Final answer:
The trace on the xy-plane of a sphere with center (-1, 3, -1) and radius 2 is a circle with center (-1, 3) and radius 2, represented by the equation (x + 1)² + (y - 3)² = 4.
Explanation:
The question asks to find the trace on the xy-plane of the sphere having a center at (-1, 3, -1) and a radius 2.
The trace on the xy-plane of a sphere is essentially the circle that is formed when the sphere intersects the xy-plane.
Since the center of the sphere is (-1, 3, -1), and the sphere intersects the xy-plane (z=0), we keep the x and y coordinates of the center the same for the circle, meaning the center of the circle will be (-1, 3). The radius of the circle remains the same as the sphere, which is 2.
The equation for a circle in the xy-plane with center (h, k) and radius r is given by (x - h)² + (y - k)² = r².
Therefore, plugging in the values for this specific circle gives us the equation (x + 1)² + (y - 3)² = 4.
This equation represents the trace of the sphere on the xy-plane.
Find the exact length of the curve. y2 = 4(x + 1)3, 0 ≤ x ≤ 1, y > 0
To find the exact length of the curve, we can use the concept of arc length. The formula for the arc length of a curve y = f(x) on the interval [a, b] is given by: L = ∫√(1 + (f'(x))^2) dx, where f'(x) is the derivative of f(x). In this case, y2 = 4(x + 1)3 can be rewritten as y = 2√(x + 1)^3. Taking the derivative of y with respect to x, we get y' = 3(x + 1)^(3/2). Plugging this into the formula for arc length: L = ∫√(1 + (3(x + 1)^(3/2))^2) dx = ∫√(1 + 9(x + 1)^3) dx. We can then evaluate this integral over the interval [0, 1] to find the exact length of the curve.
Explanation:To find the exact length of the curve y2 = 4(x + 1)3, 0 ≤ x ≤ 1, y > 0, we can use the concept of arc length. The formula for the arc length of a curve y = f(x) on the interval [a, b] is given by:
L = ∫√(1 + (f'(x))^2) dx, where f'(x) is the derivative of f(x).
In this case, y2 = 4(x + 1)3 can be rewritten as y = 2√(x + 1)^3. Taking the derivative of y with respect to x, we get y' = 3(x + 1)^(3/2). Plugging this into the formula for arc length:
L = ∫√(1 + (3(x + 1)^(3/2))^2) dx = ∫√(1 + 9(x + 1)^3) dx
We can then evaluate this integral over the interval [0, 1] to find the exact length of the curve.
A biologist studied the populations of black bear and brown bears over a 10 year period. the biologist modeled the populations, in thousands with the following polynomials where X is time , in years. BLACK BEARS : 2.3x^2-5.6X+2.3 BROWN BEARS:2.4X^2+7.2X+0.97 What polynomial models the total number of brown and black bears ? A.) 4.7x^2+1.6x+3.27 B.) 4.7x^2-1.6x-3.37 C.) 4.7x^2+1.6x-3.37 D.) 4.7x^2-1.6x+3.37 i need help ??
Can you solve this problem?
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Mailboxes plus sends packages overnight for $5 plus $0.25 per ounce. United packages cost $2 plus $0.35 per ounce. Mr.Molinari noticed that his package would cost the same to maill using either service. How much does his package weigh?
By setting up an equation equating the cost of shipping with both Mailboxes Plus and United Packages, we determine that Mr. Molinari's package weighs 30 ounces.
Mailboxes Plus charges a flat rate of $5 plus $0.25 per ounce, while United Packages charges $2 plus $0.35 per ounce. Since the cost is the same for either service, we can equate the two expressions and solve for the weight of the package in ounces.
Let x represent the weight of the package in ounces. The cost for Mailboxes Plus is then $5 + $0.25x, and for United Packages, it is $2 + $0.35x. Setting these two expressions equal to each other, we get:
$5 + $0.25x = $2 + $0.35x
Now, we will solve for x:
Subtract $2 from both sides: $3 + $0.25x = $0.35xSubtract $0.25x from both sides: $3 = $0.35x - $0.25xCombine like terms: $3 = $0.10xDivide both sides by $0.10: $3 / $0.10 = xSimplify: 30 ounces = xTherefore, Mr. Molinari's package weighs 30 ounces.
If you were only going to make a third of the recipe, how many cups of almonds would you need
Final answer:
To determine the amount of almonds needed for a third of the recipe, if one full batch requires 3 cups, you would divide 3 cups by 3, resulting in 1 cup of almonds for a third of the recipe.
Explanation:
To calculate the amount of almonds needed for a third of the recipe, we first need to determine the total number of cups used for the full recipe. If the original recipe calls for 3 cups of almonds to make one batch, and the person is making 5 batches, they would initially need 15 cups of almonds (since 3 cups per batch multiplied by 5 batches equals 15 cups).
If they only want to make a third of one batch, we would take the amount needed for one batch, which is 3 cups, and divide it by 3 to find the required amount. So, 1 cup of almonds is needed for a third of the recipe, because 3 cups divided by 3 equals 1 cup.
Which is greater 770 meters or 7 kilometers
The school is having a bake sale and the math club is bringing cupcakes. They have 180 total cupcakes, both chocolate and strawberry. The number of chocolate cupcakes is eighteen more than twice the number of strawberry cupcakes. Which system of equations can be used to find the number of chocolate cupcakes, c, and the number of strawberry cupcakes, s? A. c + s = 180 s = 2c - 18 B. c + s = 180 c = 2s + 18 C. c - s = 180 s = 2c + 18 D. c = 2s c - 180 = s
Ms. O bought 2 1/2 pounds of blueberries on Monday. She Gavs 1/4 of the blueberries to her students before school ended A. How many pounds of blueberries did she give to students on monday B.How many blueberroes were left? C. On Tuesday she ate 1/3 of the remaining blueberries. How many did she eat on Tuesday? D. Did Ms.O eat more blueberries on Monday or on Tuesday? Explain your reasoning
sin(a)+sin(b)=sqrt(5/3) and cos(a)+cos(b)=1. Compute cos(a-b).
I drew out triangles and modeled the sines and cosines of a and b, but that doesnt help me find cos(a-b). What do I do?
Twenty-four students took a test. Fourteen students earned an A and 10 students earned a B. A student will be randomly chosen.
What is the probability that the student earned an A on the last test?
Enter your answer as a fraction, in simplest form, in the box.
The probability that a student earned an A on the last test is 7/12. This is found by dividing the number of students who earned an A by the total number of students and simplifying the fraction.
To find the probability that a randomly chosen student earned an A on the last test, we need to consider the total number of students and the number of students who earned an A.
The total number of students is 24, and 14 of them earned an A. The probability is calculated by dividing the number of students who earned an A by the total number of students:
Probability = Number of Students Who Earned an A / Total Number of Students = 14/24.
Next, we simplify the fraction 14/24 by finding the greatest common divisor (GCD) of 14 and 24, which is 2. Dividing both the numerator and the denominator by 2, we get:
Simplified Probability = (14 ÷ 2) / (24 ÷ 2) = 7/12.
Therefore, the probability that a student earned an A on the last test is 7/12.
The circumference of a circle is 6.28 meters. What is the circle's radius? C=6.28 m Use 3.14 for pi
The radius of the circle is 1 meter.
We have,
The formula for the circumference of a circle is:
C = 2πr
where C is the circumference, r is the radius, and π is a constant equal to approximately 3.14.
We are given the circumference of the circle as 6.28 meters, so we can substitute this value into the formula:
6.28 = 2πr
Dividing both sides by 2π gives:
r = 6.28 / (2π)
r = 6.28 / (2 x 3.14)
r = 1
Therefore,
The radius of the circle is 1 meter.
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Final answer:
To find the circle's radius with a circumference of 6.28 meters using π=3.14, use the formula C=2πr. By rearranging and solving for r, the radius is found to be 1 meter.
Explanation:
The question is about finding the radius of a circle when the circumference is given as 6.28 meters and using 3.14 for π (pi). To find the radius, we use the formula for the circumference of a circle, C = 2πr, where C is the circumference, r is the radius, and π is Pi. Given C=6.28 m and π=3.14, we rearrange the formula to solve for r: r = C / (2π).
Plugging in the given values, r = 6.28 / (2×3.14) = 6.28 / 6.28 = 1. Therefore, the radius of the circle is 1 meter.
Given 2 points (3,6) and (-2,5) explain or show how to calculate the slope explain in words
i need to know what “x” in the angle measures
Brian spent 60% of a weeks time working on drawings for a new apartment building. If Brian spent 18 hours working on projects other than the apartment building, compute the total hours worked
Anita sees in her nutrition book that a 7.5-ounce cake has 900 calories how many calories will she save if only takes 2.5-ounce piece help please
How many inches are in a yard?
PLEASE ANSWER!!!!!! WILL MARK BRAINLIEST AND GIVE 20 POINTS:
The difference of two numbers is equal to 0.6. Their quotient is also 0.6. What are the numbers? Please answer both questions below.
What are the numbers?
What are the "or" numbers?
The numbers are:
Or numbers are"
Central High School plays Eastern High School in a basketball game. Eastern had double the score of Central before Central scored a three-pointer as the game ended.
The variable, c, represents Central's score before the three-pointer. Express the total points scored in the game as a variable expression.
Answer:
Central High School plays Eastern High School in a basketball game. Eastern had double the score of Central before Central scored a three-pointer as the game ended.
The variable, c, represents Central's score before the three-pointer. Express the total points scored in the game as a variable expression. Check all that apply.
Step-by-step explanation:
The total points scored in the game as a variable expression is 2c + c + 3.
What are equivalent expressions?Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
It is given that Central High School plays Eastern High School in a basketball game. Eastern had double the score of Central before Central scored a three-pointer as the game ended:
Let consider Central High School score be c
We knowt that the variable, c, represents Central's score before the three-pointer.
So, when Eastern doubled the score of Central, it is 2c
A Central scored a three-pointer as the game ended, it is + 3
To get the total points scored in the game, add all the actual variables
= (Eastern double points + Central single point + Central three-pointer)
= 2c + c + 3
So, the total points scored in the game as a variable expression is 2c + c + 3.
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A point undergoes two transformations. The x-coordinate's sign changes and the y-coordinate increases. What were the transformations?
Answer: The correct option is
(C) The point was reflected over the y-axis and translated up.
Step-by-step explanation: Given that a point undergoes two transformations as follows :
"The x-coordinate's sign changes and the y-coordinate increases."
We are to select the correct transformations.
We know that
when x co-ordinate's sign changes, the point (x, y) becomes (-x, y). This is reflection across y-axis.
And, if y co-ordinate increases by k units, then (x, y) becomes (x, y+k). That is, the point (x, y) is translated k units upwards.
Thus, the required transformations are
The point was reflected over the y-axis and translated up.
Option (C) is CORRECT.
Currently the Lowest tax bracket in the United States is ?
A.0%
B.1%
C.10%
D.15%
Answer: 10% -APEX
2 year late answer lol.
mr. Dell taught the six members of the chess club to play chess. each member taught three classmates. each classmate taught two more friends. how many people were taught to play chess?
Mr. Dell taught six members of the chess club who then taught 18 classmates, and those classmates taught 36 friends, resulting in 60 people being taught how to play chess in total.
To find the total number of people taught, we compute as follows:
First level (by Mr. Dell): 6 members
Second level (6 members x 3 classmates each): 18 classmates
Third level (18 classmates x 2 friends each): 36 friend
To determine the total number of people taught to play chess, we sum the three levels: 6 members + 18 classmates + 36 friends = 60 people. Therefore, a total of 60 people were taught to play chess
Carter is playing a video game he needs to score more than a hundred points to move on to the next level write an inequality to show how many points Carter needs to earn
Brian is playing a video game. He earns the same number of points for each star he picks up. He earned 2,400 points for 6 stars, 4,000 points for 10 stars, and 5,200 points for 13 stars. Which is the independent variable in the situation?
The solution is, the independent variable is number of stars, in the situation.
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
from the given information, we get,
Points are a function of stars, so stars is the independent variable.
The variable that depends on that, the dependent variable, is points.
now, we have,
2400/6= 400
4000/10= 400
5200/13= 400
we get,
y=400x
Every star is 400 points and the independent variable is number of stars Brian picks up because the amount of points he gets is dependent on the number of stars he has.
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John bought 12 books 2/3 of the books are science fiction how many of the books are science fiction
Where a linear equation crosses the y-axis, that point is called the A) x-intercept. B) y-intercept. C) point of termination. D) point of translation.
Answer:
B) Y- Intercept
Step-by-step explanation:
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The lengths of the sides of a triangle are 10, 13, and 19. Classify the triangle as acute, right or obtuse.
According to an almanac, 80 % of adult smokers started smoking before turning 18 years old. (a) if 400 adult smokers are randomly selected, how many would we expect to have started smoking before turning 18 years old? (b) would it be unusual to observe 360 smokers who started smoking before turning 18 years old in a random sample of 400 adult smokers? why?
Based on the 80% figure, we'd expect 320 out of 400 adult smokers to have started before they turned 18. Observing 360 in this situation could be unusual but would require a statistical test to confirm.
Explanation:This question pertains to concepts of probability and statistics. If 80% of adult smokers began smoking before they turned 18, then in a group of 400 randomly selected adult smokers, we would expect 80% (or 0.8) of that 400 to have started smoking before the age of 18. This means 320 out of the 400 individuals started smoking before turning 18.
As for the second part of the question, if we observed 360 smokers out of 400 who started smoking before turning 18, this number is higher than our expectation of 320. This could be seen as unusual, but it also might occur by chance. To determine how unusual it is, we would typically conduct a statistical test, which would require additional information not provided in the question.
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Find n for a series for which a649-14-01-00-00_files/i0160000.jpg = 30, d = -4, and Sn = -210.
Answer:
b.
21
Step-by-step explanation:
Look at the figure. Which step should be taken next to construct a line parallel to <-AB->?
A. Without changing the compass setting from the previous step, place the compass on point P. Draw an arc similar to the one already drawn.
B. Place the compass on point C. Open the compass to point D. Draw a small arc through point D.
C. Place the compass on point A. Open the compass to point P. Move the compass to point P and draw an arc intersecting <-AP->.
D. Without changing the compass setting from the previous step, place the compass on point B. Draw an arc similar to the one already drawn.
hat is the solution to the compound inequality 5x + 7 > −8 and 3x + 7 ≤ 19?