ABCD is a parallelogram, the value of x is 7
A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus.
The opposing sides of a parallelogram are equal and parallel.
AD = BC
5x + 3 = 38
Take 3 away from both sides.
5x + 3 - 3 = 38 - 3
5x = 35
Subtract 5 from both sides.
5x/5 = 35/5
x = 7
A two-dimensional shape with four sides, four vertices, and four angles is referred to as a quadrilateral. Convex and concave are the two main forms. Convex quadrilaterals can also be divided into a number of subgroups, including trapezoids, parallelograms, rectangles, rhombus, and squares.
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PLS HELP FAST + BRAINLIEST!!
PLEASE HELLP IM AWARDING 100 POINTS FOR THIS What is the scale factor, or constant of proportionality from Figure 1 to Figure 2?
Enter your answer as a decimal in the box.
Answer:
4:9
Step-by-step explanation:
Answer:
Scale factor = 2.25
Step-by-step explanation:
To find the scale factor between two similar shapes, we need to compare the corresponding sides of the shapes.
The scale factor is the ratio of the length of any side of one shape to the length of the corresponding side on the other shape.
From inspection of the given diagram, the ratio of the corresponding sides of the two similar figures is:
⇒ Figure 1 : Figure 2 = 8 : 18
Therefore, to find the scale factor from Figure 1 to Figure 2, divide the side length of Figure 2 by the corresponding side length of Figure 1:
[tex]\implies \sf Scale\;factor=\dfrac{18}{8}=2.25[/tex]
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.
Mark is going to an awards dinner and wants to dress appropriately. He is running behind schedule and asks his little brother to randomly select an outfit for him.
Mark has one blue dress shirt, one white dress shirt, one black dress shirt, one pair of black slacks, one pair of grey slacks, and one red tie. All six of his possible outfits are listed below.
Let
A
AA be the event that Mark's little brother selects an outfit with a white shirt and grey slacks and
B
BB be the event that he selects an outfit with a black shirt.
What is
P
(
A
or
B
)
P(A or B)P, left parenthesis, A, start text, space, o, r, space, end text, B, right parenthesis, the probability that Mark's little brother selects an outfit with a white shirt and grey slacks or an outfit with a black shirt?
let z=a+bi/a-bi where a and b are real numbers. prove that z^2+1/2z is a real number.
Answer:
Step-by-step explanation:
To prove that z^2 + 1/2z is a real number, we need to show that the imaginary part of z^2 + 1/2z is equal to zero.
We know that z = (a+bi)/(a-bi)
Multiplying the numerator and denominator by the complex conjugate of the denominator, we get
z = (a+bi)(a+bi)/(a-bi)(a+bi)
z = (a^2 + 2abi - b^2)/(a^2 + b^2)
Expanding z^2, we get:
z^2 = [(a^2 + 2abi - b^2)/(a^2 + b^2)]^2
z^2 = (a^4 + 2a^2b^2 + b^4 - 2a^2b^2 + 4a^2bi - 4b^2i)/(a^4 + 2a^2b^2 + b^4)
Simplifying, we get:
z^2 = (a^4 - b^4 + 2a^2bi)/(a^4 + 2a^2b^2 + b^4)
Now, let's compute z^2 + 1/2z:
z^2 + 1/2z = (a^4 - b^4 + 2a^2bi)/(a^4 + 2a^2b^2 + b^4) + 1/2[(a+bi)/(a-bi)]
To simplify this expression, we need to find a common denominator:
z^2 + 1/2z = (2a^5 - 2a^3b^2 + 3a^4b - 3ab^4 - 2b^5 + 3a^3bi + 3ab^3i)/(2(a^4 + 2a^2b^2 + b^4))
We can see that the imaginary part of z^2 + 1/2z is (3a^3b - 3ab^3)/(2(a^4 + 2a^2b^2 + b^4))
However, we know that a and b are real numbers, so the imaginary part of z^2 + 1/2z is zero.
Therefore, z^2 + 1/2z is a real number.
A water cooler springs a leak and empties in 2 minutes. The graph below shows the rate at which water leaks from the cooler as a function of time.
The amount of water that was in the cooler before it started leaking was 6 gallons.
Describe Integration?Integration is a mathematical process that involves finding the integral of a function. It is the reverse operation of differentiation, which involves finding the derivative of a function. The integral of a function is a measure of the area under the curve of the function, between two given limits of integration.
The graph shows the rate at which water leaks from the cooler as a function of time, which means that the y-axis represents the rate of leakage in gallons per minute (gal/min), and the x-axis represents the time in minutes.
Since we know that the cooler emptied in 2 minutes, we can integrate the leakage rate over the time interval [0, 2] to find the total amount of water that leaked out:
Total amount of water leaked = ∫[0,2] leakage rate(t) dt
The leakage rate is given by the graph, which consists of a straight line connecting two points: (0,6) and (2,0). We can express this line as a linear equation in slope-intercept form:
leakage rate(t) = mt + b
where m is the slope of the line and b is the y-intercept. To find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (0,6) and (x2, y2) = (2,0). Plugging in the values, we get:
m = (0 - 6) / (2 - 0) = -3
So the equation of the line is:
leakage rate(t) = -3t + 6
Now we can integrate this equation over the time interval [0, 2] to get the total amount of water leaked:
Total amount of water leaked = ∫[0,2] (-3t + 6) dt
= [-3t²/2 + 6t] from 0 to 2
= (-3(2)²/2 + 6(2)) - (-3(0)²/2 + 6(0))
= (6 - 0) - (0 - 0)
= 6 gallons
Therefore, the amount of water that was in the cooler before it started leaking was 6 gallons.
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The complete question is :
What is the average rate of change between
the points (17, 5) and (19, --1)?
The average rate of change between the points (17, 5) and (19, -1) is -3.
What is the average rate of change?If we have a given function y = f(x) with two known points (a, f(a)) and (b, f(b)), then the average rate of change in that interval [a, b] is:
R = ( f(b) - f(a))/(b - a)
Here we have the two points (17, 5) and (19, -1)
So we have:
a = 17 and f(a) = 5
b = 19 and f(b) = -1
Replacing that in the formula for the average rate of change we will get:
R = (-1 - 5)/(19 - 17)
R = -6/2
R = -3
The average rate of change is -3
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In △ △ ABC, CJ = 18. If CG = BG, what is KJ? Triangle A B C is divided by 4 segments. A H is the height. C J extends from C to side A B. B I extends from B to side A C. H I extends from the height on B C to I on A C. C J and B I intersect at point K. A J and B J are congruent. A I and C I are congruent.
Solving for CI in terms of the given lengths, we get: [tex]Cl=\frac{\sqrt{BG^{2} -IM^{2} } }{\sqrt{2} }[/tex]
Substituting this expression for CI and the given value for CG into the expression for BI, we get: [tex]BI=CG-\frac{\sqrt{BG^{2} -IM^{2} } }{\sqrt{2} }[/tex].
What is triangle?A triangle is a three-sided polygon, which is a closed two-dimensional shape with straight sides. In a triangle, the three sides connect three vertices, or corners, and the angles formed by these sides are called the interior angles of the triangle. The sum of the interior angles of a triangle is always 180 degrees. Triangles can be classified by their side lengths and angle measurements. For example, an equilateral triangle has three sides of equal length, and all of its angles are 60 degrees; an isosceles triangle has two sides of equal length, and its base angles are also equal; a scalene triangle has three sides of different lengths, and all of its angles are also different. Triangles are a fundamental shape in mathematics and geometry, and they have numerous applications in fields such as architecture, engineering, physics, and more.
Given by the question.
Based on the given information, we can start by drawing a diagram of triangle ABC and the segments AH, BJ, CI, CJ, and BI as described.
Since CG = BG, we can draw the perpendicular bisector of side AC passing through point G, which will intersect side AB at its midpoint M.
Now, we can see that triangle CGB is isosceles with CG = BG, so the perpendicular bisector of side CB also passes through point G. This means that G is the circumcenter of triangle ABC, and therefore, the distance from G to any vertex of the triangle is equal to the radius of the circumcircle.
Next, we can use the fact that AJ and BJ are congruent to draw the altitude from point J to side AB, which we will call JN. Similarly, we can draw the altitude from point I to side BC, which we will call IM.
Since AJ and BJ are congruent, the altitude JN will also be the perpendicular bisector of side AB, so it will pass through point M. Similarly, the altitude IM will pass through point G, which is the circumcenter of triangle ABC.
Now, we can use the Pythagorean theorem to find the lengths of JN and IM in terms of the given lengths:
[tex]JN^{2}= AJ^{2} -AN^{2} \\ = ( AH+HN)^{2} - AN^{2} \\=AH^{2} +2AH*HN+HN^{2}-AN^{2} \\[/tex]
[tex]IM^{2}= CI^{2} -CM^{2} \\=( CG-GM)^{2} -CM^{2} \\CG^{2}-2CG*GM+GM^{2} -CM^{2}[/tex]
Since CG = BG and GM = BM (since M is the midpoint of AB), we can simplify the expression for IM^2 as follows:
[tex]IM^{2}[/tex] = [tex]BG^{2}[/tex] - 2BG * BM + [tex]BM^{2}[/tex] - [tex]CM^{2}[/tex]
= [tex]BG^{2}[/tex] - [tex]BM^{2}[/tex] - [tex]CM^{2}[/tex]
Now, we can use the fact that BJ and CI intersect at point K to find the length of KJ:
KJ = BJ - BJ * (CK/CI)
= BJ * (1 - CK/CI)
= BJ * (1 - BM/CM)
To find BM/CM, we can use the fact that triangle BCI is isosceles with BI = CI, so the altitude IM is also a median of the triangle. This means that CM = 2/3 * BI. Similarly, we can find BJ in terms of JN using the fact that triangle ABJ is isosceles with AJ = BJ:
BJ = 2 * JN
Substituting these expressions into the equation for KJ, we get:
KJ = 2 * JN * (1 - 2/3 * BI/CM)
Now, we just need to find BI/CM in terms of the given lengths. Using the fact that triangle BCI is isosceles with BI = CI, we can find BI in terms of CG:
BI = CG - CI
Substituting this expression into the equation for [tex]IM^{2}[/tex]and simplifying, we get:
[tex]IM^{2}[/tex] =[tex]BG^{2}[/tex] - CG * CI
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Two cellphone companies are offering different rate plans. Rogers is offering $19.99 per month, which includes a
maximum of 200 weekday minutes plus $0.35 for every minute above the maximum. TELUS is offering $39.99 for a
maximum 300 weekday minutes, but it charges $0.10 for every minute above the maximum. Above how many minutes
would TELUS be the better choice?
If a drug has a concentration of 5.315 mg per 3.743 mL, how many mL are needed to give 4.719 gram of the drug? Round to 1 decimal.
Answer:
888.4 mL.
Step-by-step explanation:
To solve this problem, we can use the following formula:
Amount of drug (in mg) = concentration (in mg/mL) × volume (in mL)
We are given the concentration of the drug as 5.315 mg per 3.743 mL. To find the volume of the drug needed to give 4.719 g, we need to rearrange the formula to solve for volume:
Volume (in mL) = amount of drug (in mg) ÷ concentration (in mg/mL)
First, we need to convert 4.719 g to mg by multiplying by 1000:
4.719 g × 1000 mg/g = 4719 mg
Now we can substitute the given concentration and the calculated amount of drug into the formula and solve for volume:
Volume (in mL) = 4719 mg ÷ 5.315 mg/mL
Volume (in mL) ≈ 888.5 mL
Therefore, approximately 888.5 mL of the drug are needed to give 4.719 g. Rounded to 1 decimal, the answer is 888.4 mL.
ellas normal rate of pay is $10.40 an hour.
How much is she paid for working 5 hours overtime one Saturday at time-and-a-half?
Answer:
52
Step-by-step explanation:
10.40 TIMES 3
How many fractions between and inclusive can be written with a
denominator of 15?
The number of fractions between 0 and 1 (inclusive) with a denominator of 15 can be found using the formula (n-1)/n, where n is the denominator.
So, to answer your question, we can use the formula and plug in 15 for the value of n:
(15-1)/15 = 14/15
Therefore, there are 14 fractions between 0 and 1 (inclusive) with a denominator of 15.
Mary is 21 years old. She buys 50/100/25 liability insurance, and collision and
comprehensive insurance, each with $500 deductibles. What is her total annual
premium? Round to the nearest dollar. Do not state the units. Be sure to show work.
Liability Insurance
Type Amount Premium
25/50 $240
50/100 $385
100/300 $450
Property damage 25 $210
50 $150
100 $140
Collision and comprehensive premiums
$250 $172 $112
$500 $102 $87
$750 $85 $52
Rating factor
Age
17-20 male Female
3.1 1.64
21-24. 2.53. 1.22
25-29 1.73 1.0
According to the given information, Mary's total annual premium is $574 (rounded to the nearest dollar).
What is multiplication ?In mathematics, multiplication is an arithmetic operation that combines two or more numbers to produce a product. It is represented by the symbol "×" or "*", or by placing the numbers next to each other with no symbol between them.
According to the given information:Mary is 21 years old, so according to the rating factor table, her rating factor is 1.22 for a female.
For liability insurance, Mary has chosen the 50/100/25 coverage, which means $50,000 for bodily injury per person, $100,000 for bodily injury per accident, and $25,000 for property damage per accident. The premium for this coverage is $385.
For collision and comprehensive insurance, Mary has chosen a $500 deductible, so her premiums are $102 for collision and $87 for comprehensive.
To find the total annual premium, we add up the premiums for liability insurance and collision/comprehensive insurance:
Total premium = Liability premium + Collision premium + Comprehensive premium
Total premium = $385 + $102 + $87
Total premium = $574
Therefore, according to the given information, Mary's total annual premium is $574 (rounded to the nearest dollar).
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Jacobil and her friends are making a large homemade circular pizza. Jacobi cut her piece of pizza and it formed a sector with a radius of 9 Inches and a central angle measuring 75°. If the other 5 friends
equally share the remaining portion of the pizza, what is the approximate area of pizza each person receives? Use 3.14 for and round your answer to the nearest hundredth.
Jacobi get area of pizza is 52.987 in²
5 friends getting equally share each one area of pizza is 40.27 in²
Area of sectorAny point in a plane that is a certain distance away from another point forms a circle. The fixed point is known as the center of the circle and the fixed distance is known as the radius of the circle.
The formula for calculating a circle's sector's area is (∅/360°) ×π×r²
Jacobi get area of pizza =(75/360°) × π×9²=52.987in²
5 friends getting pizza with each central angle measuring=360°-75°/5
=57°
5 friends getting each one area of pizza = (57/360°) × π×9²
40.27in².
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given f(x) and g(x) find the value of (gof)(5)
Answer:
Assuming that (gof)(5) means (g(f(5))):
(gof)(5) = g(f(5)) = g(3x + 7) = 5x + 2
Therefore, (gof)(5) = 5(3x + 7) + 2 = 15x + 17.
Please help!!!!!!!!!!!!!!
Step-by-step explanation:
try this option (see the attachment), answers are marked with red colour.
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?
In the isosceles trapezoid, what is the length of LA?
A) 15
B) 17
C) 16
Answer:
A) 15 idek
Step-by-step explanation:
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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5. What is the difference between (-3)² and 3²
Answer:
the difference is the first one, (-3)^2, is negative while the other is positive
Step-by-step explanation:
HEEELLLLPPPPP MEEEEEEEEE
1. Solve.
a. 2/5t = 6
b. -4.5 = a-8
c. 1/2+p=-3
d. 1/2 = x3
e. -12 = -3y
The equation is saying that -12 is equal to -3 multiplied by y. To solve for y, divide both sides by -3. This would give an answer of 4.
What is equation?An equation is a mathematical statement that expresses the equality or inequality of two values or expressions. It consists of two expressions connected by an equals sign, inequality sign or other relational operator. Equations can involve numbers, variables, and operations such as addition, subtraction, multiplication, division and exponentiation. An equation can be used to solve problems related to mathematics, science, engineering, finance, and many other disciplines. Equations can also be used to model and describe real-world phenomena.
t = 30
a = 12.5
p = -5.5
x = 2/3
y = 4.
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a. t = 30/2; To solve this equation, divide both sides by 2/5. The resulting equation is t = 30/2.
What is equation?An equation is a mathematical statement that expresses the equality of two expressions by using an equals sign (=). It states that the two expressions on either side of the equals sign are equal in value. An equation is an example of a mathematical problem, which can be used to solve real-world problems.
b. a = 4.5; To solve this equation, add 8 to both sides. The resulting equation is a = 4.5.
c. p = -7/2; To solve this equation, add 3 to both sides. The resulting equation is p = -7/2.
d. x = 2; To solve this equation, divide both sides by 3. The resulting equation is x = 2.
e. y = 4; To solve this equation, divide both sides by -3. The resulting equation is y = 4.
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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
[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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What is the meaning of "invertible n x n matrices"?
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
PLEASE HELP ASAP! This composite figure is created by placing a sector of a circle on a triangle. What is the area of this composite figure? Use 3.14 for n. Round to the nearest hundredth. Show your work.
Answer: 24
Step-by-step explanation:
To find the area of the composite figure, we need to find the area of the sector and the area of the triangle and then add them together.
Area of sector = (θ/360) * π * r^2, where θ is the angle of the sector in degrees, r is the radius of the circle.
The angle of the sector can be found by subtracting the angle of the triangle from 360 degrees. The radius of the circle can be found by dividing the length of the arc by the angle of the sector.
Length of the arc = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 4 = 4.19
Radius of the circle = 4.19/60 = 0.07
Angle of sector = 360 - 60 = 300 degrees
Area of sector = (300/360) * 3.14 * 0.07^2 = 0.0041
The area of the triangle can be found using the formula:
Area of triangle = (1/2) * base * height = (1/2) * 8 * 6 = 24
Therefore, the total area of the composite figure is:
0.0041 + 24 = 24.0041
Rounding to the nearest hundredth, the area of the composite figure is approximately 24.00.
Determine the number of elements of a set and represent the number of elements using a symbol
We can represent the number of elements in a set using the symbol |A| or n(A). So, we can say |A| = 5 or n(A) = 5. We can make generalizations about the equality of sets based on the definition above.
What is set?In mathematics, a set is a collection of distinct objects, which can be anything such as numbers, letters, or other mathematical objects. These objects are called the elements or members of the set. Sets can be defined using various methods such as listing the elements, describing properties of the elements, or using set-builder notation. For example, we can define the set of even numbers using set-builder notation as {x | x is an integer and x is divisible by 2}. Sets play a fundamental role in various branches of mathematics, including algebra, geometry, and analysis. They are used to define mathematical structures such as groups, rings, and fields, and to study various mathematical concepts such as functions, relations, and cardinality.
Here,
11.1.4 To determine the number of elements of a set, you need to count the number of distinct elements in the set. For example, if you have a set A = {1, 2, 3, 4, 5}, then the number of elements in set A is 5.
11.1.5 Two sets are equal if they have exactly the same elements. For example, if we have set A = {1, 2, 3} and set B = {3, 2, 1}, then A and B are equal sets because they contain the same elements, even though the order of the elements is different. We can write this as A = B. If two sets are not equal, then we use the symbol ≠ to denote inequality. For example, if set A = {1, 2, 3} and set B = {4, 5, 6}, then A ≠ B.
Some of these generalizations are:
Two sets are equal if and only if they have the same elements.
The order of the elements in a set does not matter for equality.
If two sets have different elements, then they are not equal.
If two sets have the same elements, but with different multiplicities, then they are not equal.
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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
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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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?
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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Find a particular solution of the differential equation
-(9/4)y" + 4y' + y = 2xe^(3x)
using the Method of Undetermined Coefficients (primes indicate derivatives with respect to x.
yp= ?
The value of yp is equal to negative two divided by the expression 27x raised to the power of 27/4 and multiplied by e raised to the power of 3x.. This could be found using the Method of Undetermined Coefficients.
To find the particular solution using the Method of Undetermined Coefficients, we assume that the particular solution is of the form:
yp = Axⁱe⁽³ˣ⁾
where A is a constant to be determined and i is the smallest positive integer that makes yp linearly independent from the complementary function.
First, we find the complementary function by solving the characteristic equation:
r² - (4/3)r + 1 = 0
Using the quadratic formula, we get:
r = (4/3 ± √(16/9 - 4))/(-9/4) = -3/4 or -1
So the complementary function is:
yc = c₁e⁻ˣ + c₂e⁽-(3/4)x⁾
To determine the value of A, we substitute yp into the differential equation and equate coefficients of like terms.
yp' = A(xⁱe⁽³ˣ⁾)' = A(xⁱe⁽³ˣ⁾)(3e⁽³ˣ⁾ + i)
yp" = A(xⁱe⁽³ˣ⁾)" = A(xⁱe⁽³ˣ⁾)(9e⁽³ˣ⁾ + 6ie⁽³ˣ⁾ + i(i+3))
Substituting these into the differential equation and simplifying, we get:
(81/4)A(xⁱe⁽³ˣ⁾) + 4A(xⁱe⁽³ˣ⁾)(3e⁽³ˣ⁾ + i) + Axⁱe⁽³ˣ⁾ = 2xe⁽³ˣ⁾
Simplifying further, we get:
A(81/4 + 12i)e⁽³ˣ⁾xⁱ = 2x
To satisfy this equation for all x, we must have:
A(81/4 + 12i) = 0
and
A = 2/(xⁱe⁽³ˣ⁾)
Since A cannot be zero, we must have:
81/4 + 12i = 0
i = -27/4
Therefore, the particular solution is:
yp = -2/(27x⁽27/4⁾e⁽³ˣ⁾)
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△CDE∼△PQR. CD=9 m, EC=15 m, PQ=15 m. What is the length of RP?
Answer:
RP = 25
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{RP}{EC}[/tex] = [tex]\frac{PQ}{CD}[/tex] ( substitute values )
[tex]\frac{RP}{15}[/tex] = [tex]\frac{15}{9}[/tex] ( cross- multiply )
9 RP = 15 × 15 = 225 ( divide both sides by 9 )
RP = 25
Use implicit differentiation to find an equation of the tangent line to the curve sin(x+y)=8x−8y at the point (π,π)
The equation of the tangent line to the curve sin( x y) = 8x- 8y on the factor( π, π) is y = (7/9) x-( 2π/ 9).
To discover the equation of the tangent line to the curve sin( x y) = 8x- 8y on the point( π, π), we want to apply implicit differentiation to discover the pitch of the tangent line at that point.
We begin through differencing both sides of the equation with reference to xcos( x y)( 1 dy/ dx) = eight- 8dy/ dx
After, we can simplify the expression by isolating the terms beholding dy/ dx on one aspect
cos( x y) cos( x y) dy/ dx = 8- 8dy/ dx
8 cos( x y)) dy/ dx = 8- cos( x y)
dy/ dx = ( 8- cos( x y))( 8 cos( x y))
Now we're suitable to discover the pitch of the tangent line at the factor( π, π) by plugging in x = π and y = π into the expression we simply derived
dy/ dx = ( 8- cos( 2π))( 8 cos( 2π))
dy/ dx = ( 8- 1)/( 8 1)
dy/ dx = 7/ nine
Thus, the pitch of the tangent line to the curve sin( x y) = 8x- 8y at the factor( π, π) is7/9.
To find the equation of the tangent line, we can use the point- slope form of the equation
y- y1 = m( x- x1)
In which m is the pitch we simply set up, and( x1, y1) is the point( π, π). Plugging in the values, we get
y- π = ( 7/ nine)( x- π)
Simplifying, we get
y = ( 7/ nine) x-( 2π/ nine)
Thus, the equation of the tangent line to the curve sin( x y) = 8x- 8y on the factor( π, π) is y = (7/9) x-( 2π/ 9).
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