The general integral is provided by y = C1e-t + C2te-t + (1/2)(t2)e-t.
(m + 1)2 =0 is the characteristic polynomial for the differential equation y" +2y' + y = e-t.
Roots -1, -1. yh = C1e-t + C2te-t is the answer to the homogeneous equation at that point.
Use the method of variation of parameters, taking into account the independent integrals y1 = e-t, y2 = te-t, and Wronskian
W(t) = e-2t, to derive the specific integral related to f(t) = e-t.
Then, use the conventional formula yp = - y1(t)(Integral of Y2(t)f(t)dt/W(t)) +y
Obtain yp = (1/2)(t2)e-t for the given situation.
As a result, the general integral is provided by
y = C1e-t + C2te-t + (1/2)(t2)e-t.
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Determine the missing angle measure.
Answer:
19°
Step-by-step explanation:
In this problem, we have complementary angles, which add up to 90° as indicated by the right angle symbol. So, getting x° is as simple as 90°-71°=19°.
Alpha can produce either 18 oranges or 9 apples an hour, while Beta can produce either 16 oranges or 4 apples an hour. Which of the following terms of trade between apples and oranges would allow both Alpha and Beta to gain by specialization and exchange?
A. 1 orange for 0.2 apples
B. 2 apples for 3 oranges
C. 3 apples for 3 oranges
D. 1 apple for 3 orange
A nation cannot have a comparative advantage in the production of every good. Alpha can produce either 18 oranges or 9 apples an hour, while Beta can produce either 16 oranges or 4 apples an hour. The opportunity cost of producing 1 orange for Alpha and Beta, respectively, are: 0.5 apples; 0.25 apples.
What is proportion?A percentage is a component, piece, or amount that is compared to a total. It might be 0 or 1, or any number between 0 and 1. It can be stated numerically or as a percentage. In official statistics, one example would be the proportion of the Canadian population residing in a certain province.
Here,
A country cannot have a competitive advantage in producing every good. Alpha can generate 18 oranges or 9 apples per hour, whilst Beta can produce 16 oranges or 4 apples per hour. The opportunity cost of producing one orange for Alpha and Beta is 0.5 apples and 0.25 apples, respectively.
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Write the ratio. Explain what the ratio means.
butterflies : caterpillars
For every _
butterfly/butterflies, there is/are _
caterpillar(s).
The ratio is 1:4, which means for every 1 butterfly, there are 4 caterpillars.
This ratio represents the relationship between the number of butterflies and the number of caterpillars. In this case, the ratio is saying that for every 1 butterfly, there are 4 caterpillars. This could mean that for every butterfly that is observed, there are 4 caterpillars that are also present or for every butterfly that is caught, there are 4 caterpillars that are also caught.
This ratio may also indicate that for every butterfly that is born, 4 caterpillars are also born. It could also indicate the population ratio of butterflies to caterpillars in a specific habitat.
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Write each trigonometric ratio as a fraction and as a decimal rounded to
the nearest hundredth.
3. sin C
6. cos C
4. tanA
7. tan C
5. cos A
8. sin A
The trigonometric ratio as a fraction for sinC is , and the decimal is 0.80.
What are trigonometric functions?The trigonometric functions are actual functions that connect the right-angled triangle's angle to the ratios of its two side lengths.
What are the most widely used trigonometric functions?The widely used trigonometric functions are sine, cosine and tangent. The trigonometric functions also operate the inverse of the functions.
For the given triangle the trigonometric values are as follows:
For angle A the opposite side is CB, the adjacent side is AB and the hypotenuse is AC.
For angle C the opposite side is AB, the adjacent side is CB and the hypotenuse is AC.
[tex]sinC = \frac{\text{Opposite side }}{Hypotenuse} = \frac{4}{5} =0.80\\ \\ cosC = \frac{\text{Adjacent side }}{Hypotenuse} =\frac{3}{5} = 0.60\\\\tanA =\frac{\text{Opposite side }}{Adjacent side} = \frac{3}{4} = 0.75\\\\tanC= \frac{\text{Opposite side }}{Adjacent side} =\frac{4}{3} = 1.33\\\\cosA = \frac{\text{Adjacent side }}{Hypotenuse} =\frac{4}{5} = 0.80\\\\sinA= \frac{\text{Opposite side }}{Hypotenuse}=\frac{3}{5} =0.60[/tex]
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For each object, choose an appropriate scale for a drawing that fits on a regular sheet of paper.
Objects (A-E)
Scales (1 - 7)
А
Scales
AA person
1. 1:17
B A footballfeld (220 yards by 53 yards)
2. 1 cm: 1m
c The state of Washington (about 240 miles by 380 miles) 3 1:1000
The floor plan of a house
4. Itimile
E A rectangular farm (5 miles by 2 mile)
5 1:100,000
& 1 mm 1 km
7. 1:10,000,000
B
С
E
The appropriate scale for a drawing are-
2) 1 cm: 1 m 3) 1:10005) 1:100,0001) 1 in: i ft4) 1 ft : 1 mileExplain the term scale of drawing?When ever a drawing is said to be "to scale," it signifies that each piece is proportionate to the genuine or hypothetical entity; it may be smaller or larger by a specific amount.The scale describes the actual length that each length just on scale graphic corresponds to.The appropriate scale for a drawing that fits on a regular sheet of paper
A. A person : 2) 1 cm: 1m B. A football field (120 yards by 5 1/3 yards) : 3) 1:1000C. The state of Washington (about 240 miles by 360 miles) : 5) 1:100,000D. The floor plan of a house : 1 in: i ftE. A rectangular farm (6 miles by 2 mile) : 4) 1 ft : 1 mileTo know more about the scale of drawing, here
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The correct question is attached-
Tim shows his work To answer a subtraction problem. Tell how to find an equation to represent the problem Tim starts with and its answer. 863+7=870 870+30=900 900+55=955
As you can see, we turned the fraction 10100 into its decimal representation, 0.1, in a single simple computation.
what is fraction?Any number of equal portions, or parts of a whole, are described by fractions. Fractions in standard English indicate the number of pieces of a specific size. 8, 3/4 of .Part of an entire is a fraction. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. When a fraction is true, its numerator is smaller than its denominator.
With 100 as the denominator, decimal fractions in the hundredth place are written. We shall discover how each square is split into 100 equal sections in this section. A tenth is a portion that is just partially shaded. The fraction is expressed as 1/100 in decimal form.
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What does using the if __ name __ == '__ main __' syntax allow programmers to do?
The if __name__ == '__main__' syntax allows a programmer to specify that certain code should only be executed when the script is run directly, rather than when it is imported as a module into another script.
This can be useful for running code that you only want to execute when you're running the script for testing or development, rather than when you're using it as a library in another program. It also allows to use the same code in multiple script without running the main code.
When a Python script is run, the interpreter assigns the name __main__ to the script's global namespace. Therefore, when the script is run directly, __name__ will be set to __main__. When the script is imported as a module into another script, __name__ will be set to the name of the module, rather than __main__.
So, when a programmer uses the if __name__ == '__main__' syntax, they are essentially checking whether the script is being run directly or imported as a module. If the script is being run directly, the code within the if block will be executed. If the script is being imported as a module, the code within the if block will not be executed.
This allows the programmer to separate code that should only be run when the script is executed directly from code that is intended to be used as a library when the script is imported as a module. It also allows to use the same code in multiple script without running the main code.
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Nellie had $48.She spent 1/4 of it on a calculator. She also bought a book for $14.How much money did she spend all together?
Answer:
26$
Step-by-step explanation:
¼×48=12
so 12 was spent on calculator
12+14= 26
Find the perimeter of the parallelogram with these vertices.
(3, 6), (-5, 6), (6, -1), (-2, -1)
The perimeter of the parallelogram with the given vertices is 33.
What is perimeter?The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges.
Given that:
A = (3, 6)
B = (-5, 6)
C= (6 , -1)
D = (-2, -1)
The length of side is given by the formula:
[tex]L = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Substitute the values in the formula to find the sides of the parallelogram.
[tex]AB= \sqrt{(-5 -3)^2 + (6-6)^2} = 8\\ \\BC = \sqrt{(6+5)^2 + (-1 - 6)^2} = 13\\\\CD= \sqrt{(-2+6)^2 + (-1 +1)^2} = 4\\\\\DA= \sqrt{(3+2)^2 + (6+1)^2} = 8[/tex]
The perimeter is obtained by adding all the sides of the given two-dimensional shape.
P = 8+13+4+8
P = 33
Hence the perimeter of the parallelogram is 33.
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"Suppose Dave purchases a puzzle having 650 pieces. Predict the lenght of time it will take him to compleate the puzzle."
a) Attached at the end.
b) Strong positive linear correlation.
c) The length of time is 220 minutes.
What is Scatter plot?A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of connection, if any, between the values of observed quantities or events, scatter plots are crucial in statistics (called variables).
Given:
a) The Scatter plot Associated with data is attached below.
b) The Scatter plot shows the positive linear correlation between number of pieces in a jigsaw puzzle and time required for a person to complete it.
c) To complete the puzzle with 650 pieces it will take 220 minutes.
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Answer:
a) See attachment.
b) Strong positive correlation.
c) 247 minutes
Step-by-step explanation:
Part aPlot the points from the given table on the given coordinate plane.
Draw a line of best fit.
(See attachment).
Part bAs the line of best fit has a positive gradient, the two variables are positively correlated.
As the line of best fit lies close to most of the points, this indicates there may be a strong correlation.
Part cTo predict the length of time it will take Dave to complete a 650-piece puzzle, locate 650 on the x-axis of the scatter plot, trace up to the line of best fit and read the y-value:
(650, 247)Therefore, it will take Dave approximately 247 minutes to complete a 650-piece puzzle.
Simon builds this podium on a platform.
What is the combined volume of the podium and the platform?
Enter your answer in the box
The combined volume of the podium and the platform is 64 cubic feet.
This sort of figure offers several choices. We really only need to consider how to divide the front face into appropriate rectangles, since the depth of the figure is 2 feet everywhere.
The volume is the area of the front face times that depth.
1) A 2 ft × 4 ft upright atop a 12 ft × 2 ft horizontal base. The frontal area is
(2 ft)(4 ft) +(12 ft)(2 ft) = 8 ft² +24 ft² = 32 ft
so, the total volume is:
V = frontal area × depth
V= (32 ft²)(2 ft)
V=64 ft³
2) A vertical post of 2 ft × 6 ft at the left side with a horizontal protrusion of 10 ft × 2 ft from its bottom.
The frontal area calculated this way is:
(2 ft)(6 ft) +(10 ft)(2 ft) = 12 ft² +20 ft² = 32 ft²
Again, the total volume is (32 ft²)(2 ft) = 64 ft³.
3) A 6 ft × 12 ft rectangle with a 4 ft × 10 ft cutout from the upper right corner. The area calculated this way is
(6 ft)(12 ft) -(4 ft)(10 ft) = 72 ft² -40 ft² = 32 ft² . . . . . same as above
Again, the total volume is (32 ft²)(2 ft) = 64 ft³.
V=64 ft³.
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An online furniture store sells chairs for $200 each and tables for $450 each. Every day, the store can ship a maximum of 20 pieces of furniture and must sell at least $4800 worth of chairs and tables. If xx represents the number of tables sold and yy represents the number of chairs sold, write and solve a system of inequalities graphically and determine one possible solution. Inequality 1
Using the provided values and the conditions, The inequality equations required are : [tex]x+y \leq 20[/tex] and [tex]450x+200y \geq 4800[/tex].
What do you mean by equation?An equation is a mathematical statement in which two expressions are set equal to each other. It is typically written using an "=" sign, with the expressions on either side of the sign representing equivalent values. For example, the equation 2 + 2 = 4 states that the value of 2 plus 2 is equal to the value of 4. Equations can be used to express relationships and to solve problems.
What are inequalities?An inequality is a mathematical statement that compares two values or expressions. It is similar to an equation, but instead of using the "=" sign to indicate that the two sides are equal, it uses one of the following symbols: ">", "<", "≥", "≤" to indicate that the two sides are not equal. For example, the inequality 2 + 2 > 4 states that the value of 2 plus 2 is greater than 4. Similarly, the inequality 2 + 2 < 4 states that the value of 2 plus 2 is less than 4. Inequalities can be used to express constraints in a problem or to define a range of solutions. They can also be represented graphically by using a number line.
x= number of tables sold
y= number of chair sold
max furniture in a day = 20
so, [tex]x+y \leq 20[/tex].
least selling amount = 4800
so, [tex]450x+200y \geq 4800[/tex]
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Factor Completely
-3p^7+3p^3
Answer:
3p^3 (-p^4 + 1)
Step-by-step explanation:
The common factor of both -3p^7 and 3p^3 is 3p^3
Divide -3p^7 by 3p^3 and get -p^4
Divide 3p^3 by 3p^3 and get 1
So the factorisation is 3p^3 (-p^4 + 1)
A PE Teacher pays a total of $960 for 6 basketballs and 8 volleyballs. The price of 6 basketballs is equivalent to 8 volleyballs. How much does each basketball cost than each volleyball?
solve by assuming question
Answer: solving by forming simple algebra equation
Step-by-step explanation:
8x (x is the cost of 1 volleyball)
6y (y is the cost of 1 basketball)
We know that cost of 8 volleyballs is = cost of 6 basketballs
i.e. 8x = 6y
& total money spent to buy 8 volleyballs and 6 basketballs is $960
so we can write;
8x + 6y = 960
= (6y) + 6y = 960
= 12y = 960
= y or cost of 1 basketball is (960/12) = $80
& if we want to know the value of x (cost of 1 volleyball)
8x = 6y
= 8x = 6(80)
& x = 6(80/8)
= 6 (10) = 60
so the cost of basketball is $80 & 1 volleyball is $60
Hope it helps :)
p.s. that the equation I formed were made as if I was making an assumption & the conditions were kept uniform from the beginning, this is very applicable in day to day scenario; for e.g. when you go out with you friends to eat and have to split the bill - this assumption and division is called algebra - so value this education!
select the correct answer. Solve the quadratic equation. (x + 4)(x + 1) = 0
x = 4 or x = 1
x = -4 or x = 1
x = -4 or x = -1
x = 4 or x = -1
Answer:
x = -4 or x = -1
Step-by-step explanation:
Let's check
x = -4
(-4 + 4)(-4 + 1) = 0
(0)(-3) = 0
0 = 0
Let's check x = -1
(-1 + 4)(-1 + 1) = 0
(-3)(0) = 0
0 = 0
So, x = -4 or x = -1 is correct answer!
Solve for the x and y intercepts of the following. Show all steps. a)2x-5y=20
Solving for x and y intercepts when given an equation:
the x-intercept occurs when y = 0, so we can set y = 0 and solve for xthe y-intercept occurs when x = 0, so set x=0 and solve for yperform inverse operations until x or y is isolatedX-intercept:
[tex]2x-5(0)=20[/tex]
[tex]2x=20[/tex]
[tex]x=10[/tex]
x-intercept occurs at (10,0)
Y-intercept
[tex]2(0)-5y=20[/tex]
[tex]-5y=20[/tex]
[tex]y=-4[/tex]
y-intercept occurs at (0,-4)
50PTS 50PTS 50PTS [D•O•N•T E•X•P•L•A•I•N]
Answer:x=20
Step-by-step explanation:5x+9 and 3x+11 must add to 180, so you can set these equal to 180 and get 8x+20 = 180, this can be simplified to 8x=160 or x = 20
Answer:
x = 20°
Step-by-step explanation:
Given angles,
→ 5x + 9
→ 3x + 11
Forming the equation,
→ (5x + 9) + (3x + 11) = 180°
{Because, sum of two angles in a straight line leads to 180°}
Now the value of x will be,
→ (5x + 9) + (3x + 11) = 180°
→ 5x + 3x + 9 + 11 = 180°
→ 8x + 20 = 180°
→ 8x = 180° - 20
→ x = 160/8
→ [ x = 20° ]
Hence, the value of x is 20°.
Tom got a Mr. Potato Head for his birthday. It came with $3$ hairstyles, $2$ sets of eyebrows, $1$ pair of googly eyes, $2$ sets of ears, and $2$ sets of lips, a pair of regular shoes, and a bonus pair of clown shoes. If a complete Mr. Potato Head personality includes eyebrows, eyes, ears, lips, shoes and optionally hair, how many different wacky personalities can Tom come up with? Note that Mr. Potato Head can be bald. Note: You cannot "mix and match". For example, you cannot take the left eyebrow from one pair and the right eyebrow from the other pair.
Answer: Tom can come up with 13 different wacky personalities for Mr Potato Head.
Step-by-step explanation:
Tom can come up with 3 different hairstyles for Mr Potato Head, 2 sets of eyebrows, 1 pair of googly eyes, 2 sets of ears, and 2 sets of lips. He also has 2 pairs of shoes to choose from. If Mr Potato Head can be bald, Tom can also choose to not include a hairstyle.
In total, Tom can come up with 3+2+1+2+2+2+1=13 different combinations of features for Mr Potato Head. Since each combination represents a different personality, Tom can come up with 13 different wacky personalities for Mr Potato Head.
Marla is four years less than twice as old as Darla. If the sum of their ages is 47, how old is Marla?
Marla is 30 years old.
Let marla age be x and Darla age be y
Given : Marla is four years less than twice as old as Darla
What is equation ?
In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
Marla is four years less than twice as old as Darla can be represented as : 2y - x = 4
sum of their ages is 47 can be represented as : x + y = 47
Solving both the equation using addition we got ,
3y = 51
y = 17
Substituting the value of y in x + y =47 , we get
x + 17 = 47
x = 47 -17
x = 30
Hence , Marla is 30 years old.
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SU is a midsegment of QRT
If QR=-5v+96 and SU = 19v-38 than what is the value of X
Considering the given triangle, the information given helped to apply similar triangle principle to determine v to be 3.9
What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions
Examining the figure shows that pair of equivalent sides are
TS and TR , SU and QR
The solution is worked out using sides WX and XV, WY and YU
TS / TR = SU / QR
TS / TR = 1/2 since it is a mid segment
1 / 2 = (19v - 38) / (-5v + 96)
-5v + 96 = 2 * (19v - 38)
-5v + 96 = 38v - 72
96 + 72 = 38v + 5v
168 = 43v
v = 3.9
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Select the correct answer from each drop-down menu.
An axiom in Euclidean geometry states that in space, there are at least
~ points that do
The answer is that space contains at least four points that are not coplanar or not all coplanar.
What is Axioms?Axioms are statements or propositions taken to be established, accepted, or self-evident truths. In other words, a statement or mathematical statement that serves as a starting point from which other statements are logically derived. This is formulated in Hypothesis 1 as follows:
A plane contains at least three points that are not all on a straight line. Space contains at least four points that are not all in one plane. "
Simply put,
"There is at least one plane for every three points. There is exactly one plane for every three non-collinear points."
"There are at least 3 points in the plane that are not co-linear. There are at least 4 points in space that are not co-planar."
Not collinear:
Not all lined up.
Not coplanar:
do not occupy the same area or rectilinear plane
An axiom of Euclidean geometry states that there are at least four points in space that are not in the same plane.
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3. A sample of 10 networking sites for a specific month has a mean number of visits of 26.1 and a sample standard deviation of 4.2. Find a 99% confidence interval of the population mean.
The confidence interval is (22.68,29.52).
In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. Therefore, it can be concluded that there is a 95% probability that the true value falls within that range if a point estimate of 10.00 is produced using a statistical model with a 95% confidence interval of 9.50 - 10.50.
n = 10
x = 26.1
s = 4.2
Two-sided confidence interval :
CI = [tex](x-\frac{z*s}{\sqrt{n}},x+\frac{z*s}{\sqrt{n} } )[/tex]
= [tex](26.1-\frac{2.576*4.2}{\sqrt{10}},26.1+\frac{2.576*4.2}{\sqrt{10}} )[/tex]
= (26.1−3.42,26.1+3.42)
= (22.68,29.52)
Hence, the confidence interval is (22.68,29.52).
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In a survey of 2000 people who owned a certain type of car, 1200 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
The percentage of people who are satisfied with the car are 60%.
What is percentage?In mathematics →
a percentage is a number or ratio expressed as a fraction of 100.it is often denoted using the percent sign "%".Given is that in a survey of 2000 people who owned a certain type of car, 1200 said they would buy that type of car again.
The percentage of people who are satisfied with the car are -
{x}% = (1200/2000) x 100
{x}% = (12/20) x 100
{x}% = 12 x 5
{x}% = 60
Therefore, the percentage of people who are satisfied with the car are 60%.
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In the figure below, there are three right trangles. Complete the following.
A
C
D
B
(a) Write a similiarity statement relating the three right triangles.
ACDA~A~A
(b) Complete each proportion.
BD
BC
BC
DA
DC
=
0
BD
X
5
Part (a)
Let one of the angles be [tex]\theta[/tex]. After solving for all of the other angles using the triangle sum theorem, we see that [tex]\triangle CDA \sim \triangle BDC \sim \triangle BCA[/tex].
Part (b)
[tex]\frac{BD}{BC}=\frac{BC}{CA}, \frac{DA}{DC}=\frac{DC}{DB}[/tex]
2x³ + 4x = 3
has a solution between 0 and 1
Which One Doesn't Belong? Identify the linear expression that is not equivalent to the other three.
OA) (2x-1)+(-3x+7)
O B) (-5x + 3) + (4x + 3)
OC) (5x-6) + (-6x +12)
O D) (-5x-1)+(6x + 7)
The linear expression that is not equivalent to the other three is D) (-5x-1)+(6x + 7).
What is linear expression?A linear expression is an algebraic expression which is composed of constants, variables, and coefficients that are related by only addition and multiplication operations. It usually takes the form of ax + b, where 'a' and 'b' are constants and 'x' is a variable. Linear expressions can be used to describe various mathematical and physical phenomena, such as the slope of a line or the volume of a cylinder.
This linear expression is not equivalent to the other three because it does not have the same coefficient for the x terms and the constant terms. The other three expressions all have the same coefficients for the x terms and the constant terms, making them equivalent.
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Grace was born in 1995. How old will she be in 2027
Answer:
Grace will be 32 years old in 2027.
Answer: she will be 32 years old.
Step-by-step explanation:
A rectangular con lot of land is 0.4 kilometer long and 0.07 kilometer wide. What is its area in square kilometers?
Answer: 0.28 Km^2
Step-by-step explanation:
A= L x W
=0.4x0.7
=0.28
FIRST TO ANSWER GETS BRAINLIEST!! Melanie’s bank account balance is . She needs to pay $55 to her cell phone carrier and $80 to the landscaper. She also expects $250 from her sister to be added to her account.
(a) Write an expression Melanie can use to determine her bank account balance after paying these bills and receiving money from her sister.
(b) What is Melanie’s bank account balance after paying her bills and receiving money? Show any necessary work. Answer in a complete sentence.
Answer:
a 97- (55+80) +250
b Melanie has $212 left in her bank account.
Step-by-step explanation:
55 + 80 = 135
97 - 135 = -38
-38 +250 = 212
15. A pool can hold 850 gallons. It now has 598 gallons of
water and is being filled at the rate shown. How many
more minutes, m, can water continue to flow into the
pool before it overflows? Write and solve an inequality.
Then graph the solutions.