lim x→π/6 {x^2/tanx}
Answers
The limand is continuous at x = π/6, so by direct substitution
\(\displaystyle \lim_{x\to\pi/6} \frac{x^2}{\tan(x)} = \frac{\left(\frac\pi6\right)^2}{\tan\left(\frac\pi6\right)} = \frac{\pi^2}{36\times\frac1{\sqrt3}} = \boxed{\frac{\pi^2}{12\sqrt3}}\)
Related Questions
Let u(x; y) = x2 − y2 − 3x be a real-valued function of x; y 2 R. Using the
Cauchy-Riemann equations, find another real-valued function v(x; y), such that
for z = x + iy the function f(z) = u(x; y) + iv(x; y) is analytic in C. Find an
explicit expression of f as a function of z
Answers
the expression of the function f(z) = u(x, y) + iv(x, y) in terms of z is:
f(z) = (x^2 - y^2 - 3x) + i(-2xy + c)
where c is a constant.
To find the real-valued function v(x, y) that satisfies the Cauchy-Riemann equations and makes the function f(z) = u(x, y) + iv(x, y) analytic, we can use the Cauchy-Riemann equations:
∂u/∂x = ∂v/∂y (1)
∂u/∂y = -∂v/∂x (2)
Given u(x, y) = x^2 - y^2 - 3x, we can start by finding the partial derivatives of u:
∂u/∂x = 2x - 3 (3)
∂u/∂y = -2y (4)
Now, we equate equation (1) with equation (4) to find ∂v/∂x:
∂v/∂x = -2y (5)
Similarly, we equate equation (2) with equation (3) to find ∂v/∂y:
∂v/∂y = 2x - 3 (6)
To find v(x, y), we integrate ∂v/∂x with respect to x and ∂v/∂y with respect to y:
v(x, y) = -2xy + h(y) (7)
v(x, y) = x^2 - 3y + g(x) (8)
Here, h(y) and g(x) are arbitrary functions of y and x, respectively.
To make the function f(z) = u(x, y) + iv(x, y) analytic, we need v(x, y) to satisfy the Cauchy-Riemann equations. Comparing equations (5) and (7), we get:
h'(y) = 0
This implies that h(y) is a constant, which we can denote as c.
Comparing equations (6) and (8), we get:
g'(x) = 2
Integrating g'(x) with respect to x, we get:
g(x) = 2x + k
Here, k is another constant.
Substituting these values back into equations (7) and (8), we get:
v(x, y) = -2xy + c
v(x, y) = x^2 - 3y + 2x + k
Now, we have the real-valued function v(x, y) as:
v(x, y) = -2xy + c
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1. robin works as a server in a small restaurant, where she can earn a tip (extra money) from each customer she serves. the histogram below shows the distribution of her 60 tip amounts for one day of work.
Answers
The histogram below shows the distribution of her 60 tip amounts for one day of work.
a) The tips distribution is severely skewed to the right and unimodal. There is a large spread and high variability with a range of $22.50.b) The median is the average of the 30 th and 31st values, and a change in data value from $8 to $18 will not move the middle number.How to interpret Histogram?a) The distribution of tips is skewed right, whith a gap betwen 15 to 20 and a posible out lier at or above 20. The mean will be larger than the median, and the median will be in the $2,5 to $5 bar. Most tips are $5 or less, but there is some high variability with a range of $22.50.
b) The mean would increase because $18 is farther from the mean than $8. Also, more skew is added to the grapht $18 may be an out lier. This results in a larger mean.
The median: Should not change very much. The median is the average of the 30 th and 31st values, and a change in data value from $8 to $18 will not move the middle number.
Your question is incomplete, but most probably the complete question can be seen in the attachment.
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Triangle A and Triangle B have the same base. The height of Triangle B is twice the height of Triangle A. How many times greater is the area of Triangle B?
Answers
The area of Triangle B is 2 times greater than the area of Triangle A.
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
Area of the triangle = 1/2 h*b
For Triangle A, the area is:
Area_A = 1/2 * b * h
For Triangle B, the area is:
Area_B = 1/2 * b * 2h = b * h
So, the area of Triangle B is twice the area of Triangle A.
Therefore, the area of Triangle B is 2 times greater than the area of Triangle A.
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41. Which system is represented by the graph?
(1 point)
5
58
4
4
3
2
mm -m TCOO
1
+
-5 -4 -3
-2
-1
1.
2
3
4
5
-1
Answers
Answer:
the answer is the first choice please mark me brainliest
The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 85% pure fruit juice. The company is attempting to produce a fruit drink that contains pure fruit juice. How many pints of each of the two existing types of drink must be used to make pints of a mixture that is pure fruit juice
Answers
Complete question:
The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 85% pure fruit juice. The company is attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 70% pure fruit juice?
Answer:
Juice A = 15
Juice B = 35
Step-by-step explanation:
Given the following:
Juice A:
Let juice A = a
35% pure fruit juice
Juice B:
Let juice B = b
85% pure fruit juice
We need to make 50 pints of juice from both: that is ;
a + b = 50 -------(1)
In terms of pure fruit:
a = 0.35 ; b = 0.85 ;
Our mixed fruit juice from a and b should be 70% pure fruit = 0.7
Mathematically,
0.35a + 0.85b = 50(0.7)
0.35a + 0.85b = 35 -------(2)
Multiply (2) by 100
35a + 85b = 3500 --------(3)
We can then solve the simultaneous equation:
a + b = 50 -------(1)
35a + 85b = 3500 --------(3)
Multiply (1) by 35
35a + 35b = 1750 -----(4)
35a + 85b = 3500 ---(5)
Subtract (5) from (4)
-50b = -1750
b = 35
Substitute b = 35 into (2)
0.35a + 0.85(35) = 35
0.35a + 29.75 = 35
0.35a = 35 -29.75
0.35a = 5.25
a = 5.25/0.35
a = 15
Juice A = 15
Juice B = 35
Define the arrays presented in points (a) to (c) in the comment mention the fype of the aray (eg a vectoenD matrix, a column wector, a num mattix) a) a=[12245] b) b=⎣⎡12240⎦⎤=⎣⎡111222223444555⎦⎤
Answers
The array "b" is a matrix. It is represented as multiple rows and columns of numbers.
(a) The array a=[1 2 2 4 5] can be classified as a row vector.
(b) The array b=⎣⎡12240⎦⎤=⎣⎡111 222 223 444 555⎦⎤ is a matrix.
In array b, we have 5 rows and 1 column, with each element representing a separate entry in the matrix.
Let's go through the arrays presented in points (a) to (c) and identify the type of array:
a) a=[1 2 2 4 5] The array "a" is a row vector.
It is represented as a single row of numbers.
b) b=⎣⎡12240⎦⎤=⎣⎡111222223444555⎦⎤
The array "b" is a matrix. It is represented as multiple rows and columns of numbers.
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8. Maximize p=x+2y subject to 30x+20y
0.1x+0.4y
0.2x+0.3y
x≥0,y≥0
Answers
Answer:5.97
Step-by-step explanation.
you have to look at the question.
you have to look around the question
The very last step is you have to answer it
On the Ford Aquatics swim team, 11 year olds and 12 year olds swim together. The Gold team has a 2:3 ratio of 11 year olds to 12 year olds. The Silver team has a 3:8 ratio of 11 year olds to the total swimmers. If the two teams have the same number of 11 year olds what could the size of the teams be?
Answers
Answer:
The Gold team has 8 swimmers and the silver team also has 8 swimmers.
Step-by-step explanation:
Let T be the total number of swimmers on the Gold team. Since, the Gold team has a 2:3 ratio of 11 year olds to 12 year olds, the number of 11 year old is T' = 2/(2 + 3) × T = 2T/5 and the number of 12 year olds is T" = 3/(2 + 3) × T = 3T/5.
The silver team has a 3:8 ratio of 11 year olds to the total swimmers. Let T₁ be the number of 11 year old swimmers in the silver team. So, from the ratio 3:8, the number of 11 year old swimmers in the silver team is 3 and the total number of swimmers in the silver team is 8.
Since the number of 11 year old swimmers in both teams are the same, then
2T/5 = 3
T = 3 × 5 ÷ 2
T = 15/2
T = 7.5
T≅ 8
So, the Gold team also has 8 swimmers.
So, the Gold team has 8 swimmers and the silver team also has 8 swimmers.
if the perimeter of △MNO is 72 centimeters find the measure of side MN
Answers
Answer:
The answer to your question is in the file.
f(x)= 2000 (2\(2^x\)
Answers
Required value of f(x) is \(125 \times {2}^{5 + x} \)
What is function?
In mathematics, a function is a rule or a mapping that assigns each element from a set (called the domain) to a unique element in another set (called the range). The domain and range can be any set, but they are often subsets of the real numbers.
Functions are often denoted using algebraic expressions or formulas, which describe the relationship between the input values (the domain) and the corresponding output values (the range). For example, the function f(x) = 2x + 3 maps each value of x to the value 2x + 3.
Functions are important tools in many branches of mathematics, science, engineering, and other fields. They allow us to model and analyze a wide variety of phenomena, from the behavior of physical systems to the patterns of human behavior.
Here given function,
\(f(x) = 2000 \times 2( {2})^{x} \)
We know,
\( {a}^{x} \times {a}^{y} = {a}^{x + y} \)
So,
\(fx) = 2000 \times {2}^{x + 1} \\ = 2 \times 2 \times 2 \times2 \times 125\times {2}^{x + 1} \\ = 125 \times {2}^{4} \times {2}^{x + 1} \\ = 125 \times {2}^{4 + x + 1} \\ = 125 \times {2}^{5 + x} \)
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Correct question is " Simplify
\(f(x) = 2000 \times 2( {2})^{x} \)"
If ray US is an angle bisector of ∠RUT, find m∠RUT. A. m∠RUT = 80° B. m∠RUT = 40° C. m∠RUT = 20° D. m∠RUT = 10°
Answers
Answer:
Answer: m<RUT=80
Step-by-step explanation:
took the test
If ray US is an angle bisector of ∠RUT, m∠RUT = 80°.
What is a bisector in the triangle?
The angle bisector of an angle of a triangle is a straight line that divides the angle into two congruent angles. The three angle bisectors of the angles of a triangle meet in a single point, called the incenter.
What is the angle bisector formula?According to the angle bisector theorem, PQ/PR = QS/RS or a/b = x/y. An angle bisector is a line or ray that divides an angle in a triangle into two equal measures.
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Use the graph of
f(x) = x3
to write an equation for the function represented by each graph.
Answers
Answer:
y = - x³ - 3x² - 3x - 4
Step-by-step explanation:
!!!!!!
The function represented in the graph is -
\(y\ =\ -\left(x+0.9\right)^{3}-3.3\)
What is a exponent? What is logarithmic function?In mathematics, if -
xⁿ = k
then -
[n] is called exponent
[x] is called base.
Logarithm is the inverse function to exponentiation. That means the logarithm of a number [x] to the base [b] is the exponent to which [b] must be raised, to produce [x]. We can write -
\(y = log_{e}x\)
We have the function as -
f(x) = x³
Refer to the graph of the function in the modified form. The function after being translated is same as the one given in the question. The function after translation is -
\(y\ =\ -\left(x+0.9\right)^{3}-3.3\)
Therefore, the function represented in the graph is -
\(y\ =\ -\left(x+0.9\right)^{3}-3.3\)
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Marcus is rewriting a polynomial by combining like terms. which terms does he still need to combine to finish rewriting the polynomial?
Answers
Marcus needs to combine the like terms that have the same variable and exponent in order to finish rewriting the polynomial.
When rewriting a polynomial by combining like terms, Marcus needs to look for terms that have the same variable and exponent. Like terms are terms that can be added or subtracted because they share these common characteristics. For example, in the polynomial\(3x^2\)- 4x - 7, Marcus would need to combine the terms \(3x^2\) and \(5x^2\) since they have the same variable (x) and exponent (2). After combining these terms, the polynomial can be rewritten as (\(3x^2+5x^2\) + (2x - 4x) - 7.
Marcus would still need to combine the terms \(3x^2\\\)and \(5x^2\), as well as the terms 2x and -4x. By adding or subtracting these like terms, Marcus will be able to simplify the polynomial further. Once all the like terms are combined, the polynomial will be fully rewritten in a simplified form, with no more terms that can be combined.
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I need help with surface area
Answers
Answer:
Surface Area varies by object/shape.
Ask your teacher/learning helper for those formulas of surface area
Step-by-step explanation:
Surface area is the sum of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.
Could someone please solve this and explain their answer? 2x+39<9
Answers
Step-by-step explanation:
i hope you understood....
Pls help, Which shows how to solve the equation Three-fourths x = negative 6 for x in one step?
A.Three-fourths (four-thirds) x = negative 6 (four-thirds)
B.Three-fourths (4) x = negative 6 (4)
C.Three-fourths (4) x = negative 6 (3)
D.Three-fourths (four-thirds) x = negative 6 (three-fourths)
Answers
Answer:
answer A is correct
Step-by-step explanation:
3/4 * x = - 6
4/3 * 3/4 * x = 4/3 * - 6. This is answer A
12/12 * x = -24/3
1 * x = - 8
x = - 8
So you see answer A is correct.
Answer:
The correct answer is A
Which set of numbers has 21 as a common factor?
A. {126, 168, 189}
B. {84, 105, 132}
C. {40, 63, 210}
D. {42, 88, 126}
Answers
Answer:
the answer is A {126,168,189}
help me g............
Answers
Answer:
Equation: 0.165 x = 69.3
x = 420 gallons
Explanation:
Let us call x the total number of gallons the family uses. then we know that 16.5 % (WHICH WE ARE TOLD IS 69. 3 GALLONS ) of it used for cooking, meaning
\(\frac{16.5}{100}x=69.3\)\(0.165x=69.3\)Dividing both sides by 0.165 gives
\(x=\frac{69.3}{0.165}\)\(x=420.\)Hence, 420 gallons of water are used each day by a family.
A developer wants to subdivide a rectangular lot into square pieces. The lot is 600m by 2400m. What is the largest possible square? need answer asap
Answers
The largest possible square is of side 600m.
Given, a developer wants to subdivide a rectangular lot into square pieces. The lot is 600m by 2400m.
We have to find the largest possible square.
Now, to find the largest possible square we have to find the HCF of 600 and 2400.
As, the HCF of 600 and 2400 is
HCF(600 , 2400) = 600
So, the largest possible square can be of the side 600m
Hence, The largest possible square is of side 600m
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Bars of soap come in packages of 2 and packages of 8. The 2-bar pack costs $1.98, and the 8-bar pack costs $8.88. Which is the better deal? What is the price per bar of the better deal?
Answers
8.88 divided by 8= 1.11 dollars per back in the 8 pack
the better deal is the two pack
helppppppppppppppppppppppppp
Answers
Answer:
reason 1.) This is the original expression
reason 2.) you subtract 4 from both sides
reason 3.) you divide both sides by 2 to get x=5
pls hurry. 10. Select all numbers that represent a solution of the equation below.
Answers
\(x^2=196\\x=-\sqrt{196} \vee x=\sqrt{196}\\x=-14 \vee x=14\)
Therefore, it's A and D.
Please help with my work!
Answers
Answer:
x,y =3,-4
Step-by-step explanation:
// Solve equation [1] for the variable y
[1] y = 2x - 10
// Plug this in for variable y in equation [2]
[2] 3x - 2•(2x-10) = 17
[2] -x = -3
// Solve equation [2] for the variable x
[2] x = 3
// By now we know this much :
x = 3
y = 2x-10
// Use the x value to solve for y
y = 2(3)-10 = -4
Please HELP!!!! Asappppp thank you!!!!
Answers
Answer:
Step-by-step explanation:
The answer is C
If ABCD ~ EFGH, are all corresponding parts
congruent? Explain. (please answer asap!) ty!
Answers
Yes, If ABCD ≅ EFGH, are all corresponding parts congruent or same.
Congruent figures are identical in terms of both size and shape. Congruent figures have equal comparable sides and angles.
Congruent figures are identical copies of one another.
In other words, two figures are congruent if they can be converted into one another through a series of translations, rotations, and/or reflections.
Hence, Yes, If ABCD ≅ EFGH, are all corresponding parts congruent or same.
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If the _ of a parallelogram are perpendicular and a diagonal _opposite angles then the parallelogram is a _.
Answers
Given the functions below, calculate the multiplier. For ease of calculation, please round off functions to the nearest whole number. Only round off the multiplier to two decimal places.
Consumption function: C = 200 + 0.5Y
Net Exports function: NX = 150 – (25 + 0.04Y)
Government expenditure function: 0.5G = 75 – 0.2Y
Answers
The multiplier can be calculated by determining the marginal propensity to consume (MPC) and using the formula: multiplier = 1 / (1 - MPC).
What are the marginal propensities to consume (MPC) in the given functions?To calculate the multiplier, we need to find the marginal propensity to consume (MPC) from the consumption function. In this case, the MPC is the coefficient of income (Y) in the consumption function, which is 0.5.
Using the formula: multiplier = 1 / (1 - MPC), we can substitute the value of MPC into the equation:
multiplier = 1 / (1 - 0.5) = 1 / 0.5 = 2.
Therefore, the multiplier is 2.
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Determinar la pendiente, la ordenada en el origen de la siguiente ecuacion
8\3x + 1\4y = 4
Answers
The slope of the equation 8/3x + 1/4y = 4 is -32/3 and the y-intercept is 16.
To determine the slope and y-intercept of the equation 8/3x + 1/4y = 4, we need to convert it into slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. To do this, we'll isolate y on one side of the equation by subtracting 8/3x from both sides:
8/3x + 1/4y = 4
1/4y = -8/3x + 4
y = -32/3x + 16
Now we have the equation in slope-intercept form y = mx + b, where m = -32/3 and b = 16. Therefore, the slope of the equation is -32/3 and the y-intercept is 16.
The slope of a line is the ratio of the change in the vertical coordinate (rise) to the change in the horizontal coordinate (run) between any two points on the line. It tells us how steep the line is. A negative slope means that the line is decreasing from left to right, while a positive slope means that the line is increasing from left to right.
The y-intercept is the point where the line crosses the y-axis. It tells us the value of y when x is equal to zero. If the y-intercept is positive, the line intersects the y-axis above the origin, while if the y-intercept is negative, the line intersects the y-axis below the origin.
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What is the probability of picking a blue marble and rolling an odd number?
Answers
Answer:
3/6 chance.
Step-by-step explanation:
To roll an odd number on a six sided dice (Guessing it's six sided) you would have to roll either a 1, 3, or 5. That would it 3 choices. You get the six by taking the amount (like the amount of sides on the dice). You would then have a 3/6 chance of rolling an odd number.
use cylindrical coordinates. evaluate x2 dv, e where e is the solid that lies within the cylinder x2 y2 = 4, above the plane z = 0, and below the cone z2 = 36x2 36y2.
Answers
Using cylindrical coordinates ∫∫∫ (r^3cos^2θ) dz dr dθ, where r ranges from 0 to 2, θ ranges from 0 to 2π, and z ranges from 0 to √(36r^2).
To evaluate the integral ∫∫∫ x^2 dV over the solid e, using cylindrical coordinates, we need to express the integral in terms of cylindrical coordinates and determine the appropriate bounds for the variables.
In cylindrical coordinates, the solid e can be defined as follows:
Radius: r ranges from 0 to 2 (from x^2 + y^2 = 4, taking the square root).
Angle: θ ranges from 0 to 2π (full revolution around the z-axis).
Height: z ranges from 0 to the height of the cone, which is determined by z^2 = 36x^2 + 36y^2.
To convert the integral, we need to express x^2 in terms of cylindrical coordinates:
x^2 = (rcosθ)^2 = r^2cos^2θ
The integral in cylindrical coordinates becomes:
∫∫∫ (r^2cos^2θ) r dz dr dθ
Now we can determine the bounds for the variables:
r ranges from 0 to 2.
θ ranges from 0 to 2π.
z ranges from 0 to the height of the cone, which can be determined by setting z^2 = 36r^2.
Substituting the bounds and integrating, we can evaluate the integral to find the desired result.
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