Answers
The slope of the original line of the graph sis found to be 1 and the slope of perpendicular line is -1.
One of the line shown in the graph is passing through the points (0, -7) and (7, 0). Now we have to recall that the slope M of the line L passing from points (a, b) and (c, d) is given as,
M = (d-b)/(c-a)
Also, if the line L is perpendicular to line l, then the slope m of the line l will be given as,
m = -1/M.
So, now the slope of line L is,
M = (0-(-7))/(7-0)
M = 7/7
M = 1
Now, the slope of the perpendicular line l is,
m = -1/1
m = -1.
Hence, the slope of the perpendicular line and original lines are -1 and 1.
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Related Questions
200 bats in a colony are affected by a disease which causes their population to decrease by 8% every day.
the following equation represents the bat colony population as the disease effect's them
f (x)= 200 (0.92)^x
Does this equation represent exponential growth or exponential decay. Explain how you know using the function itself.
15 POINTS!!!!!
Answers
Answer:
Exponential decay--------------------------
The first explanation comes from the information given in the question.
It says the population decreases.
From the function itself, we look at the base of the exponent. The function is representing a growth if the base is greater than 1 and decay if the base is less than 1.
In our case 0.92 < 1, hence the function represents exponential decay.
total cost
of the wall = answer
Answers
Answer:
64 pounds
Step-by-step explanation:
so first what you have to do is find the perimeter of the barn:
2l+2w
2*12)+2*4)= 32 m
Then it costs 2 pounds per meter
So they you multiply
32m * 2 pounds
64 pounds
Hellooe what r the answers to these
Answers
1) The value of cos θ is,
2) The value of sin θ is,
3) The value of cos θ is,
We have to given that;
The value of sin θ is,
⇒ sin θ = 3/5
Hence,
cos θ = √1 - sin²θ
cos θ = √1 - 9/25
cos θ = √16/9
cos θ = 4/3
Since, It is quadrant II.
Hence,
cos θ = - 4/3
Since, cos θ = - 5/12
Hence,
sin θ = √1 - cos²θ
sin θ = √1 - 25/144
sin θ = √119/144
Since, It is quadrant III,
Hence,
sin θ = - √119/12
The value of sin θ is,
⇒ sin θ = - 15/17
Hence,
cos θ = √1 - sin²θ
cos θ = √1 - 225/289
cos θ = √64/289
cos θ = 8/17
Since, It is quadrant IV.
Hence,
cos θ = 8/17
Since, Value of sine is always positive,
And, Values of cosine is always greater than - 1.
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8. (Equations)
The difference between 3 times a number x and 2 is 19. What is the
value of x?
A 7
B. 6
C. 5
D. 1
Answers
Answer: A. 7
Step-by-step explanation:
3y-2=19
3y-2+2=19+2 (add 2 to both sides)
3y=21
3y/3=21/3 (divide by 3 on each side)
y=7
the mean number of words per minute (wpm) typed by a speed typist is 135 with a variance of 100 . what is the probability that the sample mean would be greater than 135.7 wpm if 43 speed typists are randomly selected? round your answer to four decimal places.
Answers
The probability that the sample mean would be greater than 135.7 WPM is 0.1686.
Calculate the standard deviation:
The standard deviation of the WPM typed by a speed typist is √100 = 10.
Calculate the z-score
The z-score is calculated by subtracting the population mean (135) from the sample mean (135.7) and dividing it by the standard deviation (10).
z = (135.7 - 135) / 10 = 0.07
Calculate the probability
The probability of the sample mean being greater than 135.7 WPM can be calculated using the z-score.
P(x > 135.7) = 1 - P(x ≤ 135.7)
P(x > 135.7) = 1 - 0.8314 = 0.1686
Therefore, the probability that the sample mean would be greater than 135.7 WPM if 43 speed typists are randomly selected is 0.1686, rounded to four decimal places.
Complete Question:
The mean number of words per minute WPM typed by a speed typist is 135 with a variance of 100. What is the probability that the sample mean would be greater than 135.7 WPM if 43 speed typist are randomly selected? round your answer to four decimal places.
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Can someone please help me answer this question, thank you in advance.
Answers
Answer:
Step-by-step explanation:
[tex]\frac{a^{3}.b^4.5^4}{b^2.5}\\ = a^3.b^2.5^3\\= 125a^3b^2[/tex]
[tex] { {a}^{3} } \times {b}^{2} \times 125[/tex]
When dividing variables with exponents, subtract the bottom exponent from the top. since there is no "a" in the denominator, we would leave it as is. The "b" at the top (numerator) has an exponent of 4, and the one in the bottom (denominator) has an exponent of 2, so we would do 4 - 2, which equals 2, so the exponent on b would be 2. Then, the exponent for 5 in the numerator is 4, and in the denominator, it's 1 (any number that with no visible exponent has an exponent of 1). 4 - 1 is 3, and 5^3 is 125.
I need some help please, which figure is a translation of figure A?
1) Figure B
2) Figure C
3) Figure D
Answers
Answer: Figure C
Step-by-step explanation:
Figure C is a translation of Figure A because it moved down. Figure A moved down 5 units in order to be Figure C. A translation is moving in a direction. Figure B and D have both been altered some other way, but Figure C has just been moved down.
2.1 You are given that m is an even integer and n is an odd integer. Which of these is an
odd integer?
A: 3m + 4n
B: 5mn
C: (m + 3n)²
D: m³n²
E: 5m + 6n
Answers
The only odd integer among the choices is 5mn.
To determine which expression is an odd integer,
we need to know that the sum of an even integer and an odd integer is always odd, and the product of an even integer and an odd integer is always even.
A: 3m + 4n = 2m + m + 4n is even
since it's the sum of two even integers.
B: 5mn is odd since it's the product of an odd and an even integer.
C: (m + 3n)² = m² + 6mn + 9n² is odd since it's the sum of two odd integers and an even integer.
D: m³n² = m * m² * n² is even since it's the product of an even integer and two odd integers.
E: 5m + 6n = 2(2m + 3n) + m is odd since it's the sum of two even integers and an odd integer.
Therefore, the only odd integer among the choices is 5mn.
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6. How many full revolutions
does a car tire with a
diameter of 25 inches
make when the car
travels one mile?
Answers
Answer:
5
Step-by-step explanation:
im right
reatest, or the mean of
node: The number that appea
POL
oss
Find the mean for 3, 9, 5, 4, 9.
Di please find mean of this question?
Answers
Answer:
The Mean is 6.
Step-by-step explanation:
Solve an equation that can be used to determine the value of k.
(11k-23)
Y
Z
(5k - 3)°
(14k - 4)°
X W
Answers
Answer:
k = 11Y = 52°Z = 98°∠WXZ = 150°Step-by-step explanation:
You want the value of the variable k and the angle measures around triangle XYZ in the given figure.
Exterior angleThe exterior angle at X is equal to the sum of the remote interior angles at Y and Z:
14k -4 = (5x -3) +(11k -23)
14k -4 = 16k -26
7k -2 = 8k -13 . . . . . . divide by 2 (because we can)
11 = k . . . . . . . . . . add 13-7k
The value of k is 11.
Angle YY = (5k -3)° = (5·11 -3)°
Y = 52°
Angle ZZ = (11k -23)° = (11·11 -23)°
Z = 98°
Angle WXZangle WXZ = Y +Z = 52° +98°
angle WXZ = 150°
__
Additional comment
The exterior angle at X is the supplement of the adjacent interior angle X. That interior angle is also the supplement of the sum of angles Y and Z. Two angles are equal when their supplements are equal. Hence angle WXZ is the sum of angles Y and Z.
#95141404393
I don’t even know if I’ve done this problem right or not please help
Answers
Step-by-step explanation:
I believe there is something missing from the description.
I base my solution and explanation on the following assumptions :
the angle theta is at the origin (0, 0).not only passes the terminal side through (20, -21), but so does also the circle around our trigonometric triangle.in other words, (20, -21) is not just any point on the line, but it is the upper vertex of the triangle.
the baseline of the triangle, which is the radius of the surrounding circle is then the distance from the origin to the point.
Pythagoras (= distance formula) gives us for the distance between 2 points (x1, y1) and (x2, y2) :
distance² = (x1 - x2)² + (y1 - y2)²
in our case
distance² = (20 - 0)² + (-21 - 0)² = 400 + 441 = 841
distance = radius = 29
remember, sine is the up/down leg, cosine is the left/right leg.
so,
sin(theta) = -21/29
FYI : theta ≈ -46.4°
cos(theta) = 20/29
tan(theta) = sin(theta)/cos(theta) = -21/29 / 20/29 =
= -21/20
you were right about tan(theta), not about sin(theta) and cos(theta).
if you mistook theta for a 0, you were still wrong :
sin(0) = 0, cos(0) = 1.
Problems 19-23 use the following scenario: A design engineer is measuring the drag force (i.e., the
force resisting motion) on a robotic submarine. As the submarine moves through the water at v
meters per second m
it experiences a drag force of F newtons (N). The table below represents
the design engineer's measurements.
Drag Force vs. Speed
Speed (in
8
10
m
F Drag Force (in N)
720
1100
The drag force can be modeled by a quadratic equation of the form F=bv+cv².
IVE
n.
19. Using (8, 720), create an equation in terms of b and c.
720=6(8) + C² (8) ²
20. Using (10, 1100), create an equation in terms of b and c.
720= 8b+ C4 C
1100=b (10) + c(10) ²
1100 = 10b + 1979 an
21. Solve the system of equations from #19 and # 20 for b and c.
720 = 8b+ Cec
2. Write a function F which serves as a model for profit.
1100-106+100c
What value of speed, in meters per second, corresponds a drag force of 120N? Includ
your answer.
Answers
Answer: =
24
X
Submit Answer
62
H
word
Answers
The value of x, which is the radius of this cone is 64 units.
How to calculate the volume of a cone?In Mathematics and Geometry, the volume of a cone can be calculated by using this formula:
Volume of cone, V = 1/3 × πr²h
Where:
V represent the volume of a cone.h represents the height.r represents the radius.By substituting the given parameters into the formula for the volume of a cone, we have the following;
512π = 1/3 × π × x² × 24
512π = π × x × 8
Radius, x = 512/8
Radius, x = 64 units
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Complete Question:
The volume of the right cone below is 512π units³. Find the value of x.
Can someone please help me with this trigonometry assignment?
Directions: Write a word problem as a STORY which will require Trigonometry to solve. What is the problem? Why do we need to solve it? Who needs us to solve it? How will it help? Solve the problem clearly and accurately.
The picture above is an example on how you could create the word problem.
Answers
The final calculation revealed that the height of the mountain was approximately 350.1 meters.
How to explain the trigonometryBack in their workshop, Alex applied the tangent function to find the mountain's height. They knew that tangent is the ratio of the opposite side (the height) to the adjacent side (the horizontal distance). Setting up the equation, they plugged in the known values:
tangent(35 degrees) = height / 500 meters
Using trigonometric tables or a calculator, they found that the tangent of 35 degrees is approximately 0.7002. Now they could solve the equation:
0.7002 = height / 500 meters
To isolate the height, they multiplied both sides of the equation by 500:
0.7002 * 500 meters = height
The final calculation revealed that the height of the mountain was approximately 350.1 meters.
With this crucial information, Alex and Sarah could now design the bridge
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Use the segment addition postulate find the value of x EF= 7x+9 FG=3x+4 EG=143
Answers
Using the segment addition postulate, we can find that the value of x is 18.
Explanation: The segment addition postulate states that for three points A, B, and C on a line, if B is between A and C, then AB + BC = AC. In this case, we have three points on a line: E, F, and G, and we are given the lengths of two line segments, EF and FG. Using the segment addition postulate, we can set up the following equation:
EF + FG = EG
Substituting the given values, we get:
(7x+9) + (3x+4) = 143
Simplifying the equation, we get:
10x + 13 = 143
Subtracting 13 from both sides, we get:
10x = 130
Dividing both sides by 10, we get:
x = 13
Therefore, the value of x is 13.
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true or false: double integral can be used to compute the area of a region d in a plane simply by integrating the function f(x,y)
Answers
True. The double integral can be used to compute the area of a region d in a plane by integrating the function f(x,y). In fact, the double integral of f(x,y) over a region D in the xy-plane gives the volume of the solid between the surface z=f(x,y) and the xy-plane over the region D.
However, if we take the function f(x,y) to be the constant function 1, then the double integral of f(x,y) over the region D is simply the area of the region D. Therefore, we can compute the area of a region D in a plane by integrating the constant function 1 over the region D using the double integral. Integrating over two variables requires calculating two separate integrals, so the answer is more than 100 words.
True. A double integral can be used to compute the area of a region D in a plane by integrating the function f(x, y). To find the area, you would integrate the function f(x, y) = 1 over the region D, as the double integral represents the sum of the function values over the entire area. The double integral can be thought of as a generalization of single-variable integration, allowing us to find the area in two dimensions.
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A cans good company manufuctured a cylinderical can of height 10cm and radus 4 cm find surface area
Answers
To find the surface area of a cylindrical can, we need to calculate the sum of the areas of its curved surface and its two circular bases.
The curved surface area (CSA) of a cylinder can be calculated using the formula:
CSA = 2πrh
In this case, the height (h) of the can is 10 cm and the radius (r) is 4 cm.
Using the formula, we can calculate the curved surface area:
CSA = 2 × 3.14 × 4 cm × 10 cm
CSA = 251.2 cm²
The area of each circular base can be calculated using the formula:
Base Area = πr²
Substituting the radius (r = 4 cm) into the formula, we get:
Base Area = 3.14 × (4 cm)²
Base Area = 50.24 cm²
Since the can has two circular bases, the total area of the bases is 2 times the base area, which is:
2 × 50.24 cm² = 100.48 cm²
To find the total surface area, we add the curved surface area and the area of the bases:
Total Surface Area = CSA + 2 × Base Area
Total Surface Area = 251.2 cm² + 100.48 cm²
Total Surface Area = 351.68 cm²
Therefore, the surface area of the cylindrical can is approximately 351.68 cm².
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the following calculation is an example of which type of measure: the number of children that had allergies in 2020 divided by an estimate of total number children in the population?
Answers
Prevalence is a commonly used metric in epidemiology and public health to describe the proportion of a population affected by a specific condition or characteristic during a specific period. In this case, it helps to understand the extent of allergies among children in 2020.
The calculation given is an example of a prevalence measure, which is used to determine the proportion or percentage of individuals in a population that have a particular health condition or disease. In this case, the number of children with allergies in 2020 is divided by an estimate of the total number of children in the population to determine the prevalence of allergies in the population.
Prevalence measures are useful for understanding the burden of a particular health condition in a population, as well as for identifying trends over time or differences between different groups within the population. However, it's important to note that prevalence measures are only as accurate as the data used to calculate them, so it's essential to use reliable sources of data and to ensure that the sample of individuals being measured is representative of the entire population.
Prevalence measures are widely used in epidemiology and public health research to understand the distribution of health conditions and diseases in populations. They can be calculated for a wide range of health outcomes, including chronic diseases, infectious diseases, mental health conditions, and more.
In addition to prevalence, other types of measures used in public health research include incidence (which measures the number of new cases of a particular health condition within a population over a specific period of time), mortality (which measures the number of deaths attributable to a particular health condition or disease), and morbidity (which measures the burden of illness associated with a particular health condition or disease, often in terms of disability-adjusted life years or quality-adjusted life years).
Ultimately, the type of measure used in a given study will depend on the research question being asked, the available data sources, and the specific health outcome being studied. However, regardless of the type of measure used, it's important to ensure that the sample of individuals being measured is representative of the entire population, and to use reliable and accurate data sources to calculate the measure.
The calculation you described, which involves dividing the number of children with allergies in 2020 by an estimate of the total number of children in the population, is an example of a prevalence measure.
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help fast and whoever gets it correct gets brainlyest
solve for x in the following equation
A. X = 16.5
B. X.= 4.125
C. X= -3
D. X= -12
Answers
Answer:
C. x = -3
Step-by-step explanation:
Given equation:
[tex]10x+57=9-6x[/tex]
Add 6x to both sides of the equation:
[tex]10x+57+6x=9-6x+6x[/tex]
[tex]16x+57=9[/tex]
Subtract 57 from both sides of the equation:
[tex]16x+57-57=9-57[/tex]
[tex]16x=-48[/tex]
Divide both sides by 16:
[tex]\dfrac{16x}{16}=\dfrac{-48}{16}[/tex]
[tex]x=-3[/tex]
Therefore, the solution to the equation is x = -3.
Hello !
Answer:
[tex] \boxed{\sf Option \: C\text{:} \: x= -3} [/tex]
Step-by-step explanation:
Solve the equation by isolating the variable 'x'.
[tex] \\ [/tex]
We are given the following equation:
[tex] \sf 10x + 57 = 9 - 6x [/tex]
[tex] \\ [/tex]
Subtract 57 from both sides and combine like terms:
[tex] \sf 10x + 57 - 57 = 9 - 6x - 57 \\ \sf 10x = -6x - 48 [/tex]
[tex] \\ [/tex]
Add 6x to both sides of the equation and combine like terms:
[tex] \sf 10x + 6x = -6x - 48 + 6x \\ \sf 16x = -48 [/tex]
[tex] \\ [/tex]
Finally, divide both sides by 16, which is the coefficient of the variable.
[tex] \sf \dfrac{16x}{16} = \dfrac{-48}{16} \\ \\ \boxed{\sf x= -3} [/tex]
Have a nice day ;)
Calculate the relative frequency of the data to determine which association the two-way table suggests.
A. None of the associations listed are correct.
B. Those who have a brother tend not to have a sister.
C. Those who have a brother tend to have a sister.
D. Those who do not have a brother tend not to have a sister.
Answers
The correct option A, "None of the associations listed are correct," is the appropriate response.To determine the association suggested by the two-way table, we need to calculate the relative frequency of the data.
The table provides information about whether individuals have a brother and a sister.
Based on the options given, let's calculate the relative frequencies to see which association is suggested:
Calculate the relative frequency for individuals who have a brother and a sister:Relative frequency = (Number of individuals with both a brother and a sister) / (Total number of individuals)
Calculate the relative frequency for individuals who have a brother but no sister:Relative frequency = (Number of individuals with a brother but no sister) / (Total number of individuals)
Calculate the relative frequency for individuals who have a sister but no brother:Relative frequency = (Number of individuals with a sister but no brother) / (Total number of individuals)
Calculate the relative frequency for individuals who have neither a brother nor a sister:Relative frequency = (Number of individuals with neither a brother nor a sister) / (Total number of individuals)
By comparing the relative frequencies, we can determine which association is suggested by the data.Unfortunately, the given two-way table is missing, so we cannot perform the necessary calculations to determine the association.
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Acceptance sampling. A company produces large cases of incandescent light bulbs. If there is a 1% chance that any one light bulb is defective, what is the probability that among 83 randomly sampled lightbulbs. A. . 1 or less are defective?
b. . 2 or more are defective?
Answers
Light bulbs can be calculated using the binomial distribution with n=83 and p=0.01. P(X≤1)=0.1808. light bulbs can be calculated as 1 minus the probability that 0 or 1 light bulbs are defective. P(X≥2)=1-P(X≤1)= 1-0.1808=0.8192.
a. The probability that 1 or less light bulbs are defective among 83 sampled light bulbs can be calculated using the binomial distribution with n=83 and p=0.01. P(X≤1)=0.1808.
b. The probability that 2 or more light bulbs are defective among 83 sampled light bulbs can be calculated as 1 minus the probability that 0 or 1 light bulbs are defective. P(X≥2)=1-P(X≤1)=1-0.1808=0.8192.
In acceptance sampling, a sample is taken from a large batch of items to determine if the entire batch should be accepted or rejected based on the number of defective items in the sample. In this problem, the probability of a light bulb being defective is given as 1%, and we are asked to find the probabilities of having 1 or less defective light bulbs or 2 or more defective light bulbs among a sample of 83 light bulbs. We can use the binomial distribution to calculate these probabilities, where X is the number of defective light bulbs in the sample. The probability of having 1 or less defective light bulbs can be calculated as the sum of the probabilities of having 0 or 1 defective light bulbs, and the probability of having 2 or more defective light bulbs can be calculated as 1 minus the probability of having 1 or less defective light bulbs.
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This is hard so don't ask why i need help -v- (90 POINTS!)
Zach has 72 cards. he gives 23 away. how many cards does Zach have left?
Answers
Answer: 49
Step-by-step explanation:
When you have 72 and subtract it by 23 you get 49
in the xy-plane, exactly how many x-intercepts does the graph of f of x equals, x times, open parenthesis, x minus 4, close parenthesis, squared, times, open parenthesis, x minus 5, close parenthesis, cubed have?
Answers
The function has three x-intercepts: x=0, x=4, and x=5. The graph of f(x) has three x-intercepts in the xy-plane.
To find the x-intercepts of a function, we need to set the value of y to zero and solve for x. In this case, the function is f(x) = x(x-4)^2(x-5)^3. To find the x-intercepts, we set f(x) = 0 and solve for x.
First, we notice that each factor is squared or cubed, which means that they cannot be negative. Therefore, we only need to consider the positive values of x.
Next, we see that the factor x will make the whole expression zero when x=0.
The factors (x-4)^2 and (x-5)^3 will make the expression zero when x=4 and x=5, respectively.
Therefore, the function has three x-intercepts: x=0, x=4, and x=5.
In conclusion, the graph of f(x) has three x-intercepts in the xy-plane. Includes the terms "parenthesis" and "squared."
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the grade point averages of the gourmet society are uniformly distributed between 2.5 and 3.5. a. find the probability distribution function, f(x) for this scenario. b. using part (a), find the probability that a randomly chosen member of the society has a grade point average between 3 and 3.2
Answers
The probability that a randomly chosen member of the society has a grade point average between 3 and 3.2 is 0.2 or 20%.
The probability distribution function (pdf), f(x), for the grade point averages of the gourmet society can be represented by a uniform distribution between 2.5 and 3.5. In a uniform distribution, the probability density is constant within the range and zero outside the range. The formula for the pdf is:
f(x) = 1 / (b - a)
where a is the lower bound (2.5 in this case) and b is the upper bound (3.5 in this case). Therefore, for this scenario:
f(x) = 1 / (3.5 - 2.5) = 1
To find the probability that a randomly chosen member of the society has a grade point average between 3 and 3.2, we need to calculate the area under the probability distribution curve within that range. Since the probability density is constant within the range, the probability is equal to the width of the range divided by the total width of the distribution.
The width of the range is 3.2 - 3 = 0.2, and the total width of the distribution is 3.5 - 2.5 = 1. Therefore, the probability is:
Probability = (width of range) / (total width)
= 0.2 / 1
= 0.2
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Select the values that make the inequality
3
�
≥
−
72
3d≥−72 true. Then write an equivalent inequality, in terms of
�
d.
Answers
The values of d that make the inequality 3d ≥ -72 true are all values greater than or equal to -24. An equivalent Inequality in terms of d is d ≥ -24.
To make the inequality 3d ≥ -72 true, we need to find values of d that satisfy the inequality.
Dividing both sides of the inequality by 3, we get:
d ≥ -24
Therefore, any value of d that is greater than or equal to -24 will satisfy the inequality.
An equivalent inequality in terms of d would be:
d + 24 ≥ 0
We can simplify this inequality by subtracting 24 from both sides:
d ≥ -24
This is the same inequality we found earlier, which means that any value of d greater than or equal to -24 will make the inequality true.
the values of d that make the inequality 3d ≥ -72 true are all values greater than or equal to -24. An equivalent inequality in terms of d is d ≥ -24.
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I really need help in this question! Lots of points as a reward for answer and I will give brainiest for best answer possible!
Answers
a) Marcus' result is likely to be more reliable.
b) Because the sample was bigger.
How to calculate a probability?The parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is then calculated as the division of the number of desired outcomes by the number of total outcomes.
The higher the total number of outcomes, the more reliable the probability calculated is.
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The mass of a substance varies directly as the volume of the substance. If a mass of 30 kg of a substance has a volume of 6 liters, what is the volume of 65 kg of the substance?
Answers
Answer:
The volume of 65 kg of the substance is 13 liters.
Step-by-step explanation:
If a substance's mass varies directly from its volume, it means that the ratio of mass to volume remains constant. In this case, we can calculate the continuous ratio and then use it to find the volume.
Given:
Mass1 = 30 kg
Volume1 = 6 liters
Let's denote the constant ratio as k.
Mass1 / Volume1 = k
30 kg / 6 liters = k
k = 5 kg/liter
Now, we can find the volume2 for a mass of 65 kg using the constant ratio:
Mass2 = 65 kg
Volume2 = ?
Mass2 / Volume2 = k
65 kg / Volume2 = 5 kg/liter
To find Volume2, we can cross multiply:
65 kg = 5 kg/liter * Volume2
Volume2 = 65 kg / 5 kg/liter
Volume2 = 13 liters
Let R be the region in the first quadrant bounded by the graph of y = 2 \sqrt x, the horizontal line y = 6, and the y-axis, as shown in the figure.
a) Find the area of R.
b) Write, but do not evaluate, an integral expression that gives the volume of the solid generated when R is rotated about the horizontal line y = 7.
c) Write, but do not evaluate, an integral expression that gives the volume of the solid generated when R is rotated about the y-axis.
Answers
a) To find the area of region R, we need to calculate the area between the curves y = 2√x and y = 6 in the first quadrant. The region is bounded by the y-axis and the horizontal line y = 6.
To find the area, we integrate the difference between the upper and lower curves with respect to x:
Area = ∫[0 to a] (6 - 2√x) dx,
where 'a' is the x-coordinate where the curves intersect.
b) To find the volume of the solid generated when region R is rotated about the horizontal line y = 7, we can use the method of cylindrical shells. Each cylindrical shell has a height of 6 - 7 = -1 (as y = 6 is below y = 7) and a radius equal to x.
The volume is given by the integral:
Volume = ∫[0 to a] 2πx(6 - 7) dx,
where 'a' is the x-coordinate where the curves intersect.
c) To find the volume of the solid generated when region R is rotated about the y-axis, we can use the method of disks. Each disk has a radius equal to y and a thickness given by dx.
The volume is given by the integral:
Volume = ∫[0 to b] π(y^2) dx,
where 'b' is the y-coordinate where the curves intersect.
To learn more about coordinate : brainly.com/question/22261383
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Which of these ordered pairs is a solution to the linear inequality y ≤ 4x – 3?
Responses
(1, 4)
(1, 4)
(1, 5)
(1, 5)
(–2, 5)
(–2, 5),
(2, 5)
Answers
Answer:
(2, 5)
Step-by-step explanation:
You want the ordered pair that is a solution to y ≤ 4x -3 from those on the list:
(1, 4)(1, 5)(-2, 5)(2, 5)GraphThe attachment shows a graph of the inequality, along with the offered solution points. The only solution among those shown is (2, 5). That solution lies on the boundary line. The "≤" symbol means the boundary line is included in the solution set.
CalculatorWe can use a calculator to check the solutions, too. Rearranging, we have ...
4x -3 -y ≥ 0
The calculator in the second attachment is able to make this calculation using the list of x-values and the list of y-values. The solution list only has one number that is not less than zero. That corresponds to (x, y) = (2, 5).
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Additional comment
We like to avoid having to enter the same equation over and over with different data. That is why we have chosen the solution methods here. A spreadsheet can repeat the calculation and comparison for you, too.
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