Rationalise the denominator of 5/√(3-√5)
Pls send the answer by today
Answers
Answer:
\(\dfrac{5(3+\sqrt{5})\sqrt{3-\sqrt{5}}}{4}\)
\(\textsf{or}\quad \dfrac{5\sqrt{3+\sqrt{5}}}{2}\)
Step-by-step explanation:
\(\textsf{Given expression}:\dfrac{5}{\sqrt{3-\sqrt{5}}}\)
Method 1
\(\textsf{Multiply by the conjugate}\quad \dfrac{\sqrt{3-\sqrt{5}}}{\sqrt{3-\sqrt{5}}}:\)
\(\implies \dfrac{5}{\sqrt{3-\sqrt{5}}} \times \dfrac{\sqrt{3-\sqrt{5}}}{\sqrt{3-\sqrt{5}}}=\dfrac{5\sqrt{3-\sqrt{5}}}{(\sqrt{3-\sqrt{5}})(\sqrt{3-\sqrt{5}})}\)
Simplify the denominator using the radical rule \(\sqrt{a} \sqrt{a} =a\):
\(\implies (\sqrt{3-\sqrt{5}})(\sqrt{3-\sqrt{5}})=3-\sqrt{5}\)
Therefore:
\(\implies \dfrac{5\sqrt{3-\sqrt{5}}}{(\sqrt{3-\sqrt{5}})(\sqrt{3-\sqrt{5}})}= \dfrac{5\sqrt{3-\sqrt{5}}}{3-\sqrt{5}}\)
\(\textsf{Multiply by the conjugate}\quad \dfrac{3+\sqrt{5}}{3+\sqrt{5}}:\)
\(\implies \dfrac{5\sqrt{3-\sqrt{5}}}{3-\sqrt{5}} \times \dfrac{3+\sqrt{5}}{3+\sqrt{5}}=\dfrac{5\sqrt{3-\sqrt{5}}(3+\sqrt{5})}{(3-\sqrt{5})(3+\sqrt{5})}\)
Simplify the denominator:
\(\implies (3-\sqrt{5})(3+\sqrt{5})=9+3\sqrt{5}-3\sqrt{5}-5=4\)
Therefore:
\(\implies \dfrac{5(3+\sqrt{5})\sqrt{3-\sqrt{5}}}{4}\)
Method 2
\(\textsf{Multiply by the conjugate}\quad \dfrac{\sqrt{3+\sqrt{5}}}{\sqrt{3+\sqrt{5}}}:\)
\(\implies \dfrac{5}{\sqrt{3-\sqrt{5}}} \times \dfrac{\sqrt{3+\sqrt{5}}}{\sqrt{3+\sqrt{5}}}=\dfrac{5\sqrt{3+\sqrt{5}}}{(\sqrt{3-\sqrt{5}})(\sqrt{3+\sqrt{5}})}\)
Simplify the denominator using the radical rule \(\sqrt{a} \sqrt{b} =\sqrt{ab}\):
\(\implies (\sqrt{3-\sqrt{5}})(\sqrt{3+\sqrt{5}})=\sqrt{(3-\sqrt{5})(3+\sqrt{5})\)
\(\implies\sqrt{(3-\sqrt{5})(3+\sqrt{5})}=\sqrt{9-5}=\sqrt{4}=2\)
Therefore:
\(\implies \dfrac{5\sqrt{3+\sqrt{5}}}{2}\)
\(\huge\color{pink}\boxed{\colorbox{Black}{♔︎Answer♔︎}}\)
To rationalise:-
\( \frac{5}{ \sqrt{3 - \sqrt{5} } } \)
There is a formula in math if there is root in denominator
for example
\( \frac{1}{ \sqrt{a - b} } \)
we can say rationalize by multiplying √(a-b) in numerator and denominator both
\( \frac{1}{ \sqrt{a - b} } \times \frac{ \sqrt{a - b} }{ \sqrt{a - b} } \\ \frac{ \sqrt{a - b} }{a - b} \)
In here
\( \frac{5}{ \sqrt{3 - \sqrt{5} } } \times \frac{ \sqrt{3 - \sqrt{5} } }{ \sqrt{3 - { \sqrt{5} } } } \\ \frac{5( \sqrt{3 - \sqrt{5} }) }{3 - \sqrt{5} } \)
but still here is root to remove this we have to multiply
3 + √5 in numerator and denominator.
\( \frac{5( \sqrt{3 - \sqrt{5} }) }{3 - \sqrt{5} } \times \frac{3 + \sqrt{5} }{3 + \sqrt{5} } \\ \frac{5( \sqrt{3 - \sqrt{5} })(3 + \sqrt{5} ) }{ {3}^{2} - { (\sqrt{5} )}^{2} } \\ \frac{5( \sqrt{3 - \sqrt{5} })(3 + \sqrt{5}) }{9 - 5} \\ \frac{5( \sqrt{3 - \sqrt{5} } )(3 + \sqrt{5}) }{4} \)
Related Questions
Please help me with this homework
Answers
Answer:
I believe it's false
Step-by-step explanation:
In a function, the x's can not be the same
PLS HELP : A school chess club needs to raise at least $750 to attend a state competition. The club has already raised $400 and there are 4 months remaining until the competition. Which inequality and statement can be used to determine the dollar amount the club will need to raise during the remaining months?
Answers
Answer:
400+4n ≥ 750; The club will need to raise an average of $87.50 or more per month.
What do I do here please help me thank you just tell me the answer thx
Answers
Answer:
3
Step-by-step explanation:
The ratio of x to y is constant
And as you can see
X×6 = y
6×6= 36
8×6=48
10×6= 60
Therefore
X×6 =18
18÷6= 3
X=3
If "a", "b" and "c" vectors are in cyclic order then:
Answers
If a, b and c vectors are in cyclic order , the scalar product is equals to zero which makes Option C to be correct.
What are scaler and vector quantities?A vector can be regarded as quantities that posses both magnitude and a direction this is the opposite to scalar quantity which posses just the magnitude without any direction.
Geometrically, the vector can be described as the line segment, having its length as the magnitude with the arrow over it showing direction.
The scalar product can be gotten with the multiplication of the magnitudes of vectors .
Hence, If a, b and c vectors are in cyclic order , the scalar product is equals to zero .
Learn more about vectors at:
https://brainly.com/question/15519257
#SPJ1
CHECK THE COMPLETE QUESTION IN THE ATTACHMENT
if a distribution of scores is shown in a bar graph, you know that the scores were measured on a(n) _________ scale of measurement.
Answers
If a distribution of scores is shown in a bar graph, it suggests that the scores were measured on an ordinal scale of measurement.
An ordinal scale is a type of measurement scale that categorizes and orders variables or data points based on their relative ranking or position. In this case, the bar graph represents the frequencies or counts of different categories or ranges of scores, indicating an ordered arrangement of the data. However, the bar graph alone does not provide information about the exact numerical differences between the scores or their precise magnitudes.
To know more about graph visit:
brainly.com/question/17267403
#SPJ11
PLS PLS i need step by step please and undefined numbers to be shown please THANK YOU!
Answers
1)The expression 4x^2-16x+12/x^2-9 is undefined when the denominator, x^2-9, equals zero because division by zero is undefined.
x^2-9 equals zero when x equals 3 or x equals -3. Therefore, the expression is undefined at x = 3 and x = -3. In all other cases, the expression is defined.
2) The given expression is:
(5-2x)/(x+2) + x^2/(x^2-4) - 5
To simplify this expression, we need to first find the LCD (least common denominator) of the two fractions. The denominator of the first fraction is x+2, and the denominator of the second fraction is x^2-4, which can be factored as (x+2)(x-2). So the LCD is (x+2)(x-2). Now we can rewrite the expression with this common denominator:
[(5-2x)(x-2) + x^2(x+2) - 5(x+2)(x-2)] / [(x+2)(x-2)]
Expanding the brackets and simplifying, we get:
(-x^3 - 3x^2 - 3x + 5) / [(x+2)(x-2)]
This expression is undefined when the denominator, (x+2)(x-2), equals zero because division by zero is undefined.
(x+2)(x-2) equals zero when x equals -2 or x equals 2. Therefore, the expression is undefined at x = -2 and x = 2. In all other cases, the expression is defined.
#SPJ1
find the absolute maximum and minimum values of the following function on the given set r.
f(x,y) = x^2 + y^2 - 2y + ; R = {(x,y): x^2 + y^2 ≤ 9
Answers
The absolute maximum and minimum values of the function f(x, y) = x^2 + y^2 - 2y on the set R = {(x, y): x^2 + y^2 ≤ 9} can be found by analyzing the critical points and the boundary of the region R.
To find the critical points, we take the partial derivatives of f(x, y) with respect to x and y, and set them equal to zero. Solving these equations, we find that the critical point occurs at (0, 1).
Next, we evaluate the function f(x, y) at the boundary of the region R, which is the circle with radius 3 centered at the origin. This means that we need to find the maximum and minimum values of f(x, y) when x^2 + y^2 = 9. By substituting y = 9 - x^2 into the function, we obtain f(x) = x^2 + (9 - x^2) - 2(9 - x^2) = 18 - 3x^2.
Now, we can find the maximum and minimum values of f(x) by considering the critical points, which occur at x = -√2 and x = √2. Evaluating f(x) at these points, we get f(-√2) = 18 - 3(-√2)^2 = 18 - 6 = 12 and f(√2) = 18 - 3(√2)^2 = 18 - 6 = 12.
Therefore, the absolute maximum value of f(x, y) is 12, which occurs at (0, 1), and the absolute minimum value is also 12, which occurs at the points (-√2, 2) and (√2, 2).
To know more about absolute maximum click here: brainly.com/question/28767824
#SPJ11
actoring Quadratic Expressions. Factor each completely. 1) x. 2 − 7x − 18. 2) p. 2 − 5p − 14. 3) m. 2 − 9m + 8.
Answers
Completely factored expressions are:
(x - 9)(x + 2)(p - 7)(p + 2)(m - 1)(m - 8)How to evaluate each part of the question?1. x² - 7x - 18 can be factored as:
(x - 9)(x + 2)
Expand the expression using FOIL:
(x - 9)(x + 2) = x² + 2x - 9x - 18 = x² - 7x - 18
2. p² - 5p - 14 can be factored as:
(p - 7)(p + 2)
Expand the expression using FOIL:
(p - 7)(p + 2) = p² + 2p - 7p - 14 = p² - 5p - 14
3. m² - 9m + 8 can be factored as:
(m - 1)(m - 8)
Expand the expression using FOIL:
(m - 1)(m - 8) = m² - 8m - m + 8 = m² - 9m + 8
Therefore, the completely factored expressions are:
(x - 9)(x + 2)(p - 7)(p + 2)(m - 1)(m - 8)Learn more about factored expressions.
brainly.com/question/19386208
#SPJ11
Find the measure of each numbered angle
Answers
Answer:
m∠1 = 54° m∠2 = 63° m∠3 = 117°
Step-by-step explanation:
We know that 117 + m∠2 = 180°, which when calculated is equal to 63. Now, we know that 63 + 63 + m∠1 = 180°. This comes out to be 54°. Finally, we know that m∠3 has to equal 117° because they are same side interior angles.
The measure of m<1, m<2 and m<3 are 54, 63 and 63 degrees respectively
The sum of angle in a straight line is 180 degrees, hence:
m<2 + 117 = 180
m<2 = 180 - 117
m<2 = 63 degrees
For the diagram, m<2 - m<3 = 63 degrees (alternate angle.)
Also, the sum of interior angle of the triangle is 180 degrees, hence:
m<2 + m<2 + m<1 = 180
63 + 63 + m<1 = 180
126 + m<1 = 180
m<1 = 180 -126
m<1 = 54degrees
Hence the measure of m<1, m<2 and m<3 are 54, 63 and 63 degrees respectively
Learn more on angles here: https://brainly.com/question/25770607
Find the equation of the line that passes through (4,4) and is parallel to y = 3 x + 4. Leave your answer in the form y = m x + c.
Answers
The equation of the line that passes through (4, 4) & parallel to y = 3x + 4 is y = 3x - 8 .
Slope intercept form:
The equation of line in slope intercept form is,
y = mx + c
Where m is slope of line and c is y-intercept.
Equation of line given that,
y = 3x + 4
So that, slope of line is 3.
We have to find the equation of the line that passes through (4,4) and is parallel to given lines.
Since, slope of all parallel lines are same.
Equation of required line is,
y = mx + c
Substitute point (4,4) in above line.
4 = 12 + c
c = 4 - 12
c = -8
So that, equation of line become,
y = 3x - 8 .
Learn more about the equation of line here:
brainly.com/question/18831322
#SPJ4
determine the general solution of
2tanx = 5sinx
Answers
To determine the general solution of 2tanx = 5sinx, we first need to rewrite the equation in terms of a single trigonometric function. We know that tanx = sinx/cosx, so we can substitute this into the equation to get:
2(sinx/cosx) = 5sinx
Multiplying both sides by cosx, we get:
2sinx = 5sinx cosx
Dividing both sides by sinx, we get:
2 = 5cosx
Solving for cosx, we get:
cosx = 2/5
Now we can use the inverse cosine function to find the solutions for x. Remember that the inverse cosine function has a range of [0,π] or [0,180°]. Therefore, we need to check if cosx = 2/5 falls within this range.
cos⁻¹(2/5) ≈ 66.42°
So one solution for x is 66.42°. To find the general solution, we need to add multiples of the period of cosx. The period of cosx is 2π, or 360°. Therefore, the general solution for 2tanx = 5sinx is:
x = cos⁻¹(2/5) + nπ, where n is an integer.
know more about general solutions here
https://brainly.com/question/32062078
#SPJ11
tyler reades 2/15 pages on monday 1/3 on tuesday and 2/9 on wendsday and 3/4 on thursday .and has 14 pages left on friday how many pages are in the book
Answers
The number of pages that are in the book is 1 31/45 pages.
How to illustrate the fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, Tyler reads 2/15 pages on Monday 1/3 on Tuesday and 2/9 on Wednesday and 3/4 on thursday .and has 14 pages left on friday how many pages are in the book.
The fraction for pages will be:
= 2/15 + 2/9 + 1/3 + 3/4 + 1/4
= 2/15 + 5/9 + 1
= 6 / 45 + 25/45 + 1.
= 1 31/45
Learn more about fractions on:
brainly.com/question/78672
#SPJ1
Complete question
tyler reades 2/15 pages on monday 1/3 on tuesday and 2/9 on wendsday and 3/4 on thursday .and has 1/4 pages left on friday how many pages are in the book
SOLVE THE EQUATION f(x)=2x^2\ x=3
Answers
Answer:
f(x)= 18
Step-by-step explanation:
f(x)= 2x^2
f(x)= 2(3)^2
f(x)= 2(9)
f(x)= 18
Let f(x) =3x+2 and g(x)=x-3 find f(x)-g(x)
Answers
The graph of the function f(x) = 5 cos (2x) is a reflection over the x-axis of the graph of g(x) =
Answers
Answer:
\(g(x)=-5\cos (2x)\)
Step-by-step explanation:
The given function is
\(f(x)=5\cos (2x)\)
If a function reflected over the x-axis, then x-coordinate remains same but the sign of y-coordinate is changed.
\(P(x,y)\Rightarrow P'(x,-y)\)
If function f(x) is a reflection over the x-axis to get the of g(x), then the resultant function is
\(g(x)=-f(x)\)
Substituting the value of function f(x), we get
\(g(x)=-5\cos (2x)\)
Therefore, the required function is \(g(x)=-5\cos (2x)\).
Anu brought an air cooler, its water tank is in the shape of a cuboid and can take 40 liters of water. Its dimensions are 50 cm x 20 cm. What will be the height of the water tank? (1000 cubic cm = 1 liter).
Answers
The height of the water tank of the air cooler brought by Anu is 40 cm.
What is the meaning of Height?Height is the vertical measurement of an object. If the measurement is not made vertically, the measurement is termed the length or width. Volume is a measure of how much space an object can occupy. Volume is used to determine the density of an object.
given,
Length = 50 cm
Width = 20 cm
Maximum tank volume = 40 liters = 40,000 cm3
Tank height?
Steps,
Tank volume = length x width x height
40,000 = 50 x 20 x height
40,000 = 1000 x height
Tank height = 40,000 : 1000
Tank height = 40 cm
So, the height of the air conditioning tank that can hold 40 liters of water is 40 cm.
Learn more about height here: https://brainly.com/question/1739912
#SPJ1
The equation of line EF is y = 1 over 2x + 6. Write an equation of a line parallel to line EF in slope-intercept form that contains point (0, −2).
Answers
Answer:
y = 1/2x -2
Step-by-step explanation:
You want the equation of a line parallel to y = 1/2x +6 that contains the point (0, -2), written in slope-intercept form.
SlopeThe slope of the line you want will be the same as the slope of the line you have. That is because parallel lines have the same slope.
The equation you are given is written in slope-intercept form:
y = mx + b . . . . . . where m is the slope and b is the y-intercept
Comparing this form to the given equation, you see that ...
m = 1/2 . . . . . the slope of the line you want
InterceptThe "intercept" in the "slope-intercept" form is the value of y when x=0. The point you are given, (0, -2), tells you that y = -2 when x = 0. So, the "intercept" in your slope-intercept equation is -2.
EquationThe equation you want is the equation of a line with slope 1/2 and a y-intercept of -2.
y = 1/2x -2
The equation of the line that is parallel to line EF and passes through point (0, -2) is y = (1/2)x - 2.To find an equation of a line that is parallel to line EF and passes through point (0, -2), we need to use the fact that parallel lines have the same slope. The slope of line EF is 1/2, so the slope of the parallel line will also be 1/2.
We can start by using the point-slope form of the equation of a line: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in m = 1/2 and (x1, y1) = (0, -2), we get:
y - (-2) = (1/2)(x - 0)
Simplifying this equation gives:
y + 2 = (1/2)x
To get this equation in slope-intercept form (y = mx + b), we can isolate y:
y = (1/2)x - 2
So the equation of the line that is parallel to line EF and passes through point (0, -2) is y = (1/2)x - 2. Note that this line intersects the y-axis at y = -2, which is the y-intercept.
learn more about slope here: brainly.com/question/16949303
#SPJ11
if p = 2^k + 1 is prime, show that every quadratic nonresidue of p is a primitive root of p.
Answers
Every quadratic nonresidue of p is a primitive root of p, when p = 2^k + 1 is primeIf p = 2^k + 1 is a prime number, we want to show that every quadratic nonresidue of p is a primitive root of p.
In other words, we aim to prove that if an element x is a quadratic nonresidue modulo p, then it is also a primitive root of p.
Let's assume p = 2^k + 1 is a prime number. To prove that every quadratic nonresidue of p is a primitive root of p, we can use the properties of quadratic residues and quadratic nonresidues.
A quadratic residue modulo p is an element y such that y^((p-1)/2) ≡ 1 (mod p), while a quadratic nonresidue is an element x such that x^((p-1)/2) ≡ -1 (mod p).
Now, let's consider an element x that is a quadratic nonresidue modulo p. We want to show that x is a primitive root of p.
Since x is a quadratic nonresidue, we know that x^((p-1)/2) ≡ -1 (mod p). By Euler's criterion, this implies that x^((p-1)/2) ≡ -1^((p-1)/2) ≡ -1^2 ≡ 1 (mod p).
Since x^((p-1)/2) ≡ 1 (mod p), we can conclude that the order of x modulo p is at least (p-1)/2. However, since p = 2^k + 1 is a prime, the order of x modulo p must be equal to (p-1)/2.
By definition, a primitive root of p has an order of (p-1). Since the order of x modulo p is (p-1)/2, it follows that x is a primitive root of p.
Learn more about Euler's criterion here:
brainly.com/question/12977984
#SPJ11
Two lighthouses flash their lights every 20 seconds and 30 seconds respectively. Given that they flash together at 8 p.m, when will they next flash together?
Answers
Which criteria can be used to prove triangles are congruent select all that apply?
Answers
The four criteria that can be used to prove triangles are congruent and can be used to prove the triangles are congruent.
Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides and all three of their corresponding angles have the same measurements. These triangles can be moved around, rotated, flipped, and turned to have a same appearance. They match up with one another when moved.
The four criteria that can be used to prove triangles are congruent are SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and SSS (Side-Side-Side). Additionally, CPCTC (Corresponding Parts of Congruent Triangles are Congruent) can be used to prove the triangles are congruent.
Learn more about triangle here
https://brainly.com/question/2773823
#SPJ4
What two factors when multiply gives you 36 but when added equals -16
Answers
Answer:-18 and +2
Step-by-step explanation:18*2=36
-18++2=-18+2=-16
please help me solve correct one gets Brainliest -6x+30
Answers
Answer:
Factor −6x+30
−6x+30
=6(−x+5)
Step-by-step explanation:
That's all there is
Assuming that someone is asked to write a code (i.e., program) for nonlinear problem using least square adjustment technique, what would be your advice for this person to terminate the program?
Answers
This criterion can be defined based on the desired level of accuracy or when the change in the estimated parameters falls below a certain threshold.
When implementing a program for a nonlinear problem using the least square adjustment technique, it is essential to determine a termination condition. This condition dictates when the program should stop iterating and provide the final estimated parameters. A common approach is to set a convergence criterion, which measures the change in the estimated parameters between iterations.
One possible criterion is to check if the change in the estimated parameters falls below a predetermined threshold. This implies that the adjustment process has reached a point where further iterations yield minimal improvements. The threshold value can be defined based on the desired level of accuracy or the specific requirements of the problem at hand.
Alternatively, convergence can also be determined based on the objective function. If the objective function decreases below a certain tolerance or stabilizes within a defined range, it can indicate that the solution has converged.
Considering the chosen termination condition is crucial to ensure that the program terminates effectively and efficiently, providing reliable results for the nonlinear problem.
Learn more about nonlinear problem: brainly.com/question/31457669
#SPJ11
What is the slope of a horizontal line that passes through the point (3,-7)?
Answers
Answer:
The slope of any horizontal line is 0.
Step-by-step explanation:
All horizontal lines have the same slope. The slope of any horizontal line is zero.
You can remember this because lines that go up (from left to right) have positive slope. The number gets smaller as the line gets flatter. Then the horizontal line has zero slope. Then lines that go down (from left to right) have negative slope.
If you need the equation of the horizontal line through (3,-7). That is y = -7
The equation of a horizontal line is "y=anumber". In the point (x,y) the 3 is the x and the -7 is the y.
y = -7
The sequence is given by the n-th term rule. Assuming this is possible, determine the recurrent input of the given sequence. If this is not possible, please justify it. an = (12^n − n^2 ), where n is a positive integer.
Answers
The recurrent input of the given sequence an = (12^n − n^2), where n is a positive integer, cannot be determined.
To determine the recurrent input of a sequence, we look for a pattern or formula that generates the terms of the sequence based on previous terms. However, in this case, the given sequence is defined directly by the formula an = (12^n − n^2).
There is no recurrence relation or dependency on previous terms in the sequence. Each term is solely determined by the value of n. Therefore, there is no underlying recurrent input or relationship between the terms that can be expressed through a recurrence relation. The sequence is entirely defined by the given formula without any recursive pattern, making it impossible to determine a recurrent input.
to learn more about sequence click here:
brainly.com/question/30762797
#SPJ11
Graph the solution set to this inequality.
3x – 11 > 7x + 9
Answers
Step-by-step explanation:
Solve the inequality:
\(3x - 11 > 7x + 9\)
Rearrange unknown terms to the left side of the equation:
\(3x - 7x > 9 + 11\)
Combine like terms:
\( - 4x > 9 + 11\)
Calculate the sum or difference:
\( - 4x > 20\)
Reduce the greatest common factor for both sides of the inequality:
\( - x > 5\)
Divide both sides of the inequality by the coefficient of variable:
\(x < - 5\)
2: plot:
\(x < - 5\)
Graph on number line:
The solution inequality that represents the solution of the given expression inequality is → x < - 5.
What is inequality? Differentiate between equation and expression? expression inequality : An inequality is used to make unequal comparisons between two expressions or numbers.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is the inequality as follows -
3x – 11 > 7x + 9
The inequality is given as -
3x – 11 > 7x + 9
3x > 7x + 9 + 11
3x - 7x > 9 + 11
- 4x > 20
x < - 5
Therefore, the solution inequality that represents the solution of the given expression inequality is → x < - 5.
To solve more questions on functions, expressions and polynomials, visit the link below -
brainly.com/question/17421223
#SPJ2
50 points need help asap plzz!!! Show that the Pythagorean identity sin^2 θ+cos^2 θ=1 is true for the given angle.
θ= 5π/3
Answers
Answer:
Pythagorean identity sin²θ+cos²θ = 1 is true for the angle θ = \(\frac{5\pi }{3}\)
Step-by-step explanation:
At first, let us simplify the left side of the identity
∵ The left side is sin²Ф + cos²Ф
∵ Ф = \(\frac{5\pi }{3}\) ⇒ lies in the 4th quadrant
∴ The left side is sin²(\(\frac{5\pi }{3}\)) + cos²(\(\frac{5\pi }{3}\))
→ Let us write the values of sin(\(\frac{5\pi }{3}\)) and cos(\(\frac{5\pi }{3}\))
∵ sin(\(\frac{5\pi }{3}\)) = \(\frac{-\sqrt{3}}{2}\) ⇒ sine an angle in the 4th quadrant is -ve
∵ cos(\(\frac{5\pi }{3}\)) = \(\frac{1}{2}\) ⇒ cosine an angle in the 4th quadrant is +ve
→ Substitute them in the left side
∵ sin²(\(\frac{5\pi }{3}\)) + cos²(\(\frac{5\pi }{3}\)) = [ \(\frac{-\sqrt{3}}{2}\)]² + [\(\frac{1}{2}\)]²
∴ sin²(\(\frac{5\pi }{3}\)) + cos²(\(\frac{5\pi }{3}\)) = [\(\frac{3}{4}\)] + [\(\frac{1}{4}\)]
∴ sin²(\(\frac{5\pi }{3}\)) + cos²(\(\frac{5\pi }{3}\)) = [\(\frac{4}{4}\)]
∴ sin²(\(\frac{5\pi }{3}\)) + cos²(\(\frac{5\pi }{3}\)) = 1
∵ The right side = 1
∴ Left side = Right side
∴ sin²(\(\frac{5\pi }{3}\)) + cos²(\(\frac{5\pi }{3}\)) = 1 ⇒ proved
∴ Pythagorean identity sin²θ+cos²θ = 1 is true for the angle θ = \(\frac{5\pi }{3}\)
To find the 95% confidence interval for the population standard deviation, you randomly sample with replacement from the original sample, thousands of times. From each new sample, you compute the sample standard deviation. Using the bootstrap method, how can you find the confidence interval for the population standard deviation from these values?.
Answers
Using the values of the 5th and 95th percentiles of these variables, the bootstrap method may be used to generate the 90% confidence interval for the population standard deviation.
What is a confidence interval?An area surrounding a measurement that indicates how accurate it is called a confidence interval. A 95% confidence interval, strictly speaking, means that if we compute a 95% confidence interval for each of the 100 independent samples, then about 95 of the 100 confidence intervals will include the true mean value (μ).So, a random sample with replacement from the original sample must be taken thousands of times in order to determine the 90% confidence interval for the population standard deviation.
We calculate the sample standard deviation from each fresh sample. The 90% confidence interval for the population standard deviation can be calculated using the bootstrap method using the values of the 5th and 95th percentiles of these variables.Therefore, using the values of the 5th and 95th percentiles of these variables, the bootstrap method may be used to generate the 90% confidence interval for the population standard deviation.
Know more about confidence intervals here:
https://brainly.com/question/15712887
#SPJ4
In a recent year, 17.3% of all registered doctors were female. If there were 48,800 female registered doctors that year, what was the total number of registered doctors?
Answers
17.3/100 = 48,800/x
where x is the total number of registered doctors.
Solving for x:
x = (48,800 x 100) / 17.3
x = 281,791.91
Therefore, the total number of registered doctors in that year was approximately 281,792.
the following table presents the probability distribution of the number of vacations X taken last year for a randomly chosen family. compute the mean X. 0. 1. 2. 3. 4p(x) 0.13. 0.61. 0.15. 0.07. 0.04
Answers
SOLUTION
The table for the x and P(x) can be shown below
From the table above, mean for the data is calculated as
\(\begin{gathered} \bar{x}=\sum_^x.p(x) \\ \sum_^x.p(x)=1.28 \end{gathered}\)Hence the answer is 1.28
