The length of the function x = 2y is 2√5 units
According to the given question.
We have a function
x = 2y
Since, we know that the length of the function in the interval [a, b] is given by
l = [tex]\int\limits^a_b\sqrt{1+(\frac{dx}{dy}) ^{2} } \,dy[/tex]
Where, l is the length of the function.
Now, differentiating the given function x = 2y w.r.t y.
Therefore,
dx/dy = 2
So, the length of the given function x = 2y from y = -1 to y = 1 is given by
l = [tex]\int\limits^1_{-1}{\sqrt{1+2^{2} } } \,dy[/tex]
⇒ l = [tex]\int\limits^1_{-1} {\sqrt{1+4} } \,dy[/tex]
⇒ l = [tex]\int\limits^1_{-1}{\sqrt{5} } \,dy[/tex]
⇒ l = √5[1 - (-1)]
⇒ l = √5(2)
⇒ l = 2√5
Hence, the length of the function x = 2y is 2√5 units.
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Seven is not an example of _____.
an expression
a term
a variable
a constant
Answer:
a variable.
Seven is a number and cannot be a variable.
Which point is the circumcenter of the triangle?
A) E
B) G
C) F
D) D
Answer: Point D
Reason:
The circumcenter is found by intersecting the perpendicular bisectors of each segment of the triangle.
As you can see, the circumcenter is the center of the circumcircle. This special circle is the smallest possible that wraps the triangle so to speak. The vertices of the triangle are on the circle. The distances AD, BD and CD are all the same.
Use the laplace transform to solve the given initial-value problem. y'' − 8y' 16y = t, y(0) = 0, y'(0) = 1
If the initial value problem is [tex]y^{11} -8y^{1} -15y=0[/tex] and [tex]y^{1}(0) =1[/tex],y(0)=0 then y(t)=[tex](e^{3t} -e^{5t} )/2[/tex].
Given the initial value problem be [tex]y^{11} -8y^{1} -15y=0[/tex]and [tex]y^{1}(0) =1[/tex],y(0)=0.
We are required to find the solution of the given initial value problem.
Laplace transform is an integral transformation that converts a function of a real variable to a function of a complex variable.
Take laplace on the DE, we get
[tex]s^{2}-sY(0)-y^{i}(0)-8[sY(s)-y(0)-15Y(s)]=0[/tex]
[tex]s^{2}Y(s)-s(0)-1-8{sY(s)-0)}+15Y(s)=0[/tex]
(Putting the values given in question)
Y(s)=([tex]s^{2} -8s+15)-1=0[/tex]
Y(s)=1/([tex]s^{2} -8s+15[/tex])
Simplifying the above:
=1/([tex]s^{2} -5s-3s+15)[/tex]
=1/[s(s-5)-3(s-5)]
=1/2 [1/(s-3)-1/(s-5)]
Taking inverse of the above we get,
y(t)=[tex](e^{3t} -e^{5t} )/2[/tex]
Hence if the initial value problem is [tex]y^{11} -8y^{1} -15y=0[/tex] and [tex]y^{1}(0) =1[/tex],y(0)=0 then y(t)=[tex](e^{3t} -e^{5t} )/2[/tex].
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-2x + 7x +34 = -2(1-7x)
[tex]\boldsymbol{\sf{-2x + 7x +34 = -2(1-7x) \ \ \longmapsto \ \ [Add \ -2x+7x]}}[/tex]
[tex]\boldsymbol{\sf{5x+34=-2(1-7x)}}[/tex]
Use the distributive property to multiply −2 by 1−7x.
[tex]\boldsymbol{\sf{5x+34=-2+14x}}[/tex]
Subtract 14x on both sides.
[tex]\boldsymbol{\sf{5x+34-14x=-2}}[/tex]
Combine 5x and −14x to get −9x.
[tex]\boldsymbol{\sf{-9x+34=-2 }}[/tex]
Subtract 34 from both sides.
[tex]\boldsymbol{\sf{-9x=-2-34 \ \ \longmapsto \ \ \ [Subtract] }}[/tex]
[tex]\boldsymbol{\sf{-9x=-36}}[/tex]
Divide both sides by −9.
[tex]\boldsymbol{\sf{x=\dfrac{-36}{-9} \ \ \longmapsto \ \ [Split] }}[/tex]
[tex]\red{\boxed{\boldsymbol{\sf{\blue{Answer \ \ \longmapsto \ \ x=4 }}}}}[/tex]
[tex] \quad\quad\quad \huge \underline{ \tt{ANSWER}}[/tex]
[tex]\quad\quad\quad\quad\quad\quad[/tex]
[tex]\tt{- 2x + 7x + 34 = - 2(1 - 7x)}[/tex]
[tex]\tt{5x + 34 = - 2(- 7x + 1)}[/tex]
[tex]\tt{5x + 34 = - (- 2 * 7x + 2)}[/tex]
[tex]\tt{5x + 34 = - (- 14x + 2)}[/tex]
[tex]\tt{(5x + 34) + (- 34 - 14x) = (14x - 2) + (- 34 - 14x)}[/tex]
[tex]\tt{5x + 34 - 34 - 14x = 14x - 2 - 34 - 14x}[/tex]
[tex]\tt{5x - 14x + 34 - 34 =14x-14x-2 - 34}[/tex]
[tex]\tt{- 9x = - 36}[/tex]
[tex]\tt{\frac{9x}{9} = \frac{36}{9}}[/tex]
[tex]\tt{x = 4}[/tex]
Can someone please help me with these problems and show work, if the answer isn’t with work I will remove your comment and you won’t get the points, please help
m∠B = 57.52°, m∠B = 70.8°, AB = 46.03 km and AC = 39.08 ft. This can be obtained using the Laws of cosine formula and Laws of sine formula.
Find the required angles and sides:Laws of cosine formula,In a triangle ABC,
⇒ a² = b² + c² - 2bc cos A
⇒ b² = a² + c² - 2ac cos B
⇒ c² = a² + b² - 2ab cos C
where a, b and c are sides of a triangle and A, B and C are the angles of a triangle.
Laws of sine formula,In a triangle ABC,
⇒ [tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]
where a, b and c are sides of a triangle and A, B and C are the angles of a triangle.
In the question we can use the laws of cosine formula and laws of sine formula,
5) Given that,
AB = c = 13 km
AC = b = 21 km
m∠A = 91°
By using Laws of cosine formula,
⇒ a² = b² + c² - 2bc cos A
a² = 21² + 13² - 2(21)(13) cos 91°
a² = 441 + 169 - 546 (-0.0174524064)
a² = 610 + 9.52901391 = 619.529014
⇒ a = 24.89 km
By using Laws of sine formula,
⇒ [tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]
sin 91°/24.89 = sin B/21
sin B = 0.999847695×21/24.89 = 0.843583833
⇒ m∠B = 57.52°
6) Given that,
AB = c = 11 cm
BC = a = 13 cm
AC = b = 14 cm
By using Laws of cosine formula,
⇒ b² = a² + c² - 2ac cos B
14² = 13² + 11² - 2(13)(11) cos B
196 = 169 + 121 - 286 cos B
196 = 290 - 286 cos B
cos B = 94/286
cos B = 0.328671329
⇒ m∠B = 70.8°
7) Given that,
AC = b = 24 km
BC = a = 26 km
m∠C = 134°
By using Laws of cosine formula,
⇒ c² = a² + b² - 2ab cos C
c² = 26² + 24² - 2(26)(24) cos 134°
c² = 676 + 576 - 1248 (-0.69465837)
c² = 1252 + 866.933646 = 2118.93365
⇒ AB = c = 46.03 km
8) Given that,
AB = c = 26 ft
BC = a = 21 ft
m∠B = 112°
By using Laws of cosine formula,
⇒ b² = a² + c² - 2ac cos B
b² = 21² + 26² - 2(21)(26) cos 112°
b² = 441 + 676 - 1096 (-0.374606593)
b² = 1117 + 410.568826 = 1527.56883
⇒ AC = b = 39.08 ft
Hence m∠B = 57.52°, m∠B = 70.8°, AB = 46.03 km and AC = 39.08 ft.
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Please help!! Which figures demonstrate a single translation?
Select each correct answer.
Answer:
the top 2 and the left bottom corner
Step-by-step explanation:
the first one in the first row is a reflection
the second one in the first row is a rotation
the one on the left bottom corner just moved a unit
Answer:
Option 3
Step-by-step explanation:
The first answer is a reflection across the y-axis, the second is a rotation, and the last one is two translations. So, the third one is correct because it's the only single translation.
Need help ASAP! This is due in an hour and this is the last question!!!
the equation with these solutions is:
0 = x^2 - 6x + 6
How to find an equation with the given solutions?
Remember that a quadratic equation with the solutions a and b is written as:
0 = (x - a)*(x - b)
Here we have the solutions:
x = 3 + √3x = 3 - √3Then we can write a quadratic equation of the form:
0 = (x - (3 + √3) )*(x - (3 - √3) )
0 = (x - 3 - √3)*(x - 3 + √3)
Expanding that, we get:
0 = x^2 - 6x + 9 - 3
0 = x^2 - 6x + 6
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As of 2018, approximately what percentage of americans rely upon television broadcasts for their news?
More than 50% of Americans rely upon television broadcasts for their news.
News, current occasions and ancient programming can help make younger humans extra aware of other cultures and those. Documentaries can help increase vital thinking about society and the arena. television can help introduce teens to classic Hollywood movies and overseas movies that they might not otherwise see.
It broadens the know-how of various cultures, and promotes tolerance and international information of worldwide issues. Through contemporary affairs, discovery, lifestyle, cooking indicates and children's programs, television encourages medical and cultural interest.
Agree with and effect: television is the most relied on a form of marketing and stays maximumly probable to make consumers chortle, circulate them to tears or cause feelings. For example, television is with the aid of a long way the maximum relied on shape of video advertising in Canada. 70% of 18-34-year-olds named tv the most truthful compared to 12% for online video.
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Consider these situations. in each situation, is the demand for the good elastic or inelastic? as the price of flat-screen televisions decreases, the quantity demanded increases significantly. as the price of bread decreases, the quantity demanded changes only slightly. as the price of a drug used to treat heart disease increases, the quantity demanded remains unchanged.
Answer:
Step-by-step explanation:
elastic, inelastic, inelastic
Answer: elastic, inelastic, inelastic
Step-by-step explanation:
A.22
B.183
C.246
D.213
Answer:
NMK= 22
Step-by-step explanation:
From N to K equals 177.
N to M equals x
K to M equals to 107
L equals 35
35 177
x 107
it equals to 21.158
Round up to the nearest ones or whole number
3. Choose the two correct transformations for:
Ay
T
R'
RSTU to R'S'T'U'.
S'
A Rotation 180°clockwise
B Reflection across y = x
OC Reflection across y = -x
OD Rotation 180°counterclockwise
My street hockey team plays three games each week. My team lost all 12 games in the first four weeks. Then, my team won two games and lost one game in the fifth week, bringing our record to 2 wins and 13 losses. Each week after that, my team won two games and lost one game. My team first wins at least 50% of all its games by the end of the first n weeks. What is n?
Using proportions, it is found that the value of n is of [tex]n \geq 11[/tex].
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
On the first 15 games, the team wins 2 games and losses 13. Then, in each week, the team plays 3 games, winning 2. Then:
After n weeks, the team will have won 2 + 2n games.After n weeks, the team will have played 15 + 3n games.The proportion of wins is given as follows:
[tex]\frac{2 + 2n}{15 + 3n}[/tex]
The proportion is of at least 50%, hence:
[tex]\frac{2 + 2n}{15 + 3n} \geq 0.5[/tex]
We solve the inequality for n, similarly to how we would solve an equality, applying cross multiplication. Then:
[tex]2 + 2n \geq 7.5 + 1.5n[/tex]
[tex]0.5n \geq 5.5[/tex]
[tex]n \geq \frac{5.5}{0.5}[/tex]
[tex]n \geq 11[/tex]
The value of n is of [tex]n \geq 11[/tex].
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A right triangle has side lengths 4 units, 5 units, and x units. It is unknown if the missing length is the longest or shortest side.
Rounded to the nearest tenth, what is the difference between the possible values of x?
3.0 units
3.4 units
6.4 units
8.0 units
Answer: B
Step-by-step explanation:
Answer:
3.4 units
Step-by-step explanation:
Pls answer I’ll mark brainliest if first person is correct
Based on these data, it is better to describe the centers of distribution in terms of: B. median for both coffee shops because the data distribution is not symmetric.
What is a median?A median can be defined as the middle number (center) of a sorted data set, which is typically when the data set is arranged in from the least to greatest or the greatest to least.
In Mathematics, the median of a data set is generally considered to be a better measure of center than the mean when there's an outlier in the data set.
Next, we would calculate the mean and median for the two coffee shops as follows.
For coffee shop A, we have:
Mean = [F(x)]/n
Mean = [12+15+33+45+46+51+52+57]/8
Mean = [311]/8
Mean = 38.875.
Median = (45+46)/2
Median = 91/2
Median = 45.5.
For coffee shop B, we have:
Mean = [F(x)]/n
Mean = [17+16+36+35+12+9+34+15]/8
Mean = [174]/8
Mean = 21.75.
Median = (16+17)/2
Median = 33/2
Median = 16.5.
Since both the mean and median are not close, we can infer and logically deduce that the data distribution isn't symmetric for both coffee shops A and B.
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Wilma worked 38 hours 52 minutes last week. She earns $25.15 per hour. What is Wilma's pay for this work period? Round your answer to the nearest hundredth..
The total pay for hours worked is $980.013
Calculating total pay for the work hours?
The method with which a daily worker's wage is being paid is by calculating the total hours worked and multiplying it with the fixed hourly pay.
From the information given:
Wilma worked for = 38 hours 52 minutesIn hours, we have:
= (38 + 0.9667) hours
= 38.9667 hours
If a fixed hourly pay of $25.15 is being paid, we have:
= $(38.9667 × 25.15)
= $980.012505
= $980.013 to the nearest hundredth.
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Compare and contrast dot plots and histograms. Make a list of the benefits and downsides of each.
A dot plot displays the individual data values and a histogram displays data ranges along the x-axis and uses rectangular bars to show the frequencies of values that fall into each range.
How to illustrate the information?It should be noted that dot plots, histograms, and box plots are all common graphical ways to represent data sets.
The dot plot represents data by placing a dot for each data point. Also, the histogram groups the data into ranges and then plots the frequency that data occurs in each range.
The similarities is that the dot plot and the histogram can more easily tell us the mode of our data set. A dot plot gives you a visual idea of your data, but histogram gives you additional information.
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10) James earned $3,000 interest
on an investment that he put in
the bank for 6 years with a 5%
interest rate. How much was his
initial deposit?
Answer:
Step-by-step explanation:
assuming that he has an annual interest of 5% then his initial deposit would be rounded to $2,238.65
20 POINTS
Here are the scores of 18 students on a history test. 55, 57, 58, 61, 62, 66, 68, 68, 71, 75, 75, 78, 82, 83, 85, 86, 88, 89. Notice that the scores are ordered from least to greatest. Make a box-and-whisker plot for the data.
The median of this box and whisker plot is 73
A box and whisker plot is defined as a graphical method of displaying variation in a set of data. In most cases, a histogram analysis provides a sufficient display, but a box and whisker plot can provide additional detail while allowing multiple sets of data to be displayed in the same graph. Box and whisker plots are very effective and easy to read, as they can summarize data from multiple sources and display the results in a single graph. Box and whisker plots allow for comparison of data from different categories for easier, more effective decision-making.
From the given data, following can be inferred
Population size: 18Median: 73Minimum: 55Maximum: 89First quartile: 61.75Third quartile: 83.5Interquartile Range: 21.75which is demonstrated in the box and whisker plot below
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The motion of an object was recorded by measuring the velocity of the object in meters per second at various times, as shown in the table. The scatterplot below was graphed from the data in the table, where t represents the time, and v represents the velocity.
Based on the scatterplot, which equation BEST represents the relationship between velocity and time?
The regression equation that represents the relationship between velocity and time is:
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
For this problem, the points (t,v), that is, time and velocity, are given as follows:
(0, 6.1), (2.1, 12.2), (5.3, 17.4), (8.2, 26.4), (10, 28.1), (12.1, 32.8).
Hence, inserting these points into a calculator, the equation is given by:
v = 2.19t + 6.7.
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Given these facts, determine how many cans of paint you would need to buy to paint 2 walls.
1st wall: 20 ft. x 8ft.
2nd wall: 40ft. x 8ft.
1 can will cover 200 square feet of wall.
Answer:
3 cans
Step-by-step explanation:
A = lw
a = 20 x 8 = 160[tex]ft^{2}[/tex]
a = 40 x 8 = 320 [tex]ft^{2}[/tex]
Together this is 480 [tex]ft^{2}[/tex]
I would need 3 cans.
Which property is shown in the following statement?
(46 + 17) + 3 = 46 + (17 + 3)
associative property of addition
commutative property of addition
identity property of addition
Answer:
Associative property of addition.
Step-by-step explanation:
The location of the parentheses makes no difference to the sum of these numbers.
The property shown in the statement "(46 + 17) + 3 = 46 + (17 + 3)" is the associative property of addition.
The associative property of addition states that when adding three or more numbers, the grouping of the numbers does not affect the sum
In the given statement, we have three numbers being added: 46, 17, and 3. The statement shows that the addition is grouped differently on each side of the equation, but the result is the same.
On the left side, we have (46 + 17) + 3.
This means we first add 46 and 17, which equals 63. Then we add 3 to the sum, resulting in 66.
On the right side, we have 46 + (17 + 3). Here, we first add 17 and 3, which equals 20. Then we add 46 to the sum, also resulting in 66.
As we can see, no matter how we group the numbers being added, the final sum is the same. This demonstrates the associative property of addition.
Therefore, the property shown in the given statement is the associative property of addition.
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Find the circumference of a circle with radius of 4.2in.
Answer: 26.39
Step-by-step explanation:
2xπxr
In the figure below, angle y and angle x form vertical angles. Angle y forms a straight line with the 60° angle and the 70° angle. A straight line is shown and is marked with three angles. The first angle measures 60 degrees. The second angle measures 60 degrees. The third angle is labeled y. The line between the 70 degree angle and angle y extends below the straight line. The angle formed is labeled angle x. Write and solve an equation to determine the measure of angle x.
The equation that solve for x is as follows;
70 + 60 + x = 180
How to find an angle?The equation that can be used to find the measure of angle x can be found as follows:
60 + 70 + y = 180
Therefore,
130 + y = 180
subtract 130 from both sides
130 - 130 + y = 180 - 130
y = 50°
70 + 60 + x = 180
130 + x = 180
x = 180 - 130
x = 50°
x and y are vertically opposite angles.
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5. During the season, the Rangers played 25 games. They won 14 of the games.
What fraction and percent of the games did they lose? Show your work in the
space below. Remember to check your solution.
suppose that a 2 by 10 rectangular grid of seats is filled with people. On the
blow of a whistle, all 20 people get up from their current seat and move to an orthogonally
adjacent seat. How many ways are there for everyone to do this so that at the end of the
move, each seat is taken by exactly one person?
There are 20! number of ways for everyone to do this so that at the end of the move, each seat is taken by exactly one person.
People are seated in a 2 by 10 rectangle grid. All 20 persons stand up from their seats and relocate to an orthogonally neighboring one upon the blowing of a whistle.
Now, we have to find the number of possible ways in which each seat is taken up by exactly one person after the move.
As the number of people is 20 and 20 seats are to filled exactly once.
So, the number of ways = 20!
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What is the value of y?
Enter your answer in the box.
y =
Answer:
64°
Step-by-step explanation:
This is a question on angle properties.
Angle y + 37 + 79 = 180 (Sum of angles in a triangle)
Angle y + 116 = 180
Angle y = 180 - 116 = 64°
Carmen has taken out a loan for $800 to buy a car. she plans to pay back the loan at a rate of $40 per month. ramona has borrowed $500 to buy a car, which she plans to pay back at a rate of $20 per month. how long will it take ramona to pay back her loan? a. 25 months b. 20 months c. 15 months d. 10 months please select the best answer from the choices provided a b c d
Answer:a
Step-by-step explanation: 20 x 25=500
which function describes this table of value x -8, -4, 4, 8, y -2, 0, 4, 6
we conclude that the linear equation represented by the given table is:
y = (1/2)*x + 2
Which function is the one described by the table?A general linear equation is given by:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through (x₁, y₁) and (x₂, y₂), then the slope is given by:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we can use just the first two points on the given line:
(-8, -2) and (-4, 0)
Then the slope will be:
[tex]a = \frac{0 - (-2)}{-4 -(-8)} = \frac{2}{4} = \frac{1}{2}[/tex]
Then the linear equation is something like:
y = (1/2)*x + b
To find the value of b, we can use one of the two given points, I will use (-4, 0), then:
0 = (1/2)*(-4) + b
0 = -2 + b
2 = b
Then we conclude that the linear equation represented by the given table is:
y = (1/2)*x + 2
Then the correct option is the first one.
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The volume of a cylindrical can of beans is 45 π cubic centimeters. if the diameter is 6 centimeters, what is the height of the can in centimeters?
Answer:
h = 5 cm
Step-by-step explanation:
Givens
d = 6cm
V = 45cubic cm
Formula
V = pi * r^2 h substitute values into the formula
Solution
d = 2*r
6 = 2*r Divide both sides by 2
6/2 = 2r / 2
3 = r
45 pi cm^3 = pi * (3)^2 * h Divide both sides by pi
45 pi/pi = pi * 9 * h / pi
45 = 9h Divide both sides by 4
45/4 = 9h/9
5 cm
How many different anagrams (including nonsensical words) can be made from the letters in the word statistics, using all the letters?
50,400 different anagrams can be made from the letters in the word statistics.
Given word : STATISTICS
Anagrams are words formed by jumbling the positions of the letters given in the word.
For such problems we do factorial of number of words and divide by the repeated letters factorials.
Total number of letters = 10
They can be permutated among themselves in 10! ways.
Some letters are repeated in word STATISTICS
Since, there are 3 S's and 3 T's and 2 I's
So, Number of anagrams = [tex]\frac{10!}{3!.3!.2!}[/tex]
= [tex]\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3!}{3! \times 3 \times 2 \times 1 \times 2 \times 1}[/tex]
= [tex]\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4}{3 \times 2 \times 2}[/tex]
= 10 × 9 × 8 × 7 × 2 × 5
= 50,400
50,400 different anagrams can be made from the letters in the word statistics.
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