Find an exact value. sin(17pi/12)
a. √6 - √2 / 4
b. -√6 - √2 / 4
c. √6 + √2 / 4
d. √2 - √6 / 4
Answers
feel free to ask if you have any doubts.
The required exact value of the given trigonometric function is sin(17π/12) = (√6 + √2)/4
What are Trigonometric functions?Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.
The trigonometric function is given in the question, as follows:
sin(17π/12)
To find the value of sin(17π/12), we can use the following trigonometric identity:
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
In this case, we can write:
sin(17π/12) = sin(π/3 + π/4)
We know that sin(π/3) = √3/2 and cos(π/3) = 1/2, and sin(π/4) = cos(π/4) = √2/2.
Therefore, we can use the above identity to get:
sin(17π/12) = sin(π/3)cos(π/4) + cos(π/3)sin(π/4)
= (√3/2)(√2/2) + (1/2)(√2/2)
= (√6/4) + (√2/4)
= (√6 + √2)/4
So the answer is option (c): √6 + √2 / 4.
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Related Questions
Kite PQRS is dilated to form LMNO. what corresponding angle is congruent to angle QRS? type the essay in the box below
Answers
By selling a stool for rupees 67.50,a carpenter loses 10%.how much percent would he gain or lose by selling it for rupees 82.50.?
Answers
So if the carpenter sells the stool x rupees he neither loses, now wins anything.
67.50 is the value x - 10% of x, that is:
67.50=x-0.1x
67.50=0.9x
x=67.50/0.9=75 (rupees) is the actual value of the stool.
Selling the stool for 82.50 rupees, the carpenter clearly would make a profit, say of y% of that actual value, that is y%*75.
So using the same method:
82.50=75+y%*75
y%*75=82.50-75=7.5
we can make the calculations, but clearly 7.5 is 10% of 75
Answer: 10% gain.
If y=12+ 3.5x ,what is the value of the y when x=10
Answers
3.5 x 10 = 35
35 + 12 = 47
Y = 47
Consider the quadratic function f(x) = 2x2 – 8x – 10. The x-component of the vertex is . The y-component of the vertex is . The discriminant is b2 – 4ac = (–8)2 – (4)(2)(–10) =
Answers
This is a parabola open upward (since a>0) with an axis of symmetry = -b/2a:
a) axis of symmetry: x = -(-8)/(2*2) = 8/4 = 2. Then x = 2, which is the x component of the vertex
b) for x = 2, f(x) = f(2) = - 18 (component of y of the vertex)
c) VERTEX(2, - 18)
d) DISCRIMINENT: b² - 4.a.c = 64 - 4*2*(-10) = 144
The x-coordinate of the vertex is 2 and the y-coordinate is -10. The discriminant is 144.
Explanation:The quadratic function can be rearranged into the form ax² + bx + c = 0, where a = 2, b = -8, and c = -10. To find the x-coordinate of the vertex, we use the formula x = -b / (2a). Plugging in the values, we get x = -(-8) / (2*2) = 2. The y-coordinate of the vertex can be found by substituting the x-coordinate into the original function. Plugging in x = 2, we get f(2) = 2(2)² - 8(2) - 10 = -10.
The discriminant is calculated as b² - 4ac. Plugging in the values, we get (-8)² - 4(2)(-10) = 64 + 80 = 144.
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Which transformations can be used to map a triangle with vertices A(2, 2), B(4, 1), C(4, 5) to A’(–2, –2), B’(–1, –4), C’(–5, –4)? a 180 (dagree) rotation about the origin a 90 (dagree) counterclockwise rotation about the origin and a translation down 4 units a 90 (dagree) clockwise rotation about the origin and a reflection over the y-axis a reflection over the y-axis and then a 90(dagree) clockwise rotation about the origin
Answers
The triangle ABC is mapped to A'B'C' through a 180-degree rotation about the origin, as all the points' x and y coordinates have changed signs, consistent with this transformation.
To determine which transformations can map the original triangle ABC to the new triangle A'B'C', we must closely examine the coordinates given and analyze the possible transformations.
Looking at the coordinates:
A(2, 2) to A'(-2, -2) suggests a reflection over the origin, which can be considered as a 180-degree rotation around the origin.
B(4, 1) to B'(-1, -4) also suggests a similar transformation, as the x and y values are negated and swapped in position.
C(4, 5) to C'(-5, -4) follows the same pattern.
All these transformations indicate that the original triangle has been rotated 180 degrees about the origin. This can also be observed by noting that the x and y coordinates have simply changed their signs, an effect of 180-degree rotation about the origin. This satisfies the claim of the classical geometry theorem which states that such transformations can be expressed as either a translation or a rotation. In this case, it's purely a rotation as there's no translation component.
Find the circumference and area of a circle with a diameter of 10 inches. Leave your answers in terms of pi.
C = 5π; A = 20π
C = 10π; A = 20π
C = 10π; A = 25π
C = 5π; A = 25π
Answers
First, let's take a look at what the formula for the circumference and area of a circle is.
The circumference is "2[tex] \pi [/tex]r", or "2 * 3.14 * r".
The area is "[tex] \pi [/tex]r^2", or "3.14 * r * r".
Let's establish what the radius is, as [tex] \pi [/tex] is equivalent to 3.14.
The radius is half of the diameter, and our diameter is 10.
Divide 10 by 2 to find our radius.
10 / 2 = 5
The radius is 5.
Now, let's plug in 5 for the radius for both formulas.
C = 2 * 3.14 * 5
10 * 3.14
31.4 is our Circumference.
Now, onto the area.
A = r * r * 3.14
5 * 5 * 3.14
25 * 3.14
78.5 is our Area.
I hope this helps!
Answer:
The answer by Equinimity is incorrect. On my test, those weren't even options. The answer is:
C = 10n; A = 25n
(the symbol that looks like 'n' anyway)
1. It's what the answer is on pretty much every other version of this question on brainly.
2. I did the math.
wahts the quotient of 92 and 5
Answers
92/5 is 18.4
_18.4___
5) 92
-5
4 2
-40
20
Final answer: 18.4
(HELP ME PLEASE) In the drawing, g > h. Which statement about the volumes of the two cylinders is true?
Answers
Answer:
The answer on Imagine Math is...
-The volume of the left-hand cylinder is less than the volume of the right-hand cylinder.
Step-by-step explanation:
I got the answer correct on Imagine Math. Hope my answer helps those who need it :)
God bless you all day every day!
The solution is, The ratio of the volumes is the cube of this: 27 : 1.
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
here, we have,
given that,
The ratio of the lengths is 75 : 25 or 3 : 1
The ratio of and area is the square of this: ie 9 : 1 or 75^2 : 25^2
(In working out the area the radius is squared)
and, we have,
The ratio of the volumes is the cube of this: ie 27 : 1 or 75^3 : 25^3
(In working out the volume the radius is cubed)
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A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle. What is the maximum area that the farmer can enclose with 2020 ft of fence? What should the dimensions of the garden be to give this area?
Answers
a and b,
such that 2a+2b=2020, (the perimeter is 2 width+2 length)
dividing by 2, we have a+b=1010
writing b in terms of a, we have b=1010-a
so f(a)=a(1010-a) is the function which calculates the area depending on a.
for example the area enclosed is the dimensions are a= 10, b=1000
is f(10)=10*(1010-10)=10*1000=10,000 square feet.
f(a) is a polynomial function of degree 2, that is a quadratic.
The graph of a quadratic polynomial is a parabola, in our case, a parabola which opens downward since the sign of the coefficient of the largest term of the quadratic, is negative.
since the quadratic is given in factorized form, we easily find that the roots are a=0 and a=1010
since f(0)=0 and f(1010)=0.
in the middle of these points, we have 1010/2=505, which is the x-coordinate of the vertex.
f(505) gives us the highest point, which is f(505)=505(1010-505)=[tex] 505^{2} [/tex]=255,025 ft squared.
the highest point of the parabola, represents the largest value of f so the largest possible area.
Answer: 255,025 ft squared.
Differences between 9/11 and pearl harbor
Answers
What is the y intercept of y=7?
A.(0,7)
B.(7,0)
C.(7,7)
D.(-7,7)
Answers
the least common multiple of 2/3 5/6 and 9/4
Answers
2/5 times 5/6 times 9/4=90/120=9/12=3/4
lcm is 3/4 then
The least common multiple of 2/3 5/6 and 9/4 is 12.
What is a fraction?A fraction represents a part of a number or any number of equal parts.
A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.
We are given that;
The numbers 2/3 5/6 and 9/4
Now,
To find the least common multiple of fractions, we need to find the least common multiple of their denominators and divide it by the greatest common factor of their numerators. The steps are:
Multiples of 3: 3, 6, 9, 12, 15, 18,
Multiples of 6: 6, 12, 18,
Multiples of 4: 4, 8, 12,
Find the greatest common factor of 2, 5 and 9. This is the largest number that can divide all three numbers without leaving a remainder. One way to do this is to list the factors of each number and find the largest one that they have in common. For example:
Factors of 2: 1 and 2
Factors of 5: 1 and 5
Factors of 9: 1,3 and9
The only common factor is 1, so this is the greatest common factor of the numerators.
Divide the least common multiple of the denominators by the greatest common factor of the numerators. This gives us:
12 /1 =12
Therefore, the LCM of given fraction will be 12.
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Describe the graph of y > mx, where m > 0.
Answers
The boundary line is dashed, and everything above it is shaded.
Answer:
The graph of y > mx, where m > 0, consists of a dashed line and a shaded half plane. The line has a positive slope and passes through the origin. The shaded half plane is above the line.
Sample ResponseStep-by-step explanation:
Hope this helps any of you! :)
Which system of equations can be graphed to find the solution(s) to x^2 = 2x + 3?
Answers
The solutions will be the points of intersection of the 2 graphs.
Karen runs 6 miles in 50 minutes. at the same rate, how many miles would she run in 35 minutes?
Answers
(5ab+2a-2)-(ab-3) find the difference.
Answers
(5ab + 2a - 2) - (ab - 3)
(5ab + 2a - 2) - ab + 3
4ab + 2a +1 <------------- That's your answer!
Vote for me as Brainliest if there is a second answer, PLEASE!!!
find the exact value of tan75
This is a question from sum and differences of trigs so it must include that. I've tried multiple things and nothing has given me one of the options for answers.
Answers
[tex]\bf tan(45^o+30^o)=\cfrac{\frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}+\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}}{1-\frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}\cdot \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}} \implies tan(45^o+30^o)=\cfrac{1+\frac{1}{\sqrt{3}}}{1-1\cdot \frac{1}{\sqrt{3}}}[/tex]
[tex]\bf tan(45^o+30^o)=\cfrac{\frac{\sqrt{3}+1}{\sqrt{3}}}{1-\frac{1}{\sqrt{3}}}\implies tan(45^o+30^o)=\cfrac{\frac{\sqrt{3}+1}{\sqrt{3}}}{\frac{\sqrt{3}-1}{\sqrt{3}}} \\\\\\ tan(45^o+30^o)=\cfrac{\sqrt{3}+1}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}-1}\implies tan(45^o+30^o)=\cfrac{\sqrt{3}+1}{\sqrt{3}-1}[/tex]
so... let's rationalize the denominator.. now, the denominator is √(3) - 1, so, we'll use her conjugate, √(3) + 1, and multiply top and bottom by it, so we end up with a "difference of squares" at the bottom, so, let's do so.
[tex]\bf \textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\\\\ -------------------------------\\\\[/tex]
[tex]\bf \cfrac{\sqrt{3}+1}{\sqrt{3}-1}\cdot \cfrac{\sqrt{3}+1}{\sqrt{3}+1}\implies \cfrac{(\sqrt{3}+1)(\sqrt{3}+1)}{(\sqrt{3}-1)(\sqrt{3}+1)}\implies \cfrac{(\sqrt{3}+1)^2}{(\sqrt{3})^2-(1)^2} \\\\\\ \cfrac{(\sqrt{3}+1)^2}{3-1}\implies \cfrac{(\sqrt{3})^2+2\sqrt{3}+1^2}{2}\implies \cfrac{3+2\sqrt{3}+1}{2} \\\\\\ \cfrac{4+2\sqrt{3}}{2}\implies \cfrac{\underline{2}(2+\sqrt{3})}{\underline{2}}\implies 2+\sqrt{3}[/tex]
On a final exam, each multiple-choice question is worth 4 points and each word problem is worth 8 points. Lorenzo needs at least 50 points on the final to earn a "B" in the class. Which inequality represents x, the number of correct multiple-choice questions, and y, the number of correct word problems, he needs to earn a "B"? 4x + 8y < 50 4x + 8y ≤ 50 4x + 8y > 50 4x + 8y ≥ 50
Answers
Hence, the inequality that will represent the marks he needs is:
4x+8y≥50
Step-by-step explanation:On a final exam, each multiple-choice question is worth 4 points and each word problem is worth 8 points.
Lorenzo needs at least 50 points on the final to earn a "B" in the class.
Let x be the number of correct multiple-choice questions, and y, the number of correct word problems.
Hence, the inequality that will represent the marks he needs is:
4x+8y≥50
A rectangular box has dimensions of length = 6, width = 4, and height = 5. the measure of the angle formed by a diagonal of the box with the base of the box is
Answers
To find the angle formed by a diagonal of a rectangular box with its base, calculate the base diagonal using the Pythagorean Theorem and then use the inverse tangent function with the height and base diagonal as arguments.
Explanation:The angle formed by a diagonal of the rectangular box with the base of the box can be found using the Pythagorean Theorem. In this case, the box has a length of 6, a width of 4, and a height of 5. The diagonal of the base can be calculated as the hypotenuse of a right triangle formed by the length and the width. According to the Pythagorean theorem, this diagonal (D) is √(6² + 4²) which is √(36 + 16) or √52. To find the angle between the box's base diagonal and the body diagonal (which includes the height), we need to use trigonometry, specifically the inverse tangent function (tan-1). So we have the length of the box's base diagonal (D) and the height (H), forming a right triangle with the body diagonal as the hypotenuse. The angle θ can be calculated using tan-1(H/D), where H is the height of the box and D is the length of the diagonal on the base. This equates to tan-1(5/√52). Evaluating this expression with a calculator gives us the angle θ formed by the body diagonal with the base of the box.
How to write 310, 763, 136 in expandes forma
Answers
Three hundred and ten
763:
Seven hundred and sixty three
136:
One hundred and thirty six
The expanded form of 310, 763, 136 is:
300,000,000 + 10,000,000 + 700,000 + 60,000 + 3,000 + 100 + 30 + 6
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
310, 763, 136
This can be written in expanded form as,
300,000,000 + 10,000,000 + 700,000 + 60,000 + 3,000 + 100 + 30 + 6
Thus,
The expanded form is:
300,000,000 + 10,000,000 + 700,000 + 60,000 + 3,000 + 100 + 30 + 6
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What is the last thing you do as a check inside the car?
Answers
I'm lost can you please tell me how to do this step by step
Answers
What is the value of y so that the line segment with endpoints A(−3, y) and B(6, −4) is parallel to the line segment with endpoints C(7, 6) and D(−2, 8)?
y = −7
y = 1
y=1/2
y = −2
Answers
To make line segment AB parallel to line segment CD, we calculate the slope of CD and ensure AB has the same slope. The slope of CD is −1/4.5, and setting the slope of AB equal to this value leads to the conclusion that y = −2 for point A.
Explanation:To determine the value of y such that the line segment with endpoints A(−3, y) and B(6, −4) is parallel to the line segment with endpoints C(7, 6) and D(−2, 8), we need to ensure that the slope of line AB is equal to the slope of line CD. The slope m of a line passing through two points (x1, y1) and (x2, y2) is given by m = (y2 − y1) / (x2 − x1).
For line CD, the slope is (8 − 6) / (−2 − 7) = 2 / (−9) = −1/4.5. To find the value of y for point A so that line AB is parallel to CD, we need to set the slope of AB equal to −1/4.5:
(−4 − y) / (6 − (−3)) = −1/4.5
(−4 − y) / 9 = −1/4.5
−4 − y = −9 / 4.5
y = −4 + 2 = −2
Therefore, the correct value of y that makes line AB parallel to line CD is −2.
In kahneman and tversky's prospect theory, they hypothesized that people tend to _____ low-probability outcomes and _____ high-probability outcomes.
Answers
Answer:
Overweight low probability outcomes
UNderweight High probability outcomes.
Step-by-step explanation:
Amos Tversky and Daniel Kahneman proposed the prospect theory that aimed to explain and understand the behavior of individuals, giving them a sample of choices to take, when put in front to the different decisions that had to be made, people often valued chances that were 99% probable to happen with a 95 to 85% chance, meaning that the didn´t give enough credit to the number and probabilities, and when facing risks of 1% probability of happening, they outweigh them with a 5 to 15 %.
Describe how the graph of y=|x| – 4 is like the graph of y= |x| – 4 and how it is different.
Answers
The graphs of y = |x| and y = |x| - 4 are similar in their overall V-shape and slope behavior, but differ in their vertical position due to the constant term difference in the equations. The second graph is essentially a downward translation of the first by 4 units.
Similarities:
Both represent absolute value functions.
Both graphs pass through the origin (0, 0)
Both graphs have a slope of 1 for positive values of x and a slope of -1 for negative values of x.
Differences:
The graph of y = |x| - 4 is shifted downwards by 4 units
The y-intercept is different for both graphs.
what is the equation of a line perpendicular to y=1/2x-1 through (0,6)
Answers
[tex]\bf \begin{array}{llll} y=&\frac{1}{2}x&-1\\ &\uparrow &~\uparrow \\ &slope&y-intercept \end{array}[/tex] so, is 1/2 ok....
now, a line that is perpendicular to that equation, will have a slope that is negative reciprocal of that.
[tex]\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{a}{b}\\\\ slope=\cfrac{a}{{{ b}}}\qquad negative\implies -\cfrac{a}{{{ b}}}\qquad reciprocal\implies - \cfrac{{{ b}}}{a}\\\\ -------------------------------\\\\ slope=\cfrac{1}{2}\qquad negative\implies -\cfrac{1}{{{ 2}}}\qquad reciprocal\implies - \cfrac{{{ 2}}}{1}\implies -2[/tex]
so, what is the equation of a line whose slope is -2 and passes through (0,6)?
[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 0}}\quad ,&{{ 6}})\quad \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies -2 \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-6=-2(x-0)\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y-6=-2x\implies y=-2x+6[/tex]
Find the surface area of a pyramid with a square base with dimensions 100 mm by 100 mm and height of 75 mm.
Answers
To solve for the surface area of the pyramid, we make use of the formula:
A= l w + l [sqrt ((w / 2)^2 + h^2)] + w [sqrt ((l / 2)^2 + h^2))
where,
l and w are the base of the pyramid = 100 mm
h is the height of the pyramid = 75 mm
Substituting the given values into the equation:
A= 100 * 100 + 100 [sqrt ((100 / 2)^2 + 75^2)] + 100 [sqrt ((100 / 2)^2 + 75^2))
A = 10,000 + 100 (sqrt 2575) + 100 (sqrt 2575)
A = 20,148.90 mm^2
Therefore the surface area of the pyramid is about 20,149 mm^2.
How many arrangements of the letters in the word o l i v e can you make if each arrangement must use three letters?
A. 60
B. 5 · 4 · 3 · 2 · 1
C. 20
D. 8 · 7 · 6 · 5 · 4 · 3 · 2 · 1
Answers
Now, we want arrangements, so the order does matter. The arrangement: OLI is not the same as ILO, since they are counted as different words.
Thus, using the permutation formula, we get:
[tex]^{5}P_3 = \frac{5!}{(5 - 3)!} = \frac{5!}{2!} = 5 \cdot 4 \cdot 3 = 60[/tex]
So, the answer is (A) 60
What's the difference between 1261⁄4 and 78 2⁄3?
A. 48 1⁄3 B. 47 7⁄12 C. 58 5⁄12 D. 57 7⁄12
Answers
505/4 - 236/3 =
1515/12 - 944/12 =
571/12 =
47 7/12 <==
Answer: The answer is (B) [tex]47\dfrac{7}{12}[/tex].
Step-by-step explanation: We are given to find the difference between the following two numbers:
[tex]n_1=126\dfrac{1}{4},~~~n_2=78\dfrac{2}{3}.[/tex]
To find the difference, we need to subtract the smaller number from the larger one.
Since, [tex]n_1>n_2[/tex], so the difference is given by
[tex]d\\\\=n_1-n_2\\\\=126\dfrac{1}{4}-78\dfrac{2}{3}\\\\=\dfrac{505}{4}-\dfrac{236}{3}\\\\=\dfrac{505\times3-236\times4}{12}\\\\=\dfrac{1515-944}{12}\\\\=\dfrac{571}{12}\\\\=47\dfrac{7}{12}.[/tex]
Thus, (B) [tex]47\dfrac{7}{12}[/tex] is the correct option.
The radii of earth and Pluto are 6,371 kilometers and 1,161 kilometers, respectively. Approximately how many spheres the size of Pluto does it take to have the same volume as earth?
Answers
Pluto volume: (3/4).π.(1171)³ = 6,555,189,765 km³
How many spheres the size of Pluto does it take to have the same volume as earth?
volume Earth/ volume Pluto = 1,0832x10¹² / 6,555,189,765 = 165.25
Answer: the answer will be 165.2
Step-by-step explanation: