Prove that: \((a+b)^{-1} . (a^{-1} + b^{-1} ) = (ab)^{-1}\)
Answers
Step-by-step explanation:
\( \frac{1}{a + b} \times ( \frac{a + b}{ab}) = \frac{1}{ab} \)
Answer with step-by-step explanation:
\((a+b)^-^1*(a^-^1+b^-^1)=(ab)^-^1\)
First, convert these into positive indices.
\(\frac{1}{(a+b)} *(\frac{1}{a} +\frac{1}{b})=\frac{1}{ab}\)
And now, let us solve the left side.
\(\frac{1}{(a+b)} *(\frac{1}{a} +\frac{1}{b})\\\\\)
First, solve the brackets. That is add the fractions inside the brackets.
\(\frac{1}{(a+b)} *(\frac{1}{a} +\frac{1}{b})\\\\\frac{1}{(a+b)}*(\frac{1*b}{a*b} +\frac{1*a}{b*a})\\\\\frac{1}{(a+b)}*(\frac{b}{ab} +\frac{a}{ab})\\\\\frac{1}{(a+b)}*\frac{(a+b)}{ab}\)
Now multiply the fractions.
\(\frac{1}{ab}\)
So, it's clear that the left side equals the right side.
Left side = Right side
\(\frac{1}{ab}=\frac{1}{ab}\)
∴ \((a+b)^-^1*(a^-^1+b^-^1)=(ab)^-^1\)
Related Questions
true or false law of sines can be used when you are given 3
sides of a triangle and you are solving for an angle
Answers
Answer:
False
Step-by-step explanation:
False, you need at least one angle and three sides to use the law of sines or two angles and two different sides.
sin A sin B sin C
------ = ------- = -------
a b c
True, the law of sines can be used when you are given 3 sides of a triangle, and you are solving for an angle.
The law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in a given triangle. Therefore, if you know the lengths of all three sides of a triangle, you can use the law of sines to solve for one of the angles.
What are angles?An angle is the measure that determines two straight lines, which when joined together create a point of origin, which is called the vertex of the angle.
The unit of measurement associated with angles is degrees.
For more information about angle, visit:
https://brainly.com/question/25716982
#SPJ11
is 0.9 greater,least than, or equal to 95%
Answers
Answer:
Less
Step-by-step explanation:
Answer:
if 1 represents 100% then it would be less than
Step-by-step explanation:
that would make the .90 90% and thus less than 95%
of girls who tried out for the lacrosse team at euclid middle school, 12 were selected. of the 40 boys who tried out , 16 were selected are the ratios of the number of students on the team to the number of students trying out the same for both boys and girls how do you know
Answers
Answer: Yes, is the same ratio.
Explanation:
For the girls we have that out of the 30 that tried out for the team, 12 were selected. The ratio for the girls is:
\(\frac{12}{30}=\frac{2}{5}\)(we simplify 12/30 by dividing the numerator and denominator by 6)
For the boys we have that out of the 40 that tried out for the team, 16 were selected. The ratio for the boys is:
\(\frac{16}{40}=\frac{2}{5}\)(we simplify 16/40 by dividing the numerator and denominator by 8)
We can see that the ratio of the number of students on the team to the number of students trying out is the same for girls and boys.
Which of the following is an example of a polynomial function?
f(x) = 5x3 + 2x2 – 6x + 7
g of x equals the quantity x squared plus 2x minus 3 end quantity divided by the quantity x minus 4 end quantity
h(x) = 750(1.04)x
p(x) = log3(x)2
Answers
A polynomial function is represented by constants and factors
The example of a polynomial is: f(x) = 5x3 + 2x2 – 6x + 7
How to determine the example of polynomial?A polynomial function is represented as:
y = ax^n + bx^n-1 + cx^n-2 + dx^n-3 + ........... + e
Where e is a constant
Using the above general form of a polynomial, we can conclude that the example of a polynomial is:
f(x) = 5x3 + 2x2 – 6x + 7
Read more about polynomials at:
https://brainly.com/question/2833285
Answer:
f(x) = 5x3 + 2x2 – 6x + 7
Step-by-step explanation:
I got it right on the test.
In the Second Law experiment, In the Second Law experiment, the acceleration is calculated by measuring the time for the cart to move from the start point to the end point and applying the kinematics equation: s= 1/2 at 2 Explain how this equation is used to find the acceleration.
Answers
The kinematics equation s = 1/2at² can be used to determine the acceleration in the Second Law Experiment, where acceleration is calculated by measuring the time taken for the cart to move from the start point to the end point.
Let's derive how the equation is used to find the acceleration from this experiment:
Drivation of kinematics equation:
The kinematics equation is derived by integrating the acceleration function twice with respect to time (t).
Acceleration, a = d²s/dt², where s is displacement, and d²s is the second derivative of displacement with respect to time.
taking integral w.r.t time twice:
∫ a dt = ∫ d²s/dt² dt integrating once gives, v = at + C₁ (where C₁ is a constant of integration)
integrating twice gives, s = 1/2at² + C₁t + C₂ (where C₂ is a constant of integration)
Thus, the kinematics equation for an object moving with constant acceleration can be represented by
s = 1/2at² + vit + s₀,
where s is the displacement, a is the acceleration, t is time, vi is initial velocity, and s₀ is initial displacement.
Know more about kinematics equation here
https://brainly.com/question/24458315
#SPJ11
a bus arrives at 2:30 p.m. in Sydney if it left port if it left port Macquarie at 6.15 a.m the trip took
Answers
Answer:
Step-by-step explanation
Left at 6:15 am
How many hours until 2:15pm? 8 hours
How many minutes from 2:15 until 2:30? 15
So it took 8 hours and 15 minutes
WILL GIVE BRAINLIEST
In the diagram below, MZABC = 42°. D (7x+2) (3x)" B С What is the value of x?
Answers
Answer:
42 = (7x +2) +3x
42 = 10x + 2 ( get rid of the 2)
40 = 10x
(get rid of the 10 by dividing 10 on each side)
x = 4
If the cost of 7m is Rs. 1470, find the cost of 5m cloth
Answers
By using unitary method, we found that the cost of 5m cloth is Rs. 1050.
According to the unitary method, the cost of 1 meter of cloth is equal to the total cost of 7 meters of cloth divided by 7. That is,
Cost of 1m cloth = Total cost of 7m cloth/7
We know that the total cost of 7m cloth is Rs. 1470. Therefore,
Cost of 1m cloth = 1470/7
Cost of 1m cloth = Rs. 210
This means that the cost of 1 meter of cloth is Rs. 210. Now, we need to find the cost of 5m cloth. To do that, we can use the unitary method again.
Cost of 5m cloth = Cost of 1m cloth x 5
Cost of 5m cloth = Rs. 210 x 5
Cost of 5m cloth = Rs. 1050
Therefore, the cost of 5m cloth is Rs. 1050.
To know more about unitary method here
https://brainly.com/question/28276953
#SPJ4
John is having a new deck built. He paid $485 for the required materials, and he will pay his brother $25 an hour to build the deck
Answers
Answer:
The answer is not finished but if John is buying the materials and paying for the labor then the answer will be $510.
Step-by-step explanation:
I’m sorry if I didn’t help but the answer is not written out enough…
Please help me with this homework
Answers
It is a rational number.
Step-by-step explanation:
Rational number means it can be denoted as a fraction and irrational numbers cannot be denoted as fractions.
square root of 4 × ⅖
square root of 4 is 2 so
2 × ⅖
it is ⅘
so it is 0.8
Hope this helps. Have a good day!
Pls give brainliest if possible.
Please help me. Much Appreciated Each part of problem mark as either a, b, c
Answers
Given:
Total number of people surveyed = 205
a) Percentage of the survey respondents that do not like both hamburgers and burritos.
Number of people that do not like both = 54
To find the percentage of the respondents that do not like both, we have:
\(\begin{gathered} \text{ \% that do not like both = }\frac{Number\text{ that }do\text{ not like both}}{\text{Total surveyed}}\ast\frac{100}{1} \\ \\ \text{ \% that do not like both = }\frac{54}{205}\ast100\text{ = }26.3\text{ \%} \end{gathered}\)Therefore, the percentage of the survey respondents that do not like both hamburgers and burritos is 26.3%
b) Marginal relative frequency of all customers that like hambugers.
Given:
Number of customers that like hamburgers = 110
To find the marginal relative frequency, we have:
\(M=\frac{110}{250}=0.54=54\text{ \%}\)The marginal relative frequency of all customers that like hambugers is 54%
c) Conditional relative frequencies:
i) Conditional relative frequency that a person likes hamburgers given that the person does not like burritos:
\(\frac{110-29}{135}=\frac{81}{135}=0.6=60\text{ \%}\)ii) Conditional relative frequency that a person likes burritos, given that the person does not like hamburgers:
\(\frac{41}{41+54}=\frac{41}{95}=0.43=43\text{ \%}\)PLEASE HELP, i’ll give brainly to correct answer
Answers
Good morning,
Have a great day ahead
Evaluate
4
21
×
15
24
Give your answer as a fraction in its simplest form
Answers
Answer:
5/4
Step-by-step explanation:
4/21 x 15/24 = 60/48 = 15/12 = 5/4
Find the slope of the tangent line to the graph of f at the given point
f(x)=x²- 2x + 3 at (-1,6)
Answers
The slope of the tangent line to the graph of f at the point (-1, 6) is -4.
To find the slope of the tangent line to the graph of f(x) = x^2 - 2x + 3 at the point (-1, 6), we need to find the derivative of f(x) and evaluate it at x = -1.
The derivative of f(x) with respect to x can be found using the power rule of differentiation. For each term in the function, we multiply the coefficient by the exponent and reduce the exponent by 1. Applying the power rule, we have:
f'(x) = 2x - 2
Now, we evaluate the derivative at x = -1 to find the slope of the tangent line at that point:
f'(-1) = 2(-1) - 2 = -4
Therefore, the slope of the tangent line to the graph of f at the point (-1, 6) is -4.
for such more question on tangent line
https://brainly.com/question/19132778
#SPJ11
Factorizar: (11x3 – 2y)2 =
Answers
Answer:
66-4y
Step-by-step explanation:
(11x3 – 2y)2
= (33 -2y)2
= 66-4y
BODMAS
(11×3-2y)2
121×9-4y2
1089-4y2
=4y2-1089
consider a plate with a radius of 3 and a radial density given by rho(x)=5 e3x2. what is the mass of the plate?
Answers
The mass of the plate is approximately 4.411 × 10¹¹.
The mass of the plate can be calculated using the formula for the mass of a circular object: M = ∫[0, R] 2πρ(x)x dx, where R is the radius of the plate, ρ(x) is the radial density, and x is the distance from the center of the plate.
In this case, the radius of the plate is R = 3 and the radial density is given by ρ(x) = 5e^(3x²). We can plug these values into the formula to find the mass of the plate:
M = ∫[0, 3] 2π(5e^(3x²))x dx
To solve this integral, we can use the substitution u = 3x^2, du = 6x dx:
M = (2π/6) ∫[0, 27] 5e^u du
M = (5π/3) ∫[0, 27] e^u du
M = (5π/3) (e^27 - e⁰)
M = (5π/3) (e^27 - 1)
Therefore, the mass of the plate is M = (5π/3) (e²⁷ - 1) ≈ 4.411 × 10¹¹.
So, the mass of the plate is approximately 4.411 × 10¹¹.
know more about mass here
https://brainly.com/question/19694949#
#SPJ11
I need some help on both of my question!
Answers
The value of x for the given triangle is x = 8.4 units. 2. For the given triangle the value of x is 2941.17 m.
What are vertically opposite angles?
The opposing angles created by the junction of two lines are known as
vertical angles
or vertically opposed angles. A pair of angles that are vertically opposed to one another are always equal. Moreover, a vertical angle and the angle to which it is next are
supplementary angles
, meaning their sum is 180 degrees.
The given triangle is a right triangle.
Using the trigonometric functions we have:
tan (35) = opposite / adjacent = x / 12
0.7 (12) = x
x = 8.4
Hence, the value of x for the given triangle is x = 8.4 units.
For the second figure, using the alternate interior angles we have angle corresponding to the segment x as 10 degrees.
Using the trigonometric function we have:
sin (10) = opposite / hypotenuse = 500/x
x = 500/0.17
x = 2941.17
Hence, the value of x is 2941.17 m.
Learn more about vertically opposite angles here:
https://brainly.com/question/18045519
#SPJ1
Write the converse, inverse, and contrapositive of each true conditional statement. Determine whether each related conditional is true or false. If a statement is false, find a counterexample. A hamster is a rodent
Answers
help plsssssssssssssss
Answers
Answer:
(- 2, - 5)Step-by-step explanation:
The solution to the linear system is the point of intersection of the lines.
This point is
(- 2, - 5)Three friends were playing a game of marbles.
At the end of the game, Marcy had 25% of the
marbles, Roger had
2
1
of the marbles, and Ann
had the rest of the marbles. If there were 100
marbles altogether, how many marbles did Ann
have at the end of the game?
Answers
The number of marbles Ann had at the end is 54.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Total marbles = 100
The number of marbles:
Marcy:
= 25% of 100
= 1/4 x 100
= 25
Roger:
= 21
Now,
The number of marbles:
Ann = 100 - (25 + 21) = 100 - 46 = 54
Thus,
Ann has 54 marbles at the end.
Learn more about percentages here:
https://brainly.com/question/11403063
#SPJ1
For a two-tailed test at 12. 66% significance level, the critical value of z is:.
Answers
for a two-tailed test at a 12.66% significance level, the critical values of z are approximately +1.53 and -1.53. We are looking for the z-score that corresponds to the area to the right of it (for the positive critical value) equal to 0.0633.
For a two-tailed test at a 12.66% significance level, we need to find the critical value of z.
Step 1: Determine the significance level for each tail.
Since this is a two-tailed test, we need to divide the overall significance level (12.66%) by 2. This gives us 6.33% (or 0.0633 in decimal form) in each tail.
Step 2: Find the z-score associated with the given significance level.
To find the critical value of z, you can use a z-table or an online calculator. We are looking for the z-score that corresponds to the area to the right of it (for the positive critical value) equal to 0.0633.
Using a z-table or calculator, you'll find that the z-score is approximately ±1.53.
So, for a two-tailed test at a 12.66% significance level, the critical values of z are approximately +1.53 and -1.53.
To know more about z-score Visit:
https://brainly.com/question/15016913
#SPJ11
Find the missing side.
27°
N
z = [? ]
Round to the nearest tenth.
Remember: SOHCAHTOA
11
![Find the missing side.27Nz = [? ]Round to the nearest tenth.Remember: SOHCAHTOA11](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/n17J8qEibIV7jTiFfZHFnRSc76nzLjad.png)
Answers
The value of hypotenuse is 24 and value of adjacent side is 11 from the triangle.
The given triangle is a right angle triangle.
The opposite side has side length of 11.
One of the angle is 27 degrees.
We have to find the length of hypotenuse and length of adjacent side.
sin27=11/z
0.45=11/z
z=11/0.45
z=24
So the length of hypotenuse is 24.
Now let us find the adjacent side by using tan function which is ratio of opposite side and adjacent side.
tan27=11/z
0.51=11/z
z=11/0.51
z=21.5
z=22
To learn more on trigonometry click:
https://brainly.com/question/25122835
#SPJ1
A construction crew will build a new railroad track which passes through the point (8,5) and is parallel to the one
modeled by the line. What equation models the path of the new track?
Answers
Answer:
y = \(-\frac{2}{9}x+\frac{61}{9}\)
Step-by-step explanation:
Let the equation of the new railroad track passing through the point \((x_1,y_1)\) and slope = m₁ is,
\(y-y_1=m_1(x-x_1)\)
Slope of the given line = \(\frac{y_2-y_1}{x_2-x_1}\)
Slope of the line passing through (-3, 1) and (6, -1) will be,
m₂ = \(\frac{1+1}{-3-6}\)
m₂ = \(-\frac{2}{9}\)
Since, railroad track and the given line are parallel,
m₁ = m₂ = \(-\frac{2}{9}\)
Therefore, equation of the railroad track passing through (8, 5) and slope = \(-\frac{2}{9}\) will be,
y - 5 = \(-\frac{2}{9}(x-8)\)
y = \(-\frac{2}{9}x+\frac{16}{9}+5\)
y = \(-\frac{2}{9}x+\frac{61}{9}\)
Answer:
BRAINLIEST PLEASEEEEEE
y-5=-2/9(x-8)
Step-by-step explanation:
I had the exact same question and just kept getting it wrong until it gave me the right one.
Help please it’s rational numbers
Answers
Answer:
3/1 ; 0/3 ; -191/32 ; 3/456
Step-by-step explanation:
We have to find all the numbers that are expressed with a fraction:
1) is a trap because the division is impossibile
2) true: 3/1 is a fraction
3) true: 0/3 is a possible division and it results 0
4) true: is a fraction
5) true: is a fraction
OKAY HELP so Raegan has a rectangular breadspread that is 238 cm by 435 cm. She wants to sew a fringe around the bread spread. what is the perimiter of the bed spread??? figured that out its 1346 but then it says raegan gets a new breadspread that is 27 cm longer. whats the perimiter now?
Answers
Answer:
The new perimeter is 1400 cm
Step-by-step explanation:
The perimeter of the bedspread is the perimeter of a rectangle, whose formula is:
Perimeter = 2 * width + 2 * length
Then the perimeter of the initial bed spread is:
Perimeter = 2 * (238 cm) + 2 * (435 cm) = 1346 cm
as you calculated.
Now, she gets a new bedspread that is 27 cm longer. So the new dimensions are 238 cm width, and (435 + 27) cm length, then the perimeter becomes:
Perimeter = 2 * (238 cm) + 2 * (462cm) = 1400 cm
Q is the equidistant from the sides of
Answers
Answer:
its B.
Step-by-step explanation:
please mark this as brainlists
the lengths of two sides of a triangle are 5 feet and 7 feet. which of the following could be the length of the third side? select all that apply.
Answers
The lengths that could be the length of the third side are any values less than 12 feet, the value of 12 feet itself, and any values greater than 2 feet.
To determine which lengths could be the third side of the triangle, we can use the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Given that the lengths of the two sides are 5 feet and 7 feet, we can evaluate the following possibilities for the length of the third side:
The third side is less than the sum of the two given sides: If the third side is less than 5 + 7 = 12 feet, it can be a valid length.
The third side is equal to the sum of the two given sides: If the third side is equal to 5 + 7 = 12 feet, it can be a valid length, forming a degenerate triangle.
The third side is greater than the difference between the lengths of the two given sides: If the third side is greater than |5 - 7| = 2 feet, it can be a valid length.
Based on these conditions, the possible lengths for the third side are:
Less than 12 feet
Equal to 12 feet
Greater than 2 feet
Know more about lengths here:
https://brainly.com/question/32060888
#SPJ11
Scores on the test are normally distributed with a mean of 79 and a standard deviation of 8.4. Find the numerical limits for a B grade. Round your answers to the nearest whole number, if necessary calculator
Answers
This is not the question, the correct question is:
A humanities professor assigns letter grades on a test according to the following scheme. A: Top 6% of scores B: Scores below the top 6% and above the bottom 59% C: Scores below the top 41% and above the bottom 17% D: Scores below the top 83% and above the bottom 7% F: Bottom 7% of scores.
Scores on the test are normally distributed with a mean of 79 and a standard deviation of 8.4. Find the numerical limits for a B grade. Round your answers to the nearest whole number, if necessary.
Answer: The numerical limits for grade B is 81 and 92
Step-by-step explanation:
Given that
mean Ж = 79
Standard deviation S = 8.4
B: Scores below the top 6% and above the bottom 59%
To find the numerical value for Grade B
Below the top bottom 6% ( 0.06) is
p ( X < Ж ) = 1 - 0.06
p ( X < Ж ) = 0.94
therefore
P( (X - ц)/S < (X - Ж) / S)) = 0.94
(X - 79) / 8.4 = 1.5548 ( from normal distribution table )
X - 79 = 13.0603
X = 13.0603 + 79
X = 92.06 ≈ 92 ( nearest whole number)
Above bottom 59% ( 0.59) is
p ( X < Ж ) = 0.59
therefore
P( (X - ц)/S < (X - Ж) / S)) = 0.59
(X - 79) / 8.4 = 0.2275 ( from normal distribution table )
X - 79 = 1.9114
X = 1.9114 + 79
X = 80.91 ≈ 81 ( nearest whole number)
So the numerical limits for grade B is 81 and 92
Let θ^θ^ and θ~θ~ be two alternative unbiased estimators for the unknown parameter θθ. θ^θ^ is said to be (the most) efficient only if
a.E(θ^)=0E(θ^)=0.
b.var(θ^)
c.E(θ^)=θE(θ^)=θ.
d.var(θ^)var(θ^) is the minimum within the group of all linear unbiased estimators for θθ.
Answers
θ^ is said to be (the most) efficient only if var(θ^) is the minimum within the group of all linear unbiased estimators for θθ. Therefore, the option d.
Given that θ^ and θ~ be two alternative unbiased estimators for the unknown parameter θθ. var(θ^) is the minimum within the group of all linear unbiased estimators for θθ. The efficiency of an estimator is measured by its variance. An efficient estimator is an estimator that attains the lowest possible variance. This is obtained by the Cramér-Rao lower bound, which states that the variance of an estimator is bounded by the reciprocal of the Fisher information. In other words, the more information in the data, the more efficient the estimator is. Moreover, in the case of unbiased estimators, the one with the smallest variance is said to be the most efficient. Furthermore, an estimator is considered the most efficient if and only if its variance is equal to the Cramér-Rao lower bound.To know more about linear unbiased estimators, visit:
https://brainly.com/question/32063886
#SPJ11
Using Laplace Transforms, find the solution of the initial value problem: d²y +9y =9. sin(t). U(t - 3), = y(0) = y'(0) = 0 dx²
Answers
The solution to the given initial value problem, obtained using Laplace transforms, is y(x) = 0. This means that the function y(x) is identically zero for all values of x.
To find the solution of the initial value problem using Laplace transforms for the equation d²y/dx² + 9y = 9sin(t)u(t - 3), where y(0) = y'(0) = 0, we can follow these steps:
Take the Laplace transform of the given differential equation.
Applying the Laplace transform to the equation d²y/dx² + 9y = 9sin(t)u(t - 3), we get:
s²Y(s) - sy(0) - y'(0) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))
Since y(0) = 0 and y'(0) = 0, the Laplace transform simplifies to:
s²Y(s) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))
Solve for Y(s).
Combining like terms, we have:
Y(s) * (s² + 9) = 9 * (1/s² + 1/(s² + 1))
Multiply through by (s² + 1)(s² + 9) to get rid of the denominators:
Y(s) * (s⁴ + 10s² + 9) = 9 * (s² + 1)
Simplifying further, we have:
Y(s) * (s⁴ + 10s² + 9) = 9s² + 9
Divide both sides by (s⁴ + 10s² + 9) to solve for Y(s):
Y(s) = (9s² + 9)/(s⁴ + 10s² + 9)
Partial fraction decomposition.
To proceed, we need to decompose the right side of the equation using partial fraction decomposition:
Y(s) = (9s² + 9)/(s⁴ + 10s² + 9) = A/(s² + 1) + B/(s² + 9)
Multiplying through by (s⁴ + 10s² + 9), we have:
9s² + 9 = A(s² + 9) + B(s² + 1)
Equating the coefficients of like powers of s, we get:
9 = 9A + B
0 = A + B
Solving these equations, we find:
A = 0
B = 0
Therefore, the decomposition becomes:
Y(s) = 0/(s² + 1) + 0/(s² + 9)
Inverse Laplace transform.
Taking the inverse Laplace transform of the decomposed terms, we find:
L^(-1){Y(s)} = L^(-1){0/(s² + 1)} + L^(-1){0/(s² + 9)}
The inverse Laplace transform of 0/(s² + 1) is 0.
The inverse Laplace transform of 0/(s² + 9) is 0.
Combining these terms, we have:
Y(x) = 0 + 0
Therefore, the solution to the initial value problem is:
y(x) = 0
To learn more about Laplace transforms visit : https://brainly.com/question/29583725
#SPJ11