The bar graph in the following graphic represents fictional net exports in billions of dollars for five countries.
Net exports are obtained by subtracting total imports from total exports; a negative net export means the
country imported more goods than it exported.
Net Exports (Billions of dollars)
United States
Denmark
China
Germany
Spain
-150 -100
-50
Net Exports (Billions of dollars)
What is the sum of net exports for Germany and China ?
a.
-80 billion dollars
b. 180 billion dollars
0 50 100 150
C. 90 billion dollars
d. 150 billion dollars
[tex]80[/tex] billion dollars' worth of net exports were made by China and Germany. The first claim is accurate.
What do the terms "export" and "import" mean?Export is the process of supplying goods and services to some other nation. Contrarily, importing is the act of acquiring goods from outside and transferring them into one's own nation.
What does GDP export mean?The domestic product (GDP) is a measure of all the products and services generated in the United States; thus, changes in exports change significantly in the demand for goods and services made in the United States abroad.
The total of China's and Germany's net exports would be:
[tex]50[/tex] billion + [tex]30[/tex] billion [tex]= 80[/tex] billion
As a result, Germany & China's consolidated net exports amounted to [tex]80[/tex] billion u.s. dollars, reflecting answer option (a).
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Oliver's normal rate of pay is $10.40 an hour.
How much is he paid for working 5 hours overtime one Saturday at time-and-a-half?
A simple random sample of size n is drawn. The sample mean, x, is found to be 18.1, and the sample standard deviation, s, is found to be 4.1.
(a) Construct a 95% confidence interval about u if the sample size, n, is 34.
Lower bound: Upper bound:
(Use ascending order. Round to two decimal places as needed.)
In response to the stated question, we may state that Hence, the 95% CI function for u is (16.72, 19.48), rounded to two decimal places in increasing order.
what is function?In mathematics, a function is a connection between two sets of numbers in which each member of the first set (known as the domain) corresponds to a single element in the second set (called the range). In other words, a function takes inputs from one set and produces outputs from another. Inputs are commonly represented by the variable x, whereas outputs are represented by the variable y. A function can be described using an equation or a graph. The equation y = 2x + 1 represents a linear function in which each value of x yields a distinct value of y.v
We use the following formula to create a confidence interval around the population mean u:
CI = x ± z*(s/√n)
where x represents the sample mean, s represents the sample standard deviation, n represents the sample size, z represents the z-score associated with the desired degree of confidence, and CI represents the confidence interval.
Because the degree of confidence is 95%, we must calculate the z-score that corresponds to the standard normal distribution's middle 95%. This is roughly 1.96 and may be determined with a z-table or calculator.
CI = 18.1 ± 1.96*(4.1/√34)
CI = 18.1 ± 1.96*(0.704)
CI = 18.1 ± 1.38
Hence, the 95% CI for u is (16.72, 19.48), rounded to two decimal places in increasing order.
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solve this proportion: 5/a = 3/4
Answer:
[tex]a = \frac{20}{3}[/tex]
Step-by-step explanation:
A box containing 5 balls costs $8.50. If the balls are bought individually, they cost $2.00 each. How much cheaper is it, in percentage terms, to buy the box as opposed to buying 5 individual balls?
Answer: The total cost of buying 5 balls individually is $2.00 x 5 = $10.00.
The box costs $8.50, which means it is $10.00 - $8.50 = $1.50 cheaper to buy the box.
To calculate the percentage difference, we can use the formula:
% difference = (difference ÷ original value) x 100%
In this case, the difference is $1.50, and the original value is $10.00.
% difference = ($1.50 ÷ $10.00) x 100%
% difference = 0.15 x 100%
% difference = 15%
Therefore, it is 15% cheaper to buy the box than to buy 5 individual balls.
Step-by-step explanation:
Between which two consecutive integers does [tex]\sqrt138[/tex]lie?
The square root of 138 lies between 11 and 12, as 11²=121 and 12²=144.
What is number?Number is a mathematical object used to count, measure, and label. Numbers are used in almost every field of mathematics and science, including algebra, calculus, geometry, physics, and computer science. Numbers can also be used to represent data, such as population, income, temperature, or time. In addition, numbers are used to represent abstract concepts, such as love, truth, beauty, and justice.
This is because the square root of a number is the number that, when multiplied by itself, produces the original number. Therefore, to find the square root of 138, we need to identify two consecutive integers such that one of them squared is smaller than 138 and the other squared is larger than 138.
To do this, we can work our way up from the integer closer to 0, in this case 11. 11 squared is 121, which is smaller than 138, so we know that the square root of 138 must be between 11 and a larger integer. Then, if we square 12, we get 144, which is larger than 138. Therefore, we can definitively say that the square root of 138 lies between 11 and 12.
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The square root of 138 lies between 11 and 12, as 11² is 121 and 12² is 144.
What is number?Number is a mathematical object used to count, measure, and label. Numbers are used in almost every field of mathematics and science, including algebra, calculus, geometry, physics, and computer science. Numbers can also be used to represent data, such as population, income, temperature, or time. In addition, numbers are used to represent abstract concepts, such as love, truth, beauty, and justice.
To calculate this, we can divide 138 by 11 and 12, and see which integer is closer to the answer.
138 divided by 11 is 12.545454545454545454545454545455.
138 divided by 12 is 11.5.
Since 11.5 is closer to the answer, the square root of 138 lies between 11 and 12.
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PLS HELP FAST 50 POINTS + BRAINLIEST
Answer:
Anna had 23 sweets in her bag at the start of the day.
Step-by-step explanation:
Let's use working backwards to find out how many sweets were in the bag at the start of the day.
At the end of lesson 4, Anna had 1 sweet left in her bag. So, before she gave a sweet to her teacher in lesson 4, she had 2 sweets left in her bag.
In lesson 3, she gave out half of the sweets left in her bag and then gave one to the teacher. So, before she gave a sweet to her teacher in lesson 3, she had 2 x 2 + 1 = 5 sweets in her bag.
In lesson 2, she gave out half of the sweets left in her bag and then gave one to the teacher. So, before she gave a sweet to her teacher in lesson 2, she had 5 x 2 + 1 = 11 sweets in her bag.
In lesson 1, she gave out half of the sweets in her bag and then gave one to the teacher. So, before she gave a sweet to her teacher in lesson 1, she had 11 x 2 + 1 = 23 sweets in her bag.
Therefore, Anna had 23 sweets in her bag at the start of the day.
Assume that x and y have been defined and initialized as int values. The expression
!(!(x < y) || (y != 5))
is equivalent to which of the following?
(x < y) && (y = 5)
The expression (x < y) && (y == 5) is an alternative way of writing the original expression, and it will be true only if two conditions are met: first, x is smaller than y, and second, y is equal to 5.
The expression !(!(x < y) || (y != 5)) is equivalent to:
(x < y) && (y == 5)
To see why, let's break down the original expression:
!(!(x < y) || (y != 5))
= !(x >= y && y != 5) (by De Morgan's laws)
= (x < y) && (y == 5) (by negating and simplifying)
So, the equivalent expression is (x < y) && (y == 5). This expression is true if x is less than y and y is equal to 5.
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Complete question:
Assume that x and y have been defined and initialized as int values. The expression
!(!(x < y) || (y != 5))
is equivalent to which of the following?
(x < y) && (y = 5)
(x < y) && (y != 5)
(x >= y) && (y == 5)
(x < y) || (y == 5)
(x >= y) || (y != 5)
let a and b be positive integers, where a and b do not equal 0. for what limit expression does l'hospital's rule apply? (1 point)
For a limit expression to be solved using L'Hospital's rule, the expression must be in the form of 0/0 or infinity/infinity, and the derivatives of the numerator and denominator must exist and approach a finite limit or infinity/negative infinity at the point of evaluation.
L'Hospital's rule applies to limit expressions of the form 0/0 or infinity/infinity. Specifically, if we have a limit expression of form f(x)/g(x), where f(x) and g(x) both approach 0 or infinity as x approaches a certain value, then L'Hospital's rule may be applied to find the limit of the expression.
It is important to note that L'Hospital's rule can only be applied if the limit of the derivative of f(x) divided by the derivative of g(x) exists and is finite, or if the limit of the derivative of f(x) divided by the derivative of g(x) approaches infinity or negative infinity.
Therefore, for a limit expression to be solved using L'Hospital's rule, the expression must be in the form of 0/0 or infinity/infinity, and the derivatives of the numerator and denominator must exist and approach a finite limit or infinity/negative infinity at the point of evaluation.
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Marcia Gadzera wants to retire in San Diego when she is 65 years old. Marcia is now 50 and believes she will need $90,000 to retire comfortably. To date, she has set aside no retirement money. If she gets interest of 10% compounded semiannually, how much must she invest today to meet her goal of $90,000?
Answer:
Step-by-step explanation:
We can use the formula for the future value of an annuity to determine how much Marcia needs to invest today to meet her retirement goal of $90,000. The formula for the future value of an annuity is:
FV = PMT x [(1 + r/n)^(n*t) - 1] / (r/n)
where:
FV = future value of the annuity
PMT = payment (or deposit) made at the end of each compounding period
r = annual interest rate
n = number of compounding periods per year
t = number of years
In this case, we want to solve for the PMT (the amount Marcia needs to invest today). We know that:
Marcia wants to retire in 15 years (when she is 65), so t = 15
The interest rate is 10% per year, compounded semiannually, so r = 0.10/2 = 0.05 and n = 2
Marcia wants to have $90,000 in her retirement account
Substituting these values into the formula, we get:
$90,000 = PMT x [(1 + 0.05/2)^(2*15) - 1] / (0.05/2)
Simplifying the formula, we get:
PMT = $90,000 / [(1.025)^30 - 1] / 0.025
PMT = $90,000 / 19.7588
PMT = $4,553.39 (rounded to the nearest cent)
Therefore, Marcia needs to invest $4,553.39 today in order to meet her retirement goal of $90,000, assuming an interest rate of 10% per year, compounded semiannually.
sams rectangular swimming pool has a volume of 600 cubic feet, the neighbors pools the same length and height but the width is three times larger. what is the volume of the neighbors pool?
Answer: Let's denote the length, width, and height of Sam's pool as l, w, and h, respectively. Then, we have:
lwh = 600
For the neighbor's pool, we know that it has the same length and height as Sam's pool, but the width is three times larger. Let's denote the width of the neighbor's pool as 3w. Then, the volume of the neighbor's pool is:
l(3w)h = 3lwh = 3(600) = 1800 cubic feet
Therefore, the volume of the neighbor's pool is 1800 cubic feet.
Step-by-step explanation:
The scale on a map is 1:320000
What is the actual distance represented by 1cm?
Give your answer in kilometres.
By answering the presented question, we may conclude that Therefore, 1 expressions cm on the map corresponds to a real distance of 3.2 km.
what is expression ?In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.
Scale 1:
320000 means that 1 unit on the map represents his 320000 units in the real world.
To find the actual distance represented by 1 cm on the map, you need to convert the units to the same scale.
1 kilometer = 100000 cm
So,
1 unit on the map = 320000 units in the real world
1 cm on the map = (1/100000) km in the real world
Multiplying both sides by 1 cm gives:
1 cm on the map = (1/100000) km * 320000
A simplification of this expression:
1 cm on the map = 3.2 km
Therefore, 1 cm on the map corresponds to a real distance of 3.2 km.
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Question 12 (2 points)
Among the seniors at a small high school of 150 total students, 80 take Math, 41
take Spanish, and 54 take Physics. 10 seniors take Math and Spanish. 19 take Math
and Physics. 12 take Physics and Spanish. 7 take all three.
How many seniors were taking none of these courses?
Note: Consider making a Venn Diagram to solve this problem.
0
5
9
22
150 - 141 = 9 seniors are not enrolled in any classes.
What is statistics, and how can it be used?The area of mathematics known as statistics is used to gather, analyse, and interpret data. To predict the future, determine the likelihood that a specific event will occur, or learn more about a survey, statistics can be employed.
The Venn diagram reveals the amount of seniors enrolling in at least one of the courses as follows:
80 + 41 + 54 - 10 - 19 - 12 + 7
= 141
Therefore, 150 - 141 = 9 seniors are not enrolled in any classes.
= 9
So, there are 9 seniors taking none of the courses. Answer: 9.
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Trains Two trains, Train A and Train B, weigh a total of 188 tons. Train A is heavier than Train B. The difference of their
weights is 34 tons. What is the weight of each train?
Step-by-step explanation:
A + B = 188
A = 188 - B - (1)
Now,
A - B = 34
188 - B - B = 34 (Substituting eqn 1 in A)
188 - 34 = 2B
154 = 2B
• B = 77 tons
Now
A = 188 - B
A = 188 - 77
A = 111 tons
given :√9+25 : π-4 : ³√-27 : 2÷3 : 18÷2 : √-27
√9+25 = 28
π-4 = -0.8571
³√-27 = -3
2 / 3 = 0.6667
18÷2 = 9
√-27 = 5.196
What is surdsIn mathematics, a surd is a term used to describe an irrational number that is expressed as the root of an integer. Specifically, a surd is a number that cannot be expressed exactly as a fraction of two integers, and is usually written in the form of a radical (e.g. √2, √3, √5, etc.).
We have √9+25 = 28
find the square root of 9 = 3
3 + 25 = 28
π-4 = 3.14 - 4
= -0.8571
³√-27 = ³√3³
= 3
2÷3 = 0.6667
18÷2 = 9
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question:
given :√9+25 : π-4 : ³√-27 : 2÷3 : 18÷2 : √-27
find the value of the terms
Find the product of 3√20 and √5 in simplest form. Also, determine whether the result is rational or irrational and explain your answer.
Answer:
30, rational
Step-by-step explanation:
[tex]3\sqrt{20}\cdot\sqrt{5}=3\sqrt{4}\sqrt{5}\cdot\sqrt{5}=(3\cdot2)\cdot5=6\cdot5=30[/tex]
The result is rational because it can be written as a fraction of integers.
QUESTION THREE (30 Marks) a) For a group of 100 Kiondo weavers of Kitui, the median and quartile earnings per week are KSHs. 88.6, 86.0 and 91.8 respectively. The earnings for the group range between KShs. 80-100. Ten per cent of the group earn under KSHs. 84 per week, 13 per cent earn KSHs 94 and over and 6 per cent KShs. 96 and over. i. Put these data into the form of a frequency distribution and obtain an estimate of the mean wage. 15 Marks
Answer:
the answer would be 100 I guess
I will mark you brainiest!
Given parallelogram STUV, what is the length of TV?
TW = y2
WV = 2y − 1
A) 2
B) 8
C) 4
The required value of TV is 2 units.
What is parallelogram?
A parallelogram is a straightforward quadrilateral with two sets of parallel edges in Euclidean geometry. A parallelogram's confronting or opposing sides are of equal length, and its opposing angles are of equal size.
According to question:
We have given that;
TW = y²
WV = 2y − 1
We know that in parallelogram
TW = WV
y² = 2y − 1
y² - 2y + 1 = 0
y² - y - y + 1 =0
y(y - 1)-1(y - 1) = 0
(y - 1)(y - 1) = 0
(y - 1)² = 0
y - 1 = 0
y = 1
So;
TV = TW + WV
TV = y² + 2y − 1
TV = 1² + 2(1) - 1
TV = 1 + 2 - 1
TV = 2 units
Thus, required value of TV is 2 units.
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Lori is moving and must rent a truck. There is an initial charge of $60 for the rental plus an additional fee per mile driven. Would a linear, quadratic or exponential function be the best type of equation to model this function? Exponential Quadratic Linear
Answer:
A linear function would be the best type of equation to model this situation. The total cost of renting the truck increases linearly with the number of miles driven. The initial charge of $60 can be considered as the y-intercept of the linear function, and the additional fee per mile driven can be considered as the slope of the line. Therefore, the equation that models this situation can be written in the form y = mx + b, where y is the total cost of renting the truck, x is the number of miles driven, m is the additional fee per mile driven (the slope of the line), and b is the initial charge of $60 (the y-intercept).
Answer:
A linear function would be the best type of equation to model this function.
Step-by-step explanation:
The total cost of renting the truck is composed of two parts:
Initial charge of $60.Additional fee per mile driven.The initial charge of $60 is the fixed charge, and the additional fee is the variable charge that is proportional to the number of miles driven.
Let "x" be the number of miles driven and "y" be the total cost of the rental (in dollars), then the linear equation is:
y = mx + 60
where "m" is the additional fee (in dollars) per mile driven.
Therefore, a linear function, in the form y = mx + b, where m represents the slope or rate of change, and b represents the initial fixed charge, is the most appropriate function to model this situation.
Allan painted the circular patch on his driveway. He used the formula below to calculate the area of the circular patch. The diameter of the circular patch was 20 meters. What was the area of the patch? Assume pi=3.14
Answer: 314 square meters
Step-by-step explanation:
The formula for the area of a circle is given by A = πr^2, where r is the radius of the circle. Since the diameter of the circular patch is given as 20 meters, the radius would be half of that or 10 meters.
So, using the formula, we can calculate the area of the circular patch as follows:
A = πr^2
A = π(10)^2
A = 3.14(100)
A = 314 square meters
Therefore, the area of the circular patch is 314 square meters.
In the year 1985, a house was valued at $108,000. By the year 2005, the value had appreciated to $148,000. What was the annual growth rate percentage between 1985 and 2005? Assume that the value continued
to grow by the same percentage. What was the value of the house in the year 2010?
Answer:
To find the annual growth rate percentage, we can use the formula:
annual growth rate = [(final value / initial value)^(1/number of years)] - 1
where "final value" is the value in the ending year, "initial value" is the value in the starting year, and "number of years" is the total number of years between the starting and ending years.
Using the given values, we have:
annual growth rate = [(148,000 / 108,000)^(1/20)] - 1
= 0.0226 or 2.26%
So the house appreciated at an annual growth rate of 2.26%.
To find the value of the house in 2010, we can use the same growth rate to project the value from 2005 to 2010:
value in 2010 = 148,000 * (1 + 0.0226)^5
= $175,465.11 (rounded to the nearest cent)
Therefore, the value of the house in the year 2010 was $175,465.11.
Joann had a vegetable stand where she sold tomatoes. She sold 15 tomatoes the first day. The second day she sold half of what was left. On the third day she sold 12 and sold half of what was left on the fourth day. On the fifth day there were 4 tomatoes left to be sold. How many tomatoes did she have to begin with?
On the fifth day there were 4 tοmatοes left tο be sοld. Jοann had 71 tοmatοes tο begin with.
What is prοbability?Prοbability is a measure οf the likelihοοd οr chance οf an event οccurring. It is a number between 0 and 1, where 0 indicates that the event is impοssible, and 1 indicates that the event is certain tο οccur.
Let's wοrk backwards frοm the last day and figure οut hοw many tοmatοes Jοann had οn the fοurth day.
On the fifth day, there were 4 tοmatοes left tο be sοld, which means she sοld half οf what was left οn the fοurth day. Sο she must have started with 8 tοmatοes οn the fοurth day (since half οf 8 is 4).
On the fοurth day, she sοld half οf what was left, which means she had 16 tοmatοes befοre she sοld any.
On the third day, she sοld 12 tοmatοes, which means she had 28 tοmatοes befοre she sοld any.
On the secοnd day, she sοld half οf what was left, which means she had 56 tοmatοes befοre she sοld any.
Finally, οn the first day, she sοld 15 tοmatοes.
Therefοre, Jοann had 71 tοmatοes tο begin with.
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one ticket is drawn at random from each of the two boxes below: 1 2 6 1 4 5 8 find the chance that the both numbers are even numbers.
The chance that both numbers drawn are even numbers is 8/21.
The probability refers to the measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain.
There are 4 even numbers and 3 odd numbers in the first box, and 2 even numbers and 1 odd number in the second box.
The probability of drawing an even number from the first box is 4/7, and the probability of drawing an even number from the second box is 2/3.
By the multiplication rule of probability, the probability of drawing an even number from both boxes is
(4/7) × (2/3) = 8/21
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the values or variables listed in the function declaration are called _____ paramters to the function.
The values or variables listed in the function declaration are called formal parameters to the function.
They are used to store the data that is passed into the function when it is called. The formal parameters are local variables, meaning that the values stored in them are only available within the function.
The arguments are the values passed to the function when it is called. These values are then assigned to the formal parameters and are used within the function to perform the desired task.
Formal arguments are produced at function entry and removed at function exit, behaving similarly to other local variables inside the function.
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PLEASE HELP 30 POINTS!
Answer:
57
57
123
123
57
57
123
that's all.
Answer:
m<1 = 57°
m<2 = m<1 = 57°
m<3 = x = 123°
m<4 = x = 123°
m<5 = m<1 = 57°
m<6 = m<5 = 57°
m<7 = m<4 = 123°
Step-by-step explanation:
[tex]{ \tt{m \angle 1 + x = 180 \degree}} \\ { \colorbox{silver}{corresponding \: angles}} \\ { \tt{m \angle 1 = 180 - 123}} \\ { \tt{ \underline{ \: m \angle 1 = 57 \degree \: }}}[/tex]
To approximate binomial probability plx > 8) when n is large, identify the appropriate 0.5 adjusted formula for normal approximation. O plx > 7.5) O plx >= 9) O plx > 9) O plx > 8.5)
The appropriate 0.5 adjusted formula for normal approximation is option (d) p(x > 8.5)
The appropriate 0.5 adjusted formula for normal approximation to approximate binomial probabilities when n is large is
P(Z > (x + 0.5 - np) / sqrt(np(1-p)))
where Z is the standard normal variable, x is the number of successes, n is the number of trials, and p is the probability of success in each trial.
To approximate binomial probability p(x > 8) when n is large, we need to use the continuity correction and find the appropriate 0.5 adjusted formula for normal approximation. Here, x = 8, n is large, and p is unknown. We first need to find the value of p.
Assuming a binomial distribution, the mean is np and the variance is np(1-p). Since n is large, we can use the following approximation
np = mean = 8, and
np(1-p) = variance = npq
8q = npq
q = 0.875
p = 1 - q = 0.125
Now, using the continuity correction, we adjust the inequality to p(x > 8) = p(x > 8.5 - 0.5)
P(Z > (8.5 - 0.5 - 8∙0.125) / sqrt(8∙0.125∙0.875))
= P(Z > 0.5 / 0.666)
= P(Z > 0.75)
Therefore, the correct option is (d) p(x > 8.5)
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The given question is incomplete, the complete question is:
To approximate binomial probability p(x > 8) when n is large, identify the appropriate 0.5 adjusted formula for normal approximation. a) p(x > 7.5) b) p(x >= 9) c) p(x > 9) d) p(x > 8.5)
Find the missing length indicated
The answer of the given question based on finding the missing length of a triangle the answer is , None of the answer choices match this value exactly, but the closest one is D) 15. Therefore, the answer is D) 15.
What is Triangle?In geometry, triangle is two-dimensional polygon with three straight sides and three angles. It is one of basic shapes in geometry and can be defined as closed figure with three line segments as its sides, where each side is connected to two endpoints called vertices. The sum of interior angles of triangle are 180° degrees.
Triangles are classified based on length of their sides and measure of their angles. A triangle can be equilateral, isosceles, or scalene based on whether all sides are equal, two sides are equal, or all sides are different, respectively.
To find the missing length indicated, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs (the sides adjacent to the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle).
In this triangle, we can see that the two legs have lengths of 9 and 16, and the hypotenuse has length X. So we can write:
9²+ 16² = X²
Simplifying the left-hand side:
81 + 256 = X²
337 = X²
Taking the square root of both sides (and remembering that X must be positive, since it is a length):
X = sqrt(337)
X ≈ 18.3575
So the missing length indicated is approximately 18.3575. None of the answer choices match this value exactly, but the closest one is D) 15. Therefore, the answer is D) 15.
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Consider the initial value problem y⃗ ′=[33????23????4]y⃗ +????⃗ (????),y⃗ (1)=[20]. Suppose we know that y⃗ (????)=[−2????+????2????2+????] is the unique solution to this initial value problem. Find ????⃗ (????) and the constants ???? and ????.
The unique solution to the initial value problem of differential equation is y(t) = -t^2 + 2t + 3sin(3t) - 1 with e(t) = -t^2 + 2t + 3sin(3t) - 9, a = 2, and B = -21.
To find the solution to the initial value problem, we first need to solve the differential equation.
Taking the derivative of y(t), we get:
y'(t) = -2t + a
Taking the derivative again, we get:
y''(t) = -2
Substituting y''(t) into the differential equation, we get:
y''(t) + 2y'(t) + 10y(t) = 20sin(3t)
Substituting y'(t) and y(t) into the equation, we get:
-2 + 2a + 10(-2t + a) = 20sin(3t)
Simplifying, we get:
8a - 20t = 20sin(3t) + 2
Using the initial condition y(0) = 2, we get:
y(0) = -2(0) + a = 2
Solving for a, we get:
a = 2
Using the other initial condition y'(0) = 21, we get:
y'(0) = -2(0) + 2(21) + B = 21
Solving for B, we get:
B = -21
Therefore, the solution to the initial value problem is:
y(t) = -t^2 + 2t + 3sin(3t) - 1
Thus, we have e(t) = y(t) - 8, so
e(t) = -t^2 + 2t + 3sin(3t) - 9
and a = 2, B = -21.
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_____The given question is incomplete, the complete question is given below:
Consider the initial value problem >= [22. 2.1]+20). 361) = [2] Suppose we know that (t) = -2t + a 21? + is the unique solution to this initial value problem. Find e(t) and the constants and B. a = B= 8(t) =
Find X using the picture below.
Answer: 37.5
Step-by-step explanation:
75 - 180 = 105
105 degrees = the obtuse angle, bottom triangle.
75/2= 37.5 (since both sides of the bottom triangle are equal angles)
An inlet pipe on a swimming pool can be used to fill the pool in 16
hours. The drain pipe can be used to empty the pool in 24
hours. If the pool is 13
filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?
Answer:
Step-by-step explanation:
