The equivalent double integral with the order of integration reversed is:
∫4_0 ∫√(x/4)_0 4y dydx = 8/3. The correct option is B.
The given double integral is:
∫∫R 4y dxdy, where R is the region bounded by the curves x=0, x=4y^2, and y=0.
To reverse the order of integration, we need to draw the region R and express it in terms of the other variable. The region R is a triangle in the first quadrant, bounded by the x-axis, the curve y=√(x/4), and the vertical line x=4.
Therefore, the equivalent double integral with the order of integration reversed is:
∫∫R 4y dydx,
where R is the region bounded by the curves y=0, y=√(x/4), and x=4.
To evaluate this integral, we integrate with respect to y first, keeping x as a constant. The limits of integration for y are y=0 and y=√(x/4).
Therefore, the integral becomes:
∫4_0 ∫√(x/4)_0 4y dydx.
Integrating with respect to y, we get:
∫4_0 2y^2 |_0^√(x/4) dx,
which simplifies to:
∫4_0 x/2 dx = 8/3.
Therefore, the equivalent double integral with the order of integration reversed is:
∫4_0 ∫√(x/4)_0 4y dydx = 8/3.
This matches the limits of integration for the inner integral.
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Proof : tan10 x tan20 x tan…70 x tan80=1
This follows from the identity
[tex]\cot(x) = \dfrac1{\tan(x)} = \tan(90^\circ - x)[/tex]
The overall product is 1 because
[tex]\tan(10^\circ) \tan(80^\circ) = \cot(80^\circ) \tan(80^\circ) = 1[/tex]
[tex]\tan(20^\circ) \tan(70^\circ) = \cot(70^\circ) \tan(70^\circ) = 1[/tex]
[tex]\tan(30^\circ) \tan(60^\circ) = \cot(60^\circ) \tan(60^\circ) = 1[/tex]
[tex]\tan(40^\circ) \tan(50^\circ) = \cot(50^\circ) \tan(50^\circ) = 1[/tex]
Can someone help me with these problems please!!
a.
i. In standard form y = 5x² - 20x + 27ii. The y intercept is (0, 27)iii. Find the graph in the attachmentb.
i. In standard form is y = 3x² + 6x + 15ii. The y-intercept is (0, 15)iii. Find the graph in the attachmentWhat is a quadratic function?A quadratic function is a function of the form y = ax² + bx + c
a. i. How to write the quadratic function y = 5(x - 2)² + 7 in standard form?To write y = 5(x - 2)² + 7, we expand the bracket and simplify.
So, y = 5(x - 2)² + 7
y = 5(x² - 4x + 4) + 7
y = 5x² - 20x + 20 + 7
y = 5x² - 20x + 27
So, the quadratic function y = 5(x - 2)² + 7 in standard form is y = 5x² - 20x + 27
ii. The y-intercept
The y intercept is gotten when x = 0.
So, y = 5x² - 20x + 27
y(0) = 5(0)² - 20(0) + 27
y(0) = 0 - 0 + 27
y(0) = 27
The y intercept is (0, 27)
iii. The graph of y = 5(x - 2)² + 7Find the graph in the attachment
b. i. How to write the quadratic function y = 3(x + 1)² + 12 in standard form?To write y = 3(x + 1)² + 12, we expand the bracket and simplify.
So, y = 3(x + 1)² + 12
y = 3(x² + 2x + 1) + 12
y = 3x² + 6x + 3 + 12
y = 3x² + 6x + 15
So, the quadratic function y = 3(x + 1)² + 12 in standard form is y = 3x² + 6x + 15
ii. The y-intercept
The y intercept is gotten when x = 0.
So, y = 3x² + 6x + 15
y(0) = 3(0)² - 6(0) + 15
y(0) = 0 - 0 + 15
y(0) = 15
The y-intercept is (0, 15)
iii. The graph of y = 3(x + 1)² + 12Find the graph in the attachment
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WILL VOTE BRAINLIEST FOR THE FIRST RIGHT ANSWER
Answer:
1st option
Step-by-step explanation:
let y = h(x) and rearrange making x the subject , that is
y = 6x - 6 ( add 6 to both sides )
y + 6 = 6x ( divide both sides by 6 )
[tex]\frac{y+6}{6}[/tex] = x
change y back into terms of x with x = [tex]h^{-1}[/tex] (x)
[tex]h^{-1}[/tex] (x) = [tex]\frac{x+6}{6}[/tex]
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
As part of your retirement planning, you purchase an annuity that pays 5.75% annual interest compounded quarterly If you make quarterly payments of $1600 how much will you have saved in 5 years? Instead, if you make quarterly payments of $800, how much will you have saved in 10 years?
Tatiana has a special puzzle in which all of the pieces fit together in any way. There is no goal picture. Instead, the goal of the puzzle is to make different patterns and pictures using the pieces. If Tatiana has 50 unique puzzle pieces and she plans to use all of them, how many possible pictures can she create
It is an example of Permutation without repetition.
To find the number of pictures can create.
what is permutation and combination?An arrangement of things in a certain sequence is what we refer to as a permutation. The constituents or components of sets are presented in this section in a sequential or chronological fashion. A coming together or merging of several parts or characteristics in which each of the constituent parts or traits retains its unique identity.
Given that:
50 unique pieces of puzzle
Use them all to solve puzzle
No repetition is allowed therefore
Since no repetition is allowed because all puzzle pieces are required to be used.
Therefore each of the 50 pieces can be used max one time
Therefore if we start with piece like this " 1 2 3 .. up to ... 50 " it is one combination
Another could be "2 1 3 .. up to .. 50" or "3 1 2 .. up to 50" and so on
So we see that we can see that we can select the first piece in 50 ways 49 left which could be selected for second piece then 48, 47 respectively
Therefore 50X49X48X47X46X....X1 = 50!
Hence, It is an example of Permutation without repetition.
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Option is missing
A. Combination with repetition
B. Permutation with repetition
C. Combination without repetition
D. Permutation without repetition
PLEASE HELP DUE TONIGHT
1. The time taken for the water to fall that much is 0.2 s
2. The initial speed of the water is 4 m/s
1. How to determine the time Height (h) = 20 cm = 20 / 100 = 0.2 mAcceleration due to gravity (g) = 9.8 m/s²Time (t) =?h = ½gt²
0.2 = ½ × 9.8 × t²
0.2 = 4.9 × t²
Divide both side by 4.9
t² = 0.2 / 4.9
Take the square root of both side
t = √(0.2 / 4.9)
t = 0.2 s
2. How to determine the initial speedHorizontal distance (s) = 80 cm = 80 / 100 = 0.8 mTime (t) = 0.2 sInitial speed (u) =?s = ut
Divide both sides by t
u = s / t
u = 0.8 / 0.2
u = 4 m/s
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John noticed that the angle formed by the minute hand and hour hand on a standard 12-hour clock was 110 degrees when he left home after 6 p.m.; it was also 110 degrees when he returned before 7 p.m. that same night. If he left home for more than five minutes, for how many minutes was he away
Jhon was between 6:12 p.m and 6:52 p.m. So, Jhon left home for exact 40 minutes. Using the angle made by the hands in the clock, the required value is calculated.
How to find the angle between the minute hand and hour hand?The general formula for finding the angle between the minute hand and the hour hand is
M = [tex]\frac{2}{11}[/tex] (H × 30 ± θ)
Calculation:It is given that,
Jhon left home after 6 p.m with an angle of 110° formed by the minute hand and hour hand.
So,
M = [tex]\frac{2}{11}[/tex] (H × 30 - θ)
= [tex]\frac{2}{11}[/tex] (6 × 30 - 110)
= [tex]\frac{2}{11}[/tex] (180 - 110)
= [tex]\frac{2}{11}[/tex] × 70
= 140/11
So, he left after 6:12 p.m
Jhon returned home before 7 p.m with angle of 110° formed by the minute hand and hour hand.
M = [tex]\frac{2}{11}[/tex] (H × 30 + θ)
= [tex]\frac{2}{11}[/tex] (6 × 30 + 110)
= [tex]\frac{2}{11}[/tex] (180 + 110)
= [tex]\frac{2}{11}[/tex] × 290
= 580/11
So, he returned before 6:52 p.m
Then,
The time taken for returning home = 580/11 - 140/11 = 440/11 = 40 minutes.
Therefore, he took 40 minutes to return home.
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At the store, there were 6 bags of chips for every 8 cookie boxes. If there were 104 cookie boxes, how many bags of chips were there?
Answer: There were 78 bags of chips.
Can someone help solve both of these? ASAP
Question 4
[tex]\sin 30^{\circ}=\frac{y}{14\sqrt{3}}\\\\\frac{1}{2}=\frac{y}{14\sqrt{3}}\\\\\boxed{y=7\sqrt{3}}\\\\\\\\\cos 30^{\circ}=\frac{x}{14\sqrt{3}}\\\\\frac{\sqrt{3}}{2}=\frac{x}{14\sqrt{3}}\\\\\boxed{x=21}[/tex]
Question 5
[tex]\cos 45^{\circ}=\frac{x}{28}\\\\\frac{1}{\sqrt{2}}=\frac{x}{28}\\\\x=\frac{28}{\sqrt{2}}\\\\\boxed{x=14\sqrt{2}}\\\\\\\\\sin 45^{\circ}=\frac{y}{28}\\\\\frac{1}{\sqrt{2}}=\frac{y}{28}\\\\y=\frac{28}{\sqrt{2}}\\\\\boxed{y=14\sqrt{2}}[/tex]
←
Which equation is represented by the graph below?
-5
oy-ex
40
3
2
-¹11
7 ?T?
3 45 x
The equation that is represented by the graph below is y = e^x - 4.
How to illustrate the graph?From the graph, it can be seen that the only exponential function n to hat intercept the function at equal to 3 is y = e^x - 4.
Let's equate y to 0.
y = e^x - 4.
e^x - 4 = 0
e^x = 4
In(e^x) = In(4)
x = 1.386
The x intercept is located at (1.386, 0).
In conclusion, the correct option is D.
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help me please im in a rush
Answer:
a.1
b. 17
Step-by-step explanation:
So the | | around an equation makes it an absolute value which can be defined as the "distance from zero" or in other words, if a value is positive, it stays positive, and if a value is negative, it becomes positive.
|-8 + 9| = |1| = 1
|-8| + 9 = 8 + 9 = 17
Which of the following is the complete factorization of the polynomial below?
2x² +13x² +17x-12
a
jfjoydx9tdzrzfzixitxxytxixutx
A potato was launched in the air using a potato gun. the function for the situation was h(t) = -16t2 + 100t + 10, where t was the time in seconds and h(t) was the height in feet. (3 points each) a. what was the maximum height of the potato? b. what was the lowest height of the potato? c. what was the lowest time that applies to the actual situation? d. what is the greatest time that applied to the actual situation? e. using your answers to parts a through d, what are the domain and range of the function, as they apply to this situation? use set builder notation.
The answers to all the parts are given below.
To find the answers using a function:The height equation is:
h(t) = - 16t^2 + 100t + 10
A) To find the maximum height, we must find the time where the velocity is 0, so we must derive it with respect to the time.
v(t) = - 2 * 16 * t + 100 = 0
t = 100/(2*16) = 3.125s
Now we put this time in our height equation:
h(3.125s) = -16*3.125^2 + 100*3.125 + 10 = 166.25 ft.
B) The lowest height of the potato will be h = 0ft when the potato hits the ground.
C) the lowest time that works for that function is t = 0s when the potato is fired by the gun.
D) the maximum time can be found when the potato hits the ground, after that point the equation does not work anymore, let's find it,
h(t) = 0 = -16t^2 +100t+10
we can solve it using Bhaskara's equation:
[tex]t=\frac{-100+-\sqrt{100^{2} +4*16*10} }{-2*16} =\frac{-100+-103.2}{-32}[/tex]
So the two solutions are:
t = 6.3s
t = -0.1s
We need to choose the positive time, as we already discussed that the minimum time that works for the equation is t = 0s.
so here the answer is t = 6.3s
E) the domain is 0s ≤ t ≤ 6.3s
The range is 0ft ≤ h ≤ 166.25 ft.
Therefore, the answers to all the parts are shown.
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In 2016, Alberta had about 4.2 million people.
Assuming they follow the same population
growth rate, it is predicted they will have 6.65
million people in 20 years. At what rate is the
province's population growing?
the population of province is growing at the rate of 2.91%
What is the formula of the rate of growth of a population?the formula of the rate of growth of a population =
[(future population- initial population/initial population)*100]/time
population in 2016 = 4.2 milllion = 4200000
Population predicted in 20 years = 6.65 million = 6650000
so, initial population = 4200000
future population = 6650000
rate of growth = {(6650000- 4200000/4200000)*100]/20
= 58.33/20
= 2.91%
the population is growing at the rate of 2.91%
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The function f(x) = 0.11(3)x is reflected over the x-axis to produce function g(x). Function g(x) is then reflected over the y-axis to produce function h(x). Which function represents h(x)?
h(x) = –0.11(3)x
h(x) = 0.11(3)–x
h(x) = 0.11(3)x
h(x) = –0.11(3)–x
Answer:
[tex]h(x)=-0.11(3)^{-x}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=0.11(3)^x[/tex]
Reflection in the x-axis:
When reflecting a function in the x-axis, make the whole function negative:
[tex]\implies g(x)=-f(x)[/tex]
[tex]\implies g(x)=-0.11(3)^x[/tex]
Reflection in the y-axis:
When reflecting a function in the y-axis, make the x variable negative:
[tex]\implies h(x)=g(-x)[/tex]
[tex]\implies h(x)=-0.11(3)^{-x}[/tex]
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Answer:
the answer to this question is d
Step-by-step explanation:
h(x)=-0.11(3)^-x
Apply the distributive property to factor out the greatest common factor 15+21
Jordan is studying whether or not race affects high school graduation in utah. in this example, high school graduation is the?
The high school graduation is the dependent variable.
In this question,
Jordan is studying whether or not race affects high school graduation in utah.
A dependent variable is a variable in an expression that depends on the value of another variable. It is a variable that represents a quantity that changes based on other quantities being manipulated in an experiment. It is the variable being tested, and therefore, it is called the dependent variable.
In the above statement, the high school graduation gets affected by race. So, the the high school graduation is the dependent variable.
Hence we can conclude that the high school graduation is the dependent variable.
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[tex](9x^{2} +9x-4)(9x^{2} +9x-10)-72[/tex]
Quadratic expressions are mathematical expressions that have the power of one of its alphabets being equal to and not more than two. The given expression in the question can be simplified as 81[tex]x^{4}[/tex] + 162[tex]x^{3}[/tex] - 45[tex]x^{2}[/tex] - 54x - 112
Algebraic expressions are mathematical expressions that consist of given number(s) and alphabet(s). When the power (exponential) of one of the alphabets is given as two, then the expression can be classified as a quadratic expression.
Thus the given expansion of the quadratic expression can be simplified as follows:
([tex]9x^{2}[/tex] + 9x - 4)([tex]9x^{2}[/tex] + 9x - 10) - 72
But,
([tex]9x^{2}[/tex] + 9x - 4)([tex]9x^{2}[/tex] + 9x - 10) = [tex]9x^{2}[/tex]([tex]9x^{2}[/tex] + 9x - 10) + 9x([tex]9x^{2}[/tex] + 9x - 10) - 4([tex]9x^{2}[/tex] + 9x - 10)
= 81[tex]x^{4}[/tex] + 81[tex]x^{3}[/tex] - 90[tex]x^{2}[/tex] + 81[tex]x^{3}[/tex] + 81 [tex]x^{2}[/tex] - 90x - 36 [tex]x^{2}[/tex] + 36x - 40
= 81[tex]x^{4}[/tex] + 162[tex]x^{3}[/tex] - 45[tex]x^{2}[/tex] - 54x - 40
So that we have;
(81[tex]x^{4}[/tex] + 162[tex]x^{3}[/tex] - 45[tex]x^{2}[/tex] - 54x - 40) - 72 = 81[tex]x^{4}[/tex] + 162[tex]x^{3}[/tex] - 45[tex]x^{2}[/tex] - 54x - 40 -72
= 81[tex]x^{4}[/tex] + 162[tex]x^{3}[/tex] - 45[tex]x^{2}[/tex] - 54x - 112
Thus the simplification of the given expression is 81[tex]x^{4}[/tex] + 162[tex]x^{3}[/tex] - 45[tex]x^{2}[/tex] - 54x - 112
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The polynomial
f(x) =3x³+ 2x2 + 3x + 6
has *insert answer here*
possible rational roots.
options- 10, 14, 16, 11, 12
I keep getting 6 but that’s not an option lol
The Polynomial Roots are given as follows:
x₁=−1.2085
x₂=0.2709+1.2576i
x₃=0.2709−1.2576i
It is to be noted that the Polynomial 3x³+ 2x2 + 3x + 6 has no real rational roots that can be found using the rational root text. Hence, this was solved using the Qubic Formulas.
What are Polynomial Roots?
The roots (also known as zeroes or solutions) of a polynomial P (x) P(x) P(x) are the x values for which P (x) P(x) P(x) equals zero.
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Answer: 12
Step-by-step explanation:
I got it right
Fatima wants to find the value of sine theta, given cotangent theta = four-sevenths. which identity would be best for fatima to use? cosine theta = startfraction 1 over secant theta endfraction sine squared theta cosine squared theta = 1 cosecant theta = startfraction r over y endfraction
Answer:
Step-by-step explanation:
From the right triangle with cot theta = 4/7 = (adjacent side / opposite side), Fatima can find the length of the hypotenuse using Pythagoras. This gives a value of 8.0823. So cos theta = 4 / 8.0823 = 0,49614,
Then she could find the values of sin theta using
sine squared theta + cos squared theta = 1.
Answer: its D or 1 + cotangent squared theta = cosecant squared theta
Step-by-step explanation:
Which test represents the best choice if you wanted to compare the average mean time to repair (mttr) of your office for the last month to the division’s mttr?
The test that represents the best choice if you wanted to compare the average mean time to repair (mttr) of your office for the last month to the division’s mttr is one sample t-test
The purpose of the one sample t-test is to determine if a sample observations could follow a specific parameter like the mean.
This test is used to determine whether an unknown population mean is different from a specific value.
one sample t-test is used to compare the mean of a single group against that of a known mean.
We wanted to compare the average mean time to repair (mttr) of your office for the last month to the division’s mttr
So this test (one sample t-test ) would be the best choice to compare mttr.
Therefore, the test that represents the best choice if you wanted to compare the average mean time to repair (mttr) of your office for the last month to the division’s mttr is one sample t-test
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What is the range of function g if g (x) = f(x) + 3?
A. (3,00)
B. (-3, 3)
C. (-∞0, ∞0)
D. (-∞0, 3)
Based on the 2009 Kaiser Family Foundation survey, adding up the daily media use figures to obtain a report of weekly media use leads to the staggering number of more than _____ hours a week of media use by 11- to 14-year-olds.
The survey shows that adding up the daily media use figures to obtain a report of weekly media use leads to the staggering number of more than 60 hours a week of media use by 11- to 14-year-olds.
What is a survey?It should be noted that a survey simply means a list of questions that are used to get information about a group.
In this case, the daily media use figures to obtain a report of weekly media use leads to the staggering number of more than 60 hours a week of media use by 11- to 14-year-olds.
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NEED HELP ASAP
Lucy pays $275 in advance on her account at the athletic club. Each time she uses the club, $5 is
deducted from the account. Write a linear function that gives the value remaining in her
account after x visits to the club. Find the value remaining in the account after 11 visits.
Answer:
Step-by-step explanation:
Porfa urgente para hoy
Si triplicamos la cantidad de cada artículo, el subtotal será de 2 940 soles, el impuesto al consumo será de 529,20 soles y el total será de 3 469,20 soles.
¿Cual es el coste total y los impuestos por cambiar la cantidad de artículos comprados?
En esta pregunta tenemos un recibo con una lista de productos, cantidades, precios unitarios y precios de compra, además de un impuesto que se aplica al consumo por concepto de los productos comprados y el total, el cual refleja tanto el subtotal como el concepto por impuestos.
En cuanto a la compra de una determinada cantidad para un artículo, el coste total respectivo es igual a producto del número de artículos por el precio unitario.
El subtotal se determina mediante la suma de los costes totales asociados a cada artículo y luego se le recarga con el impuesto al consumo. Por último, el total de compra es la suma del subtotal y los pagos tributarios.
Si triplicamos el número de cada artículo comprado, tenemos los siguientes costes para cada artículo:
Chompas de dralom
12 / 4 × 280 = 840
Chompas de Orlon
6 / 2 × 100
300
Chompas de lana de alpaca
15 / 5 × 600
1 800
El subtotal es 2 940 soles y el impuesto al consumo es 18 / 100 × 2 940 = 529,20 soles. Por tanto, el total es 3 469,20 soles.
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The number of pollinated flowers as a function of time in days can be represented by the function. f(x)
The average increase in the number of flowers pollinated per day between days 4 and 10 is 39, given that the number of pollinated flowers as a function of time in days can be represented by the function [tex]f(x) = (3)^{\frac{x}{2} }[/tex].
In the question, we are asked for the average increase in the number of flowers pollinated per day between days 4 and 10, given that the number of pollinated flowers as a function of time in days can be represented by the function [tex]f(x) = (3)^{\frac{x}{2} }[/tex].
To find the average increase in the number of flowers pollinated per day between days 4 and 10, we use the formula {f(10) - f(4)}/{10 - 4}.
First, we find the value of the function [tex]f(x) = (3)^{\frac{x}{2} }[/tex], for f(10) and f(4).
[tex]f(x) = (3)^{\frac{x}{2} }\\\Rightarrow f(10) = (3)^{\frac{10}{2} }\\\Rightarrow f(10) = 3^5 = 243[/tex]
[tex]f(x) = (3)^{\frac{x}{2} }\\\Rightarrow f(4) = (3)^{\frac{4}{2} }\\\Rightarrow f(10) = 3^2 = 9[/tex]
Thus, the average increase
= {f(10) - f(4)}/{10 - 4},
= (243 - 9)/(10 - 4),
= 234/6
= 39.
Thus, the average increase in the number of flowers pollinated per day between days 4 and 10 is 39, given that the number of pollinated flowers as a function of time in days can be represented by the function [tex]f(x) = (3)^{\frac{x}{2} }[/tex].
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For complete question, refer to the attachment.
Write [tex]sec^2x[/tex] in two equivalent forms
The two equivalent forms of [tex]sec^2x[/tex] are [tex]\frac{1}{cos^2x}[/tex] and [tex]1+tan^2x[/tex]
Equivalent forms forms of trigonometric expressionsThe given trigonometric expression is:
[tex]sec^2x[/tex]
Note that:
[tex]sec(x)=\frac{1}{cos(x)}[/tex]
Substitute this equivalence to the given expression
[tex]sec^2(x)=\frac{1}{cos^2(x)}[/tex]
Also from [tex]cos^2(x)+sin^2(x)=1[/tex]
Divide through by [tex]cos^2x[/tex]
[tex]\frac{cos^2x}{cos^2x} +\frac{sin^2x}{cos^2x}=\frac{1}{sin^2x}[/tex]
Simplifying the resulting expression:
[tex]1+tan^2x=sec^2x\\\\sec^2x=1+tan^2x[/tex]
Therefore, the two equivalent forms of [tex]sec^2x[/tex] are [tex]\frac{1}{cos^2x}[/tex] and [tex]1+tan^2x[/tex]
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Light travels at a speed of approximately Light travels at a speed of approximately 1,000,000,000 kilometers per second (621,118,012 miles per second). 80,500 kilometers per hour (50,000 mph). 300,000 kilometers per hour (186,336 mph). 300,000 kilometers per second (186,333 miles per second).
The speed of light is 300,000 kilometers per hour. hence option c is correct.
According to the statement
we have to explain that the by how much speed the light travels.
So, Firstly
Light is the natural agent that stimulates sight and makes things visible.
and speed of light means that the distance covered by the light with respect to time.
So, it means those distance which is covered by the light with respect to time is called the speed of light.
The speed of light is measures in km, meters and in other units also.
And we can calculate the speed of light per hour or per minute or in other time measurements.
So, The speed of light is 300,000 kilometers per hour. hence option c is correct.
Learn more about speed of light here https://brainly.com/question/104425
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Write an expression equivalent to the following problems using the fewest number of terms. ( number 1)