With convolution theorem the equation is proved.
According to the statement
we have given that the equation and we have to evaluate with the convolution theorem.
Then for this purpose, we know that the
A convolution integral is an integral that expresses the amount of overlap of one function as it is shifted over another function.
And the given equation is solved with this given integral.
So, According to this theorem the equation becomes the
[tex]\mathscr{L} \left( \int_{0}^{t} e^{-\tau} \cos \tau d \tau \right) = \frac{ \mathscr{L} (e^{-\tau} \cos \tau ) }{s} \\\mathscr{L} \left( \int_{0}^{t} e^{-\tau} \cos \tau d \tau \right) = \frac{\frac{s+1}{(s+1)^2+1}}{s} \\\mathscr{L} \left( \int_{0}^{t} e^{-\tau} \cos \tau d \tau \right) = \frac{1}{s}\left (\frac{s+1}{(s+1)^2+1} \right).[/tex]
Then after solving, it become and with theorem it says that the
[tex]\mathscr{L} \left( \int_{0}^{t} f(\tau) d\tau \right) = \frac{\mathscr{L} ( f(\tau))}{s} .[/tex]
Hence by this way the given equation with convolution theorem is proved.
So, With convolution theorem the equation is proved.
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b)Find z
: (√z+√22)(√z-√22) = 35
Answer: [tex]\Large\boxed{z=57}[/tex]
Concept:
Here, we need to know how to expand expressions like (a - b)(a + b).
For expressions like (a - b)(a + b), the expanded form must be:
a² - b²
For checking whether it is true:
(a - b)(a + b)
= a² - ab + ba - b²
= a² - b²
Solve:
Given equation
[tex](\sqrt{z}+\sqrt{22})(\sqrt{z}-\sqrt22)}=35[/tex]
Expand the parenthesis by the concept
[tex](\sqrt{z})^2-\sqrt{22}^2=35[/tex]
Simplify the exponents
[tex]z-22=35[/tex]
Add 22 on both sides
[tex]z-22+22=35+22[/tex]
[tex]\Large\boxed{z=57}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
can someone help with this algebra problem?
Answer:
g(1) = 1
Step-by-step explanation:
Since 1 ≠ -2 and 1 ≠ -1
Then we must use the expression:
g(x) = x³ - x² + 1 ,to calculate g(1).
Therefore
g(1) = (1)³ - (1)² + 1
= 1 - 1 + 1
= 0 + 1
= 1
What is the slope of a line perpendicular to the line whose equation is 3x + y = -9.
Fully simplify your answer.
Considering the definition of perpendicular line, the slope of a line perpendicular to the line whose equation is 3x+y= -9 is [tex]\frac{1}{3}[/tex].
Linear equationA linear equation o line can be expressed in the form y = mx + b.
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Perpendicular linePerpendicular lines are lines that intersect at right angles or 90° angles.
Two nonvertical lines are perpendicular if the slope of one is the negative reciprocal of the slope of the other. In other words, if you multiply the slopes of two perpendicular lines, you get –1.
Equation of perpendicular line in this caseIn this case, the line is 3x+y=-9. Expressed in the form y = mx + b, you get: y= -9 - 3x or, what is the same, y= -3x -9
If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of -3. So:
(-3)× slope perpendicular line= -1
slope perpendicular line= (-1)÷ (-3)
slope perpendicular line= [tex]\frac{1}{3}[/tex]
Finally, the slope of a line perpendicular to the line whose equation is 3x+y= -9 is [tex]\frac{1}{3}[/tex].
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Explain type i error and give an example. explain type ii error and give an example. what is the best way to reduce both kinds of error? find a current scenario that has a type i error and a type ii error. is this scenario an example of an inverse relationship? why or why not?
Type I error says that we suppose that the null hypothesis exists rejected when in reality the null hypothesis was actually true.
Type II error says that we suppose that the null hypothesis exists taken when in fact the null hypothesis stood actually false.
What is Type I error and Type II error?In statistics, a Type I error exists as a false positive conclusion, while a Type II error exists as a false negative conclusion.
Making a statistical conclusion still applies uncertainties, so the risks of creating these errors exist unavoidable in hypothesis testing.
The probability of creating a Type I error exists at the significance level, or alpha (α), while the probability of making a Type II error exists at beta (β). These risks can be minimized through careful planning in your analysis design.
Examples of Type I and Type II error
Type I error (false positive): the testing effect says you have coronavirus, but you actually don’t.Type II error (false negative): the test outcome says you don’t have coronavirus, but you actually do.To learn more about Type I and Type II error refer to:
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A company did a quality check on all the packs of trail mix it manufactured. each pack of trail mix is targeted to weigh 9.25 oz. a pack must weigh within 0.23 oz of the target weight to be accepted. what is the range of rejected masses, ×, for the manufactured trail mixes? (1 point) 0 x<9.02 or x> 9.48 because lx - 9.251 > 0.23 o x<9.25 or x > 9,48 because ix - 0.231 9.25 > 0 0 x€ 9.02 or x> 9.48 because ix - 0.231 9.25 > 0 o x< 9.25 or x> 9.48 because ix - 9.25| > 0.23
Rejected masses x are those that weigh less than 9.02 oz or more than 9.48 oz.
What is the range?In mathematics, the range of a function can refer to one of two notions that are closely related.The function's codomain, the function's visual representation.A binary relation f between two sets X and Y is a function if for every x in X there is exactly one y in Y such that f relates x to y.To find the rejected masses:
If each pack of trail mixes is supposed to weigh 9.25 oz and must be within 0.23 oz of that weight to be accepted, then rejected masses x are those that weigh less than 9.02 oz or more than 9.48 oz.Therefore, rejected masses x are those that weigh less than 9.02 oz or more than 9.48 oz.
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The correct question is given below:
A company did a quality check on all the packs of trail mix it manufactured. each pack of trail mix is targeted to weigh 9.25 oz. a pack must weigh within 0.23 oz of the target weight to be accepted. what is the range of rejected masses, ×, for the manufactured trail mixes?
Pls help!
using the numbers 1-9 fill in the boxes so that it meets the criteria. use each number only once per red box and once per blue box
To fill in the values we have the following
a. log6⁰, log 2 . 1, log 8/3
b. log 1 .4 , 1 , log 4. 6
c. log 9/2, log 3. 5 , log 5⁷
How to find the logarithm of a numberTo do this, you have to decide on that particular number that you want to find the logarithm on. Next you have to find the base of that number.
The logarithm of the number is the power that it would have to be raised for us to obtain a different number. You have to note that the logarithm of the number is the exponent that a base would have to be raised up to in order to get a particular number.
Log6⁰ for instance would give us the solution of 1 as the answer. While telling us that we have that the exponent is 0 while the base is 6.
One good property of logarithm is that log m/n = log m - log n also when we have log mn, it is the same as log m * log n
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math related pls help
Answer:
(a) (f +g)(x) = √(x-2) +√(x)
Step-by-step explanation:
The sum of two functions is the sum of their definitions.
Application(f +g)(x) = f(x) +g(x)
(f +g)(x) = √(x -2) +√(x)
Note: the radicals can only be combined if they can be reduced to a form that has the same expression under the radical. Here, that is not the case, so there is no way to simplify the sum.
PLS HELP!!!!
The half-life of Carbon-14 is 5730 years. Suppose a fossil is found with 27% of Carbon-14 as compared to a living sample. How old is the fossil?
Answer: 1547.10
Step-by-step explanation: Since you are not in a physics class, in which case requires the usage of the radioactive decay formula, definite integrals, and natural logarithms) but an Algebra class which deploys the usage of percentages, this should be rather simple.
I believe they want you to find 27% of the half life of Carbon-14 since it is below 50%. To find the percent of a number (in this case 27%), you multiply the number by 0.27.
5730 * 0.27 = 1547.10
Hope this helped! And if I'm wrong, please don't hesitate to correct me.
Give the missing angle as a bearing.
North
70⁰
Answer:
30°
Step-by-step explanation:
To make sure it's complete
What number is the height changing by each minute?
The height is changing by 0.5 units per minute as evident in the given table.
By what number is the height changing?It follows from the task content that the table given indicates that at, 0min, the height was 150.
While at 1 min, the height is 150.5. On this note, it follows that the height increases by 0.5 units for after every minute.
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What is the measure of 28?
O 90⁰
O 60°
O 180°
O 120°
Answer: 120
Step-by-step explanation:
Answer:
B. 60°
Step-by-step explanation:
Angle 4 and angle 8 are equal. Find the measure of angle 4 to know the measure of angle 8.
∠4=∠8
180-120=60
∠4=60°
Since angle 4 equals 60 degrees, angle 8 also equals 60 degrees.
Hope this helps!
.
y = x2 + 3
y = x + 5
The diameter of a circle is 8 mm. What is the circumference of the circle?
25 and 1/7mm?
50 and 2/7mm?
11/28mm?
Or
19 and 1/4mm?
Answer:
25.12 rounded.
Step-by-step explanation:
C = 2[tex]\pi[/tex]r
C=[tex]\pi[/tex]d
C = [tex]\pi[/tex](8)
C = 25.12 rounded.
Answer:
25 and 1/7 mm
Step-by-step explanation:
Diameter = circunference / π
π = 3.1416 aprox.
Then:
8 = citcunference / 3.1416
8 * 3.1416 = circunference
25.1428 = circunference
1/7 = 0.1428
Then:
25.1428 = 25 + 1/7
= 25 1/7
Solve x
1.6x+3=21
2.15(x - 5)=75
Answer:
11.25
77.85
Step-by-step explanation:
1.6x + 3 = 21
use inverse operation (+ = -, x = ÷) by taking 3 to the opposite side and changing it's integer to negative
1.6x = 21 - 3
divide 2 sides by 1.6
1.6x = 18
1.6x/1.6 = 18/1.6
x = 11.25//
2.15(x-5)=75
inverse operation
x= 75 - 2.15 + 5
x= 77.85//
Planes X and Y are perpendicular. Points A, E, F, and G are points only in plane X. Points R and S are points in both planes X and Y. Lines EA and FG are parallel.
Planes X and Y are shown. Lines A E and F G are vertical and are on plane X. Line R S is at the intersection of the 2 planes.
Based on this information, which pair of lines, together, could be perpendicular to RS? Select two options.
The pair of the line together that could be perpendicular to RS and should be considered will be EA and FG.
What is a perpendicular line?It should be noted that in terms of elementary geometry, two geometric objects should be considered as perpendicular when they intersect at a right angle.
In such a case, a line is treated to be perpendicular to another line in the case when the two lines intersect at a right angle.
Therefore, based on the information, the pair of the line together that could be perpendicular to RS and should be EA and FG.
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Area=
What is the area?
Help me asap! Please!! Thanks so much:)
Answer:
area = 10
Step-by-step explanation:
Triangle BOC is a right triangle. You can see this because the slope of BO and OC are negative reciprocals (opposite sign and flipped over) You can calculate the slope, m.
m = (y-Y)/(x-X)
Slope of BO is 4/2,
slope of OC is -2/4.
see image.
So then you can use BO and OC as the base and height in an area calculation.
But first you have to calculate the length of each. Luckily they are the same length. You can use distance formula, but when you have a picture, you can just see to use Pythagorean theorem (distance formula comes from PythagThm anyway)
Both BO and OC have legs length 2 and 4. See image. They are both length sqrt20.
Use Area= 1/2bh to find the area. See image.
Elliott is standing at the top of a store escalator that leads to the ground floor below. the angle of depression from the top of the escalator to the floor is 42.51°, and the escalator is 16 feet long. how far is the top of the escalator from the ground floor? round your answer to the nearest foot.
By using what we know about right triangles, we conclude that the height is 11ft.
How far is the top of the escalator from the ground floor?We can think of this as a right triangle.
Where the length of the escalator is the hypotenuse
We know that the angle of depression is 42.51°, then the top angle of our right triangle is:
90° - 42.51° = 47.49°
Now, the height of the top of the escalator would be the adjacent cathetus to said angle, then we can use the relation:
cos(a) = (adjacent cathetus)/(hypotenuse)
Replacing what we know:
cos(47.49°) = height/16ft
cos(47.49°) *16ft = height = 10.8ft
Rounding to the nearest foot, we get:
height = 11ft
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(2x² + 6x + 6) (3x - 2)
Answer:
6x³ + 14x² + 6x - 12
Step-by-step explanation:
(3x - 2)(2x² + 6x + 6)
6x³ - 4x² + 18x² - 12x + 18x - 12
6x³ + 14x² + 6x - 12
Answer: 6x³+14x²+6x-12
Step-by-step explanation:
Here, we can use the distributive property to multiply one of the factors by each term in the other. Below, I multiplied [tex]2x^2 + 6x + 6[/tex] by both 3x and -2.
[tex](2x^2+ 6x + 6) (3x - 2)\\3x(2x^2+ 6x + 6)-2(2x^2+ 6x + 6)\\6x^3+18x^2+18x-4x^2-12x-12[/tex]
Now, we can rearrange so that like terms are next to each other. Then, we can combine them to simplify.
[tex]6x^3+18x^2+18x-4x^2-12x-12\\6x^3+18x^2-4x^2+18x-12x-12\\6x^3+14x^2+6x-12[/tex]
Pls help me,this is Canadian MO 1998 question,i'm very confuse with this
The solution to the equation is x = 1.62
How to solve the equation?The equation is given as:
[tex]x =\sqrt{x\ -\ \frac{1}{x}}+\sqrt{1-\ \frac{1}{x}}[/tex]
Next, we split the equations as follows:
y = x
[tex]y =\sqrt{x\ -\ \frac{1}{x}}+\sqrt{1-\ \frac{1}{x}}[/tex]
Next, we graph the equations (see attachment)
From the attached graph, the equations intersect at
(x, y)= (1.62, 1.62)
Remove the y value
x = 1.62
Hence, the solution to the equation is x = 1.62
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Rationalize the right side first. Expand and simplify.
[tex]x = \sqrt{x - \dfrac1x} + \sqrt{1 - \dfrac1x}[/tex]
[tex]x \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right) = \left(\sqrt{x - \dfrac1x} + \sqrt{1 - \dfrac1x}\right) \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right)[/tex]
[tex]x \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right) = \left(\sqrt{x - \dfrac1x}\right)^2 - \left(\sqrt{1 - \dfrac1x}\right)^2[/tex]
[tex]x \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right) = \left(x - \dfrac1x\right) - \left(1 - \dfrac1x\right)[/tex]
[tex]x \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right) = x - 1[/tex]
Rearrange terms as
[tex]\dfrac{x - 1}x = \sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}[/tex]
[tex]\dfrac{x - 1}x + \sqrt{\dfrac{x - 1}x} = \sqrt{x - \dfrac1x}[/tex]
Substitute
[tex]y = \sqrt{\dfrac{x-1}x} = \sqrt{1 - \dfrac1x} \\\\ \implies y^2 = 1 - \dfrac1x \implies x = \dfrac1{1-y^2}[/tex]
(noting that [tex]y>0[/tex]) so that
[tex]x - \dfrac1x = \dfrac1{1-y^2} - (1-y^2) = \dfrac{2y^2 - y^4}{1-y^2}[/tex]
and the equation transforms to
[tex]y^2 + y = \sqrt{\dfrac{2y^2 - y^4}{1-y^2}}[/tex]
[tex]y + 1 = \sqrt{\dfrac{2 - y^2}{1-y^2}}[/tex]
Solve for [tex]y[/tex].
[tex](y+1)^2 = \left(\sqrt{\dfrac{2-y^2}{1-y^2}}\right)^2[/tex]
[tex]y^2 + 2y + 1 = \dfrac{2 - y^2}{1 - y^2}[/tex]
[tex]-y^4 - 2y^3 + 2y + 1 = 2 - y^2[/tex]
[tex]y^4 + 2y^3 - y^2 - 2y + 1 = 0[/tex]
[tex]\left(y^4 + 2y^3 + y^2\right) - 2y^2 - 2y + 1 = 0[/tex]
[tex](y^2 + y)^2 - 2(y^2 + y) + 1 = 0[/tex]
[tex]\left(y^2 + y - 1\right)^2 = 0[/tex]
[tex]y^2 + y - 1 = 0[/tex]
[tex]y = \dfrac{-1 \pm \sqrt5}2[/tex]
Since [tex]y>0[/tex], we take the positive root. Then
[tex]y = \sqrt{\dfrac{x-1}x} = \dfrac{-1 + \sqrt5}2[/tex]
Solve for [tex]x[/tex].
[tex]\left(\sqrt{\dfrac{x-1}x}\right)^2 = \left(\dfrac{-1 + \sqrt5}2\right)^2[/tex]
[tex]\dfrac{x-1}x = \dfrac{6 - 2\sqrt5}4 = \dfrac{3 - \sqrt5}2[/tex]
[tex]x - 1 = \dfrac{3-\sqrt5}2x[/tex]
[tex]\dfrac{-1+\sqrt5}2 x = 1[/tex]
[tex]x = \dfrac2{-1+\sqrt5}[/tex]
Rationalize to clean up the answer.
[tex]x = \dfrac2{-1+\sqrt5}\cdot\dfrac{-1-\sqrt5}{-1-\sqrt5} = \boxed{\dfrac{1+\sqrt5}2} \approx 1.6108[/tex]
i.e. the golden ratio constant.
Find the area of the blue shape below. Use 3.14 for π
If anyone knows the answer please help!
Answer:
1413.86 ft^2.
Step-by-step explanation:
The diameter of the circle = 50 - 2(18)
= 50-36
= 14 ft.
So its radius is 7 ft.
The total area of the blue shape
= 2(35 * 18) + 3.14*7^2
= 1413.86 ft^2.
Which statements accurately describe how to determine the y-intercept and the slope from the graph below? On a coordinate plane, a line goes through points (0, negative 6) and (3, 0). To find the y-intercept, begin at the origin and move horizontally to the graphed line. To find the slope, use two ordered pairs on the line and substitute into the equation m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction. To find the y-intercept, begin at the origin and move horizontally to the graphed line. To find the slope, use two ordered pairs on the line and substitute into the equation m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction. To find the y-intercept, begin at the origin and move vertically to the graphed line. To find the slope, use two ordered pairs on the line and substitute into the equation m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction. To find the y-intercept, begin at the origin and move vertically to the graphed line. To find the slope, use two ordered pairs on the line and substitute into the equation m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction.
Answer:
To find the y-intercept, begin at the origin and move vertically to the graphed line. To find the slope, use two ordered pairs on the line and substitute into the equation m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction.
The table represents an exponential function. what is the multiplicative rate of change of the function? a. 1/5 b. 2/5 c. 2 d. 5
Find the rectangular coordinates of the point with spherical coordinates (rho,θ,ϕ) : (4,π6,2π3)
The spherical coordinate (4,6π,2π/3) is (5,2π3,0.927) in spherical coordinates.
I’m going to assume that your values are in the form of:
(r,θ,z)=(4,6π,2π/3)
where
(r,θ)are the polar coordinates of the point’s projection in the xy-plane
z is the usual z-coordinate in the Cartesian coordinate system
Now solving for Cartesian coordinates:
x=rcosθ=4cos(6π)=4(0.86)=3.44
y=rsinθ=4sin(6π)=2
Now for spherical transformation, note that:
(ρ,θ,ϕ)
ρ is the distance between P and the origin
θ is the same angle used to describe the location in cylindrical coordinates
ϕ is the angle formed by the positive z-axis and line segment from the origin and point in space, note that0≤ϕ≤π
OK, now that we have that out of the way, let’s compute:
ρ=r2+z2 = 5
θ=θ=6π
ϕ=arccos(zr2+z2−−−−−−√)=arccos(35)≈0.927rad
The spherical coordinate (4,6π,2π/3) is (5,2π3,0.927) in spherical coordinates.
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what is the missing number?
Answer:
17
Step-by-step explanation:
the pattern
x is the blank
1+5 = 6
5+6 = 11
6+11 = x
11 + x = 28
so x = 17
ANSWER ASAP!!
what is the missing word in the pattern below?
Monday, Tuesday, Wednesday, __, Tuesday, Wednesday, Monday
A. Tuesday
B. Monday
C. Monday
D. Tuesday
Answer:
b
Step-by-step explanation:
Answer:
B. Monday
Step-by-step explanation:
Monday, Tuesday, Wednesday, Monday, Tuesday, Wednesday, Monday
hope it helps
Quick algebra 1 question for 25 points!
Only answer if you know the answer, Tysm!
Using a quadratic regression equation, it is found that the prediction of the number of songs that Kimberly will download on Month 9 is of:
c. 16.
How to find the equation of quadratic regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
In this problem, we have that the function initially decreases, then it increases , which means that it is a quadratic function. The points (x,y) to be inserted into the calculator are given as follows:
(1,8), (2,6), (4,5), (6,7), (7,9)
Inserting these points into the calculator, the prediction of y for a value of x is given as follows:
y = 0.391x² - 2.937x + 10.455
Hence, when x = 9, the prediction is:
y = 0.391 x 9² - 2.937 x 9 + 10.455
y = 15.69
Rounded to 16, hence option c is correct.
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25points if u solve these questions
Answer:
Step-by-step explanation:
1. yes
2. 0.048955
3. equal, not equal, less than and equal to, less than, greater than and equal to, greater than
4. 9 51/250
5. 387.5%
does someone mind helping me with this? Thank you!
Find the critical numbers of the function. (enter your answers as a comma-separated list. if an answer does not exist, enter dne. ) f(x) = x4/5(x − 8)2
The critical values of the function are x = 0 and x = 64
The critical values of a function f(x) are the values of x for which f'(x) = 0.
Given,
f(x) = [tex]\frac{x^{4} }{5(x-8)^{2} }[/tex]
The derivative is found as follows, applying the quotient rule:
f'(x) = [tex]\frac{[5(x^{4} )(x-8)^{2}-5x^{4} [(x-8)^{2} ]' }{[5(x-8)^{2} ]^{2} }[/tex]
= [tex]\frac{2x^{3}(x-64) }{5(x-8)^{3} }[/tex]
The zeros of the function are the zeros of the numerator, thus:
[tex]2x^{3} (x-64) =0\\2x^{3} =0-------- > x =0\\[/tex]
x - 64 = 0------------->x = 64
The critical values are x = 0 and x = 64
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. Factorise the following expression fully
(a+1)²-4b²
The factoring the equation (a + 1)² - 4b² we get (a+1+2b)(a+1-2b).
What is the factoring function of (a + 1)² - 4 b²?Given: (a + 1)² - 4b²
Apply Perfect Square Formula, and we get
(a + b)² = a² + 2 a b + b²
(a + 1)² = a² + 2a1+1²
= a² + 2a1 + 1² - 4 b²
simplifying the equation, we get
a² + 2a1 + 1² = a² + 2a + 1
= a² + 2a + 1 - 4b²
Factor, a² + 2a + 1 = (a + 1)²
= (a + 1)² - 4 b²
Simplify 4 b² = (2 b)²
= (a + 1)² - (2b)²
Apply the Difference of Two Squares Formula, and we get
x² - y² = (x + y)(x - y)
(a + 1)² - (2b)² = ((a + 1) + 2b)((a + 1) - 2 b)
simplifying the equation, we get
= ((a + 1) + 2b)(a + 1) - 2 b)
= (a + 1 + 2b)(a + 1 - 2b)
Therefore, the correct answer is (a+1+2b)(a+1-2b).
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