What is the exact value of the trigonometric expression? State your answer in simplified radical form and include all work.
*Please reference included picture for problem. Thank you!
Answers
Answer:
The exact value of the given trigonometric expression is undefined.
Step-by-step explanation:
Given trigonometric expression:
[tex]\dfrac{\cos\left(\dfrac{2 \pi}{3}\right)}{\tan\left(-\dfrac{7 \pi}{4}\right)}+\csc(\pi)[/tex]
To find the exact value of the given trigonometric expression, begin by finding the exact values of each of the trigonometric functions in the expression
The exact value of cos(2π/3) is:
[tex]\implies \cos\left(\dfrac{2 \pi}{3}\right)=-\dfrac{1}{2}[/tex]
The exact value of tan(-7π/4) is:
[tex]\implies \tan\left(-\dfrac{7 \pi}{4}\right)=1[/tex]
Since the cosecant function is the reciprocal of the sine function, the exact value of csc(π) is:
[tex]\implies \csc (\pi)=\dfrac{1}{\sin(\pi)}=\dfrac{1}{0}=\textsf{unde\:\!fined}[/tex]
Therefore:
[tex]\begin{aligned}\implies \dfrac{\cos\left(\dfrac{2 \pi}{3}\right)}{\tan\left(-\dfrac{7 \pi}{4}\right)}+\csc(\pi)&=\dfrac{-\dfrac{1}{2}}{1}+\dfrac{1}{0}\\&=-\dfrac{1}{2}+\dfrac{1}{0}\\\\&=\textsf{unde\:\!fined}\end{aligned}[/tex]
Related Questions
a relationship that is noted between two or more variables is termed
Answers
The relationship that is noted between two or more variables is termed a correlation. Correlation refers to the statistical association or relationship between two or more variables.
It indicates the degree to which the variables are related or how they are related to each other. Correlation can be positive, negative, or zero, depending on the direction and strength of the relationship between the variables.
A positive correlation indicates that as one variable increases, the other variable also increases. A negative correlation indicates that as one variable increases, the other variable decreases. Zero correlation indicates that there is no relationship between the variables.
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Find the length of the side labeled x. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth.
Answers
The length of the side labeled x is 75.3 when rounded to the nearest tenth which can be determined by using Pythagorean theorem.
What is Pythagorean theorem?The Pythagorean theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
To find the length of the side labeled x, we will first need to calculate the length of the other two sides.
For the first triangle, the hypotenuse is equal to the side labeled x, so the length of the side labeled x can be calculated using the formula:
x = √(35² + 42²) = 50.1
For the second triangle, the hypotenuse is the side opposite the right angle, which is equal to the side labeled x. We can calculate the length of the side labeled x using the formula:
x = √(60² + 50²) = 75.3
For the third triangle, the hypotenuse is the side opposite the right angle, which is equal to the side labeled x. We can calculate the length of the side labeled x using the formula:
x = √(28² + 34²) = 39.6
Therefore, the length of the side labeled x is 75.3 when rounded to the nearest tenth.
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The rounded value of x in the triangles is:
25) x ≈ 76
27) x ≈ 21
29) x ≈ 104
Give a brief account on trigonometric relations.All trigonometric identities are based on six trigonometric ratios. Sine, cosine, tangent, cosecant, secant, and cotangent. All these trigonometric ratios are defined using the sides of a right triangle as follows: Adjacent side, opposite side, and hypotenuse side.
25) Since, Sinθ = Opposite side/hypotenuse
Sin35° = 39/hypotenuse
hypotenuse = 39/Sin35°
Sin35° = 0.57
hypotenuse = 39/0.57
hypotenuse = 68.42
Now, using Pythagoras theorem:
hypotenuse² = base² + perpendicular²
68.42² = 39² + perpendicular²
4681.29 - 1521 = perpendicular²
4681.29 - 1521 = perpendicular²
3160.29 = perpendicular²
√3160.29 = perpendicular
56.21 = perpendicular
For the calculation of x:
Cosθ = Adjacent side/hypotenuse
Cos42° = 56.21/x
0.74 = 56.21/x
x = 56.21/0.74
x = 75.95
x ≈ 76
27) Cosθ = Adjacent side/hypotenuse
Cos60° = 14/hypotenuse
0.5 = 14/hypotenuse
hypotenuse = 14/0.5
hypotenuse = 28
Now, using Pythagoras theorem:
hypotenuse² = base² + perpendicular²
28² = 14² + perpendicular²
784 - 196 = perpendicular²
588 = perpendicular²
√588 = 24.24
perpendicular = 24.24
For the calculation of x:
Sinθ = Opposite side/hypotenuse
Sin50 = 24.24/hypotenuse
0.76 = 24.24/hypotenuse
hypotenuse = 24.24/0.76
hypotenuse = 31.89
Using Pythagoras theorem:
hypotenuse² = base² + perpendicular²
31.89² = x² + 24.24²
1016.97 = x² + 587.57
x² = 1016.97 - 587.57
x² = 429.4
x = √429.4
x = 20.72
x ≈ 21
29) Sinθ = Opposite side/hypotenuse
Sin28° = 44/hypotenuse
0.46 = 44/hypotenuse
hypotenuse = 44/0.46
hypotenuse = 95.65
Using Pythagoras theorem:
hypotenuse² = base² + perpendicular²
95.65² = 44² + perpendicular²
perpendicular² = 9148.92 - 1936
perpendicular² = 7212.92
perpendicular = √7212.92
perpendicular = 84.92
For the calculation of x:
Cosθ = Adjacent side/hypotenuse
Cos34 = 84.92/x
x = 84.92/0.82
x = 103.56
x ≈ 104
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How do you find height when you are doing volume with cubic units?
Answers
Answer:calculate the cube root of a cube's volume.
Step-by-step explanation:
Select the correct answer. Solve for x. x2 - 2x - 24 = 0
A.
-4, -6
B.
-4, 6
C.
2, -6
D.
4, 6
Answers
Answer:
B. -4, 6
Step-by-step explanation:
x2-2x-24=0
1st you must factor
x2+4x-6x-24=0
next factor by grouping and find gcf
x(x+4)-6(x+4)=0
you now have your factors so set then to 0 and solve for x
x+4=0
-4 -4
x=-4
x-6=0
+6 +6
x=6
7) A long piece of wire of length 90 cm is bent to form an equilateral triangle. What will be the length of each side of the triangle?
Answers
Answer:
30cm
Step-by-step explanation:
Perimeter of an equilateral triangle = 3L
Mathematically we have;
P = 3L
Where P = perimeter of the triangle
L = Length
Therefore;
90 = 3L
Divide both side by 3
L = 30cm
Therefore, the length of each side of the triangle is 30cm.
assume that 1 laborer produces 6 units of output, 2 laborers produce 15 units of output, 3 laborers produce 25 units of output, and 4 laborers produce 34 units of output. diminishing returns to labor set in when the firm hires the
Answers
The marginal product of labor initially increases from 6 to 9, but then starts to decrease as more labor is added. Therefore, the firm experiences diminishing returns to labor when it hires a third laborer.
Diminishing returns to labor occur when the marginal product of labor (i.e., the additional output produced by adding one more unit of labor) decreases as more labor is added. We can calculate the marginal product of labor for each level of labor as follows:
1 laborer: 6 units of output (marginal product = 6)
2 laborers: 9 units of additional output (total output = 15, marginal product = 9)
3 laborers: 10 units of additional output (total output = 25, marginal product = 10)
4 laborers: 9 units of additional output (total output = 34, marginal product = 9)
The law of diminishing marginal returns is a concept from economics that explains how the marginal output of a production process starts to decrease as the input goes up. It is also used to refer to a point at which output increases at a diminishing rate as more units of labor are added to a production process. This can also be called the point of decreasing marginal productivity.
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what is the messure or the vertex angle of an isosceles triangle if one of its base angle measures 16 degrees
Answers
Since the sum of the angles in any triangle is 180 degrees, we can find the measure of the vertex angle by subtracting the sum of the base angles from 180 degrees.
So, the measure of the vertex angle of the isosceles triangle is:
180 - 32 = 148 degrees.
which of the following was traditionally an assumption underlying the independent samples t-test question 10 options: a) scores must be drawn from a normally distributed population b) variances should be unequal in both groups c) data should be at the nominal level d)all of the above
Answers
The assumption underlying the independent samples t-test is that the scores must be drawn from a normally distributed population. Option A is correct.
What is a t-test?A t-test is a statistical method that determines whether two groups of observations are significantly different from one another. When comparing the means of two populations, the t-test is commonly used. The t-test is used to determine whether two groups' means are significantly different when the samples are drawn from normally distributed populations with equal variances.
The t-test is a powerful tool for determining whether a sample is significantly different from a population or whether two samples are significantly different from one another. The independent samples t-test, as opposed to the dependent samples t-test, is a t-test that compares the means of two independent groups. In this situation, the groups are separate and distinct.
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The neck of a gifaffe is 4 1/2 feet in length. Its neck is 30 perocent of it height whats the higet of the giffae
Answers
The giraffe is 15 feet tall based on the relation between the length of neck of giraffe and it's height.
Firstly convert the mixed fraction to fraction.
Length of neck of giraffe = (4×2)+1/2
Length of neck = 9/2 feet
Now, let us assume the height of giraffe be x. So, equation will be -
30% × x = 9/2
Rewriting the equation
30/100 × x = 9/2
Cancelling zero
3x/10 = 9/2
Again rewriting the equation
x = 90/6
Performing division on Right Hand Side of the equation
x = 15 feet
Thus, height of giraffe is 15 feet.
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Let P be some predicate. Check the box next to each scenario in which ∀n ∈ N, P(n) must be true.
a) For every natural number k > 0 , if P(i) holds for every natural number i < k, then P(k) holds.
b) P(0) holds and for every natural number k > 0, if P(i) does not hold, then there is some natural number i < k such that P(i) does not hold.
c) For every natural number k, if P(i) holds for every natural number i < k, then P(k) holds.
d) For every natural number k, if P(k) does not hold, then there is a smaller natural number i < k such that P(i) does not hold.
Answers
Answer:
A
Step-by-step explanation:
a) ✔️
This is the principle of mathematical induction. If P holds for the base case k=1 and we can show that if it holds for any arbitrary k (e.g. k=n) then it must also hold for the next value (e.g. k=n+1), then we have shown it holds for all natural numbers.
b) ❌
There is no guarantee that P holds for all natural numbers from the statement alone. It only guarantees that for any k where P does not hold, there exists a smaller number i where P does not hold.
c) ❌
This is the principle of weak mathematical induction. It only shows that if P holds for a given k and for all smaller values i then it must hold for k+1. It does not guarantee that P holds for all natural numbers.
d) ❌
This statement is the negation of the principle of mathematical induction. It is known as the "strong induction" principle, which assumes that if P does not hold for k, then there exists a smaller i where P does not hold. However, this principle is not sufficient to prove that P holds for all natural numbers k.
if cell phone companies screen text messages, then freedom of speech is threatened. thus, freedom of speech is not threatened, because cell phone companies do not screen text messages. which of the following correctly expresses the form of this argument? a. if c then f. b. not f. c. all c are f. d. if c then f. e. if c then f. not
Answers
The correct option that expresses the form of the given argument is "d. if c then f."Explanation:In the given argument, it is stated that if cell phone companies screen text messages, then freedom of speech is threatened.
But as cell phone companies do not screen text messages, so freedom of speech is not threatened. This is a conditional argument, and it can be expressed in the form of a hypothetical syllogism.
The hypothetical syllogism is a syllogism that has a conditional statement in its premises. It is also called a chain argument or transitive argument. The form of the hypothetical syllogism is "If A, then B. If B, then C.
Therefore, if A, then C."In the given argument, it can be expressed in the form of the hypothetical syllogism as follows:If cell phone companies screen text messages, then freedom of speech is threatened. If freedom of speech is threatened, then cell phone companies screen text messages. Therefore, if cell phone companies do not screen text messages, then freedom of speech is not threatened.This can also be represented as "if C then F."Therefore, the correct option that expresses the form of the given argument is "d. if c then f."
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what is the sum of all integer values of $x$ such that $\frac{31}{90} < \frac{x}{100} < \frac{41}{110}$ is true?
Answers
\begin{align*}
\frac{31}{90} < \frac{x}{100} &\iff 3100 < 90x < 31\cdot 100 \
\frac{x}{100} < \frac{41}{110} &\iff 100x < 41\cdot 110
\end{align*}
Solving the first inequality, we have $3100/90 < x < 31\cdot 100/90$, or $31/9 < x < 310/9$. Multiplying both sides by $9$ gives $31 < 9x < 310$, so $x$ can be any integer between $32$ and $34$ inclusive.
Solving the second inequality, we have $x < 41\cdot 110/100$, or $x < 45.1$. Since $x$ is an integer, the largest possible value of $x$ that satisfies this inequality is $45-1=44$.
Therefore, the possible values of $x$ are $32, 33, 34,$ and $44$, and their sum is $32+33+34+44=\boxed{143}$.
y is inversely proportional to the square of x. It is given that y = 8 for a particular value of x. k= When x increases by 300%, find the new value of y,
Answers
Answer:
1/2 or .5
Step-by-step explanation:
If y is inversely proportional to the square of x, we can express this relationship using the formula:
y = k/x^2
where k is a constant of proportionality. We are told that y = 8 for a particular value of x, so we can substitute these values into the equation:
8 = k/x^2
To find the value of k, we can solve for it:
k = 8x^2
Now we are asked to find the new value of y when x increases by 300%. This means that the new value of x will be 4 times the original value (since an increase of 300% means an increase by a factor of 3, and we need to add the original value to get the new value). So we can substitute 4x for x in our equation:
y = k/(4x)^2 = k/16x^2
We already know the value of k, so we can substitute it in and simplify:
y = (8x^2)/(16x^2) = 1/2
Therefore, the new value of y is 1/2 when x increases by 300%.
which of the following is an incorrect statement? if a density curve is skewed to the right, the mean will be larger than the median. in a symmetric density curve, the mean is equal to the median. the mean of a skewed distribution is pulled toward the long tail. the median is the balance point in a density curve.
Answers
In a skewed distribution, the long tail pulls the mean toward it. In a density curve, the median is where everything level out.
what is mean ?The median, a statistician's measure of central tendency, divides a dataset into two equally sized half. When the data is organized from smallest to largest, it is the midway value (or largest to smallest). The median is the average of the two middle values when there are an even number of values. Since it is unaffected by extreme values, the median is frequently employed as a measure of central tendency when a dataset contains outliers or is skewed.
given
None of the claims are untrue.
The mean will be greater than the median if a density curve is tilted to the right.
The mean and median are equal in a density curve that is symmetric.
In a skewed distribution, the long tail pulls the mean toward it. In a density curve, the median is where everything level out.
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What geometric shapes can you draw that have exactly one pair of parallel sides? Use pencil and paper. Sketch examples for as many different types of shapes as you can. Use appropriate marks to show the pairs of parallel sides.
A. regular pentagon
B. square
C. Trapezoid
D. parallelogram
Answers
Write each polynomial in Standard form and name it based on its degree an number of terms.
9x²-213
Standard --
Degree
Terms
Answers
We would name this polynomial as a quadratic polynomial with two terms.
In standard mathematics, what is a polynomial function?A polynomial function is one that involves only non-negative integer powers or positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, and so on.
In the standard form of a polynomial, the terms are written in descending order of degree. The standard form for a polynomial of degree n is:
a1x + a0 + anxn + an-1xn-1 +...
We have the polynomial in this case:
9x² - 213
To write it in standard form, rearrange the terms in descending order of degree as follows:
213 + 9x²
As a result, the standard form of the polynomial is:
9x² - 213
This polynomial has degree 2 (because x's highest exponent is 2) and two terms (since there are two distinct parts to the expression, a constant and a term with an x squared coefficient).
As a result, we'd call this polynomial a quadratic polynomial with two terms.
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25 out of 68 students have vanilla ice cream and the rest have chocolate. What is the ratio of the number of students who have vanilla to the total number of students?
Answers
Answer: The total number of students is the sum of the number of students who have vanilla and those who have chocolate:
Total = 25 + (68 - 25) = 43
The ratio of the number of students who have vanilla to the total number of students is:
Vanilla : Total = 25 : 43
This ratio cannot be simplified any further because 25 and 43 do not have any common factors other than 1. Therefore, the ratio of the number of students who have vanilla to the total number of students is:
25 : 43
Step-by-step explanation:
The daily temperatures for the winter months in Virginia are Normally distributed with a mean of 59 F and a
standard deviation of 10°F. A random sample of 10 temperatures is taken from the winter months and the mean
temperature is recorded. What is the standard deviation of the sampling distribution of the sample mean for all
possible random samples of size 10 from this population?
Answers
The standard deviation of the sampling distribution of the sample mean for the given sample size is equal to 3.1623°F.
For the normally distributed data,
Mean of the population distribution 'μ' = 59F
Population standard deviation 'σ' = 10°F
Sample size 'n' = 10
Formula for the standard deviation of the sampling distribution of the sample mean (also known as the standard error of the mean) is equal to ,
= σ / √(n)
Substitute the value to get the standard deviation of the sampling distribution of the sample mean we get,
= 10°F / √(10)
= 3.1623°F
Therefore, the standard deviation of the sampling distribution of the sample mean for all possible random samples of size 10 from this population is approximately 3.1623°F.
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How much was one movie ticket in 2008
Answers
Answer: 7 dollars 18 cents.
Step-by-step explanation:
Let sin(2x) = cos(x), where 0° ≤ x < 180°. what are the possible values for x? a. 30° only b. 90° only c. 30° or 150° d. 30°, 90°, or 150°
Answers
If sin(2x) = cos(x), where 0° ≤ x < 180°, then, The possible angle values of x are 90°, 30° and 150°.
The sine and the cosine are trigonometric functions of the angles. The sine and cosine of an acute angle are defined in the context of a right triangle: for a given angle, its sine is the ratio of the length of the side opposite the angle to the length of the longest side of the angle. triangle (the hypotenuse ), and the cosine is the adjacent side The ratio of the length to the hypotenuse.
According to the Question:
Given that,
sin(2x) = cos(x) where 0° ≤ x < 180°
We know that:
sin(2x) = 2 sin(x) cos(x)
⇒ 2 sin(x) cos(x) = cos(x)
Subtract cos(x) on both sides
2 sin(x) cos(x) - cos(x) = 0
cos(x) (2sinx-1)=0
It means, cos(x) = 0 and (2sin x -1 ) = 0
cos x = cos0 and sinx(x) = 1/2
x = 90° and x = 30°, 150°
Hence, the possible values of x are 90°, 30° and 150°.
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What is the solution to -1/2 [x-1] =0?
x=1
x=-1 or x=1
x=1 or x=2
No solutions exists
Answers
Answer:
x=1
Step-by-step explanation:
If p and q vary invarsely and p is 11 when q is 28, determine q when p is equal to 4
Answers
77 is the value of Q in linear equation.
What in mathematics is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
P ∝ 1/Q
PQ = K
AT P= 11
Q = 28
11 * 28 = K
K = 308
AT P = 4
4Q = 308
Q = 77
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suppose 46.37% of all voters in the last election supported the current governor. a telephone survey contacts 328 voters from the last election and asks if they voted for the current governor. what is the probability that at least half of the voters contacted supported the current governor in the last election?
Answers
The probability that at least half of the 328 voters contacted in the telephone survey supported the current governor in the last election is 0.0532.
What is the probability?To calculate the probability that at least half of the 328 voters contacted in the telephone survey supported the current governor in the last election, we can use the binomial probability formula.
The formula is: P(x) = (ⁿCₓ) × pˣ × (1-p)⁽ⁿ⁻ˣ⁾
In this case, n = 328, p = 46.37%, and x = 164 (since half of 328 is 164).
Plugging in the numbers we get:
P(x) = ³²⁸C₁₆₄ × (0.4637)¹⁶⁴ × (0.5363)⁽³²⁸⁻¹⁶⁴⁾ = 0.0532
Therefore, the probability that at least half of the 328 voters contacted in the telephone survey supported the current governor in the last election is 0.0532.
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part c question consider two groups of randomly selected peppers, where neither group has all big or all small peppers. a mean difference of zero indicates the peppers are well distributed between the two groups.a. true b. false
Answers
False. A mean difference of zero does not necessarily indicate that the peppers are well distributed between the two groups.
What is number?Number is a mathematical object used to count, measure, and label. It is one of the most fundamental concepts in mathematics and is used to describe a wide variety of physical, logical, and abstract objects. Numbers are used to represent quantities, lengths, temperatures, money, and many other measurements. They are also used to represent abstract ideas, such as the number of days in a year or the number of colors in a rainbow.
Although the mean may be equal between the two groups, the distribution of the peppers could be skewed and not evenly distributed. For example, one group could have all large peppers and the other all small peppers and the mean would be equal. This would not be considered well distributed. To ensure the peppers are evenly distributed, one should check the standard deviation or range of the data to see if the peppers are spread across both groups.
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Answer: A mean difference of zero indicates the peppers
are not well distributed between the two groups.
Why: Part B Answers
What do large differences of the means of each group indicate? Select the correct answer.
The peppers with different weights aren’t properly distributed between the two groups.
So they arent distributed well
A man sells an article at rs 600and makes a profit of 20%. Calculate his profit percentage
Answers
Answer:
120
Step-by-step explanation:
20 percent of 600 is 120 so he will get 120
At the book store, you purchased some $3 clearance mystery books and $8 regular-priced science fiction books. How many of each did you buy if you spent a total of $77?
Answers
Answer:
we bought 12 $3 clearance mystery books and 5 $8 regular-priced science fiction books.
Step-by-step explanation:
14. The perimeter of the table shown is 18 feet. Write an equation
in the form px + q = r to solve for x.
6
Answers
Answer:
its 3
Step-by-step explanation:
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Kate plans to save 5% of her income. She just earned 80.Howmuchmoneyshouldsheputintosavings?
Answers
$4
Multiply 80 by 0.05 to get the answer of $4
Answer:
4 (insert the currency needed)
Step-by-step explanation:
To find our answer we have to find 5% of Kate's wages and to do this we have to do 5 divided by 100. Then that answer is multiplied by 80!
5 ÷ 100 = 0.0580 × 0.05 = 4This means she has to put £4 into her savings!
Hope this helps, have a lovely day! :)
Use the following circle to solve for x
Answers
We know that the product of lengths of the same chord is equal to the product of the other chord intersecting it.. So;
[tex] \purple{ \mathfrak{x \times 6 = 12 \times 5}}[/tex]
[tex] \large \purple{ \mathfrak{x = \frac{12 \times 5}{6}}}[/tex]
[tex] \large \purple{ \mathfrak{x = \frac{ \cancel{12} \times 5}{ \cancel6}}}[/tex]
[tex] \large \purple{ \mathfrak{x = 2 \times 5}}[/tex]
[tex] \large \boxed{ \red{ \mathfrak{x =10}}}[/tex]
I need some help please
Answers
Given:-
[tex] \texttt{c = 1}[/tex][tex] \: [/tex]
[tex] \texttt{d = 3}[/tex][tex] \: [/tex]
Solution:-
[tex] \texttt{3(2c + d ) -4 ( c - d ) + d² }[/tex][tex] \: [/tex]
put the given values in tha equation
[tex] \texttt{= 3( 2 ( 1 ) + 3 ) -4 ( 1 - 3 ) + ( 3 )² }[/tex][tex] \: [/tex]
[tex] \texttt{= 3 ( 2 + 3 ) -4 ( -2 ) + 9}[/tex][tex] \: [/tex]
[tex] \texttt{= 3 ( 5 ) -4 ( -2 ) + 9}[/tex][tex] \: [/tex]
[tex] \texttt{= 15 + 8 + 9}[/tex][tex] \: [/tex]
[tex] \texttt{= 23 + 9}[/tex][tex] \: [/tex]
[tex] \boxed{ \texttt{ \purple{= 32}}}[/tex][tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
hope it helps ⸙
