The initial-value is x(t)=F0/2w^2 (sin wt-wt cos wt)
An initial-value hassle is a differential equation wherein is an open set of, together with a point within the domain called the initial situation. A technique to an initial cost hassle is a function that is a technique to the differential equation and satisfies.
Inside the discipline of differential equations, preliminary cost trouble (additionally called Cauchy trouble by using a few authors) is a normal differential equation collectively with a detailed fee, called the preliminary situation, of the unknown function at a given factor in the domain of the solution.
In multivariable calculus, an initial-value hassle is a normal differential equation collectively with a preliminary circumstance that specifies the fee of the unknown characteristic at a given factor in the area. Modeling a system in physics or different sciences often amounts to fixing an initial cost problem.
Consider a differential equation x+x=F, sin wt, x(0) = 0,X(0) = 0
Apply Laplace transformation on both sides, and we get
(s²L{x(t)}-sy(0)-y'(0)) + w²L {x(t)} =·
Fow
Fow
(s² + w² ) { x(t)} = 3 + w²
L{x(t)}=
Fow
(5²+w²)²
x(t)=FwL
[(s² + w²)²]
Fow
x(t)=(sin wt-wt coswt)
2w
x(t)=
Fo
wtcos
2w (sin wt-wt cos wt),
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James covers a distance of 8 meters in the first second of a 100 meter race. then, he sprints at a speed of 9 meters per second. how far is james from the finish line 9 seconds after the race has started? a. 11 c. 28 b. 20 d. 80 please select the best answer from the choices provided a b c d
James is (B) 20 meters far from the finish line 9 seconds after the race has started.
What is the distance?Distance is a numerical measurement of the distance between two objects or places. The distance can refer to a physical length or an estimate based on other criteria in physics or common usage. The distance between two points A and B is commonly expressed as |AB|.To find the distance:
James covers 8 meters in the opening second of the 100-meter race.Then he sprints at a 9-meter-per-second pace.We need to figure out how far James is from the finish line 9 seconds after the race begins.James travels 8 meters in the first second.After running 8 meters, the time remaining in 9 seconds is 9 - 1 = 8 seconds.James completes the distance = speed time = 9 8 = 72 meters in another 8 seconds.The total distance traveled in 9 seconds is equal to 8 + 72 = 80 meters.After 9 seconds, the distance remaining in a 100-meter race is 100 - 80 = 20 meters.9 seconds into the race, James is 20 meters from the finish line.Therefore, James is (B) 20 meters far from the finish line 9 seconds after the race has started.
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The complete question is given below:
James covers a distance of 8 meters in the first second of a 100-meter race. Then, he sprints at a speed of 9 meters per second. How far is James from the finish line 9 seconds after the race has started?
a. 11
b. 20
c. 28
d. 80
Use the figure to the right to identify each pair of angles as alternate exterior,
alternate interior, consecutive interior, or corresponding.
7. ∠I and ∠M are corresponding angles.
8. ∠J and ∠P are alternate exterior angles.
9. ∠K and ∠M are alternate interior angles.
10. ∠L and ∠M are consecutive interior angles..
11. ∠I and ∠O are alternate exterior angles.
12. 7. ∠K and ∠O are corresponding angles.
What are Alternate Exterior Angles?Angles that are formed outside the parallel lines that are intersected by a transversal and lie alternate to each other on along the transversal are alternate exterior angles.
What are Alternate Interior Angles?
Angles that are formed inside of the parallel lines that are intersected by a transversal and lie alternate to each other on along the transversal are alternate interior angles.
What are Consecutive Interior Angles?
Angles that are formed inside of the parallel lines that are intersected by a transversal and lie on the same side of the the transversal are consecutive interior angles.
What are Corresponding Angles?
Angles that are formed in relative corner position on each of the parallel lines that are intersected by a transversal and lie along the transversal in the same side are called corresponding angles.
Thus, from the image given, we have the following special angles:
7. ∠I and ∠M are corresponding angles.
8. ∠J and ∠P are alternate exterior angles.
9. ∠K and ∠M are alternate interior angles.
10. ∠L and ∠M are consecutive interior angles..
11. ∠I and ∠O are alternate exterior angles.
12. 7. ∠K and ∠O are corresponding angles.
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The volume of the fish tank needs to be tripled. What scale factor should be applied to the dimensions to produce a fish tank with three times the volume
Answer:
assuming it's a perfect world and that the fish lives in a 1 cubic meter fish tank 1*1.4422 will increase the volume my a factor of 3
Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles
The height of the triangle is 11.3 in. The correct option is C. 11.3 in
Calculating height of triangleFrom the question, we are to determine the height of the given triangle
The height of the given triangle is x in.
Now, we will determine the value of x
In the diagram, we can observe that the height divides the triangle into two equal halves
Thus,
By the Pythagorean theorem, we can write that
12² = x² + 4²
144 = x² + 16
144 - 16 = x²
∴ x² = 144 - 16
x² = 128
x = √128
x = 11.3
Hence, the height of the triangle is 11.3 in. The correct option is C. 11.3 in
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7. Which of these statements is true?
A. 1-(-4)<4- (-2)
B. (-2)(3) > (-1)(-6)
C. 6÷
D.-(5-3)=-5-3
Answer:
A. because 5 < 6. 1-(-4)=5. and 4-(-2) =6
Two students compared the scores on their math tests. Their results on 9 tests are shown in the box plots below.
Which statements are true?
Ben has the smaller range of test scores.
The lower quartile and upper quartile of Nadia’s data are both higher than the lower quartile and upper quartile of Ben’s data.
The median of Nadia’s data is equal to the median of Ben’s data.
Nadia had the highest score on a test.
Ben’s lowest score was equal to Nadia’s lowest score.
The statements which are true regarding the students whose results on 9 tests are as shown are; The median of Nadia's data is equal to the median of Ben's data.
Nadia had the highest score on a test.
Which statements are true regarding the scores on the tests?According to the task content, it follows that the results of the students in discuss are indicated by means of a box plot as in the attached image.
Consequently, it follows from observation that the median of Nadia and Ben as indicated in the attached box plot is 92 in both cases as indicated by the vertical line in both boxes.
Additionally, the highest score by Nadia is 100 while that for Ben is; 99.
Hence, Nadia had the highest score on a test.
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When comparing the f(x) = –x2 + 2x and g(x) = log(2x + 1), on which interval are both functions positive?
(–∞, 0)
(0, 2)
(2, ∞)
(∞, ∞)
Considering their graphs, the interval in which both functions are positive is:
(0, 2)
When are the functions positive?A function is positive when it's graph is positioned above the x-axis.
Looking at the graph, the functions are positive for x between 0 and 2, hence the interval in which both functions are positive is stated as follows:
(0, 2)
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what is 2^c=8 (please help)
Answer:
c=3.
Step-by-step explanation:
∵2*2*2=8,
∴2^3=8.
∵2^c=8,
∴c=3.
Mr. Nero drives to work each day 35 miles one way. If he were in a hurry, could he legally make it to work in less than a half hour with the legal speed limit set to 65 MPH? Reference the formula, d = rt, when explaining the answer.
Answer:
Nope. It would take 32 and 4/13 minutes, which is longer than 30 min.
Step-by-step explanation:
The distance is 35 miles and the speed 65 miles/hour
Dividie the distance by the speed to obtian the time required,
(35 miles)/(65 miles/hour) = 0.538 hours
No, 35 miles at the speed limit of 65 mph would require 0.538 hours, 0.038 hours more than 1/2 hour. 2 and 4/13 minutes more than 30 minutes.
The data set below has a lower quartile of 13 and an upper quartile of 37.
1, 12, 13, 15, 18, 20, 35, 37, 40, 78
Which statement is true about any outliers of the data set?
The dataset 78 is an outlier of the dataset
How to determine the true statement about the outlier?The dataset is given as:
1, 12, 13, 15, 18, 20, 35, 37, 40, 78
Where
Q1 = 13
Q3 = 37
The boundaries of the outliers are given as:
L = Q1 - 1.5 * (Q3 - Q1)
U = Q3 + 1.5 * (Q3 - Q1)
Substitute the known values in the above equation
L = 13 - 1.5 * (37 - 13) = -23
U = 37 + 1.5 * (37 - 13) = 73
This means that the data elements outside the range -23 to 73 are outliers.
78 is outside this range
Hence, 78 is an outlier of the dataset
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What is the 7th term of an AP: 50+45+40
Answer:
20
Step-by-step explanation:
using the arithmetic progress formula
tn=a+(n-1)d
from the series given above a which is your first term is 50
the d which is the common difference.. you minus the first term from the second term which is 45-50=-5
so the 7th term which our n=7
we have:
t7=50+(7-1)(-5)
t7=50+(6)(-5)
t7=50-30
t7=20
Answer:
a₇ = 20
Step-by-step explanation:
the nth term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 50 and d = 45 - 50 = - 5 , then
a₇ = 50 + (6 × - 5) = 50 + (- 30) = 50 - 30 = 20
Which equation can be solved by using this system of equations?
[y=3x5 - 5x³ + 2x² - 10x+4
y=4x4 +6x³-11
the equation that we can solve using the given system of equations is:
3x^5 - 4x^4 - 11x^3 + 2x^2 - 10x + 15 = 0
Which equation can be solved using the given system of equations?
Here we have the system of equations:
y = 3x^5 - 5x^3 + 2x^2 - 10x + 4
y = 4x^4 + 6x^3 - 11
Notice that both x and y should represent the same thing in both equations, then we could write:
3x^5 - 5x^3 + 2x^2 - 10x + 4 = y = 4x^4 + 6x^3 - 11
If we remove the middle part, we get:
3x^5 - 5x^3 + 2x^2 - 10x + 4 = 4x^4 + 6x^3 - 11
Now, this is an equation that only depends on x.
We can simplify it to get:
3x^5 - 4x^4 - 11x^3 + 2x^2 - 10x + 15 = 0
That is the equation that we can solve using the given system of equations.
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what is the Pythagorean theorem
Answer:
a^2+b^2=c^2
Step-by-step explanation:
leg1=a
leg2=b
hypotenuse=c
a^2+b^2=c^2
Answer:
u see this is how the Pythagorean theorem works a^2 + b^2 = c^ i hope this helps have a great day bye please mark as brainliest :D
Step-by-step explanation:
Kamden is a mind-reading alien. He had each friend draw and look at a card, then he guessed whether the card had a star on it.
The two-way frequency table below shows data on guess and true status of the cards the friends drew.
Complete the following two-way table of column relative frequencies.
The completed table will have values filled into it accordingly from left to right and the downwards.
What values are required to complete the table?The concept of relative frequencies involves expressing the frequency of occurrence of events as a fraction of a whole frequency.
Hence, it follows that the blank space on the top-leftmost corner of the table can be filled with the value; 4/5 = 0.8.
For the top-rightmost blank space in the table, the required value is; 2/754 = 0.0027.
For the bottom-leftmost blank space, the required value to fill the table is; 1/5 = 0.2.
For the bottom-rightmost blank space, the required value is; 752/754 = 0.9973.
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What type of construction is illustrated in the figure?
A
The bisection of ∠D
B
A line segment congruent to segment AB
C
An angle congruent to ∠D
D
The bisection of segment BD
Option A is correct. The type of construction that we have here is the bisection of the <D.
What is the bisection of an angle?The bisection of angle can be defined to be the construction of a ray that would help to divide a particular angle into two equal halves.
In this diagram we can see that the angle here is at D. Hence the construction is aimed at dividing this particular angle into 2. Therefore the answer to the question is The bisection of ∠D.
The bisector does the job of creating an equal measure. The given bisector is known to have the midpoint of the segment. It cuts through this angle and creates two different angles that are of the same size.
If we draw the line in that shape, we will be having the division of that angle. From the explanation here, we can see the answer is the first option
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Find the explicit form of the arithmetic function of p if the first term is 12 and the common difference is 2. Then find the seventh term.
The explicit form of the arithmetic function as described is; f(p) = 2(p-1) + 12. and the seventh term is; 24.
What is the seventh term of the arithmetic function?Since it follows from the task content, that the first term is 12 and the common difference is 2.
It therefore follows from convention that the explicit function is; f(p) = 2(p-1) + 12 and by substituting n= 7 into, the equation, we have; f(7) = 24.
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Here are yesterday's high temperatures (in Fahrenheit) in 12 U.S. cities. 48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80 Notice that the temperatures are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary Minimum: Lower quartile: Median: Upper quartile: Maximum: Interquartile range:
The five number summary can be calculated as follows:
lower quartile(Q₁) = 54 + 56 / 2 = 55
Median = 63.5
Upper quartile(Q₃) = 74
Maximum = 80
Interquartile range = Q₃ - Q₁ = 74 - 55 = 19
How to find the five number summary ?The five number summary can be found as follows;
48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80
minimum = 48
lower quartile(Q₁) = 54 + 56 / 2 = 55
The median is the middle number when the data is arranged in ascending or descending order.
Median = 63 + 64 / 2 = 127 / 2 = 63.5
Upper quartile(Q₃)= 74 + 74 / 2 = 148 / 2 = 74
Maximum = 80
Interquartile range = Q₃ - Q₁ = 74 - 55 = 19
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Test the claim that the proportion of people who own cats is larger than 60 t the 0. 10 significance level?
The null hypothesis to test the claim that the proportion of people who owns cats is larger than 60% of the significance level is [tex]H_{0}[/tex]:μ<0.06.
Given that the significance level is 0.10.
We are required to form the null hypothesis to test the claim that the proportion of people who owns cats is larger than 60% the significance level.
Hypothesis is a statement which is tested for its validity. Null hypothesis is the statement which is accepted or not by z test,t test,f test ,chi-square test or any other test.
We have to take opposite of the statement to form a null hypothesis. Since we have to check whether the proportion of people who owns cats is larger than 60% of the significance level, we have to assume that it is smaller than 60% of the significance level.
60% of the significance level=0.60*0.10=0.06.
Null hypothesis is [tex]H_{0}[/tex]:μ<0.06
Hence the null hypothesis to test the claim that the proportion of people who owns cats is larger than 60% of the significance level is [tex]H_{0}[/tex]:μ<0.06.
Question is incomplete.The question should include the following:
Find the null hypothesis for the testing.
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1/?
Which number produces a rational number when Multiplied 1/5
Answer:
-2/3
Step-by-step explanation:
A rational number is a number that can be expressed as a fraction so when you add 2 fractions it’s a rational number
A substance decays so that the amount a of the substance left after t years is given by: a = a0 • (0.7)t, where a0 is the original amount of the substance. what is the half-life (the amount of time that it takes to decay to half the original amount) of this substance, rounded to the nearest tenth of a year?
The half-life of the substance is 1.94 years.
What is exponential decay formula?The exponential decay formula aids in determining the exponential drop, which is a rapid reduction over time. To calculate population decay, half-life, radioactivity decay, and other phenomena, one uses the exponential decay formula. F(x) = a [tex](1-r)^{x}[/tex] is the general form.
Here
a = the initial amount of substance
1-r is the decay rate
x = time span
The correct form of the equation is given as:
[tex]a=a_{0}[/tex]×[tex](0.7)^{t}[/tex]
where t is an exponent of 0.7 since this is an exponential decay of 1st order reaction
Now to solve for the half life, this is the time t in which the amount left is half of the original amount, therefore that is when:
a = 0.5 a0
Substituting this into the equation:
0.5 [tex]a_{0}=a_{0}[/tex]×[tex](0.7)^{t}[/tex]
0.5 = [tex](0.7)^{t}[/tex]
Taking the log of both sides:
t log 0.7 = log 0.5
t = log 0.5 / log 0.7
t = 1.94 years
The half life of the substance is 1.94 years.
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If 12 oz. of sausage contains 300 calories, how many calories w ould 7 oz, contain? how would i write a formula
Answer:
175 cal
Step-by-step explanation:
if 12oz = 300 cal
then, 7 oz = ?
cross multiplication
12×?= 7×300
? = 2100/12
? = 175 cal
NB: you can replace the question mark with any variable.
Last week a painter painted 6 houses in 2 days. this week she painted 5 houses in 4 days. in which week was the painter more productive?
Answer:
The painter was more productive in week a.
Step-by-step explanation:
Find the unit rate. How many houses could be painted in 1 day?
6/2 means that she could paint 3 houses per day
5/4 means that she could paint 1.25 houses per day.
The painter was more productive in the last week.
Explanation:In this problem, we need to find in which week did the painter paint the most.
To find the solution to this problem, first, we need to divide 6 by 2 (last week)
which equals 3.
Next, divide 5 by 4 (this week)
which equals 1.25
Now, compare the two quotients and identify the larger number (3 and 1.25).
Basically, we can see that the number 3 is larger.
This means that the painter could paint 3 houses per day in the last week, and 1.25 houses per day in this week.
Therefore, we can say that the painter was more productive in the last week.
I hope this helps :)
johns first three test scores out of 100 are 84,78,82. what did he score on his fourth test if the average for all four tests is 80 out of 100
Answer:
76
Step-by-step explanation:
Formula
[tex]\sf Average=\dfrac{\textsf{sum of all the numbers}}{\textsf{amount of numbers}}[/tex]
Given values:
First three test scores: 84, 78 and 82Total number of tests = 4Average score for all four tests = 80Let x be the score of the fourth test.
To find the score of the fourth test, substitute the given values into the formula and solve for x:
[tex]\begin{aligned} \sf Average & =\dfrac{\textsf{sum of all the numbers}}{\textsf{amount of numbers}}\\\\\implies \sf 80 & = \sf \dfrac{84+78+82+x}{4}\\\sf 80 & = \sf \dfrac{244+x}{4}\\\sf 80 \cdot 4 & = \sf 244 + x \\\sf 320 & = \sf 244 + x\\\implies \sf x & = \sf 320 - 244\\& = \sf 76\end{aligned}[/tex]
Therefore, John scored 76 on his fourth test.
If a 650-cm leader is placed against a building at a certain angle, it just reaches a point on the building that is 520 cm above the ground. If the ladder is moved to reach a point 80 cm higher up, how much closer will the foot of the ladder be to the building
Answer:
140 cm
Step-by-step explanation:
The distance of the foot of the ladder from the building can be found using the Pythagorean theorem (or your knowledge of Pythagorean triples). Once the two distances are found, their difference can be found.
Position 1The 650 cm ladder reaches 520 cm up the side of the building. The ratio of these side lengths is 650/520 = 5/4, suggesting these are the sides of a 3-4-5 right triangle. The distance from the building is ...
(3/5)×650 cm = 390 cm.
Alternatively, the distance (a) from the building can be found using the Pythagorean relation ...
a² +b² = c²
a² +520² = 650²
a = √(422500 -270400) = √152100 = 390 . . . cm
Position 2The 650 cm ladder reaches 520 +80 = 600 cm up the side of the building. The ratio of these side lengths is 650/600 = 13/12, suggesting these are the sides of a 5-12-13 right triangle. The distance from the building is ...
(5/13)×650 cm = 250 cm
Again, the Pythagorean theorem can be used to obtain the same result:
a = √(422500 -360000) = √62500 = 250 . . . cm
DifferenceThe difference between the two distances is ...
390 cm -250 cm = 140 cm
The foot of the ladder will be 140 cm closer to the building.
What expression represents the volume of the prism, in cubic units? one-halfx3 one-halfx2 x 2x3 2x2 x
Volume of prism = [tex]\frac{1}{2x^{3} } + x^{2}[/tex]
Given that:
The oblique prism below has an isosceles right triangle base and the length of the base is x
=> the area of the base: [tex]\frac{1}{2}[/tex] × x × x = [tex]\frac{1}{2}[/tex]
The vertical height of the prism is (x + 2)
=> The volume of the oblique prism is:
V = the base area * the vertical height
<=> V = [tex]\frac{1}{2}[/tex] [tex]x^{2}[/tex] (x + 2)
<=> V = [tex]\frac{1}{2x^{3} } + x^{2}[/tex]
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Hurry A total of $6000 is invested: part at 5% and the remainder at 10%. How much is invested at each rate if the annual interest is $510?
Answer:
Step-by-step explanation:
We know a total of 6000 is being turned into 510, in two accounts which equal to 15%, to find how much is in each account we can create the following equation:
[tex]5x+10x=510[/tex]
Solve for x
[tex]15x=510\\x=34[/tex]
Now multiply x by the corresponding percentages to find how much was invested into each percentage.
[tex]34*5=170[/tex]
[tex]34*10=340[/tex]
Therefore we now know that 170 dollars was invested into the 5% division, and 340 dollars was invested into the 10% division.
We can of course check our answer by adding 170+340 which equals our original investment of 510.
$1800 is invested at 5% and the remainder, $4200, is invested at 10%.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Let us consider the amount invested at 5% x.
The amount invested at 10% is then the remainder, which is:
$6000 - x
Now we can set up an equation for the total interest earned:
0.05x + 0.10($6000 - x) = $510
Simplifying and solving for x:
0.05x + $600 - 0.10x = $510
-0.05x + $600 = $510
-0.05x = -$90
Divide both sides by 0.05
x = $1800
Hence, $1800 is invested at 5% and the remainder, $4200, is invested at 10%.
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If the graph of a budget function has an x-intercept at 2 and the y-intercept at 5, name two ordered pairs that would fall on this line.
(2, 0) (0, 5)
(0, 2) (5, 0)
(2, 0) (2, 5)
(0, 2) (2, 5)
Based on the graph of the budget function with the x-intercept and the y-intercept, the two ordered pairs that would fall on this line are (2, 0) (0, 5).
What points fall on this line?The x-intercept is the point on the graph where the budget function would cross the x-intercept.
At this point, the value of y would be 0 because the x-axis intersects the y-axis at y = 0.
An x-intercept of 2 would therefore have the point, (2,0).
The y-intercept would be the point where the y axis is crossed. At this point, x will be zero because the y-axis intercepts the x-axis at the value, x = 0.
A y-intercept of 5 would therefore yield a point of (0, 5).
In conclusion, option A is correct.
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define ratio (maths short definition)
Answer:
division
Step-by-step explanation:
ratio compares 2 numbers by dividing them
example
2 out of 3 dentists like gum
2 ÷ 3 = .67 = 67%
so you can say
67% of dentists like gum
A ratio can be defined as the relationship or comparison between two numbers of the same unit to check how bigger is one number than the other one. For example, if the number of marks scored in a test is 7 out of 10, then the ratio of marks obtained to the total number of marks is written as 7:10.
Which expression is equivalent to RootIndex 4 StartRoot StartFraction 24 x Superscript 6 Baseline y Over 128 x Superscript 4 Baseline y Superscript 5 Baseline EndFraction EndRoot? Assume x not-equals 0 and y
The expression [tex]\sqrt[4]{\frac{24x^6y}{128x^4y^5} }[/tex] is equivalent to the expression [tex]\frac{\sqrt[4]{3x^2}}{2y}[/tex]
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
Given the expression:
[tex]\sqrt[4]{\frac{24x^6y}{128x^4y^5} }\\ \\Simplifying:\\\\=\frac{\sqrt[4]{3x^2}}{2y}[/tex]
The expression [tex]\sqrt[4]{\frac{24x^6y}{128x^4y^5} }[/tex] is equivalent to the expression [tex]\frac{\sqrt[4]{3x^2}}{2y}[/tex]
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Answer:
The answer is D
Step-by-step explanation:
Please help me solve!
Answer:
Step-by-step explanation:
Comment
There are a number of ways of doing this problem. I don't know which method you are intended to use. One sure way in this case is graphing the equation, I have done this for you. See below. The maximum volume occurs where x = 2
The graph shows that there is a peak at x = 2. That is where the maximum volume is,
Answer
x = 2
