The area of the parking lot is 2,025 .81 meter2.
How do you calculate a triangle's area?In essence, it is equal to 1/2 of the height times the base, or A = 1/2 b h. Therefore, we need to know the triangular polygon's base (b) and height (h) in order to calculate its area.
A triangular parking lot has sides measuring 90 meters, 54 meters, and 128 meters.
Triangle Height Determination Using Area
Now that you are aware of the triangle's area, you may use the triangle formula A=1/2bh to get the triangle's height.
s = a + b+ c /2
90 + 54 + 128 / 2 = 136
A = [tex]\sqrt{s (s-a) (s-b) (s-c)}[/tex]
A = [tex]\sqrt{136(136-90)(136-54)(136-128}[/tex])
A = 2,025 .81
The area of the parking lot is 2,025 .81 meter2.
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TRANSLATE EACH PHRASE INTO AN ALGEBRAIC EXPRESSION
1) 4 times a number,increased by 11.
2) 8 times the sum of a number and 7.
3) 1 less than twice a number.
4) the sum of a number and 3 times that number.
5) 12 more than 5 times a number.
6) 16 increased by 1 more than a number.
7) 20 decreased by 5 less than a number.
8) 6 less than a number increased by 15.
Answer:
Step-by-step explanation:
Let the number be x then,
1) 4 * x + 11
2) 8 * (x + 7)
3) 2x - 1
4) x+ 3x
5) 5x + 12
6) 16 + 1 + x = 17 + x
7) 20 - ( x - 5) = 20 - x + 5 = 25 - x
8) x - 6 + 15 = x +9
David invested $220 in an account paying an interest rate of 1. 7% compounded
continuously. Assuming no deposits or withdrawals are made, how much money, to
the nearest ten dollars, would be in the account after 10 years?
David's deposit of $220 compounded continuously at a rate of 1.7% will become $260 after 10 years.
Here we have been given that David invested $220.
The interest rate was 1.7%
Since the amount was compounded continuously, there is no fixed date of when it was compounded, the whole process is taken as an exponential distribution.
There were no withdrawals or additional deposits to this, so our Principal is constant. Hence we can write the formula
Amount = Principal X eᵃˣ
where a = rate of interest/100
x = time
Therefore, we can say that
Ampunt after 10 years = 220 X e¹⁰ ˣ ⁰°⁰¹⁷
= $260.76707
rounding off to the nearest 10 dollars we get
= $260
Hence David's deposit of $220 compounded continuously at a rate of 1.7% will become $260 after 10 years.
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Gas is $2. 09 per gallon at the gas station. If
Nate filled up his car and spent $33. 44, how
many gallons did he put in his car?
Nate's car was filled with 16 gallons of gas.
The concept is used in this is equations. An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. An equation is the set of variables, constants, and mathematical operations like addition, subtraction, multiplication, or division balanced by an equal sign. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic, etc.
As gas is $2. 09 per gallon at the gas station.
$2. 09 → per gallon
and Nate filled up his car and spent $33. 44.
$33. 44 for fully filled → how many gallons ?
So,
33.44 / 2.09 = 16 gallons.
Therefore, Nate filled 16 gallons gas in his car.
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Your family travels from Bazooka, Iowa, to Dentyne, Missouri, a distance of 348 miles. Your car averages 14.5 miles per gallon on open road driving. If you filled your vehicle at a station where regular gasoline cost $1.83 per gallon, how much would the
Consequently, it would take polynomials roughly 690,64 years for the disintegrations to disappear.
what are polynomials?A polynomial is a mathematical statement made up of coefficients and uncertainty that exclusively uses additions, subtractions, multiplications, and positive integer powers of variables. A single indeterminate x polynomial is represented by the expression x2 4x + 7. A polynomial is an expression in mathematics that consists of variables (sometimes referred to as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. A polynomial is an algebraic expression made up of coefficients and variables. The only operations that an expression can contain are addition, subtraction, multiplication, and non-negative integer exponents. These expressions are known as polynomials.
The formula for this is Activity = decay constant x atoms.
1238 = 2.64 x 1010 times the decay constant
decay constant is equal to 4.76 x 10-8 min-1.
Currently, the disintegrations are being slowed to 809 disintegrations per minute.
Ln(809) = Ln(2.64 x 1010) - Ln(4.76 x 10-8 x t)
t=3.63x108min = 690.64y
Consequently, it would take roughly 690,64 years for the disintegrations to disappear.
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What literary device did Oscar Wilde use?
Oscar Wilde creates a hilarious tone by using puns, situational irony, dramatic irony, satire, and epigrams.
Who is Oscar Wilde?Oscar Fingal O'Flahertie Wills, an Irish poet, and playwright, lived from 16 October 1854 to 30 November 1900.
He wrote in a variety of genres throughout the 1880s before becoming one of London's most well-known playwrights in the early 1890s.
The Picture of Dorian Gray, his plays and epigrams, as well as the circumstances surrounding his meningitis-related early death at age 46 and criminal conviction for gross indecency for consensual homosexual activities in "one of the earliest celebrity trials," is what people will remember him for most.
Using puns, situational irony, dramatic irony, satire, and epigrams, Oscar Wilde establishes a humorous tone.
Therefore, Oscar Wilde creates a hilarious tone by using puns, situational irony, dramatic irony, satire, and epigrams.
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A convenience store sell pre-paid mobile phones. It purchases them for $12 each and uses a mark up rate of 250%.
a. The markup rate is the constant of proportionality in the equation y= kx. Write an equation that can be used to find the amount of markup on the cost x of a phone
b. Use the equation to calculate the markup amount. What is the retail price of a phone?
c. Next week the store is going to reduce the price to $31. 50. Calculate what percent the sale price is of the retail price.
d. Based on your answer to part C, what is an equation in the form y = kx that relates the sale price to the retail price x?
Answer:
a. y = 2.5x
b. markup: $30; retail price: $42
c. 75%
d. y = 0.75x
Step-by-step explanation:
You want equations relating markup, retail price, and sale price on a phone that costs $12, is marked up 250%, then put on sale for $31.50.
a. Markup equationThe problem statement tells you the markup is 250% of the cost. You could write the equation as ...
y = (250%)x
Or you can simplify it to a decimal number:
y = 2.5x
b. Markup amountThe markup amount is ...
y = 2.5(12) = 30
The markup amount is $30.
That is added to the cost to get the retail price:
retail = $12 +30 = $42
The retail price of the phone is $42.
c. Sale priceThe sale price as a percent of the retail price is ...
percent = (sale price)/(retail price) × 100%
percent = 31.50/42 × 100% = 75%
The sale price is 75% of the retail price.
d. Sale price equationAs in part (a), we could write this as ...
y = (75%)x
or, in decimal, as ...
y = 0.75x
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Russel is doing an experiment for a science fair project. He fills a beaker with water three times. He puts 16.5 mililiters of water in each test tube. How many full test tubes can Russel fill with water? 1. Describe one way to estimate the solution to this problem. 2. Russel calculates correctly and says the answer to the problem is 36.36 test tubes. Is Russel's answer reasonable? Explain
The number of full test tubes Russel fill with water must be discrete number and not rational. 36 test tubes is the answer.
How to Know Cylinder Volume ?Volume of a cylinder can be known either by the use of formula (V = πr²h) or by measuring with the volume of a known liquid.
Given that Russel is doing an experiment for a science fair project. He fills a beaker with water three times. He puts 16.5 milliliters of water in each test tube. How many full test tubes can Russel fill with water?
1. Describe one way to estimate the solution to this problem.
By dividing the amount of milliliters of water in the baker by 16.5 ml
2. Russel calculates correctly and says the answer to the problem is 36.36 test tubes. Is Russel's answer reasonable?
No! The reason is based on the fact that the answer must be a whole number and not a decimal number since the question centered on number of full test tubes filled with water.
Therefore, the correct answer should be 36 test tubes.
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What are the 3 linear equations?
The 3 linear equations are
1. y = mx + b
2. ax + by = c
3. x/a + y/b = 1
1. y = mx + b is a linear equation in two variables, x and y. The equation is in the slope-intercept form, where m is the slope of the line and b is the y-intercept.
2. ax + by = c is a linear equation in two variables, x and y. The equation is in the standard form, where a and b are constants and c is the result of the equation.
3. x/a + y/b = 1 is a linear equation in two variables, x and y. The equation is in the general form, where a and b are constants and 1 is the result of the equation.
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HELP!!!! Due to inflation, there were two price increases. After the second increase, the price of an item was twice its original price. By what percent did prices increase the first time if prices increased by 25% the second time?
The increase was 250% over the original price.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
let 'x' represent the original price, then 'x+0.25x' represents the first increase of 25%
six times greater, converted to a percentage:
(x+0.25x)×2×100 a second increase of six-fold
1.25x×2×100
250
The increase was 250% over the original price.
Hence, the increase was 250% over the original price.
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Arithmetic sequence please help
10. a. The sequence is arithmetic as the difference between the next term and the previous term is constant.
b. The 200th term of the sequence is 1382.
c. 100 is not a member of the sequence.
11. a. u₁ is even and d is also even.
b. u₁ is odd and d is even.
What are arithmetic and geometric sequence?An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference
d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.
In a geometric sequence numbers are written in the same constant ratio(r).
It means every next number is a multiple of a common constant and the previous number.
r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.
Given, u₁ = - 12 and uₙ₊₁ = uₙ + 7.
So,
u₂ = u₁₊₁ = - 12 + 7 = - 5.
Similarly, u₃ = - 5 + 7 = 2 and u₄ = 9.
So, The terms have a common difference o 7 and hence it is an arithmetic sequence.
We know, uₙ = u₁ + (n - 1)d.
Therefore, u₂₀₀ = u₁ + (200 -1)×7.
u₂₀₀ = - 12 + 199×7.
u₂₀₀ = - 12 + 1393.
u₂₀₀ = 1382.
Now, Determining whether 1000 is a member of the sequence.
Let, 1000 = - 12 + (n - 1)×7.
1012 = 7n - 7.
1019 = 7n, Here is not completely divisible hence 1000 is not a member of the sequence.
11. When all the terms of an AP is even the first term u₁ is even and the common difference would also be even and when all the terms of an AP are odd the first term u₁ would be odd and the common difference d would e even, as odd - odd = even.
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The question is in the picture I would appreciate if you could explain how to get the answer thank you.
The equation that is modeled to the situation is x - 2y + 2 = 0 and the slope of the line is 1/2.
The slope of an equation:
A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in determining if the lines are parallel, perpendicular, or none at all.
The slope intercept form of a line is y = mx + c
Where, c - y-intercept and m - the slope of the line
Given that
The cost of using the internet at an internet cafe is equal to a fee plus a certain rate per minute.
4 minutes of internet costs $ 3
8 minutes of internet costs $ 4
[ We can represent the given situation as given below ]
And the coordinates formed are (4, 3) and (8, 4)
The slope of the line formed = (4 - 3)/(8 - 4) = 1/4
Let y = mx + c be the equation to the model situation
=> y = (1/2)x + c
=> 2y = x + c ---- (1)
As we know (1) will pass through (4, 3)
=> 2(3) = 4 + c
=> 6 = 4 + c
=> c = 6 - 4
=> c = 2
=> 2y = x + 2
=> x - 2y + 2 = 0
Therefore,
The equation that is modeled to the situation is x - 2y + 2 = 0 and the slope of the line is 1/2.
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H)
find the exact value of sec 7pi / 4
Answer: sqrt(2)
Step-by-step explanation:
Remember that sec x = 1/cos x.
That means that sec 7pi/4 = 1/cos(7pi/4)
cos(7pi/4) = -cos(7pi/4 - pi)
= -cos(3pi/4)
cos(3pi/4) is a special angle which evaluates to -sqrt(2)/2.
Hence, -cos(3pi/4) evaluates to simply sqrt(2)/2
Since cos(7pi/4) is equal to -cos(3pi/4),
cos(7pi/4) is equal to sqrt(2)/2.
Lastly, sec 7pi/4 = 1/cos(7pi/4) , which is the reciprocal of sqrt(2)/2, that is 2/sqrt(2).
Rationalizing the answer 2/sqrt(2) gives sqrt(2)
Multiply: 1) (5xy+3yz) and 2xz
2) 6/7x2y and (35/6xy + 14/3 xy2
3) (2x3-3x2+6x-8) and (-5x2)
Therefore, the multiple of the given equations is 10x^2yz + 6xyz^2, 5x^3y^2 + 14x^3y^3, and -10x^5 + 15x^4 - 30x^3 + 40x^2.
Define Polynomial Multiplication.The process of multiplying two or more polynomials together is known as polynomial multiplication. Applying the distributive property to the multiplication of polynomials allows us to conduct polynomial multiplication.
What is multiplication?Multiplication in mathematics is essentially just adding a number repeatedly in relation to another number. For instance, if we multiply 2 by 3, then implies that 3 gets multiplied by itself twice, meaning 3 + 3 = 6. Children can multiply numbers easily with the help of this method.
1. (5xy+3yz) * 2xz = 10x^2yz + 6xyz^2
2. (6/7x2y) * (35/6xy + 14/3 xy2) = 5x^3y^2 + 14x^3y^3
3. (2x3-3x2+6x-8) * (-5x2) = -10x^5 + 15x^4 - 30x^3 + 40x^2
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Quadrilateral ABCD is similar to quadrilateral A'B'C'D'. Write 2 equations that could be used to solve for missing lengths?
2 equations that could be used to solve for missing lengths are:
[tex]\frac{AD}{A'D'} = \frac{BC}{B'C'}[/tex]
Now, According to the question:
Two quadrilaterals are similar if their corresponding angles are equal and also their corresponding sides must be proportional.
Quadrilateral ABCD is similar to quadrilateral A'B'C'D'.
ABCD ~ A'B'C'D'
So,
[tex]\frac{AB}{A'B'} = \frac{BC}{B'C'}\\ \\ \frac{CD}{C'D'} = \frac{AD}{A'D'}[/tex]
Hence, 2 equations that could be used to solve for missing lengths are:
[tex]\frac{AD}{A'D'} = \frac{BC}{B'C'}[/tex]
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What unit is equal to Avogadro's number ?
Avogadro's number is a unitless object. It represents a number.
What is unit?
The mass of a particular piece of metal or the length of a particular rod are examples of quantities (specific properties) of objects that have historically been used to define measurement units. An object that has no units is known as unitless.
The proportionality factor that connects the number of constituent particles (often molecules, atoms, or ions) in a sample with the amount of material in that sample is called the Avogadro constant, also known as NA or L. It has a precise value of 6.02214076 × 10²³ reciprocal moles and serves as a SI defining constant.
The value of Avogadro's number is 6.02214076 × 10²³.
One mole of the chemical compound consists of 6.02214076 × 10²³ atoms.
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Can you help me with this
Answer:
m = 2
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
We see the y increase by 4 and the x increase by 2, so the slope is
m = 4/2 = 2
So, m = 2
1. A school held several events last month- a music concert, a basketball game, a drama play, and
literacy night. The music concert was attended by 250 people. How many people came to each of
the events? 250 people attended the events.
a. The attendance to the basketball game was 30% of attendance at the concert. 75 people
attended the basketball game.
b. Attendance at the drama play was 140% of attendance at the concert.
C. Attendance at the literacy night was 44% of the attendance at the concert.
70% of those who went to the music concert and the play also did so.
What is meant by percentage?A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a percentage. Divide the number by the total and multiply by 100 to find the percent of a given number. A portion per hundred is what the percentage denotes. Percentage refers to one in a hundred. The word "%" stands in for it.
In addition to being stated as a decimal or a fraction, a percentage is a number that indicates how many out of 100 it is. Three for the price of one! Simply enter the % as the numerator and 100 as the denominator to convert the percentage to a fraction.
We know that 350 people attended the drama play.
50% of 350 = (0.5) · 350 = 175 people attended both the drama play and music concert.
We know that 250 people attended the music concert.
The percentage of the people who attended the music concert even attended the drama play would be 175 ÷ 250 · 100% = 70%
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70% of those who went to the music concert and the play also did so.
Hence, the option A is correct.
What is meant by percentage?In mathematics, a value or ratio that can be expressed as a fraction of 100 is known as a percentage. In order to get the percentage of a given number, divide the number by the total and multiply by 100. The percentage is a chunk out of one hundred. One out of 100 is referred to as a percentage. The symbol for it is "%".
A % is a number that, in addition to being expressed as a decimal or a fraction, also specifies how many out of 100 it is. For the price of one, get three! To convert a percentage to a fraction, just enter the% as the numerator and 100 as the denominator.
We know that 350 people attended the drama play.
50% of 350 = (0.5) · 350 = 175 people attended both the drama play and music concert.
We know that 250 people attended the music concert.
The percentage of the people who attended the music concert even attended the drama play would be 175 ÷ 250 · 100% = 70%
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32. Hannah's gross wage is 1250perweek, buther' takehome' payisonly785 What percentage is this of her gross wage? Give your answer correct to the nearest whole percentage.
Therefore , the solution of gross pay problem is 62% is this of her gross wage.
What percentage is this of her gross wage?Hannah's take home pay of percentage 785 is 62.8% of her gross wage of 1250. This can be calculated by dividing 785 by 1250 and multiplying the answer by 100.
Here,
62.8% is the same as 0.628.
This can be calculated by dividing 785 by 1250.
To get the answer to the nearest whole percentage, we round up 0.628 to 0.63 which is 63%.
This means that Hannah's take home pay of 785 is 63% of her gross wage of 1250.
63% is the answer to the question: what percentage is Hannah's take home pay of her gross wage? This is correct to the nearest whole percentage.
To summarise, Hannah's take home pay of 785 is 63% of her gross wage of 1250, correct to the nearest whole percentage.
Hannah's take-home pay is 62.8% of her gross wage. This percentage is the result of taxes and other deductions taken by her employer.
Knowing this percentage can help Hannah better understand how much money she is taking home each week and how much money is being withheld from her paychecks.
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Which of the following statements is not equivalent to the others?
16-34
|34 -16|
34-16
|16 -34
Answer:
the one that is not equivalent to the others would be 116-34
Step-by-step explanation:
because its 116 and the others dont have anything to do with 116 :)
Answer: The statement that is not equivalent should be D. |16-34
What is the difference of the two polynomials 9x2 8x 2x2 3x?
The difference between the polynomials 9x² + 8x and 2x² + 3x is 7x² + 5x.
What is polynomials?A polynomial is formed mathematically by combining one or more algebraic terms (monomials). The roots of "polynomial" are poly- (many) and -nomial (terms). A polynomial can have exponents (powers), constants (numbers), and variables (letters), but not negative exponents or variable division.
Polynomials are typically expressed in standard form. Furthermore, because there are no similar terms among the exponents, they are arranged in descending order (largest to smallest).
To find the difference between
(9x² + 8x) - (2x² + 3x)
We do calculation
= 9x² + 8x - 2x² - 3x
= 9x² - 2x² + 8x - 3x
= 7x² + 5x
Thus, the difference between the polynomials is 7x² + 5x.
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Explain how you decided to divide your wholes into fractional parts and how you decided where your number scale should begin and end. Due 1-2-23
On solving the provided question, we can say that - on doing the fraction we have [tex]\frac{1}{10} ; \frac{1}{100} ; \frac{1}{10000}[/tex]
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. 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. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
here we have,
0.1 = 1/10
0.01 = 1/100
0.0001 = 1/10000
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How do you find the height of an acute triangle?
The height of an acute triangle can be calculated using the Pythagorean Theorem. The formula for this theorem is a2 + b2 = c2, where a and b are the two legs of a right triangle and c is the hypotenuse.
To find the height of an acute triangle, we must first identify the two legs of the triangle. The length of the two legs can be determined by measuring the lengths of the three sides of the triangle. Once we have the lengths of the two legs, we can apply the Pythagorean Theorem to calculate the length of the hypotenuse.
Once the length of the hypotenuse is determined, we can use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle. This formula states that the square of the height of the triangle is equal to the square of the hypotenuse minus the square of the two legs. So, to find the height of an acute triangle, we first measure the lengths of the three sides, then use the Pythagorean Theorem to calculate the hypotenuse, and finally use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle.The height of an acute triangle can be calculated using the Pythagorean Theorem. The formula for this theorem is a2 + b2 = c2, where a and b are the two legs of a right triangle and c is the hypotenuse. To find the height of an acute triangle, we must first identify the two legs of the triangle. The length of the two legs can be determined by measuring the lengths of the three sides of the triangle. Once we have the lengths of the two legs, we can apply the Pythagorean Theorem to calculate the length of the hypotenuse.
Once the length of the hypotenuse is determined, we can use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle. This formula states that the square of the height of the triangle is equal to the square of the hypotenuse minus the square of the two legs. So, to find the height of an acute triangle, we first measure the lengths of the three sides, then use the Pythagorean Theorem to calculate the hypotenuse, and finally use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle.
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Is the y-intercept 0 or 1?
Coordinate (0,1) of y-intercept implies that a line or curve cross the Y axis
at 1.
What is y-intercept?
The location of a point on the cartesian coordinate plane where a straight line or curve line as well as a plane crosses the Y axis is called Y-intercept. The coordinate of y-intercept is expressed as (0, y). This y value is y-intercept. The X coordinate of y intercept is zero.
In case of an equation of line while writing in slope-intercept form it is denoted by b such as y = mx+ b
in the above equation, b is y-intercept and m is the slope.
What means y-intercept (0, 1)?The y -intercept given by coordinate (0, 1) defines that a straight-line or curve line cross the Y axis at 1. The x coordinate of y -intercept is always zero because over the Y axis there is no value of X.
The y-intercept can have negative or positive value.
Suppose we have an equation of line 4x + 8y + 10 = 0
we will write it in a slope-intercept form
8y = -4x - 10
y = - 4x/8 - 10/8
y = -1/2x - 5/4
In the above equation - 5/4 or -1.25 is the y-intercept that means the line crosses the Y-axis at -1.25
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Zasha spent $6 on packages of gum. How many more packages of gum that cost $1.20 each can she buy if she has a $20 bill?
Answer: Zasha spent $6 on packages of gum, which means that she bought 6 / $1.20 = 5 packages of gum.
If she has a $20 bill, she has $20 - $6 = $14 left to spend on gum.
Zasha can buy an additional 14 / $1.20 = 11.6666666666666666666666667 packages of gum with this money.
Rounded down, Zasha can buy an additional 11 packages of gum.
Therefore, Zasha can buy a total of 5 + 11 = 16 packages of gum.
Step-by-step explanation:
Angel missies 4% of the free throws he attempts in a season. How many total free throws did he attempt if he missed 55
Answer:
Step-by-step explanation:
55 times 25, making Angel attempt 1375 free throws
Answer:
Step-by-step explanation:
Its 700% because 7x3 = 11
6. Given:
Prove: AB = DC
I need helpppp PLEASEEEEEEE
The point Q has coordinates (2,3) The point R has coordinates (a,b) A line perpendicular to QR is given by the equation 5x+2y=9 Find an expression for b in terms of a
B = (2a + 11)/5 is an expression for b when expressed in terms of a.
What exactly are slopes and lines?
We are aware that lines might have several kinds of equations; the typical form is
The equation of a line in slope-intercept form is Ax + By + c = 0, and
y = mx + b.
m is the slope, and b is the y-intercept.
The y-intercept, or (0,b), is the point where the line crosses the y-axis when x = 0. The slope represents the rate of change of the y-axis relative to the x-axis.
Given:
Coordinates of point Q = (2,3)
Coordinates of point R = (a,b)
The equation of the line is 5x + 2y = 9 ⇒ 2y = - 5x + 9
Therefore, y = (-5/2)x + 9/2.
We know slope m = (y2 - y1) / (x2 - x1)
∴ m = (b - 3)/(a - 2).
∴ (2/5) = (b - 3).(a - 2).
2(a - 2) = 5(b - 3).
2a - 4 = 5b - 15.
2a + 11 = 5b.
b = (2a + 11)/5.
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What does each of these represent in this situation (0,0),(1,55), and (5,275
A grocer makes a display of cans in which the top row has one can and each lower row has two more cans than the row above it. If the display contains $100$ cans, how many rows does it contain
A grocer makes a display of cans in which there are 10 rows.
The top row has one can and each lower row has two more cans than the row above it.
We can write it as sequence:
1, 3, 5, 7, . . .
We can observe that it's an arithmetic sequence: 1, 3, 5, 7, . . . , 2n-1
We know that the formula for the sum of n-terms of arithmetic sequence:
S(n) = (n/2)(1 + 2n-1)
Here, Sn = 100
So, (n/2)[1 + 2n-1] = 100
n(1 + 2n + 1)
n(2n) = 200
2n^2 = 200
n^2 = 100
n = 10
Hence, the number of rows = 10
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Find the general solution of the given system. dx/dt = 4x+ 5y dy/dt = 10x + 9y
(x(t), y(t)) =
x(t) = [tex]c_1e^1^4^t+c_2e^-^t[/tex] , y(t) = [tex]2c_1e^1^4^t-c_2e^-^t[/tex] is the general solution of the sytem of differention eqution dx/dt = 4x+ 5y , dy/dt = 10x + 9y .
given dx/dt = 4x+ 5y and dy/dt = 10x + 9y
X'(t) = [tex]\left[\begin{array}{ccc}4&5\\10&9\end{array}\right][/tex] X
where X = [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex]
so A = [tex]\left[\begin{array}{ccc}4&5\\10&9\end{array}\right][/tex]
now we need to find eigen value of the matrix and the corresponding eigen vector.
| A- λI | = 0
so after equation the value to zero
λ = 14 and λ = -1
now for the λ = 14 corresponding eigen vector = [tex]\left[\begin{array}{ccc}1\\2\\\end{array}\right][/tex]
for λ = -1 corresponding eigen vector = [tex]\left[\begin{array}{ccc}1\\-1\\\end{array}\right][/tex]
So general equation is given by:
X(t) = [tex]c_1e^1^4^t[/tex] [tex]\left[\begin{array}{ccc}1\\2\\\end{array}\right][/tex] + [tex]c_2e^-^t[/tex] [tex]\left[\begin{array}{ccc}1\\-1\\\end{array}\right][/tex]
after solving this
x(t) = [tex]c_1e^1^4^t+c_2e^-^t[/tex]
y(t) = [tex]2c_1e^1^4^t-c_2e^-^t[/tex]
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