What is the area of the region in the first quadrant bounded on the left by the graph of x=y^2/2 and on the right by the graph of x=3y−4 for 2≤y≤4 ?
Answers
The area of the region is -2/3 square units
The area bounded by the regionSince the region is bounded on the left by x = y²/2 and on the right by x = 3y - 4 for 2 ≤ y ≤ 4, the area of the region is given by
[tex]A = \int\limits^4_2 {\frac{y^{2}}{2} } \, dy - \int\limits^4_2 {(3y - 4)} \, dy \\[/tex]
Integrating, we have
A = [y³/6]₂⁴ - [3y²/2 - 4y]₂⁴
A = [4³/6 - 2³/6] - [3(4)²/2 - 4(4) - {3(2)²/2 - 4(2)]}]
A = [64/6 - 8/6] - [3(16)/2 - 16 - {3(4)/2 - 8]}]
A = [64/6 - 8/6] - [3(16)/2 - 16 - {3(4)/2 - 8]}]
A = [64/6 - 8/6] - [3(8) - 16 - {3(2) - 8]}]
A = [(64 - 8)/6] - [3(8) - 16 - {3(2) - 8]}]
A = [56/6] - [24 - 16 - {6 - 8}]
A = [56/6] - [8 - {-2}]
A = [56/6] - [8 + 2]
A = [56/6] - [10]
A = 56/6 - 10
Taking the L.C.M, we have
A = (56 - 10 × 6)/6
A = (56 - 60)/6
A = -4/6
A = -2/3 square units
So, the area of the region is -2/3 square units
Find the graph in the attachment
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Related Questions
if p:q=2:3 and q:r=6:5 find p:r
Answers
Step-by-step explanation:
p/q=2/3
q/r=6/5
First q is to be made same . So take LCM of 3 and 6 which is 6 only.
Now,
p/q=2×2/3×2=4/6
q/r=6/5 only
Cancel both the 6.
Therefore the answer is p/r=4/5.
Hope this helps
Answer:
p:r =4:5
hope it helps
Given the following geometric sequence find the common ratio {0.45, 0.9, 1.8}
Answers
Answer:
Given the following geometric sequence, find the common ratio. {0.45, 0.9, 1.8, ...} 0.45 0.9 2
Given the following geometric sequence {0.45, 0.9, 1.8, ...}, the common ratio is 2. The common ratio = 1.8/0.9 = 0.9/0.45 = 2
Are 4/7 and 12/21 equivalent fractions? Why or why not?
Answers
Answer:
Yes
Step-by-step explanation:
12/21 simplified is 4/7. if you divide the numerator (12) by 3 and the denominator (21) by 3, you get 4 and 7, or 4/7 if you put it together.
4/7 and 12/21 are equivalent fractions
What is Fraction?A fraction represents a part of a whole.
We need to check whether the fractions 4/7 and 12/21 are equivalent or not.
Equivalent fractions are the fractions that have different numerators and denominators but are equal to the same value.
12/21 we have to simplify.
12 and 21 are the multiples of 3, so divide numerator and denominator by 3
which gives 4/7
12/21=4/7
Hence, 4/7 and 12/21 are equivalent fractions
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2. Simplify the expression (6.8 x 106) +
(3.4 X 106). Express
your answer in
scientific notation.
someone help
Answers
Answer:
1081.2x10
Step-by-step explanation:
A survey found that women's heights are normally distributed with mean 63.9 in. and standard deviation 2.4 in. The survey also found that men's heights are normally distributed with mean 67.9 in. and standard deviation 3.9 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 57 in. and a maximum of 63 in. Complete parts (a) and (b) below.
a. Find the percentage of men meeting the height requirement.
What does the result suggest about the genders of the people who are employed as characters at the amusement park?
Answers
Craig saved $10,950 in a year. He saved $75 more than what he saved the previous
month. How much did he save in the first month?
Answers
Answer: $10,875
Step 1: Subtract.
10,950 - 75 = 10,875.
Step 2: Add a dollar sign.
$10,875
Hope this helps!
An insurance company regularly reviews official police reports of traffic accidents in a particular region of the country so that it can price its premiums in that region appropriately. A review of a random sample of 582 accident reports showed that in 91 accidents, a teenage driver was found to be at fault.
Required:
Report the upper bound of a 90% confidence interval for the true proportion of accidents in the area that are caused by teenagers, to three decimal places.
Answers
Answer:
The upper bound of the 90% confidence interval is 0.181
Step-by-step explanation:
From the question we are told that
The sample size is n = 582
The number of accidents is k = 91
Generally the sample proportion is mathematically represented as
[tex]\r p = \frac{ k}{n} = \frac{582}{91 }[/tex]
=> [tex]\r p = 0.1564[/tex]
Generally the confidence level is 90% , the level of significance is [tex]\alpha = (100-90)\%[/tex]
=> [tex]\alpha = 0.10[/tex]
From the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p (1 - \r p)}{n} }[/tex]
=> [tex]E = 1.645* \sqrt{\frac{ 0.1564 (1 - 0.1564)}{582} }[/tex]
=> [tex]E = 0.0248[/tex]
Generally the 90% confidence interval is mathematically represented as
[tex]0.1564 - 0.0248 < p < 0.1564 -0.0248[/tex]
=> [tex]0.1316 < p < 0.1812[/tex]
Answer and Step-by-step explanation:
Random sample = 582
No. of accidents = 91
P = 91 / 582 = 0.156
Confidence interval for proportion of accidents:
P ± z √(p(1-p)/n)
Where,
n = 582
p = 0.156
z = 1.645
Formula:
P ± z √(p(1-p)/n)
put these values in formula, we get:
= 0.156 ± 1.645 √(0.156(1-0.156)/582)
= 0.156 ± 1.645 √(0.1316/582)
= 0.156 ± 1.645 (0.01483)
= 0.156 ± 0.0244
= (0.1804, 0.1316)
How you do this work ?
Answers
Answer:
24
Step-by-step explanation:
1 ant = 6 legs
6 legs ×2 ants= 12 legs of ants
1 butterfly = 6 legs
2 butterfly ×6 legs = 12 legs of butterfly
total
12 legs of butterfly + 12 legs of ants
= 24 legs in total
Answer:
24
Step-by-step explanation:
1 ant = 6 legs
2 ants = 6 + 6 = 12
2 ants = 12 legs
1 butterfly = 6 legs
2 butterflies = 6 + 6 = 12
2 butterflies = 12 legs
12 + 12 = 24
There were 24 legs all together.
Solve by substitution. 5x + 4y = -14 y = -7x - 15
Answers
Answer:
(-2,-1)
Step-by-step explanation:
The solution is, x = 3.06 and, y = -7.33..
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
5x + 4y = -14 ..(1)
y = -7x - 15
i.e. 7x + y = -15 ...(2)
for solving now, we multiply (2) by 4 , then subtract from (1),
we get,
5x + 4y = -14
20x + 4y = -60
------------------------
15x = 46
or, x = 3.06
and, y = -7.33
Hence, The solution is, x = 3.06 and, y = -7.33.
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As Mercury revolves around the sun, it travels at a speed of approximately 30 miles per second.Convert this speed to miles per minute. At this speed, how many miles will Mercury travel in 3 minutes? Do not round your answers.
Answers
Answer:
Step-by-step explanation:
30*1.6 = 48 km per second
48 * 2 = 96 kilometres
this is not rounded!!
Help please
Is it possible that the lengths of the sides of a triangle are proportional to the numbers 1, 2, and 3?
Answers
Answer:
No
Step-by-step explanation:
Triangular Inequalities state that in a triangle, the sides must always be less than the sum of the other two.
You would have sides x, 2x, 3x in this case and use the inequality a+b>c.
if...
a=x, b=2x, c=3x
then...
x+2x>3x
3x>3x which is false.
Therefore you cannot make a triangle with sides proportional to 1, 2, and 3.
find the sum for (2w-9) + (-4w - 5)
Answers
Answer:
The solution to this problem is −2−14
Step-by-step explanation:
Suppose a sample of radioactive substance weighs 40 mg. One year later the sample weighs 29.5 mg. What is the half life of the substance?
Answers
Answer:Use the radioactive decay formula: A = Ao*2^(-t/h), where:
A = Amt of remaining after t time
Step-by-step explanation:
Ao = Initial amt
t = time of decay
h = half-life of the substance
in this problem
A = 21.5
Ao = 38
t = 1 year
h = half life of substance
Please help fill it in I’ll mark you as brainlist
Answers
Answer:
it so blurry
Step-by-step explanation:
= ?[tex]\sqrt{x} \sqrt{x} -(-9)^2\\[/tex]
Answers
Answer:
Step-by-step explanation:
[tex]\sqrt{x} \sqrt{x} -(-9)^{2} \\=x-81\\x=81[/tex]
Find x - someone help me please
Answers
Answer:
-10
Step-by-step explanation:
x + 75 + x + 125 = 180 add like terms
2x + 200 = 180 subtract 200 from both sides
2x = -20 divide both sides by 2
x = -10
What is the product of StartFraction 4 Over 9 EndFraction and StartFraction 1 Over 11 EndFraction
Answers
Answer:
4/99
Step-by-step explanation:
Which of the following numbers is a factor of 555555?
Choose 1 answer:
Answers
Answer: You didn't give choices but here are all of them
Step-by-step explanation: 1, 3, 5, 7, 11, 13, 15, 21, 33, 35, 37, 39, 55, 65, 77, 91, 105, 111, 143, 165, 185, 195, 231, 259, 273, 385, 407, 429, 455, 481, 555, 715, 777, 1001, 1155, 1221, 1295, 1365, 1443, 2035, 2145, 2405, 2849, 3003, 3367, 3885, 5005, 5291, 6105, 7215, 8547, 10101, 14245, 15015, 15873, 16835, 26455, 37037, 42735, 50505, 79365, 111111, 185185, 555555
Answer
The factors of 55 are 1, 5, 11, and 55.
Step-by-step explanation:
Need the answer ASAP. -6x-4>-2(x-4)
Answers
The ratio of butterflies to bees in Lucy's insect collection is 3 to 4. If there are 32 bees, how many butterflies would there be?
Answers
Answer:
24:32
Step-by-step explanation:
When I saw that you wrote 'the ratios of BUTTERFLIES TO BEES' it tells me that I need to do the order of But. to Bees. I saw you had 3:4, and you said, '32 bees' I know because of that, 32 bees needs to be the second.
I got my answer, by seeing 4x_=32. I actually multiplied 4x8=32, and then multiplied 3x8 as well, to get 24. Then I got my answer: 24:32!
HOPE I HELPED:)
-Adiel, Age 11, 6th Grade
Try This question out and I’ll give you brainliest
Answers
Answer:
B
Step-by-step explanation:
2d represents the amount sold on Tuesday
subtracting 150 from this amount fits the question
how do you round 0.313265 to the nearest tenth of a percent
Answers
Answer:
.313265*100 is 31.3265
rounded is 31.3
Step-by-step explanation:
Answer:
Step-by-step explanation:
CJ = 2x – 1 and
JT = 82 – 43
Answers
Answer:
CT = 10x-44
Step-by-step explanation:
Since J is the midpoint you would set your equation up like this
2x-1+8x-43Now you would add like terms
10x-44Hope this helps!
Solve this equation
-(C^5)⁴
Answers
Answer:
[tex]-(C^5)^4\\= -(C^2^0)\\= -C^2^0[/tex]
a teacher has a 12 lb bag of sand the sand will be divided evenly into 0.8 pound container if using all the saying how many 0.8 pound containers does the teacher use
Answers
The quotient of a number and -5 has a result of 2. What is the number?
Type the correct answer in the box. Use numerals instead of words.
n =
Answers
Answer:
Answer is -10
Step-by-step explanation:
Explanation:
First, define the variable. Let n represent the unknown number.
Next, write an equation to represent the situation. Because a quotient is the result of division, divide the unknown number by -5:
.
Then, use opposite operations and the properties of equality to solve for n. Notice that the variable, n, is divided by -5. So, to isolate n, do the opposite and multiply both sides of the equation by -5:
Finally, to check the solution, substitute -10 for n in the original equation:
The resulting statement is true, so the solution is correct.
Please answer this correctly without making mistakes
Answers
Answer:
The point G represents: "60 dollars is the cost to dry clean 6 suits."
Step-by-step explanation:
If you look at the graph, on the bottom it shows number of suits, which is the independent. On the left it shows the cost of suits which is the dependent.
The dependent (Money) depends on the independent (Suits) so when you look at the point G you see that it is graphed on 6 suits for 60 dollars.
If the discriminant of a quadratic equation is equal to -8, which statement describes the roots?
There is one real root.
There are two complex imaginary roots.
There is one complex imaginary root.
There are two real roots.
Answers
Answer:
Step-by-step explanation:
A discriminate of -8 is never going to give you a real root. D is wrong
You cannot have just 1 complex root, nor can you have just 1 real root unless the discriminate is 0. A and C are both wrong for the same reason. 1 complex root is impossible. They come in pairs.
So the answer is B. You have 2 complex roots.
Explain how you can find the missing number in 3 4/5 divided by x equal 2 5/7. Then find the missing number.
Answers
Answer:
You multiply
Step-by-step explanation:
You multiply 3 4/5 and 2 5/7
Answer is 10 1/3
erika says that no matter how many decimal places she divides to when she divides 1 by 3, the digit 3 in the quotient will just keep repeating. is she correct?n
Answers
Answer:
Yes
Step-by-step explanation:
When u divide 1 by 3 the answer is repeating 0.3333....