solve please and thank you it’ll help a lot. 15 points.

Solve Please And Thank You Itll Help A Lot. 15 Points.

Answers

Answer 1

Parallelogram (Opposite sides have the same length). Parallelogram (Area is one-half the base times the height). Parallelogram (Opposite sides are parallel). Parallelogram (Angles can be right angles)

What is the assertion of the parallelogram?

According to the parallelogram law, the sum of the squares of a parallelogram's four sides is equal to the sum of the squares of its two diagonals. It is essential for the parallelogram to have equal opposite sides in Euclidean geometry.

Are a parallelogram's opposing sides parallel?

A parallelogram is a particular sort of polygon. It is a quadrilateral in which the opposite side pairs are parallel to one another. There are six crucial parallelogram characteristics to be aware of: Congruent sides are those when AB = DC.

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Related Questions

the values or variables listed in the function declaration are called _____ paramters to the function.

Answers

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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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)

Answers

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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The scale on a map is 1:320000

What is the actual distance represented by 1cm?

Give your answer in kilometres.

Answers

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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solve this proportion: 5/a = 3/4

Answers

Answer:

[tex]a = \frac{20}{3}[/tex]

Step-by-step explanation:

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?

Answers

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.

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?

Answers

Answer:

Step-by-step explanation:

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)

Answers

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)

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

Answers

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.

Find the product of 3√20 and √5 in simplest form. Also, determine whether the result is rational or irrational and explain your answer.

Answers

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.

Can I please get help it's an EMERGENCY!

Answers

The number of hours it will take the same dog to run 26 1/10 miles is 7.2 hours

How long will it take the dog to run 26 1/10 miles?

7 1/4 miles in 2 hours

26 1/10 miles in x hours

Equate miles ratio hours

7 ¼ miles : 2 hours = 26 ⅒ miles : x hours

7.25 / 2 = 26.10 / x

cross product

7.25 × x = 26.10 × 2

7.25x = 52.20

divide both sides by 7.25

x = 52.20 / 7.25

x = 7.2 hours

Ultimately, it will take 7.2 hours for the dog to run 26⅒ miles.

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Find X using the picture below.

Answers

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)

look at this square: 2 mm 2 mm if the side lengths are tripled, then which of the following statements about its area will be true?

Answers

Therefore, the only statement that is true is: "The new area is 6 times the original area."

What is area?

Area is a measure of the size or extent of a two-dimensional surface or region, such as the surface of a square, rectangle, circle, triangle, or any other shape. It is expressed in square units, such as square meters, square feet, or square centimeters.

Here,

If the side lengths of a square are tripled, the new side length will be 2 mm x 3 = 6 mm.

The original area of the square is:

Area = side length x side length = 2 mm x 2 mm = 4 mm²

The new area of the square with tripled side lengths will be:

New area = new side length x new side length = 6 mm x 6 mm = 36 mm²

Therefore, the new area of the square will be 36 mm².

To determine which of the following statements about its area will be true, we need to see which statements are true for the new area of 36 mm²:

A. The new area is 6 times the original area. This statement is true because 36 mm² is 6 times larger than 4 mm².

B. The new area is 3 times the original area. This statement is false because 36 mm² is 9 times larger than 4 mm², not 3 times larger.

C. The new area is equal to the original area. This statement is false because the new area of 36 mm² is much larger than the original area of 4 mm².

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Complete question:

look at this square: 2 mm 2 mm if the side lengths are tripled, then which of the following statements about its area will be true?

The ratio of the new area to the old area will be 2:1

The ratio of the new area to the old area will be 6:1.

The ratio of the new area to the old area will be 1:2.

The ratio of the new area to the old area will be 4:1.

Between which two consecutive integers does [tex]\sqrt138[/tex]lie?

Answers

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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What is the meaning of "invertible n x n matrices"?

Answers

Answer: A matrix A of dimension n x n is called invertible if and only if there exists another matrix B of the same dimension, such that AB = BA = I, where I is the identity matrix of the same order.

Step-by-step explanation:

hope it helped! <3

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.)

Answers

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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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​

Answers

Answer:

the answer would be 100 I guess

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)

Answers

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)

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?

Answers

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:

Roberto must make his costume for the school play. He needs a piece of fabric that is 2 2/3 yards long and 1 1/2 yard wide. What is the area of the piece of fabric Roberto needs?

Answers

Roberto needs 4 square yards of fabric to make his costume.

What is improper fraction?

A fraction that has the numerator higher than or equal to the denominator is said to be inappropriate. For instance, the fraction 7/3 is incorrect since 7 is bigger than 3. Mixed numbers, which combine a whole number and a correct fraction, can be created from improper fractions.

Given that, piece of fabric that is 2 2/3 yards long and 1 1/2 yard wide.

Convert the length from a mixed number to an improper fraction:

2 2/3 = (2 x 3 + 2)/3 = 8/3

1 1/2 = 3/2

The area of the rectangle is:

Area = Length x Width

Substituting the values we have:

Area = (8/3) x (3/2) = 4

Hence, Roberto needs 4 square yards of fabric to make his costume.

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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.

Answers

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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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?

Answers

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:

PLEASE HELP 30 POINTS!

Answers

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]

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?

Answers

For this problem you want to multiply your hourly rate by your time worked and then you also want to multiply it by you time and a half factor so your problem should look like, 10.40 x 5 x 1.5 = ? And if you plug that all into a calculator you will get $78

Point E represents the center of this circle. Angle DEF
has a measure of 80%.
Drag and drop a number into the box to correctly
complete the statement.
An angle measure of 80° is the size of an angle
that turns through
20
50
one-degree turns.
80
100
K

Answers

The measure of the arc intercepted by the angle and the vertical angles make up the angle subtended at the center. As a result, XYZ has a value of 35°.

What are angles?

Two lines intersect at a location, creating an angle.

An "angle" is the term used to describe the width of the "opening" between these two rays. The character is used to represent it.

Angles are frequently expressed in degrees and radians, a unit of circularity or rotation.

In geometry, an angle is created by joining two rays at their ends. These rays are referred to as the angle's sides or arms.

An angle has two primary components: the arms and the vertex. T

he two rays' shared vertex serves as their common terminal.

Hence, The measure of the arc intercepted by the angle and the vertical angles make up the angle subtended at the center. As a result, XYZ has a value of 35°.

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given :√9+25 : π-4 : ³√-27 : 2÷3 : 18÷2 : √-27​

Answers

√9+25 = 28

π-4 = -0.8571

³√-27 = -3

2 / 3 = 0.6667

18÷2 = 9

√-27​ = 5.196

What is surds

In 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 missing length indicated

Answers

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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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

Answers

[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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6 TH GRADE MATH , WHAT IS THE SLOPE? TY

Answers

Answer:

Step-by-step explanation:

The slope of a line is the measure of the steepness and the direction of the line. Finding the slope of lines in a coordinate plane can help in predicting whether the lines are parallel, perpendicular, or none without actually using a compass.

The slope of any line can be calculated using any two distinct points lying on the line. The slope of a line formula calculates the ratio of the "vertical change" to the "horizontal change" between two distinct points on a line. In this article, we will understand the method to find the slope and its applications.

That is what Slope is.

Answer:

Step-by-step explanation:

Slope :( 1,1)

You start on the y-axis point which is (0,1) as you can see it is going up so I used the “up left” strategy. You go up 1 to the left 1 since the line intersects at point (1,2)

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 ????.

Answers

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.

To know more about differential equation:

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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) =

PLS HELP FAST 50 POINTS + BRAINLIEST

Answers

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.

SORRY IF THIS IS WRONG
1+1 = 2 2x2 = 4 = what was left at the start of lesson 4
4 + 1 = 5
5 x 2 = 10 = what was left at the start of lesson 3
10 + 1 = 11
11 x 2 = 22 = what was left at the start of lesson 2
22 + 1 = 23
23 x 2 = 46
So at the start of the day there was 46 sweets
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