Thus, the coordinates of Y and Z after the translation is obtained as :
Y'(-2,4) and Z'(-4, 3).
Define about the translation:A figure is translated when it is moved from one point to another without changing in size, form, or rotation.
A figure can be translated to move it up, down, left, or right while maintaining the same size. This is carried out using a coordinate system in order to be done properly and accurately.The pre-image is the original object that needs to be translated, and the image is the translated object.Given translation:
Point X(1,4) ---> point X'(0,6)
There is 1 unit shift to left as 1 is subtracted to x coordinate to get 0.
There is 2 unit shift to upward as 2 is added to y coordinate to get 6..
Translation:
(x,y) --->(x - 1, y + 2)
Applying same on points Y and Z,
Y(-1,2) --> Y'(-2,4)
Z(-3,1) --> Z'(-4, 3)
Thus, the coordinates of Y and Z after the translation is obtained as :
Y'(-2,4) and Z'(-4, 3).
Know more about the translation
https://brainly.com/question/1574635
#SPJ1
High school competency test a mandatory competency test for high school sophomores has a normal distribution with a mean of 400 and a standard deviation of 100. the top 3% of students receive $500. what is the minimum score you would need to receive this award? the bottom 1.5% of students must go to summer school. what is the minimum score you would need to stay out of this group?
A score of at least 183 is required to stay out of the bottom 1.5%. To find the minimum score required to receive the award, we need to determine the z-score corresponding to the top 3% of students.
Since the distribution is normal, we can use the standard normal distribution table to find the z-score. From the table, we find that the z-score corresponding to the top 3% is approximately 1.88.
Therefore, we can use the formula z = (x - μ) / σ, where μ = 400 and σ = 100, to find the minimum score required: 1.88 = (x - 400) / 100
Solving for x, we get: x = 1.88(100) + 400 = 488. Therefore, a score of at least 488 is required to receive the award.
To find the minimum score required to stay out of the bottom 1.5%, we need to determine the z-score corresponding to the bottom 1.5%.
From the standard normal distribution table, we find that the z-score corresponding to the bottom 1.5% is approximately -2.17. Therefore, we can use the same formula as before to find the minimum score required: -2.17 = (x - 400) / 100.
Solving for x, we get: x = -2.17(100) + 400 = 183. Therefore, a score of at least 183 is required to stay out of the bottom 1.5%.
To know more about standard normal distribution, refer here:
https://brainly.com/question/29509087#
#SPJ11
The height of Mount Rushmore is 5900 feet. What is the height of Mount Rushmore in
centimeters? (1 in = 2. 54 cm)
Answer:
the answer is 14,986 centimetres
X-1 if x < 2 Let f(x)=1 if 2sxs6 X+4 if x > 6 a. Find lim f(x). X-+2 b. Find lim f(x). X-6 Select the correct choice and, if necessary, fill in the answer box to complete your choice. O A. lim = X-2 O B. The limit is not - oo or co and does not exist. Select the correct choice and, if necessary, fill in the answer box to complete your choice. O A. lim = X-6 OB. The limit is not - oor oo and does not exist.
a. The limit does not exist.
b. The limit is equal to 4.
a. To find the limit as x approaches 2, we need to evaluate the left-hand and right-hand limits separately and check if they are equal.
Left-hand limit: lim f(x) as x approaches 2 from the left
We have f(x) = x - 1 for x < 2. So, as x approaches 2 from the left, f(x) approaches 1.
Right-hand limit: lim f(x) as x approaches 2 from the right
We have f(x) = 1 for 2 ≤ x ≤ 6 and f(x) = x + 4 for x > 6. So, as x approaches 2 from the right, f(x) approaches 6.
Since the left-hand and right-hand limits are not equal, the limit as x approaches 2 does not exist.
b. To find the limit as x approaches 6, we need to evaluate the left-hand and right-hand limits separately and check if they are equal.
Left-hand limit: lim f(x) as x approaches 6 from the left
We have f(x) = 1 for 2 ≤ x ≤ 6 and f(x) = x + 4 for x > 6. So, as x approaches 6 from the left, f(x) approaches 1.
Right-hand limit: lim f(x) as x approaches 6 from the right
We have f(x) = x + 4 for x > 6. So, as x approaches 6 from the right, f(x) approaches 10.
Since the left-hand and right-hand limits are not equal, the limit as x approaches 6 does not exist.
Therefore, the correct choices are:
a. The limit is not -oo or co and does not exist.
b. lim = 4.
Learn more about limit Visit: brainly.com/question/282767
#SPJ11
Find the average x-coordinate of the points in the prism D={(x,y,z):0 ≤ x ≤ 6,0 ≤ y ≤ 18-3x, 0 ≤ z ≤ 4}. The average x-coordinate of the points in the prism is (Simplify your answer.)
The average x-coordinate of the points in the prism is 3.
What is a prism?A prism is a polyhedron that has two parallel and congruent polygonal bases that are linked by parallelogram faces that are lateral. The height of the prism is the perpendicular distance between the bases.
The formula for calculating the average x-coordinate of the points in the prism D = {(x,y,z):0 ≤ x ≤ 6,0 ≤ y ≤ 18-3x, 0 ≤ z ≤ 4} is$$\frac{\text{sum of all x-coordinates}}{\text{number of vertices}}$$
The vertices of a prism are the points where two adjacent edges meet. There are eight vertices in a rectangular prism, and the x-coordinate of each vertex is either 0 or 6. The x-coordinates of the vertices are $$0,0,0,0,6,6,6,6.
$$The sum of all the x-coordinates is 24. Thus, the average x-coordinate of the points in the prism is$$\frac{24}{8}=\boxed{3}.
$$Hence, the average x-coordinate of the points in the prism is 3.
To know more about x-coordinate, visit:
https://brainly.com/question/16634867#
#SPJ11
Consider a metal plate on [0,1] ×[0,1] with density rho(x,y) = αx
+ βy g/cm2, where α and β are positive constants. Show that the
center of mass must lie on the line x + y = 7/6 .
The center of mass of the metal plate with density rho(x,y) = αx+ βy g/cm2 must lie on the line x + y = 7/6.
To find the center of mass of the metal plate, we need to calculate the coordinates of its centroid (X, Y). The coordinates of the centroid are given by:
X = (1/M) ∬(R) x ρ(x,y) dA, Y = (1/M) ∬(R) y ρ(x,y) dA
where M is the total mass of the plate, R is the region of integration (0 ≤ x ≤ 1, 0 ≤ y ≤ 1), and dA is the differential area element.
We can calculate the total mass M of the plate as follows:
M = ∬(R) ρ(x,y) dA = α/2 + β/2 = (α + β)/2
Using the given density function, we can calculate the integrals for X and Y:
X = (1/M) ∬(R) x ρ(x,y) dA = (2/αβ) ∬(R) x(αx+βy) dA = (2/3)(α+β)
Y = (1/M) ∬(R) y ρ(x,y) dA = (2/αβ) ∬(R) y(αx+βy) dA = (2/3)(α+β)
Thus, the coordinates of the centroid are (X, Y) = ((2/3)(α+β), (2/3)(α+β)).
Now, if we substitute X + Y = (4/3)(α+β) into the equation x + y = 7/6, we get:
x + y = 7/6
2x + 2y = 7/3
2(x+y) = 4/3(α+β)
x+y = (2/3)(α+β)
which shows that the centroid lies on the line x + y = 7/6. Therefore, the center of mass must also lie on this line.
For more questions like Integral click the link below:
https://brainly.com/question/22008756
#SPJ11
Color the stars, so it is unlikely impossible to choose a red one.
Part C
What does the absolute value of the correlation coefficient say about the predictions in part B? How do you know? Write
an explanation of about one to two sentences.
BI U x
х
Font Sizes
A-A-DEE 3
✓
Characters used: 0 / 15000
Submit
o
The shows that Luther can expect the speed to be 51 miles/hour when he throws 80 pitches and 64 miles/hour when he throws 54 pitches.
How to calculate the speed?The average speed of Luther's pitches when he throws 80 pitches will be:
y = -0.511x + 91.636
= -0.511(80) + 91.636
= 50.756
= 51
Also, the number of pitches that Luther can throw when the speed is 64 miles per hour will be:
y = -0.511x + 91.638
64 = -0.511x + 91.638
0.511x = 91.638 - 64
0.511x = 27.636
x = 54
Therefore, the number of pitches will be 54.
Learn more about line of best fit on:
brainly.com/question/21241382
#SPJ4
Answer:
Because the absolute value of the correlation coefficient, 0.9672, is very close to 1, Luther can be very confident in the predictions.
Step-by-step explanation: Edmentum Answer
15 POINTS IM GOING TO BE BROKE AFTER THESE QUESTIONS
Two cars leave from the same location with one car traveling north and the other traveling west. When the northbound car has traveled 18 miles, the straight-line distance between the two cars is 30 miles. How far has the westbound car traveled?
We know that the westbound car has traveled 24 miles.
When the northbound car has traveled 18 miles and the straight-line distance between the two cars is 30 miles, you can use the Pythagorean theorem to determine the distance the westbound car has traveled. The theorem states that a² + b² = c², where a and b are the legs of a right triangle and c is the hypotenuse.
In this case, the northbound car's distance (18 miles) represents one leg (a) and the westbound car's distance represents the other leg (b). The straight-line distance between the cars (30 miles) represents the hypotenuse (c). The equation can be set up as follows:
18² + b² = 30²
Solving for b:
324 + b² = 900
b² = 900 - 324
b² = 576
b = √576
b = 24
So, the westbound car has traveled 24 miles.
To know more about miles refer here
https://brainly.com/question/23245414#
#SPJ11
MARKING BRAINLEIST IF CORRECT PLS ANSWER ASAP
Answer:
7.6 cm
Step-by-step explanation:
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
[tex]a^{2}[/tex] + [tex]6.5^{2}[/tex] = [tex]10^{2}[/tex]
[tex]a^{2}[/tex] + 42.25 = 100 Subtract 42.25 from both sides
[tex]a^{2}[/tex] = 57.57
[tex]\sqrt{\a^{a} }[/tex] = [tex]\sqrt{57.57}[/tex]
a ≈ 7.6
Helping in the name of Jesus.
Answer:
7.6 cm
Step-by-step explanation:
a^2+ b^2=c^2
a^2+6.5^2=10^2
a^2+42.25=100 subtract 42.25 from both sides
a^2=57.57
a=√57.57
a=7.6 cm
Give the Laplace transform of f(x)= (-2x-3)/4
The Laplace transform of f(x)= (-2x-3)/4 is (-2L{x}-3L{1})/4, where L{x} is the Laplace transform of x and L{1} is the Laplace transform of 1.
Hi! The Laplace transform of a given function f(t) is denoted by L{f(t)} and is defined as the integral of f(t) multiplied by e^(-st), where s is a complex variable. For the function f(x) = (-2x - 3)/4, the Laplace transform can be calculated as follows:
L{f(t)} = L{(-2t - 3)/4}
To find the Laplace transform, we will treat the function as two separate parts:
L{(-2t - 3)/4} = (-2/4) * L{t} + (-3/4) * L{1}
The Laplace transforms of t and 1 are well-known:
L{t} = 1/s^2
L{1} = 1/s
Now, substitute these transforms back into our expression:
L{f(t)} = (-1/2) * (1/s^2) + (-3/4) * (1/s)
L{f(t)} = -1/(2s^2) - 3/(4s)
And that's the Laplace transform of f(x) = (-2x - 3)/4.
To learn more about Laplace transform visit;
brainly.com/question/31041670
#SPJ11
In a class of students, the following data table summarizes how many students passed a test and complete the homework due the day of the test. What is the probability that a student chosen randomly from the class passed the test and completed the homework? Passed the test Failed the test Completed the homework 11 3 Did not complete the homework 2 5
The probability that a student chosen randomly from the class passed the test or completed the homework is 20/27.
What is the probability?The probability that a student chosen randomly from the class passed the test or completed the homework is calculated as follows:
Let the probability that a student completed the homework be P(B).
Also, let the probability that a student passed the test be P(A)
P(A or B) = P(A) + P(B) - P(A * B)
From the data table:
The number of students who passed the test = 18
The number of students who completed the homework = 17
The number of students who both passed the test and completed the homework = 15.
Total number of students = 27
P(A) = 18/27
P(B) = 17/27
P(A*B) = 15/27
Therefore,
P(A or B) = 18/27 + 17/27 - 15/27
P(A or B) = 20/27
Learn more about probability at: https://brainly.com/question/24756209
#SPJ1
Let
Ф(u, v) = (3u + 9v, 9u + 9v). Use the Jacobian to determine the area of
Ф(R) for: (a)R = [0,91 × [0, 6]
(b)R = [2,20] × [1, 17]
(a)Area (Ф(R)) =
(b) Area (Ф(R)) =
a) Area (Ф(R)) = 5184 (b) Area (Ф(R)) = 25920
Let J be the Jacobian of Ф. We have J = det(DФ) = det([3 9; 9 9]) = -72.
(a) For R = [0,9] × [0,6], we have
Ф(R) = {(3u+9v,9u+9v) | 0 ≤ u ≤ 9, 0 ≤ v ≤ 6}.
The area of Ф(R) is given by the double integral over R of the Jacobian:
Area (Ф(R)) = ∬R |J| dudv
= ∫0^9 ∫0^6 72 dudv
= 5184.
Therefore, the area of Ф(R) is 5184.
(b) For R = [2,20] × [1,17], we have Ф(R) = {(3u+9v,9u+9v) | 2 ≤ u ≤ 20, 1 ≤ v ≤ 17}. The area of Ф(R) is given by the double integral over R of the Jacobian:
Area (Ф(R)) = ∬R |J| dudv = ∫2^20 ∫1^17 72 dudv = 25920.
Therefore, the area of Ф(R) is 25920.
To learn more about integral click here
brainly.com/question/18125359
#SPJ11
hello! are these correct?
if you can not see my answers :
1. right triangle
2. isosceles triangle
3. equilateral triangle
4. acute triangle
5. isosceles triangle
6. right triangle
( if im incorrect, please tell me the correct answer )
Answer: Yes those are correct good job
Step-by-step explanation:
A circle with center (7,3) and radius of 5 is graphed below with a square inscribed in
the circle.
Part A: Dillon and Chelsey are discussing how to write the equation of a tangent line
to circle A through point B. Both agree that they start the problem by drawing the
radius AB and find the slope of that segment. They also know that a tangent line is
perpendicular to the radius.
The area of the shaded region is (9/500)π.
To find the area shaded below in circle K, we first need to find the radius of the circle.
Let O be the center of the circle, and let N be the midpoint of segment LM. We can draw a radius ON to segment LM such that it is perpendicular to LM, and then draw another radius OL to point L. This forms a right triangle LON with the hypotenuse equal to the radius of circle K.
Since segment LM is given to have a length of 11/9π, we can find the length of LN by dividing it in half:
LN = (11/9π)/2 = 11/18π
We can then use trigonometry to find the length of OL:
sin(55°) = OL / LN
OL = LN sin(55°)
OL = (11/18π) sin(55°)
Next, we can use the Pythagorean theorem to find the length of ON:
ON² = OL² + LN²
ON² = [(11/18π) sin(55°)]² + [11/18π]²
ON ≈ 1.022
Therefore, the radius of circle K is approximately 1.022.
The area of the shaded region can now be found by subtracting the area of sector LOM from the area of triangle LON:
Area of sector LOM = (110/360)π(1.022)² ≈ 0.317π
Area of triangle LON = (1/2)(11/18π)(1.022) ≈ 0.326π
Area of shaded region = (0.326π) - (0.317π) = (9/500)π
So the area of the shaded region is (9/500)π.
To learn more about trigonometry here
https://brainly.com/question/31896723
#SPJ1
1. Sanchez deposited $3,000 with a bank in a 4-year certificate of deposit yielding 6% interest
compounded daily. Find the interest earned on the investment. (4pts)
The compound interest generated on the investment is roughly $813.67, which is the solution to the question based on compound interest.
What is Principal?The initial sum of money invested or borrowed, upon which interest is based, is referred to as the principle. The principal is then periodically increased by the interest, often monthly or annually, to create a new principal sum that will accrue interest in the ensuing period.
Using the compound interest calculation, we can determine the interest earned on Sanchez's investment:
[tex]A = P(1 + \frac{r}{n} )^{(n*t)}[/tex]
where A is the overall sum, P denotes the principal (the initial investment), r denotes the yearly interest rate in decimal form, n denotes the frequency of compounding interest annually, and t denotes the number of years.
In this case, P = $3,000, r = 0.06 (6%), n = 365 (compounded daily),
and t = 4.
Plugging in the values, we get:
[tex]A = 3000(1 + \frac{0.06}{365} )^{(365*4)}[/tex]
A= $3813.67
The difference between the final amount and the principal is the interest earned.
Interest = A - P
Interest = $3813.67 - $3000
Interest = $813.67
As a result, the investment's interest yield is roughly $813.67.
To know more about compound interest, visit:
brainly.com/question/20406888
#SPJ1
A right triangle has legs that are 17 centimeters and 28 centimeters long.
What is the length of the hypotenuse?
Enter your answer as a decimal, Round your answer to the nearest hundredth.
Answer: 4.5
Step-by-step explanation:
Megha bikes 20km north, 30km east, 20 km south and then 30 km west and then stopped. What is her displacement
Megha's total movement involves biking 20km north, 30km east, 20km south, and 30km west, resulting in a displacement of zero as she ends up back at her starting point.
Given that,
Megha bikes 20km north.
Megha then bikes 30km east.
After that, Megha bikes 20km south.
Lastly, Megha bikes 30km west.
Megha stops after completing the above movements.
Megha's displacement can be calculated by finding the straight-line distance between her starting point and ending point.
In this case,
She initially bikes 20km north, then 30km east, followed by 20km south, and finally 30km west.
Let's break it down:
The north and south distances cancel each other out, as she ends up back at her starting point vertically.
The east and west distances also cancel each other out, as she ends up back at her starting point horizontally.
Hence,
Megha's displacement is zero. She has returned to her original position.
To learn more about number straight lines visit:
https://brainly.com/question/32029748
#SPJ12
the sales tax rate in your city is 7.5%. What is the total amount you pay for a $6.84 item.
Answer:
$7.35
Step-by-step explanation:
Why do Markets behave in the same ways as Individual Consumers?
Answer:
Markets behave the same way as individual customers because markets are made up of individual consumers.
Step-by-step explanation:
"The times for the mile run of a large group of male college students are approximately Normal with mean 7. 06 minutes and standard deviation 0. 75 minutes. Use the 68-95-99. 7 rule to answer the following questions. (Start by making a sketch of the density curve you can use to mark areas on. ) (a) What range of times covers the middle 95% of this distribution
According to the 68-95-99.7 rule, approximately 68% of the distribution falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
In this case, the mean is 7.06 minutes and the standard deviation is 0.75 minutes. Therefore, the range of times that covers the middle 95% of the distribution would be from the mean minus two standard deviations (7.06 - 2 x 0.75 = 5.56 minutes) to the mean plus two standard deviations (7.06 + 2 x 0.75 = 8.56 minutes).
In other words, 95% of the male college students' mile run times are expected to fall between 5.56 and 8.56 minutes. This means that most of the students' mile run times will be within this range, and only a small percentage will be outside of it.
To know more about standard deviation click on below link:
https://brainly.com/question/23907081#
#SPJ11
.PLEASEEEEEEEEEEEEEE
Answer:
#1 (176 - x)°
#2 m∠3 = m∠4 = 90°
Step-by-step explanation:
If a pair of parallel lines are cut by a transversal, there are several angles that are either equal to each other or are supplementary(angles add up to 180°).
For the specific questions...
For #1.
Angles ∠1 and ∠2 are supplementary angles since they are adjacent to each other and lie on the same straight line
Therefore
m∠1 + m∠2= 180°
Given m∠1 = (x + 4)° this becomes
(x + 4)° + m∠2 = 180°
m∠2 = 180° - (x + 4)°
= 180° - x° - 4°
= (176 - x)°
For #2
∠3 and ∠4 are supplementary angles so m∠3 + m∠4 = 180°
If m∠3 = m∠4 each of these angles must be half of 180°
So
m∠3 = m∠4 = 180/2 = 90°
Pls Answer Soon!
A college professor asked every student in his statistics class to flip a coin 100 times and report how many times the coin landed on heads. The results followed a normal distribution, with a mean of 50 and a standard deviation of 5.
If there were 70 students in the class, how many of the students most likely got heads between 45 times and 60 times?
Round your answer to the nearest whole number of students
57 students most likely got heads between 45 and 60 times.
To determine the number of students who got heads between 45 and 60 times, we'll use the normal distribution properties. First, we need to calculate the z-scores for 45 and 60:
Z = (X - μ) / σ
For 45 heads:
Z1 = (45 - 50) / 5 = -1
For 60 heads:
Z2 = (60 - 50) / 5 = 2
Next, we need to find the probability that a student falls between these z-scores. We can do this by looking up the z-scores in a standard normal distribution table or using a calculator. The probabilities corresponding to these z-scores are:
P(Z1) = 0.1587
P(Z2) = 0.9772
Now, subtract P(Z1) from P(Z2) to get the probability of a student's result falling between 45 and 60 heads:
P(45 ≤ X ≤ 60) = P(Z2) - P(Z1) = 0.9772 - 0.1587 = 0.8185
Finally, multiply this probability by the total number of students (70) and round to the nearest whole number:
Number of students = 0.8185 * 70 ≈ 57
So, approximately 57 students most likely got heads between 45 and 60 times.
To learn more about probability, refer below:
https://brainly.com/question/30034780
#SPJ11
The ratio of runners to walkers at the 10k fund-raiser was 5 to 7. if there
were 350 runners, how many walkers were there?
There were 490 walkers at the 10k fund-raiser.
The ratio of runners to walkers is 5:7, that means that the every five runners, there are 7 walkers so therefore we will use ratio formula.
If there have been 350 runners, we can use this ratio to discover what number of walkers there were:
5/7 = 350/x
Where x is the number of walkers.
To solve for x, we will cross-multiply:
5x = 7 * 350
5x = 2450
x = 490
Consequently, there were 490 walkers at the 10k fund-raiser.
Learn more about ratio formula:-
https://brainly.com/question/2328454
#SPJ4
The table shown below gives the approximate distance from the sun for a few different planets how much further (in km) from the sun is Saturn than Venus
The distance that shows how much farther (in km) from the sun is Saturn than Venus is: [tex]1.2 * 10^9[/tex] km.
How to calculate the distanceAccording to the table, the distance of Saturn from the Sun is [tex]1.4 * 10^{9}[/tex] and the distance of Venus from the Sun is [tex]1.1 * 10^{8}[/tex] .
Now to determine how much further from the Sun is Saturn than Venus, we will subtract the distance of the planet with the higher distance span from the one with the lower distance.
So our calculation will go thus:
[tex]1.4 * 10^9 - 1.1 * 10^8 = \\140000000 - 11000000 = 1290000000\\= 1.29 * 10^9[/tex]
From the calculation above, we can see how much further from the sun, is Saturn than Venus.
Complete Question:
The table shown below gives the approximate distance from the sun for a few different planets. How much farther (in km) from the sun is Saturn than Venus? Express your answer in scientific notation.
_______km
Learn more about distance calculation here:
https://brainly.com/question/26046491
#SPJ1
a time capsule has been buried 98m away from the cave at a bearing of 312 degrees how far west of the cave is the time capsule buried? give your answer in 1 decimal places
If a time capsule has been buried 98m away from the cave at a bearing of 312. the time capsule is buried about 82.2 meters west of the cave.
What is the time capsule?To find how far west the time capsule is buried, we need to find the horizontal component of the displacement vector that points from the cave to the location of the time capsule. We can use trigonometry to do this:
cos(312°) = adjacent/hypotenuse
The hypotenuse is the distance between the cave and the time capsule, which is 98m. The adjacent side represents the horizontal distance between the two points, which is what we want to find. Rearranging the equation, we get:
adjacent = cos(312°) x hypotenuse
adjacent = cos(312°) x 98
adjacent ≈ 82.2
Therefore, the time capsule is buried about 82.2 meters west of the cave.
Learn more about time capsule here:https://brainly.com/question/27400520
SPJ1
Complete the proof that △QST≅△QRT.
The congruent triangles is solved and the triangles are congruent by AAS postulate
Given data ,
Let the two triangles be represented as ΔRQT and ΔTQS
And , the side TQ is the common side of both the triangles
Now , the measure of ∠TQR ≅ measure of ∠TQS ( given )
And , the measure of ∠TRQ ≅ measure of ∠TSQ ( given )
So , Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Hence , the triangles are congruent by ASA postulate
To learn more about congruent triangles click :
https://brainly.com/question/26131452
#SPJ1
Use any method to determine whether the series converges а. น k2 sk (5 pts) b 6. Ex 2+(-1){ 5k (5 pts)"
To determine whether the series น k2 sk converges, we can use the Integral Test. Let f(x) = x2, then f'(x) = 2x. Since 2x is continuous, positive, and decreasing on [1,∞), In summary, the series Σ (1/k^2) converges, while the series Σ (2 + (-1)^{5k}) does not converge.
∫1∞ f(x) dx = ∫1∞ x2 dx = lim (t → ∞) [1/3 x3]1t = ∞
Since the integral diverges, the series น k2 sk also diverges.
b. To determine whether the series 2+(-1){ 5k converges, we can use the Alternating Series Test. The series has alternating signs and the absolute value of each term decreases as k increases. Let ak = 2+(-1){ 5k, then:
|ak| = 2+1/32k ≤ 2
Also, lim (k → ∞) ak = 0. Therefore, by the Alternating Series Test, the series 2+(-1){ 5k converges.
a. For the series Σ (1/k^2) (denoted as น k2 sk), we can use the p-series test. A p-series is a series of the form Σ (1/k^p), where p is a constant. If p > 1, the series converges, and if p ≤ 1, the series diverges. In this case, p = 2, which is greater than 1. Therefore, the series Σ (1/k^2) converges.
b. For the series Σ (2 + (-1)^{5k}), we can use the alternating series test. An alternating series is a series that alternates between positive and negative terms. In this case, the series alternates because of the (-1)^{5k} term. However, the series does not converge to zero as k goes to infinity, since there is a constant term 2. Therefore, the series Σ (2 + (-1)^{5k}) does not converge.
In summary, the series Σ (1/k^2) converges, while the series Σ (2 + (-1)^{5k}) does not converge.
Visit here to learn more about integral test:
brainly.com/question/28157842
#SPJ11
The base radius and height of a right circular cone are measured as 10 cm and 25 cm, respectively, with a possible error in measurement of as much as 0.1 cm in each dimension. Use differentials to estimate the maximum error in the calculated volume of the cone. (Hint: V = 1/3 πr²h)
The estimated maximum error in the calculated volume of the cone is 20π cubic centimeters.
How to estimate the maximum error in the calculated volume of the cone?Let V = (1/3)πr²h be the volume of the cone, where r and h are the base radius and height of the cone, respectively.
Let dr and dh be the possible errors in the measurements of r and h, respectively.
Then, the actual dimensions of the cone are (r+dr) cm and (h+dh) cm, respectively.
The differential of V is given by:
dV = (∂V/∂r)dr + (∂V/∂h)dh
We have:
∂V/∂r = (2/3)πrh and ∂V/∂h = (1/3)πr²
Substituting the given values, we get:
∂V/∂r = (2/3)π(10 cm)(25 cm) = 500π/3
∂V/∂h = (1/3)π(10 cm)² = 100π/3
Substituting into the differential equation, we get:
dV = (500π/3)dr + (100π/3)dh
Using the given maximum error of 0.1 cm for both r and h, we have:
|dr| ≤ 0.1 cm and |dh| ≤ 0.1 cm
Therefore, the maximum possible error in V is given by:
|dV| = |(500π/3)(0.1 cm) + (100π/3)(0.1 cm)|
|dV| = 50π/3 + 10π/3
|dV| = 60π/3
|dV| = 20π cm³
Therefore, the estimated maximum error in the calculated volume of the cone is 20π cubic centimeters.
Learn more about maximum error
brainly.com/question/15082959
#SPJ11
HERE IS A HARD QUESTION , COULD U PLEASE ANSWER B PLEASE? I DID A ! 1ST ANSWER WOULD BE MARKED BRAINLIEST AND GET 5/5 WITH A THANKS! ILL ALSO COMMENT ON YOUR ANSWER ! BUT IF IT ISNT CORRECT , I WONT MARK BRAINLIEST! Thank you for your answers!!!!
Answer:
D(6,4).
Step-by-step explanation:
The shape ABCD is a square.
By definition, the diagonals are equal.
The diagonal from A to C is 6 units long. Therefore, you should get your point D by drawing across from B to the right by 6.
D(6,4).
A square pyramid is contained within a cone such that the vertices of the base of the pyramid are touching the edge of the cone. They both share a height of 20 cm. The square base of the pyramid has an edge of 10 cm. Using 3.14 as the decimal approximation for T, what is the volume of the cone? 1046.35 cubic centimeters 2093.33 cubic centimeters O 4185.40 cubic centimeters 06280.00 cubic centimeters
To find the volume of the cone, we first need to find its radius. Since the pyramid is contained within the cone such that the vertices of the base of the pyramid are touching the edge of the cone, the diagonal of the square base of the pyramid is equal to the diameter of the base of the cone. The diagonal of the square base of the pyramid is:
d = √(10^2 + 10^2) = √200 = 10√2 cm
Therefore, the diameter of the base of the cone is 10√2 cm, and the radius is 5√2 cm.
The volume of the cone can be calculated using the formula:
V = (1/3)πr^2h
where r is the radius of the base of the cone and h is the height of the cone.
Substituting the given values, we get:
V = (1/3)π(5√2)^2(20)
V = (1/3)π(50)(20)
V = (1/3)(1000π)
V = 1000/3 * π
Using 3.14 as the decimal approximation for π, we get:
V ≈ 1046.35 cubic centimeters
Therefore, the volume of the cone is approximately 1046.35 cubic centimeters. The answer is A.
