Answers
Step-by-step explanation:
15t + 30 = 20t | -15t
30 = 5t
t = 30/5 = 6
20 + 5t = -6t + 86 | + 6t
20 + 11t = 86 | -20
11t = 66
t = 6
18t + 20 = 24t + 50 | -18t
20 = 6t + 50 | -50
-30 = 6t
t = -30/6 = -5
18t - 2 = 10t + 54 | -10t
8t - 2 = 54 | +2
8t = 56
t = 56/8 = 7
7t - 5 = 15t + 91 | -7t
-5 = 8t + 91 | -91
-96 = 8t
t = -96/8 = -12
Related Questions
lify.
(√-4)(4√-25) help me i dont get how to do this
Answers
Answer:
-40
Step-by-step explanation:
The Concept here is Complex Numbers
where [tex]\sqrt{-1}=i \ and \ i^{2} = -1[/tex]
Then [tex]\sqrt{-4}=\sqrt{4i^{2} } =\sqrt{(2i)^{2} } =2i[/tex]
Also [tex]\sqrt{-25}=\sqrt{25i^{2} } =\sqrt{(5i)^{2} } =5i[/tex]
Then [tex](\sqrt{-4} )(4\sqrt{-25} )=(2i)(4*5i)=40i^{2} =40*-1=-40[/tex]
Glad to Help:)
3. One batch of pancakes needs 1½ cups of pancake mix. One box has 9 cups of pancake mix.
How many batches of pancakes can be made with one box of pancake mix?
Answers
In linear equation, 27/2 pancakes are in the box .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a " of two variables," where x and y are the variables.Number of b pancake mix to be need = 1½ cups
Number of box has pancake mix = 9 cups
Therefore, in order to get the total number of batches of pancakes needed for the batches will be calculated thus
= 1½ * 9
= 3/2 * 9
= 27/2
therefore 27/2 pancakes are in the box .
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I NEED HELP!!
Information:
Ryan conducted a 6-day study observing the effects of an organic plant food on the growth of his sprouting bean plant. He tracked these two pieces of information:
1. the amount of plant food remaining in the container after each day’s feeding
2. the height of the plant over time
(There was a total of 72 millimeters of plant food)
Question:
Write a function rule for the relationship between the amount of plant food remaining, f(x), and the number of days that have passed, x.
Answers
This relationship is not a function because more than one amount of plant food remains each day.
What is a function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that, Ryan did an experiment by observing the effects of plant food and the growth of the sprouting bean plant. He made a note of the height of the bean plant and the amount of food remaining in the container for the plant after feeding each day.
Thus, he observed that the plant food in the container decreases by an equal amount every day as the bean plant grew. Thus, this states that it is not a function between the two, as there are more than one plant food remaining each day for the plant.
Hence, This relationship is not a function because more than one amount of plant food remains each day.
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A right triangle's hypotenuse is 1 cm longer than twice the length of the shortest side.
The third side is 1 cm less than twice the shortest side.
Find the length (in cm) of the hypotenuse.
Answers
The length (in cm) of the hypotenuse is 17 cm.
What is Pythagoras' theorem?According to Pythagoras' theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides.
H² = P² + B²
Let the hypotenuse = H
Shortest side = B
Third side = P
So, according to the question
H = 2B +1 ..... (1)
P = 2B -1 ..... (2)
Use Pythagoras' theorem,
H² = P² + B²
(2B+1)² = (2B-1)² + B²
4B² + 1 + 4B = 4B² + 1 - 4B + B²
4B = - 4B +B²
B² =-8B
B = - 8
But the length cannot be negative, so B = 8 cm
The length of the shortest side = 8 cm
So the hypotenuse will be
H = 2B + 1
= 2(8) + 1
= 17 cm
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assume that the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. the u.s. marine corps requires that the heights of men be between 64 and 78 inches. if 500 men want to enlist in the u.s. marine corps, how many would you not expect to meet the height requirements?
Answers
The percentage of men who didn't expect to meet the height requirements be 96.29%
Given, that the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches.
Find the percentage of men who meet the height requirements.
z(64) = (64-69)/2.8 = 1.7857
z(78) = (78-69)/2.8 = 3.2143
P(64 <= x <= 78) = P(1.78457<= z <=3.2143) = 0.0371 = 3.71%
So, the percentage of men who meet the height requirements be 3.71%
Now, the percentage men who didn't expect to meet the height requirements be
100 - 3.71 = 96.29%
Hence, the percentage of men who didn't expect to meet the height requirements be
96.29%
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Students in a classroom have eaten 20% of jellybeans from a jar. There are now only 100 jellybeans left! How many jellybeans were in the jar to begin with?
Answers
Using percentages we calculate in the beginning there were 125 jellybeans in the jar.
Let the number of jellybeans in the jar was x.
Now student ate 20% of the jellybeans.
Number of jellybeans students ate = 20% of x = 0.2x
Number of jellybeans left = x - 0.2x = 0.8x
But the number of jellybeans is given as 100.
Therefore 0.8x = 100
or, x = 100 /0.8 = 125
Hence there were 125 jellybeans in the jar.
The English word "percentage" derives from the Latin phrase "per centum," which means "by the hundred." Percentages are fractions with a denominator of 100.
In other words, that is a relationship where it is always assumed that the value of the whole is 100.
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Suppose U = {2,3,6,9,10,13,14,17,19) is the universal set and A = {2,9,10). What is A'?
Answers
The complement of set A is { 3, 6, 13, 14, 17, 19}
What is the complement of a given set?The complement of a set is the set that includes all the elements of the universal set that are not present in the given set. Let's say A is a set of all coins which is a subset of a universal set that contains all coins and notes, so the complement of set A is a set of notes (which do not includes coins).
U = {2,3,6,9,10,13,14,17,19}, A = {2,9,10}
set A complement are all the elements in the Universal set U not contained in set A. Those elements are in set A' = { 3, 6, 13, 14, 17, 19}
In conclusion the complement of set A is { 3, 6, 13, 14, 17, 19}
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Can someone help me on this question? I think it’s the 2nd answer but I’m not sure
Answers
From the properties of a right triangle is found that the missing length x= [tex]5\sqrt{3}[/tex].
RIGHT TRIANGLEA triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.
The Pythagorean Theorem says: (hypotenuse)²= (leg1)²+(leg2)² . And the main trigonometric ratios are: sin (x) , cos (x) and tan (x) .
The sum of the internal angles of a right triangle also is equal to 180°.
The question gives a figure which is compound for two right triangles.
For each triangle is informed two angles, then:
Triangle 1 - It is given the angle 45° and 90°, thus the third angle will be:45+90+ x = 180
135 + x =180
x=180-135
x=45°
Triangle 2 - It is given the angle 60° and 90°, thus the third angle will be:60+90+ y = 180
150+ y =180
y=180-150
y=30°
Thus, the angles for the given triangle are:
Triangle 1 - 45°, 45° and 90°Triangle 2 - 60°, 30° and 90°From the trigonometric ratio sinФ, you can find the hypotenuse the triangle 2. See below.
[tex]sin \theta =\frac{opposite\ leg }{hypotenuse} \\ \\ sin 45 =\frac{hypotenuse \ triangle 2 }{hypotenuse \ triangle 1} \\ \\ \frac{\sqrt{2} }{2}=\frac{hypotenuse \ triangle 2 }{10\sqrt{2} }\\ \\ 2*hypotenuse \ triangle 2 = 10*2\\ \\ hypotenuse \ triangle 2 = \frac{10*2}{2} \\ \\ hypotenuse \ triangle 2 =10[/tex]
If the hypotenuse of triangle 2 is 10, you can apply again the trigonometric ratio sinФ for finding x
[tex]sin \theta =\frac{opposite\ leg }{hypotenuse} \\ \\ sin 60=\frac{x }{hypotenuse \ triangle 2} \\ \\ \frac{\sqrt{3} }{2}=\frac{x }{10}\\ \\2x=10 \sqrt3\\ \\ x=5\sqrt3[/tex]
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(y+6) (y+13) find the product
step by step explanation pls
Answers
Answer:
(y + 6)(y + 13) = y² + 19y + 78
Step-by-step explanation:
[tex] \rm \implies (y + 6)(y + 13) \\ \\ \rm \implies y(y + 13) + 6(y + 13) \\ \\ \rm \implies {y}^{2} + 13y + 6y + 78 \\ \\ \rm \implies {y}^{2} + 19y + 78[/tex]
Multiply 1st y by 2nd y = y^2
Multiply 1st y by +13 = +13y
Multiply +6 by 2nd y = +6y
Multiply +6 by +13 = +78
[y^2 + 13y + 6y + (6x13)]
y^2 + 19y + 78
:. (y+6) (y+13) = y^2 + 19y + 78
Fill in the missing values from the similar figures in the table
Answers
Step-by-step explanation:
9 × 1/2 = 4.5
8 × 1/2 = 4
hope it's helpful
James knows that he eventually wants to buy a motocycle, and the model he has in mind cost $5000. he has found a bank that will let him open a saving account with 7% interest that is compounded monthly. if he wants to buy his motocycle in 5 years ( he's still nervious) how much money should he invest in the account now
Answers
He should invest $86.29 in the account now, which has a 7% interest compounded monthly.
Compound interest refers to the amount of interest added on the principal amount plus interest. The formula for compound interest is:
B = P(1 + r/n)^t
where B is the ending balance, P is the principal amount or original balance, r is the interest rate in decimal form, n = number of times interest is compounded monthly, and t is the time in number of months
Based on the given information, P is the unknown and
B = $5000
t = 5 years = 60 months
r = 7% = 0.07
n = 1
Plug in the values and solve for P or the amount that should be invested today.
B = P(1 + r/n)^t
$5000 = P(1 + 0.07/1)^60
$5000 = P(1.07)^60
P = $5000/(1.07)^60
P = $86.29
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Which compound inequality does not belong with the other three? Explain your reasoning.
1) a>4 or a<-3
2) a< -2 or a>8
3) a>7 or a<-5
4) a < 6 or a>-9
PLEASE HELP!
Answers
The a < 6 or a>-9 compound inequality is different than the rest as it involves one interval instead of a reunion of two intervals.
What is compound inequality?A phrase having two inequality statements connected by the words "or" or "and" is referred to as a compound inequality. The conjunction "and" denotes the simultaneous truth of both truths in the compound phrase. It is when the solution sets for the various assertions to cross over or intersect.
When the word and is used to connect two inequalities, the compound inequality is solved when both inequalities are true at the same time. It is the intersection or overlap of each inequality's solutions.
1)(−∞,−3)∪(4,∞)
2)(−∞,−2)∪(8,∞)
3)(−∞,−5)∪(7,∞)
4)(−∞,6)∪(−9,∞)=(−9,6)
The fourth compound inequality is different than the rest as it involves one interval instead of a reunion of two intervals.
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In a wildlife park they were 18 gray wolves after three years they were 27 gray wolves. What is the percent gain?
Answers
Answer: 66.66.....% (6 recurring) / 66.67%
Step-by-step explanation: To get the percent form of this, you'll need to turn this into a fraction, which would be 18/27, then you can simplify it to 2/3 and convert it to a percent which would be 66.66..... .
Find the least common denominator. Then express each fraction using the least common denominator. 3/4 and 5/6
I need a answer
Answers
Answer:
The least coomon denominator is 12, so
9/12 and 10/12
a circle is always sometimes or never similar to the other circle because we can always sometimes or never map one onto the other using dilations and rigid transformations
Answers
Answer: always, always
Step-by-step explanation:
Every circle is similar to every other circle.
Jeremy has a huge display of holiday decorations outside his home. He used 6 kilowatt hours (KWH) of electricity in November and used a total of 120KWH during the holiday season until he took them down on December 30. Set up and solve an equation that can be used to calculate the amount of electricity Jeremy used per day during the month of December.
Answers
The equation that can be used to find the amount of electricity Jeremy used per day during the month of December is 3.8KWH per day and Jeremy used 3.8KWH per day electricity in the month of December.
How to write and solve an equation?Electricity Jeremy used in November = 6 kilowatt hours (KWH)
Total electricity used in the holiday season = 120KWH
He took the decorations down on December 30
Amount of electricity Jeremy used per day during the month of December =
(Total electricity used in the holiday season - Electricity Jeremy used in November) / 30 days
= (120KWH - 6KWH) / 30
= 114KWH / 30
= 3.8KWH per day
In conclusion, the amount of electricity Jeremy used per day in December is 3.8KWH per day.
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3z + 6(z-5) = -48
What does this equal please help
Answers
Answer: z=-2
Step-by-step explanation:
3z+6z-30=-48
9z-30=-48
9z-30=-48+30
9z=-18
z=-2
Deshaun works as a busboy making $9 per hour and as a theater usher making $10 per hour. Let b be the number of hours he works as a busboy this
month, and let u be the number of hours he works as an usher.
His goal this month is to earn more than $1400 total
Answers
Answer:
[tex]9b + 10u > 1400[/tex]
when x = -2, y = []
when x = 0, y = []
when x = 2, y = []
when x = 4, y = []
Answers
The values of y respective to x values are when x = -2 then y = 12 when x = 0 then y = 2 when x = 2 then y = -8, & when x = 4 then y = -18.
What is a function rule?
The equation-based relationship between the dependent and independent variables is known as a function rule. In simple words, a function is an association between inputs in which each input is connected to precisely one output.
Given, y = -5x + 2
when x= -2, y = (-5)* (-2) + 2 = 10 + 2 = 12, y = 12
when x= 0, y = (-5)* (0) + 2 = 0 + 2 = 2, y = 2
when x= 2, y = (-5)* (2) + 2 = -10 + 2 = -8, y = -8
when x= 4, y = (-5)* (4) + 2 = -20 + 2 = -18, y = -18
Hence, these are the required values of y to the respective input value of x.
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The diameter of a quarter is 2.4 cm. You trace around the edge of the quarter on a sheet of paper. What is the area of the circle on the paper? Use 3.14 as an approximation for π. Round your answer to the nearest tenth.
Answers
The area of the circle on the paper is 4.5 cm when traced around the edge of the quarter on a sheet of paper.
What is the area of the circle?The area of the circle is equal to the product of the square of the radius of the circle and pi.
A = πr²
where 'r' is the radius of the circle
The diameter of a quarter is 2.4 cm. You trace around the edge of the quarter on a sheet of paper.
The area of the circle on the paper = πr²
Here r = (diameter of a quarter)/2 = 2.4/2 = 1.2 cm
The area of the circle on the paper = π(1.2)²
The area of the circle on the paper = π × 1.44
The area of the circle on the paper = 4.5238
Round the answer to the nearest tenth.
The area of the circle on the paper = 4.5 cm
Thus, the area of the circle on the paper is 4.5 cm
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Answer:its 4.5
Step-by-step explanation:
i will literally do ANYTHING for doordash mcdonalds literally Anything for 20 dollars
Answers
Answer: Nice
Step-by-step explanation:
Joe and Chris share a locker at school. if they each have 8 classes and each class has 2 books, how many books are in the locker. Please show the work! :)
Answers
Answer:
32 books
Step-by-step explanation:
Well if each have 8 classes and 2 books per class then to get the total of books you'd multiply 8x2 and you get 16 for one alone. Since its two people sharing a single locker than add 16 with another 16 and you get 32!
sorry I can't physically show the work but writing down a 8x2 on the side and then adding 16 to that answer should show it off! :]
700% of what number is 1,540
Answers
If 700% of a number is 1540, then the number is 220
The given percentage = 700%
The percentage of a number is defined as the ratio that can be expressed as the fraction of 100.
Consider the number as x
Here the 700% of the number is 1540
Then the equation will become
x × 700% = 1540
Solve the equation and find the value of x
x × (700/100) = 1540
Divide the terms first
x × 7 = 1540
Move the 7 to the right hand side of the equation
x = 1540/7
Divide the terms
x = 220
Hence, if 700% of a number is 1540, then the number is 220
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kumiko decides to buy the same number of apps and games, and she decides to spend as much of the $50 as possible. how many apps and games does she buy? how much money does she have left on her gift card?
Answers
The linear inequality representing the number of apps and games that Kumiko can buy is [tex]1.25a+2.5g\leq50[/tex].
Expressions using linear inequalities compare any two values using inequality symbols like "," ">," "," or "."
The linear inequality representing the number of apps and games that Kumiko can buy is [tex]1.25a+2.5g\leq50[/tex].
What is Inequality?Expressions using linear inequalities compare any two values using inequality symbols like "," ">," "," or "." These values might be either numerical, algebraic, or both.
The number of apps Kumiko buy is a and the number of games she can buy is g.
The gift card has 50$.
Total amount of apps = 1.25a
Total amount of games = 2.5g
So, the linear equality will be [tex]1.25a+2.5g\leq50[/tex].
She can can only games and apps for amount less than and equal to $50.
Therefore, The linear inequality representing the number of apps and games that Kumiko can buy is [tex]1.25a+2.5g\leq50[/tex].
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The given question is Incomplete. Here is the complete question:
Kumiko has a $50 gift card for a Web site that sells apps and games. Games cost $2.50 each, and apps cost $1.25 each. Write an inequality that represents the number of apps a and the number of games g that Kumiko can buy and describe any constraints.
The shaded area below is 79 m².
Work out the area of the smaller rectangle.
If your answer is a decimal, give it to 2 d.p.
x+4 m
x + 3 m
x+2m
2x+5 m
Not drawn accurately
Answers
Answer:
[tex](x + 4)(2x + 5) - (x + 3)(x + 2) = 79 \\ 2x {}^{2} + 5x + 8x + 20 - {x}^{2} - 2x - 3x - 6 = 79 \\ {x}^{2} + 8x + 14 = 79 \\ {x}^{2} + 8x - 65 = 0 \\ {x}^{2} + 13x - 5x - 65 = 0 \\ x(x + 13) - 5( x + 13) = 0 \\ (x - 5)(x + 13) = 0[/tex]
x-5=0
x=5
the length of smaller rectangle= 8 m
and breadth of s. rectangle= 7 m
l x b = 8 x 7
[tex]56 {m}^{2} [/tex]
hopefully this will u
The sequence below is arithmetic. Complete parts (a) through (d) below.
- 1, 2, 5, 8, ...
(a) Find the common difference.
The common difference is d= . (Type a whole number.)
(b) Find the eighth term.
The eighth term is ag =
(Type a whole number.)
(c) Find a recursive rule for the nth term.
(Type an equation.)
(d) Find an explicit rule for the nth term.
(Type an equation.)
Answers
Answer:
see explanation
Step-by-step explanation:
- 1, 2, 5, 8
(a)
the common difference
d = a₂ - a₁ = 2 - (- 1) = 2 + 1 = 3
(b)
to find a term in the sequence add d = 3 to the previous term
a₅ = = 8 + 3 = 11
a₆ = 11 + 3 = 14
a₇ = 14 + 3 = 17
a₈ = 17 + 3 = 20
(c)
the recursive rule is
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 3 : a₁ = - 1
(d)
the explicit rule for an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = - 1 and d = 3 , then
[tex]a_{n}[/tex] = - 1 + 3(n - 1) = - 1 + 3n - 3 = 3n - 4
a random sample of 42 college graduates revealed that they worked an average of 7.3 years on the job before being promoted. the sample standard deviation was 2.9 years. using the 0.99 degree of confidence, what is the confidence interval for the population mean?
Answers
The confidence interval for the population mean with 99% confidence interval is (6.90;8.50).
What is meant by confidence interval?A confidence interval is a set of values that, with a particular level of certainty, includes a population value. When a population mean is between an upper and lower interval, it is frequently stated as a percentage.
The population mean is mean [tex]\bar{x}[/tex]=7.3.
The sample's standard deviation is 2. 9
Number of samples: 42
The range of possibilities for the mean, [tex]\bar{x}[/tex]
The confidence interval for the mean is
[tex]\bar{x}[/tex] ± (σ/√n)
To calculate the critical value, we must first determine the degrees of freedom, which are given by:
df=n-1
df=42-1
df=41.
Since the confidence level is 0.99 or 99%, the values of and can be used to calculate the critical value using Excel, a calculator, or a table is 2.701
7.3-2.701(2.9/√42)=6.9013
7.3+2.701(2.9/√42)=8.5086
The 99% confidence interval in this instance would therefore be provided by (6.90;8.50).
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Can someone help me with this please! I really need it done
increase the amount of the ingredients by 5 and by 20
Answers
Using simple mathematical operations, the missing values are as follows:
(B) Dijon Mustard: 18g
Increased by 20 = 360g(C) Barbeque sauce: 70g
Increased by 5 = 350gIncreased by 20 = 1,400g(D) Worcestershire sauce: 10.35g
Increased by 5 = 51.75gIncreased by 20 = 207g(E) Kosher salt: 1.5g
Increased by 5 = 7.5gIncreased by 20 = 30g(F) Ground black pepper: 2.3g
Increased by 5 = 11.5gIncreased by 20 = 46g(G) Crushed red pepper: 1.15g
Increased by 5 = 5.75gIncreased by 20 = 23gWhat do we mean by mathematical operations?A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.There are predefined rules associated with the math operator's symbol that must be applied to the supplied operands or numbers.The order of operations is a rule that outlines the proper steps to take when analyzing a mathematical equation.We can recall the PEMDAS steps in the following order: Parentheses, Exponents, Multiplication, Division (from Left to Right), Addition, and Subtraction (from left to right).So, we can calculate missing values as follows:
(B) Dijon Mustard: 18g
Increased by 20 = 18×20 = 360g(C) Barbeque sauce: 70g
Increased by 5 = 70×5 = 350gIncreased by 20 = 70×20 = 1,400g(D) Worcestershire sauce: 10.35g
Increased by 5 = 10.35×5 = 51.75gIncreased by 20 = 10.35×20 = 207g(E) Kosher salt: 1.5g
Increased by 5 = 1.5×5 = 7.5gIncreased by 20 = 1.5×20 = 30g(F) Ground black pepper: 2.3g
Increased by 5 = 2.3×5 = 11.5gIncreased by 20 = 2.3×20 = 46g(G) Crushed red pepper: 1.15g
Increased by 5 = 1.15×5 = 5.75gIncreased by 20 = 1.15×20 = 23gTherefore, using simple mathematical operations, the missing values are as follows:
(B) Dijon Mustard: 18g
Increased by 20 = 360g(C) Barbeque sauce: 70g
Increased by 5 = 350gIncreased by 20 = 1,400g(D) Worcestershire sauce: 10.35g
Increased by 5 = 51.75gIncreased by 20 = 207g(E) Kosher salt: 1.5g
Increased by 5 = 7.5gIncreased by 20 = 30g(F) Ground black pepper: 2.3g
Increased by 5 = 11.5gIncreased by 20 = 46g(G) Crushed red pepper: 1.15g
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F(x,y) = x^2 + y^2 - 2x, D is the closed triangular region with vertices (0,0), (0,2), and (0,-2). Find the absolute maximum and minimum values of f on the set D. I know the maximum and minimum are f(0,+-2) = 4, minimum f(1,0) = -1. I need a step by step process on how to get to this answer
Answers
The absolute maximum value is f(0,±2) = 4 and the absolute minimum value is f(1,0) = -1.
The given function is F(x,y) = [tex]x^{2}[/tex] + [tex]y^{2}[/tex] - [tex]2x[/tex] → 1
D is the closed triangular region with the vertices (0,0), (0,2) and (0,-2).
Differentiate 1 partially with respect to x:
df/dx = [tex]x^{2}[/tex] + [tex]y^{2}[/tex] - [tex]2x[/tex]
[tex]f^{'}[/tex](x) = 2x - 2
Differentiate 1 partially with respect to y:
df/dy = [tex]x^{2}[/tex] + [tex]y^{2}[/tex] - [tex]2x[/tex]
[tex]f^{'}[/tex](y) = 2y
Consider [tex]f^{'}[/tex](x) = 0 and [tex]f^{'}[/tex](y) = 0 to find the critical points.
[tex]f^{'}[/tex](x) ⇒ 2x -2 =0
x = 1
[tex]f^{'}[/tex](y) ⇒ 2y
y = 0
Thus, the critical point is (x,y) = (1,0).
Calculate the values of f(x,y) at (0,0), (0,2), (0,-2) and (1,0).
At (x,y) = (0,0)
f(0,0) ⇒ 0 + 0 - 0 = 0
At (x,y) = (0,2)
f(0,2) ⇒ 0 + 4 - 0 = 4
At (x,y) = (0,-2)
f(0,-2) ⇒ 0 + 4 - 0 = 4
At (x,y) = (1,0)
f(1,0) ⇒ 1 + 0 - 2 = -1
Therefore, the absolute maximum is f(0,±2) = 4 and the absolute minimum is f(1,0) = -1.
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Write the prime factorization of 27.
Order the factors from least to greatest (for example, 2 × 2 × 3 × 5).
Answers
Answer:
3*3*3 or 3^3
Step-by-step explanation:
27/3=9/3=3
so 3*3*3 or 3^3