50 POINTS!!!
I NEED STEPS
Answer:
[tex]\dfrac{3}{a-6}\quad \textsf{if}\;\;a \neq -6,a \neq 6[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{a^2}{36-a^2}[/tex]
Rewrite the third fraction:
[tex]\implies \dfrac{a^2}{36-a^2}=\dfrac{-a^2}{-(36-a^2)}=\dfrac{-a^2}{a^2-36}[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Difference of two squares }\\\\$x^2-y^2=(x-y)(x+y)$\\\end{minipage}}[/tex]
Apply the difference of two squares to the denominator of the third fraction:
[tex]\implies a^2-36=a^2-6^2=(a-6)(a+6)[/tex]
Therefore the expression can be written as:
[tex]\implies \dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{-a^2}{(a-6)(a+6)}[/tex]
[tex]\implies \dfrac{a}{a-6}-\dfrac{3}{a+6}-\dfrac{a^2}{(a-6)(a+6)}[/tex]
The least common multiplier (LCM) of the denominator is (a - 6)(a + 6).
Adjust the fractions based on the LCM:
[tex]\implies \dfrac{a(a+6)}{(a-6)(a+6)}-\dfrac{3(a-6)}{(a-6)(a+6)}-\dfrac{a^2}{(a-6)(a+6)}[/tex]
Simplify:
[tex]\implies \dfrac{a^2+6a}{(a-6)(a+6)}-\dfrac{3a-18}{(a-6)(a+6)}-\dfrac{a^2}{(a-6)(a+6)}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}-\dfrac{d}{c}=\dfrac{a-b-d}{c}:[/tex]
[tex]\implies \dfrac{a^2+6a-(3a-18)-a^2}{(a-6)(a+6)}[/tex]
Simplify:
[tex]\implies \dfrac{3a+18}{(a-6)(a+6)}[/tex]
Factor out 3 from the numerator:
[tex]\implies \dfrac{3(a+6)}{(a-6)(a+6)}[/tex]
Cancel the common factor (a + 6):
[tex]\implies \dfrac{3}{a-6}[/tex]
Therefore:
[tex]\dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{a^2}{36-a^2}=\dfrac{3}{a-6}\quad \textsf{if}\;\;a \neq -6,a \neq 6[/tex]
Pls help me with math
The correct expression to represent the similarity of these two triangles is,
21/35 = x/30.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know two triangles are similar if the ratio of their corresponding sides is equal.
Therefore, The correct way to represent the similarity is,
21/35 = x/30.
We can solve for x here,
35x = 21×30.
5x = 3×30.
x = 3×6.
x = 18.
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Gregory(g) is 20 years older than his cousin Mark(m). Mark is 6 years younger than his
sister Louanne(L). Write an expression to represent the sum of their ages.
An expression to represent the sum of their ages is as follows.
g = 14 + L
How do you figure up the total age?If the ratio of the ages of X and Y is p:q and their sum is X, then the following formula can be used to calculate Y's age: Age of Y = Y/Total Ages x Total Ratios. Age of Y = (p+q) q x A.
According to the given information:Assume that L is Louannel's sister's age, m is Mark's age, and g is Gregory's age.
Gregory's age difference with his cousin Mark, who is 20 years older (m).
∴ g = 20 + m .............(1)
Also given that Mark is 6 years younger than his sister Louanne(L)
∴ m = L - 6 ............(2)
Now, substituting m = L - 6 from (2) in (1),
∴ g = 20 + L - 6
∴ g = 14 + L
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Q1. In the given figure, ABCD is a parallelogram. Complete each statement along with the definition or property used.
(i) AD = ……….. (ii) DC = ……….. (iii) ∠DCB = ………..
(iv) ∠ADC = ……….. (v) ∠DAB = ……….. (vi) OC = ………..
(vii) OB = ……….. (viii) m∠DAB + m∠CDA = ………..
Step-by-step explanation:
i. AD = BC= 6cm (each two opposite sides are equal in length in parallelogram)
ii.DC=AB=9cm (each two opposite sides are equal in length in parallelogram)
iii.DCB=60 ,, bec DC and AB are parallel so their interior angles are supplementary their sum equals 180°
so DCB = 180-120=60°
iv.ADC=ABC = 120° because each two opposite angles are equal in measure in parallelogram
v. DAB=DCB =60° because each two opposite angles are equal in measure in parallelogram
vi. OC=AO =7cm because the diagonals of parallelogram bisect each other
vii. OB=DO=5cm because the diagonals of parallelogram bisect each other
viii . DAB=60° ,, CDA= 120 °
DAB+CDA =180°
or you could simply say that because DC and AB are parallel their interior angles are supplementary their sum is 180°
Kate loves to read. She wants to read all 70 books in her bookcase and has already finished 2. Write an equation to represent the time it will take for Kate to read all 70 books if she can read 3 books per month.
Answer:
simply do 70 divided by 12, then that divided by 3, in total it should take 1, 2, or 3 hours to read 3 books a month
Step-by-step explanation:
~50 POINTS~ don’t explain.
A
B
C
Answer:
C
Step-by-step explanation:
The angles at point A have to be congruent so that you have two congruent angles. and one congruent side, which give SAA.
From the image, we can see than angle B and angle D are congruent. We also know that line AC is congruent to itself since it shared between the two triangles. Since we need one more angle, that angle has to be angle A.
Find the 66th term of the arithmetic sequence 25, 10, -5, ...
On solving the provided question, we can say that - The provided arithmetic sequence's 66th term is -950.
Arithmetic sequence is what?An arithmetic sequence is a set of integers that are ordered and have a common difference between each following word.An ordered group of integers with a shared difference between each word is known as an arithmetic sequence.
The given arithmetic sequence is,
25, 10, -5, .....
The sequence's initial word, a, equals 25, while the common difference, d, equals -15.
Use the formula nth term of arithmetic series = a+ (n-1)d to determine the 66th term of the sequence.
66th term =
[tex]25 + (66-1)(-15)\\ = 25 + 65× (-15)\\ = 25 - 975\\ = -950\\[/tex]
The 66th term of the arithmetic sequence is -950.
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Solve the differential equation by variation of parameters. y + 2y' + y = e^-t ln t y(t)=
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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13. Which situation can be represented bya true proportion?
A car used 3 gallons of gas to drive 72 miles on a highway and used 4 gallons of gas to drive 72 mileš town.
A store charged $20 for 2 shirts and charged $25 for 3 shirts.
A signal light flashed yellow 7 times in 28 seconds and flashed red 5 times in 35 seconds.
An alarm on a clock beeped 7 times in 6 seconds and beeped 14 times in 12 seconds.
The example of a proportion, is An alarm on a clock beeped 7 times in 6 seconds and beeped 14 times in 12 seconds.
What is a proportion?The term proportionality describes any relationship that is always in the same ratio.
Given are some statements,
a) A car used 3 gallons of gas to drive 72 miles on a highway and used 4 gallons of gas to drive 72 miles in a town.
Solution:- In this case, we see, a car is using 3 and 4 gallons of gas for driving in a highway and in a town for 72 miles respectively.
Since, the distance is same and quantity of gases is different therefore, this can not be represented as a proportion.
b) A store charged $20 for 2 shirts and charged $25 for 3 shirts.
Solution:- In this, let's first find the unit prices for each,
for $20 there are 2 shirts, therefore, for 1 shirt it will be $10, and for 3 shirts it costs $25, therefore, for 1 shirt it will cost $8.3
Since, unit price for both is not equal, therefore, this can not be represented as a proportion.
c) A signal light flashed yellow 7 times in 28 seconds and flashed red 5 times in 35 seconds.
Solution:- As in 2nd option, will here also find unit rate, since, yellow light is flashing 7 times in 28 seconds, therefore, in 4 seconds it will be flashed for 1 time, similarly, red light is flashing 5 times in 35 seconds, therefore, in 7 seconds it will be flashed for 1 time,
Since, both unit rates are not equal, therefore, this can not be represented as a proportion.
d) An alarm on a clock beeped 7 times in 6 seconds and beeped 14 times in 12 seconds.
Solution:- Again we will find unit rate, since, the alarm is beeping 7 times in 6 seconds, therefore, it will beep for 1 time in 6/7 seconds, similarly, it is beeping 14 times in 12 seconds, so for 1 time it will beep in 12/14 = 6/7 seconds.
Here, we see that, both the unit rates are equal, therefore, this is an example of a proportion.
Hence, the last option is the correct example.
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The table shows the balances of two bank accounts for 3 months. In what month will the balance of account A be equal to the balance of account B?
As per Given data,
The month in which the balance of two bank accounts A is become equal to the balance of account B is 30thmonths,
How to find unknown values?Unknown variables are used to find the unknown values of the problem using the algebraic expressions.
Month Account A Account B
0 $ 100 $ 250
1 $ 125 $ 270
2 $ 150 $ 290
Clearly
The amount in account A is growing with $25 each month. Thus, the amount in this account in nth month is,
100+25[tex]n[/tex]
The amount in account B is just growing with $20. Thus, the amount in this account in nth month is,
250+20[tex]n[/tex]
x month
balances of two
account becomes equal,
then
100 + 25x =250 + 20x
25x - 20x = 250 - 100
5x = 150
x =30
Therefore, in 30th month balance of account A equal to balance of account B
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Q. The table shows the balances of two bank accounts for 3 months. In 30th month will the balance of account A be equal to the balance of account B?
Month Account A Account B
0 $100 $250
1 $125 $270
2 $150 $290
Papa Bear ate a quarter of the pie. Mama Bear ate a third of what was left. Baby Bear ate half of what was left. How much of the pie was left for Goldilocks
Mama bear only ate (1/4) of the pie, leaving Goldilocks with the remaining (1/8) fraction.
Which fraction is it?The fraction is expressed in the form a/b, where an is referred to as the numerator and b is referred to as the denominator. The fraction is a rational number that only divides two integers.
Let the pie's largest portion be a.
Half of the pie was consumed by Papa Bear.
Papa Bear then consumed = (1/2)a.
Rest of the pie is equal to a- (1/2).
a= (1/2)a
Mama bear consumed (half) of the remaining pie.
Mother bear consumed (1/2)(1/2).
pie portion a= (1/4) pie portion after mom bear has eaten = (1/2)
a- (1/4)a= (1/4)a
Baby bear afterwards consumed (half) of the remaining pie.
Baby bear ate (1/2)(1/4), thus. After the young bear has finished eating, the remaining pie is equal to (1/4) a- (1/8)a= (1/8)
The remainder of the component was given to GoldLiocks.
As a result, mom bear only ate (1/4) of the pie, leaving Goldilocks with the remaining (1/8) portion.
The complete question is Papa Bear ate 1/2 of a pie. Mama Benr ate 1/2 of what was left Baby Bear ate 1/2 of what
was left after Mama Bear finished.
3) What fractional part of the pie did Mama Bear eat?
4) What fractional part of the pie was left for Goldilocks?
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Which transformation produces another triangle that has the same area as the one shown
A reflection in the line y = -2 and then translation of 2 units right will create the same area so option (C) will be correct.
How to plot a graph?f we shift the triangle anywhere then there will be no change in the area but if we apply the scale factor then since the dimension changes so its area will also change.
In all options, there is a scale factor so it will change area but in option C
A reflection in the line y = -2 reflection gives a mirror image about y = -2 but no changes in area then translation of 2 units right will shift triangle 2 units right but no effect in the area.
Hence "A reflection in the line y = -2 and then translation of 2 units right will create the same area".
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Which of the following are irrational numbers?
Choose two correct answers.
3.05
√17
√27
√81
Answer:√17
√81
√27
This 3 numbers are irrational number
Answer:
17 and 27 are irrational
Step-by-step explanation:
What is a binomial Class 8?
The Binomial Expression is defined as the type of algebraic expression that consists of exactly two terms .
What is Binomial Expression ?
The algebraic expression which contains exactly only two terms is termed as binomial expression . It is called a two term polynomial.
the binomial is also called a sum or a difference between two or more monomials. Binomial is the simplest form of a polynomial.
Some Examples of Binomial Expression are ⇒ [tex]4x^{2} +6y^{2}[/tex] , [tex]xy^{3} +xy[/tex] ;
Various Mathematical Operations can be performed on Binomial Expression such as Addition , Subtraction , Multiplication and Division .
and The Equation that contains one or more binomial expression is called as a Binomial Equation.
The given question is incomplete , the complete question is
What is a Binomial Expression ?
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in a right triangle, the two sides adjacent to the right angle are known as the
Answer:legs
Step-by-step explanation: I cannot give a explanation since it is simply math, anything adjacent to a right angle is called a leg.
Answer: the legs? or opposite and hypotenuse.
Step-by-step explanation:
How do you find the zero’s algebraically?
To find the zeros of a polynomial algebraically, you can use the following steps:
Write the polynomial in standard form, with the terms arranged in descending order of the degree of the term. For example, if the polynomial is 3x^2 - 2x + 5, it is already in standard form.
Set the polynomial equal to zero. For example, if the polynomial is 3x^2 - 2x + 5, you would set the equation equal to zero like this:
3x^2 - 2x + 5 = 0
Use the quadratic formula to find the solutions (i.e., the zeros) of the equation if the polynomial is a quadratic (degree 2). The quadratic formula is:
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
where a, b, and c are the coefficients of the polynomial, and sqrt represents the square root.
For example, if the polynomial is 3x^2 - 2x + 5, the solutions would be:
x = (-(-2) +/- sqrt((-2)^2 - 4 * 3 * 5)) / (2 * 3)
x = (2 +/- sqrt(4 - 60)) / 6
x = (2 +/- sqrt(-56)) / 6
Since the square root of a negative number is not a real number, there are no real solutions (zeros) for this polynomial.
Use the Rational Root Theorem to find the solutions of the equation if the polynomial is not a quadratic. The Rational Root Theorem states that if a polynomial of degree n has a rational root p/q (where p and q are integers and q is not equal to zero), then p must be a divisor of the constant term and q must be a divisor of the coefficient of the term of highest degree.
For example, if the polynomial is x^3 - 2x^2 + x - 6, the constant term is -6 and the coefficient of the term of highest degree is 1. The divisors of -6 are -6, -3, -2, -1, 1, 2, 3, and 6. The divisors of 1 are 1 and -1. Therefore, the possible rational roots of this polynomial are -6, -3, -2, -1, 1, 2, 3, and 6.
To find the actual roots, you can try each of these numbers as a root and see if it works. For example, if you try -6 as a root, you would get:
(-6)^3 - 2(-6)^2 + (-6) - 6 = 0
(-216) - (-72) + (-6) - 6 = 0
-144 - 6 - 6 = 0
-156 = 0
This equation is not true, so -6 is not a root of the polynomial. You can repeat this process for each of the other possible rational roots until you find all of the roots of the polynomial.
In the Himalaya Mountains along the border of Tibet and Nepal, Mount Everest reaches a record height of 29,035 feet. How high is Mt. Everest in miles
The height of the mt. Everest in miles exists 5.499 miles.
What is meant by unit conversion?By changing the unit of measurement, a quality can be expressed differently. In contrast to distance, which can be stated in miles, kilometers, feet, or any other unit of length, time can also be expressed in minutes rather than hours.
By multiplying or dividing a number, a conversion factor can be used to change one set of units to another. The right conversion factor to an equal value must be used when a conversion is required. The correct conversion factor, for instance, is 12 inches to 1 foot when converting between inches and feet.
The height of the mt. Everest is : 29035 feet.
The unit conversion is given as :
5280 feet = 1 mile
1 feet = 1/5280 mile
So, 29035 feet =29035 × 1/5280 miles
29035 feet = 29035/5280 miles
29035 feet = 5.499 miles
So, the height of the mt. Everest in miles is 5.499 miles.
The complete question is:
In the Himalaya mountains along the border of Tibet and Nepal, mount Everest reaches a record height of 29,035 feet. how high is mt. Everest in miles? use the conversion equivalency of 1 mile = 5280 feet.
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Answer: The height of the Mount Everest in miles is 5.499 miles
Step-by-step explanation:
1 miles = 5,280 feet
For feet to miles conversion, you should multiply your length value by 0.0001894: mi = ft × 0.0001894 .For miles to feet conversion, you should multiply your length value by 5,280: ft = mi × 5,280 .1 feet = 1/5280 mileso So, 29035 feet = 29035×1/528029035 feet = 29035/5280in the given question, 29035 feet = 5.499 milesSo, the height of the mt. Everest in miles is 5.499 mileTo learn more about it refer to:
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For one kindergarten class in his district, a researcher determines which children already can read simple words and which children cannot upon entering kindergarten. The children are followed until third grade, at which point they are tested to determine the grade level at which they are reading. Those children who were reading simple words upon entering kindergarten are found to be reading at a higher level than those who could not read simple words upon entering kindergarten. Fill in the Blank: The researcher _____________________________. Select one: a. can conclude that children should be taught to read in preschool, as there are clear benefits to reading early. b. needs to check the reading level of the children's parents. c. cannot establish a cause-and-effect relationship because the study did not use a random sample of kindergarten students. d. finds these results beneficial, as there may be confounding variables in this study. e. needs to retest in sixth grade or no conclusions can be reached.
The correct answer is that we cannot conclude that being able to read is beneficial for them as there can be various cause and effect relation.
A research is conducted to collect information about a specific topic for the purpose of study. A group of population is asked to fill a survey form or answer questions based on the research topic.
This data is collected and analyzed to get the required result.
Here, in this question kindergarten students are the population from whom data is collected . Here, the conclusion is that having the ability to read and write from before only doesn't means they will have academic intelligence later.
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Help i got some more math
x = 5
AB = 6
BC = 13
What is a line?A line can be defined as a straight set of points that extend in opposite directions, It has no ends in both directions(infinite). It has no thickness. It is one-dimensional.
Given,
AB = 2x - 4
BC = 3x - 2
AC = 19
By the figure
AB + BC = AC
2x - 4 + 3x - 2 = 19
5x - 6 = 19
5x = 25
x = 5
AB = 2 × 5 - 4 = 10 - 4 = 6
BC = 3 × 5 - 2 = 15 - 2 = 13
Hence the value of x, AB and BC is 5, 6, 13 respectively.
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write the equation of the line in fully simplified slope intercept form
The equation of a line can be written in both slope-intercept form and standard form.
Write the equation of the line in fully simplified slope intercept form?The equation of a line in slope intercept form is written as y = mx + b, where m is the slope of the line, and b is the y-intercept of the line.The simplified form of the equation of a line is obtained by first identifying the slope of the line. The slope of a line is the ratio of the vertical change (rise) over the horizontal change (run). The slope of a line is written as m = (y2 - y1)/(x2 - x1).Next, the y-intercept of the line is found. The y-intercept is the point where the line intersects the y-axis. To find the y-intercept, substitute the slope into the equation of the line and solve for b.Once the slope and y-intercept have been determined, the equation of the line can be written in fully simplified slope intercept form as y = mx + b.For example, if the slope of a line is 4 and the y-intercept is 6, then the equation of the line in slope intercept form is y = 4x + 6.To learn more about slope intercept form refer to:
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Select all the equation that depicts one of the properties of exponents
Answer:
1st, 4th and 5th are correct.
Step-by-step explanation:
There are 96 girls in a junior class of 176 students. Find the ratio of girls to boys.a.11:6c.6:11b.5:6d.6:5
The ratio tells us how often one number is contained in another. In the class, there are six girls for every five boys. D is the right answer.
What is a Ratio?A ratio is an ordered pair of numbers a and b, expressed as a / b, where b is not equal to 0. A percentage is an equation in which two ratios are made equal to one another. For instance, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls) One-fourth are boys and three-fourths are girls.
The ratio tells us how often one number is contained in another.
Considering that 96 of the 176 junior students are female. Consequently, the class's gender distribution is,
96 girls are present.
80 boys out of 176, or 96 boys.
Currently, the junior class's gender distribution is as follows:
Girls to Boys in Ratio
96 girls and 80 boys.
Divide the numerator and denominator by 16 to simplify.
Boys/Girls: 6 to 5.
Therefore, the answer is option d) 6:5.
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Alexis deposited $6,000 into an account that pays 3% interest compounded annually. He doesn’t withdraw or deposit any money for 4 years. How much interest did he earn in that time?
Answer:
$720
Step-by-step explanation:
The formula is:
A = P(1 + rt)
We know
P = $6000
r = 3% = 0.03
t = 4 years
A = 6000( 1 + 0.03 x 4) = $6720
Now we have to find the interest by taking
$6720 - $6000 = $720
So, he earns $720 in interest in 4 years.
How much water and how much drink mix should Jerome use to make enough energy drink for all the runners? Create a table to show your work and explain your results in writing.
Answer:
well, you didnt give me any numbers or variables, so ill do it like this. if the container is the size of a pint, and there are 8 runners, and a pint equals 16 fluid ounces, in turn it should end as that each runner gets 2 fluid ounces of energy drink
Step-by-step explanation:
PLEASE HELP ASAP I WILL GIVE BRAINLIEST!!!
Answer:
try -5
Step-by-step explanation:
mainly because it says -3 plus 5 and there's only 4 and 5 so It can't really go further
Answer:try -5
Step-by-step explanation:
mainly because it says -3 plus 5 and there's only 4 and 5 so It can't really go further
ASAP PLEASE WILL GIVE BRAINLIEST
The two (2) possible locations of point F include the following: F. [7, 9.5].
How to determine the coordinates of F?In this scenario, line ratio would be used to determine the coordinates of the point on the directed line segment that partitions the segment into a ratio of 5 to 3.
Mathematically, line ratio can be used to determine the coordinates of F and this is modeled by this mathematical expression:
F(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
Given the following parameters:
Point (x, y)= (4, 11)
Point (x, y) = (8, 9)
m:n = 3:1
Substituting the given parameters into the line ratio formula, we have;
F(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
F(x, y) = [(3(8) + 1(4))/(3 + 1)], [(3(9) + 1(11))/(3 + 1)]
F(x, y) = [(24 + 4)/(3 + 1)], [(27 + 11)/(3 + 1)]
F(x, y) = [(28)/(4)], [(38)/(4)]
F(x, y) = [7, 9.5]
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The equation yˆ=−2. 5x+222. 5 models the amount of cholesterol, LDL , for a person, in mg/dl , where x is the time spent exercising per day, in minutes. According to the regression equation, what is the amount of cholesterol for a person exercising 20 minutes a day?
61. 5 mg/dl
81. 5 mg/dl
172. 5 mg/dl
272. 5. 5 mg/dl
The equation y^ = -2.5x + 222.5 models the amount of cholesterol, LDL, for a person in mg/dl, where x is the time spent exercising per day in minutes.
What in mathematics is a quadratic equation?
Definitions: x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
To find the amount of cholesterol for a person exercising 20 minutes a day, we need to substitute x = 20 into the equation:
y^ = -2.5(20) + 222.5
Solving this equation, we get:
y^ = -50 + 222.5
y^ = 172.5
So, the amount of cholesterol for a person exercising 20 minutes a day is 172.5 mg/dl.
Therefore, the answer is 172.5 mg/dl
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Solve the differential equation by variation of parameters.
y'' + y = sin2 x
The solution to the differential equation y'' + y = sin2x is y = -2sin2x + (Acos2x + Bsin2x).
This differential equation can be solved by the method of variation of parameters. This method involves finding two arbitrary functions, U and V, such that U' = V and V' = -U + sin2x, so that the general solution of the differential equation is y = U + V. Solving the two equations yields U = Acos2x + Bsin2x and V = -2sin2x, where A and B are arbitrary constants. Substituting U and V into the general solution of the differential equation yields the final solution y = -2sin2x + (Acos2x + Bsin2x).
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Answer:
Step-by-step explanation:
a. we konw triangle have 180°
b. A straight line have 180°， so
∠abc=180-5x-12=168-5x,
∠bca=180-10x+37=217-10x
∠cab=180-9x-1=179-9x
then add them all 564 - 24x = 180
c.384=24x, x=16
d.so ∠bca=217-10·16=57.
Answer:
m∠BCA = 57°-------------------------------------------
Sum of exterior angles is 360°:
9x + 1 + 5x + 12 + 10x - 37 = 36024x - 24 = 36024x = 384x = 384/24x = 16The exterior angle at vertex C is:
10x - 37 = 10*16 - 37 = 160 - 37 = 123The ∠BCA is the linear pair with 123°:
m∠BCA = 180° - 123° = 57°What is the formula for this operation of functions?
The sum of two functions, f and g: (f + g)(x) = f (x) + g(x) and The difference of two functions f and g: (f - g)(x) = f (x) - g(x).
What is operation function ?
The operations function refers to all the activities that focus on producing goods and services for the customers. It includes the production process of converting raw material into final products. It helps to reduce costs and make process improvements.
Have given ,
Two function f and g then ,
There is one more way that functions can be combined. The fifth operation is called the composition of two functions. The composition of the functions f (x) and g(x) is symbolized this way: (fog)(x). It is equivalent to f (g(x)). It is read "f of g of x." The concept is simple. First, the value of g at x is taken, and then the value of f at that value is taken. Let's try an example to clear things up.
So , The sum of two functions, f and g: (f + g)(x) = f (x) + g(x) and The difference of two functions f and g: (f - g)(x) = f (x) - g(x).
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