]

[tex]sin\theta = \frac{perpendicular}{hypotenuse}\\\\cos\theta = \frac{base}{hypotenuse}\\\\tan\theta = \frac{perpendicular}{base}\\\\cot\theta = \frac{base}{perpendicular}\\\\sec\theta = \frac{hypotenuse}{base}\\\\cosec\theta = \frac{hypotenuse}{perpendicular}[/tex]

Trigonometry is a very important tool in mathematics.

Here, the trigonometric equation is

sec 2a = 3

cos 2a = [tex]\frac{1}{3}[/tex]

we know,

[tex]1 - cos 2a = 2 sin^2a\\\\1 - \frac{1}{3} = 2sin^2a\\\\2 sin^2a = \frac{2}{3}\\\\sin^2a = \frac{2}{3} \times \frac{1}{2}\\\\sin^2a = \frac{1}{3}\\\\ sina = \pm \frac{1}{\sqrt{3}}[/tex]

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Related Questions

PR is a chord of a circle Center 0 and radius 20CM - POR = 120° calculate (a) length of the Chord PR (b) length of are PQR ​

Answers

Answer:

i have the similar question just radius is changed frm 12 to 20 cm..

hopefully this will help u ...^⁠_⁠^

What is the interest on a $1900 investment at 3% for 1 year?

Answers

The interest is $57 on a $1900 investment at 3% for 1 year

Given,

In the question:

Principal = $1900

Rate of interest = 3%

Time = 1

Now, According to the question:

Principal = $1900

Rate of interest = 3%

Time = 1

Substitute:

Principal = $1900

Rate of interest = 3%

Time = 1  into formula Interest = P x R x T

I = 1900 x 0.03 x 1

Calculate the product or quotient:

I = 57

Hence, The interest is $57 on a $1900 investment at 3% for 1 year.

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marjore needs to earn a C in her class. her current test scores are 67,78,75,78 and .her final exam is worth 6 test scores. In order to earn a C marjorties average must lie between 70 and 79 inclusive. What range of scores can marjorie's receive on the final exam to earn a C in the​ course?

Answers

The range of scores that Marjorie's can receive in the final exam to earn a C in the course is 67 to 82  .

in the question ,

it is given that

the Marjorie's score in the tests are 67 , 78 , 75 , 78 .

let the score in the final exam be "x"

it is given that the final exam score is worth 6 test scores , which means

the score in final exam is = 6x

and the total number of tests = 6+4 = 10

given that to get the grade C minimum average is = 70

that is  (67 + 78 + 75 + 78 + 6x)/10 = 70

67 + 78 + 75 + 78 + 6x = 700

298 + 6x = 700

6x = 700 - 298

6x = 402

x = 402/6

x = 67

given that to get the grade C maximum average is = 79

that is  (67 + 78 + 75 + 78 + 6x)/10 = 79

67 + 78 + 75 + 78 + 6x = 790

298 + 6x = 790

6x = 790 - 298

6x = 492

x = 492/6

x = 82

the range of scores is 67 to 82 .

Therefore , The range of scores that Marjorie's receive in the final exam to earn a C in the course is 67 to 82  .

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Teresa estimates that the height of a giraffe in a zoo is 18 feet. In fact, it is 16 feet tall. What is Teresa’s percentage error? Use proportional relationships to solve the problem. Show all your work and round your answer to the nearest tenth.

Answers

Answer: 11.1%

Step-by-step explanation:

The formula for percent error is:

|Actual-predicted/predicted| * 100%

In the context of the problem:

Actual = 16 ft

Predicted = 18 ft

Plug these values into the equation:

|16-18/18| * 100% = percent error

11.11% = percent error
If you have any other problems about percent error, you should be able to just plug these values into the formula

Show all your work!
First find the k= COP x
K=18-12=1.5
X=1.5(10)
Y=1.5 =
y
४/५
es, Show all your work!
y
of
y
First find the k= COP x

Answers

Answer:

Step-by-step explanation:

COP = Constant of Proportionality. • y varies directly to x. > If 10 miles varies directly to 5 minutes,. – then 10 = y and 5 = x. • Unit Rate (1, r). > (x, y).

the letters that spell mississippi are each written on separate tiles lying facedown on a table. a tile is selected at random, the letter is recorded, and then the tile is placed facedown on the table. then the process repeats. what is the theoretical probability of choosing a tile with the letter p? responses 14 1 fourth 411 4 over 11 111 1 over 11 211

Answers

The theoretical probability of choosing a tile with the letter p is 1/8

The letter of the word MISSISSIPPI are written on separate tiles lying down on the table and tile is chosen at random and the the letter is noted and then the tile is lied again on the table.

Probability of the event is,

P(E) = Total favorable outcomes/Total possible outcomes.

Total possible outcomes in this case are 11 because there are a total of 11 letters.

The total favorable outcomes that the chosen letter is P is,

Total favorable outcomes = ¹¹C₁/(2!)(2!)(2!)

Total favorable outcomes = 11/8

Probability P that chosen number is P is,

P = (11/8)/11

P = 1/8

So, the probability that the chosen tile is with letter P is 1/8.

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Which of the following rational functions is graphed below?

Answers

Answer:

C

Step-by-step explanation:

In the graph, you can see an asymptote is happening for x=-5, so look for an equation that divides by 0 for x=-5. That is clearly C, for x=-5 the denominator is 0.

A sphere has a diameter of 24 mm.
What is the volume of the sphere?

48pi mm³
192pi mm³
2304pi mm³
I don't know.

Answers

Answer:

Step-by-step explanation:

volume of a sphere = ⁴/3 π r³. r = D/2. V = 4/3 × π × (D/2)³. V = 4/3 × π × D³/8. V = ⅓ × π × D³/2. V = ⅓× π × (24mm)³/2.

8. If a population doubles every 5 years, how many years will it take for the population to increase by 10 times
its original amount?
First: If the population gets multiplied by 2 every 5 years, what does it get multiplied by each year? Use this
to help you answer the question.

Answers

After ≈16.61 years the population will increased by  times it's original amount.

What do you mean by population?

A population is the entire set of people in a group, whether that group is a country or a collection of people who share a certain trait. A population is the group of people from which a statistical sample is taken in statistics.

Given: If a population doubles every 5  years.

Assume,  'A' is the starting population, and 't' is the passing time in years.

Given the fact that a population doubles every five years, our population is growing exponentially, as per the question.

Here, the equation can be written as follows: [tex]A(t) = A(2)^{\frac{t}{5} }[/tex]                    (1)

We now need to determine when the population will have multiplied by 10 by that time.

Let's substitute [tex]A(t) = 10A[/tex]  in the above equation.

[tex]10A = A(2)^{\frac{t}{5} }[/tex]

[tex]10 = (2)^{\frac{t}{5} }[/tex]

Taking the natural log of both sides we get:

[tex]ln10 = \frac{t}{5} \times ln2[/tex]                        {[tex]ln(a)^n= nln(a)[/tex]}

2.3025 x 5 = t x 0.6931

[tex]t = \frac{2.3025}{0.6931}\\t = 16.6096[/tex]

Therefore, After ≈16.61 years the population will increased by  times it's original amount.

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let nn denote the smallest positive integer that is divisible by both 44 and 9,9, and whose base-1010 representation consists of only 44's and 99's, with at least one of each. what are the last four digits of nn?

Answers

The last four digits of the number nn are 4944

Given that,

Let nn stand for the lowest positive integer that can be represented in base-1010 using only the numbers 44 and 99, with at least one of each. This number must be divisible by both 44 and 9,9.

The last two digits of n must be divisible by 4 for n to be divisible by 4.

So last digits of n will be 44.

And for divisiblity by 9, sum of all digits of n has to be divisible by 9.

As two digits are fixed and their total is 8, next feasible total will be 45 so 9 can be atleast one time in n.

And as statement says n has to be smallest number n will be 4444444944

So last 4 digits of n are 4944.

Therefore, nn's last four numbers are 4944.

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y≥x²+2x-8 factor the quadratic equation to find x intercepts

Answers

The factors of the quadratic equation are x≥-4, x≥2 and lies in the interval (-∞, -4]∪[2, ∞)

What is meant by quadratic equation?

A quadratic equation is any equation that can be rearranged in standard form as ax²+bx+c=0 where x represents an unknown value and a, b, and c represent known numbers. In general, a = 0; equations with a = 0 are considered degenerate because the equation becomes linear or even simpler. The numbers a, b, and c are the equation's coefficients, and they can be distinguished by referring to them as the quadratic coefficient, linear coefficient, and constant or free term, respectively.

To find x-intercept y=0

y≥x²+2x-8

x²+2x-8≥0

x²+4x-2x-8≥0

x(x+4)-2(x+4)≥0

(x-2)(x+4)≥0

∴x≥-4, x≥2

∴(-∞, -4]∪[2, ∞)

Therefore, the factors of the quadratic equation are x≥-4, x≥2 and lies in the interval (-∞, -4]∪[2, ∞)

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how do i solve 1) −10+ r = 3+r-7

Answers

Answer: No Solution

Explanation: 10 + r = 3 + r - 7

Combine like terms: 10 + r = -4 + r

Subtract R to both sides: 10 = 4

There is NO SOLUTION

Find the slope of the line that passes through the pair of points (8, −2), (1, 1)

Answers

The slope of the line that passes through the given pair of points is, -3/7.

What is slope of the line?

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. where "m" represents a line's slope. So, the slope of a line is tanθ.

Given: (8, -2), (1, 1)

Since, if two points [tex](x_1, y_1), (x_2, y_2)[/tex] are given then slope (m) is defined as,

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex].

Here,

[tex](x_1, y_1) = (8, -2)\\(x_2, y_2)=(1, 1)[/tex]

So, the slope can be defined as,

[tex]m = \frac{1-(-2)}{1-8} \\m=\frac{3}{-7} \\m=-\frac{3}{7}[/tex]

Hence, the slope of the line that passes through the given pair of points is, -3/7.

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Help please
Find the values of the variables and the measures of the angles.

Answers

Answer:

X= 29 because it is a right angle, and all right angles are = to 90, so you subtract 61 from 90.Y= 29Z= 61

Step-by-step explanation:

Answer:

Step-by-step explanation:

Summation of all angles within a triangle is equal to 180 degrees.

y+61+90=180

Therefore, y = 180-61-90 = 29 degrees

61+x = 90

Therefore, x = 90-61 = 29 degrees

z+90+29 = 180

Therefore, z = 180 - 90 - 29 = 61 degrees

how many 44-digit positive integers (that is, integers between 10001000 and 99999999, inclusive) having only even digits are divisible by 55?how many 44-digit positive integers (that is, integers between 10001000 and 99999999, inclusive) having only even digits are divisible by 55?

Answers

There are 100 4-digit positive integers are possible between 1000 and 9999.

Our first step is to divide the four digit number into four places: tens, hundreds, and thousands.

To solve this problem, we must start from the right-hand side and find how many even numbers should be placed where the desired answer can be obtained.

There are a total of [0, 2, 4, 6, and 8] objects

There should only be one digit on one place, since it is the only digit that makes the number divisible by five

There are 1 ways to fill the one's place, so the total number is 1.

It is possible to take any number from the given sets of even numbers in the tens place,

There are five ways to fill one place, so there are five ways to fill it.

Taking a look at the hundreds place,

All numbers can be placed in the hundreds place from the given sets, so all numbers can be taken from the hundreds place.

Therefore, there are five ways to fill the hundreds place.

Taking a look at the thousands,

It is possible to fill thousands of places with 4 numbers from a given set of even numbers.

Therefore, there are four ways to fill the thousands place

The next step is to use the concept of factorial to find the number of ways to make a 4-digit number from even numbers that are divisible by 5.

To fill the respective places, we will multiply all the ways we calculated

= 4 × 5 × 5 × 1

= 100

Hence, there 100 4-digit positive integers possible.

Question

how many 4-digit positive integers (that is, integers between 1000 and 9999, inclusive) having only even digits are divisible by 5?

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length of 3 feet, a width of 2 feet, and a height of 5 feet. What is the volume of the refrigerator?

Answers

Answer:

30 feet^3

Step-by-step explanation:

length x width x height

3 x 2 x 5

=30

The answer to this is 30 ft always multiply the L•w•h

Can anyone write the equation this graph?

Answers

The equation of the graph given in the diagram which represents an absolute value function is: y = |x - 3| + 5.

What is the Equation of the Graph of an Absolute Value Function?

The equation, in vertex form, of a absolute value function is expressed as y = a|x – h| + k, where:

(h, k) = vertex of the graph a = this value determines if the graph opens up or opens down.h = horizontal translation factork = vertical translation factor

From the graph, we know that:

Vertex (h, k) = (3, 5)

Substitute h = 3 and k = 5 into the equation, y = a|x – h| + k:

y = a|x - 3| + 5

A point on the graph is (5, 7). To find the value of a, substitute x = 5 and y = 7 into the equation y = a|x - 3| + 5:

7 = a|5 - 3| + 5

7 = 2a + 5

7 - 5 = 2a + 5 - 5 [subtraction property of equality]

2 = 2a

Divide both sides by 2

2/2 = 2a/2 [division property of equality]

Substitute a = 1 into y = a|x - 3| + 5:

y = |x - 3| + 5 [equation of the absolute value function]

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Solve the system of equations by the addition method.
3x + 4y = 7
6x - 4y= 2

Answers

3x + 4y = 7
6x - 4y = 2
* Delete 4y together because they are the same *
=> 9x = 9 * we divide it by 9
x = 1

17 ÷ 2578
Please help I need an answerrrr

Answers

Answer:   17/2578  (Decimal: 0.006594)

Step-by-step explanation:

That's the answer :)

2 times 221 divide 4 ?

Answers

The answer is 110.5 as 221/4 is 55.25 so double that u will get 110.5 or if anything can do half of 221 which would be 110.5

The cost of a pizza varies directly as the square of its radius. If a
pizza with a 6 inch radius costs $8.00, how much should a pizza with
an 11 inch radius cost?

Answers

The cost of a pizza with an 11 inch radius is  $26.86

In this question, the cost of a pizza varies directly as the square of its radius.

Let C be the cost of pizza and r be the radius of Pizza.

We have been given the direct proportionality between the cost of pizza and the radius of Pizza.

C ∝ r²

If a pizza with a 6 inch radius costs $8.00

8 = k * 6^2

where k is the proportionality constant.

8 = k * 36

k = 0.222

We need to find the cost of pizza with an 11 inch radius.

so, we get an equation,

C = k * 11^2

substitute above value of k

C = 0.222 * 11^2

C = 0.222 * 121

C = $26.86

Therefore, the cost of a pizza with an 11 inch radius is  $26.86

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A roofing contractor uses shingles at a rate of 3 bundles for every 96 square feet of roof covered. At this rate, how many bundles of shingles will he need in order to cover a roof that is 416 square feet?

Answers

Answer:

13

Step-by-step explanation:

416/96 = 4.33333

416 is 4.333 times 96, so he needs 4.333 times 3 bundles.

4.3333 × 3 = 13

Answer: 13

Answer:

13

Step-by-step explanation:

you see how much it covers initially. (96/3=32) then 416/32=13

The triangle on the right is a scaled copy of the triangle on the left. Identify the scale factor. Express your answer as a fraction in simplest form.

Answers

The scale factor in the simplest form of a fraction of the triangles will be 43/78.

What is dilation?

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

There is no effect of dilation on the angle.

The triangle on the right is a scaled duplicate of the triangle on the left.

The ratio of the side of a big triangle to the side of a small triangle. Then we have

Scale factor = 43 / 78

The scale factor in the simplest form of a fraction of the triangles will be 43/78.

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if x is a number in the interval 2 6 state all integers that satisfy the given inequality

Answers

Answer:

it is because I haven't completed the answer from THE WORK OF THE BEST ways to solve a question

Step-by-step explanation:

do I

Which is equivalent to 3√8x?

Answers

It is equivalent to 8^x/3

What is equivalent equations?OBJECTIVES FOR EQUALITY EQUATIONSAfter finishing this section, you need to be able to:Sort an equation into a conditional or an identity category.Mentally solve simple equations.Check to see if some equations are equal.A mathematical equation is a statement that two numerical expressions are equal.Equations go into one of two categories.

acc to our question-

to write a square root into fraction. To do that, you just have to apply the formula :

x^power/root

Then, here it gives . 8^x/3

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A housepainter mixed 5 gal of blue paint with every 9 gal of yellow paint in order to make a green paint. Which ratio of gallons of blue paint to gallons of yellow paint will NOT make the same shade of green paint?

Answers

The ratio of gallons of blue paint to gallons of yellow paint will NOT make the same shade of green paint 4:9.

What is Ratio?

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

A housepainter mixed 5 gal of blue paint with every 9 gal of yellow paint.

So, the ratio of gallons of blue paint to gallons of yellow paint is

= 5 to 9  or 5:9

Now, ratio of gallons of blue paint to gallons of yellow paint will NOT make the same shade of green paint

= 1- 5/9

=4/9

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In the figure below, a pole has two wires attached to it, one on each side, forming two right triangles.



Based on the given information, answer the questions below. Round each answer to the nearest tenth.

Part A: How tall is the pole? Show your work.

Part B: How far from the base of the pole does Wire 2 attach to the ground? Show your work.

Part C: How long is Wire 1? Show your work.

Answers

A. Applying the trigonometric ratio, the length of pole = 29.6 ft.

B. 23.1 ft.

C. Length of wire 1 = 45.1 feet.

How to Apply the Trigonometric Ratios?

The trigonometric ratios are:

sin ∅ = opposite length/hypotenuse length cos ∅ = adjacent length/hypotenuse lengthtan ∅ = opposite length/adjacent length.

Part A: Apply the trigonometric ratio, tan ∅ = opp/adj, to find the length of the pole

∅ = 41°

Opp. = length of pole

Adj. = 34 ft

Substitute

tan 41 = length of pole/34

Length of pole = (tan 41)(34) = 29.6 ft.

Part B:

Let the distance between the base of the pole and wire 2 be represented as x. Therefore, apply tan ∅ = opp/adj.

∅ = 38

Opp. = x

Adj. = 29.6 ft

Therefore:

tan 38 = x/29.6

x = (tan 38)(29.6)

x = 23.1 ft.

Part C: Use the Pythagorean theorem to find the length of wire 1.

Length of wire 1 = √34² + 29.6²)

= 45.1 feet.

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Find the value of x and 3x

Answers

Step-by-step explanation:

remember, the sum of all angles in a triangle is always 180°.

now let's consider the white, "cut-out" triangle on the left side.

the purple one angles at the top and bottom corner are 45°.

the withe outer angles at the same corners (they are the inner angles for the white triangle) are complementary angles (together they have 90°) to the purple ones, because due to the equal angles at the top and bottom we know the connection between the 2 45° angles (the white baseline) is at a 90° angle to the 45° to 135° sides.

so the 2 baseline angles of the left white triangle are also 45° (45+45 = 90).

and that means that the third white angle is

180 - 45 - 45 = 90°.

and because a full circle around the 3x° point must have 360° (as any full circle), we know that both angles (90° and 3x°) together are 360°.

360 = 90 + 3x

270 = 3x

x = 90°

3x = 270°

Which relation is a function?

Answers

The relation that is a function in the option is graph C.  

What is a function?

A function relates an input to an output.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

In a simpler term, a function relates each element of a set with exactly one element of another set (possibly the same set).

In a function, the x value is exactly related to a single y value,  exactly, means that a function is single valued. It will not give back 2 or more results for the same input.

Therefore, the only graph that follows the rule of a function is graph C.

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Which statement is true?

This table does not show a probability distribution.
This table shows a probability distribution.

Answers

After using the probability distribution table, the given table does not show a probability distribution. The statement 1 is correct.

In the given question, we have to check which statement is correct regarding to the given option.

The given statements are:

(1) This table does not show a probability distribution.

(2) This table shows a probability distribution.

Before checking the statement we learn about a probability distribution table.

In a probability distribution table every result of a statistical experiment is connected to the likelihood that the result will actually occur. An experiment's result is recorded as a random variable, which is typically written with a capital letter.

As we can see that there is given the probability of having the blue, green, yellow and red color.

So the given table does not show a probability distribution.

So the statement 1 is correct.

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