Answer:
Step-by-step explanation:
The gold vein is at (-3,9) and the farthest gold dust strike is at (33,9). The distance between the two points is 36 miles.
23- Find unit vectors that satisfy the stated conditions (a) Oppositely directed to v = (3,-4 ) and half the length of v.
The unit vector that is oppositely directed to v = (3, -4) and half its length is approximately u = (-0.5547, 0.8321).
How to find a unit vector that satisfies the given conditions?To find a unit vector that is oppositely directed to v = (3, -4) and half its length, we can follow these steps:
Find the length of vector v:
|v| = sqrt(3^2 + (-4)^2) = 5
Divide vector v by 2 to get a vector with half its length:
v/2 = (3/2, -2)
To get a vector that is oppositely directed to v, we can reverse the direction of v/2:
-(3/2, -2) = (-3/2, 2)
Finally, we can find the unit vector in the direction of (-3/2, 2) by dividing it by its length:
|(-3/2, 2)| = sqrt((-3/2)^2 + 2^2) = sqrt(13/4)
u = (-3/2, 2) / sqrt(13/4) = (-3/2) * (2/sqrt(13))/2 + (2/sqrt(13)) * (1/2)
Therefore, the unit vector that is oppositely directed to v = (3, -4) and half its length is approximately u = (-0.5547, 0.8321).
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Use The Fundamental Theorem of Calculus, Part 2 to evaluate / - (13 – 12) dt.
The value of the integral [tex]\int -1^1 (13 - 12) dt[/tex] is 26.
How to evaluate the integral?To evaluate the integral [tex]\int-1^1 (13 - 12) dt[/tex] , we need to find an antiderivative of the integrand, which is simply:
∫ (13 - 12) dt = 13t - 12
Using this antiderivative, we can evaluate the definite integral by applying the theorem:
[tex]\int-1^1 (13 - 12) dt = [13t - 12]_{(-1)^1[/tex]
Evaluating this expression at the limits of integration (-1 and 1), we get:
[13(1) - 12] - [13(-1) - 12]
Simplifying, we get:
= 13 - 12 + 13 + 12
= 26
Therefore, the value of the integral [tex]\int-1^1 (13 - 12) dt[/tex] is 26.
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Find dy/dx. x =^9root (t) y = 9 - t dy/dx = _____
To find dy/dx, we need to take the derivative of y with respect to x. On evaluating the value of dy/dx is [tex]-9t^{8/9}[/tex]
However, we are given x in terms of t. So first, we need to use the chain rule to find dx/dt:
x = [tex]t^{1/9}[/tex]
dx/dt = (1/9) * [tex]t^{-8/9}[/tex]
Now, we can use the chain rule again to find dy/dt:
y = 9 - t
dy/dt = -1
Finally, we can use the formula for the chain rule to find dy/dx:
dy/dx = (dy/dt) / (dx/dt)
dy/dx = (-1) / ((1/9) * [tex]t^{-8/9}[/tex]
dy/dx = [tex]-9t^{8/9}[/tex]
So, the final answer is dy/dx = [tex]-9t^{8/9}[/tex]
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Jorge bought a pedometer to measure how many miles he walks each day. he walks 1.4 miles on monday. this was 1/6 of his totalfor the week. what is his total distance ?
The total distance of Jorge for the week is 8.4 miles.
Let's assume that Jorge walks x miles in a week. According to the problem, he walks 1.4 miles on Monday, which is 1/6 of his total for the week. We can use this information to set up the following equation:
1/6 x = 1.4
To solve for x, we can multiply both sides by 6:
x = 1.4 x 6
x = 8.4
Therefore, Jorge walks a total distance of 8.4 miles in a week.
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The height in meters of a projectile can be modeled by h = -4. 9t^2 + vt + s where t is the time (in seconds) the
object has been in the air, v is the initial velocity
(in meters per seconds) and s is the initial height (in meters). A
soccer ball is kicked upward from the ground and flies through the air with an initial vertical velocity of 4. 9
meters per second. Approximately, after how many seconds does it land?
The soccer ball will land approximately 1 seconds after it was kicked upward. This is found by setting the height equation to 0 and solving for t using the quadratic formula.
To solve for the time the soccer ball lands, we need to find the time when h = 0. We can use the given equation
h = -4.9t² + vt + s
where v = 4.9 m/s (since it's kicked upward) and s = 0 (since it starts at ground level).
Substituting those values, we get
0 = -4.9t² + 4.9t
Factoring out 4.9t, we get
0 = 4.9t(-t + 1)
So, either t = 0 or -t + 1 = 0
Since time cannot be negative, we discard the second solution and solve for t
-t + 1 = 0
t = 1
Therefore, the soccer ball lands after approximately 1 second.
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In the given diagram, L is the midpoint of KM
I need to find x, LM, and KM
Answer:
KM = 34
Step-by-step explanation:
Since L is the midpoint of KM that makes KL and LM equal. If LM and KL are congruent that means that the measure of KL is also 17. Therefore KM is just double 17 therefore being 34.
If f(x) is an exponential function where f(4. 5) = 22 and f(14) = 40,
then find the value of f(26. 5), to the nearest hundredth.
So, to the nearest hundredth, the value of f(26.5) is approximately 59.81.
To find the value of f(26.5) for the given exponential function f(x), we will first determine the base and initial value of the function using the given points f(4.5) = 22 and f(14) = 40.
An exponential function has the form f(x) = ab^x, where a is the initial value and b is the base.
1. Write the two equations using the given points:
22 = ab^(4.5)
40 = ab^(14)
2. Divide the second equation by the first to eliminate the initial value, a:
(40/22) = (ab^(14))/(ab^(4.5))
3. Simplify and solve for the base, b:
1.81818 = b^(9.5)
b ≈ 1.05459
4. Now, plug b back into one of the original equations to solve for the initial value, a:
22 = a(1.05459)^4.5
a ≈ 16.08364
5. With a and b found, we can now find the value of f(26.5):
f(26.5) = 16.08364 * (1.05459)^26.5
f(26.5) ≈ 59.81
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The value of exponential function f(26. 5), to the nearest hundredth is 144.42.
To find the value of f(26.5) for the exponential function, we can use the given data points and apply the exponential function formula.
Let's assume the exponential function is of the form: f(x) = a * b^x, where a and b are constants.
Using the given data points:
f(4.5) = 22
f(14) = 40
Substituting these values into the exponential function equation:
22 = a * b^4.5 ---(1)
40 = a * b^14 ---(2)
Dividing equation (2) by equation (1), we can eliminate the constant 'a':
40/22 = (a * b^14) / (a * b^4.5)
1.8182 = b^(14 - 4.5)
1.8182 = b^9.5
To find the value of b, we take the 9.5th root of 1.8182:
b ≈ 1.109
Now we can substitute the value of b into equation (1) to solve for 'a':
22 = a * (1.109)^4.5
a ≈ 4.95
Therefore, the exponential function can be approximated as: f(x) ≈ 4.95 * (1.109)^x
Now we can find the value of f(26.5):
f(26.5) ≈ 4.95 * (1.109)^26.5 ≈ 144.42
Hence, the value of f(26.5), to the nearest hundredth, is approximately 144.42.
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The average weight of Carl, Carla, Carmen, Clark, and Cathy is 107.6 lb. Cathy weighs 115 lb. What is the average weight of the other four? Show your work.
Answer:
Step-by-step explanation:
Let's start by finding the total weight of all five people:
Total weight = Average weight x Number of people
Total weight = 107.6 x 5
Total weight = 538
We know that Cathy weighs 115 lb, so we can subtract her weight from the total weight to find the total weight of the other four people:
Total weight of other four = Total weight - Cathy's weight
Total weight of other four = 538 - 115
Total weight of other four = 423
To find the average weight of the other four, we can divide the total weight of the other four by the number of people:
Average weight of other four = Total weight of other four / Number of people
Average weight of other four = 423 / 4
Average weight of other four = 105.75 lb
Therefore, the average weight of the other four is 105.75 lb.
If the solutions to 4x² + 1 = 81 are tg√/5, what is the value of g?
9 =
PLEASE HELP
Answer: 2√5, -2√5
Step-by-step explanation:
Work out the size of angle t.
t
40°
Rate of US adults who use the internet can be modeled by dI dt -0.5t+16.9, 5
The rate of change after 5 years is 14.4%, indicating that the percentage of US adults using the internet is increasing at a rate of 14.4% per year.
Based on the provided information, the rate of US adults who use the internet can be modeled by the equation dI/dt = -0.5t + 16.9, where t represents the time in years and I represents the percentage of adults using the internet.
To determine the rate of change at a specific time, we need to substitute the value of t into the equation.
For example, to find the rate of change after 5 years, we would substitute t = 5:
dI/dt = -0.5(5) + 16.9
dI/dt = -2.5 + 16.9
dI/dt = 14.4
Therefore, the rate of change after 5 years is 14.4%, indicating that the percentage of US adults using the internet is increasing at a rate of 14.4% per year.
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What is the value of 45 nickels as a decimal number ?
Answer:
2.25
Step-by-step explanation:
45 nickels
45*5=225
225 cents
2.25
The value of 45 nickels in decimal number can be 2.25.
In the decimal system, each digit's value depends on its position or place value within the number.
A nickel is worth 0.05 dollars.
To find the value of 45 nickels, multiply the number of nickels by the value of each nickel:
So, Value = Number of nickels × Value of each nickel
= 45 × 0.05
= 2.25
Therefore, the value of 45 nickels is $2.25 as a decimal number.
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For this problem, a table has been started for you based on the information given in the problem. use inductive reasoning to complete the table.
an electronics store finds that over a period of three months, sales of stereos decreased. in march, the store sold 325 stereos. in april, the store sold 280 stereos, and in may, the store sold 235 stereos.
month
stereos sold
march
325
april
280
may
235
june
july
august
incorrect feedback has been removed from the screen.
type your answers and then click or tap done.
make a conjecture about the number of stereos sold in june. fill in the blank text field 1
190
make a conjecture about the number of stereos sold in july.
make a conjecture about the number of stereos sold in august.
Using inductive reasoning, we can observe a pattern in the given data: the number of stereos sold decreases by 45 each month.
We can apply this pattern to make conjectures about the number of stereos sold in June, July, and August.
June: 235 (May's sales) - 45 = 190 stereos
July: 190 (June's sales) - 45 = 145 stereos
August: 145 (July's sales) - 45 = 100 stereos
So, the conjectures for the number of stereos sold are:
June: 190
July: 145
August: 100
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A. johnny translated abcd 3 units to the right and 4 units up to a new position, efgh. draw and label efgh.
b. tom rotated abcd to a new position, ijkl, 90º clockwise about the origin, o. draw and label ijkl.
c. tony placed a smaller car, represented as mnop, on the coordinate plane. mnop is a dilation of abcd with its center at the origin and a scale factor of -0.5. draw and label mnop.
A. To obtain the position of EFGH, Johnny translated ABCD by 3 units to the right and 4 units up. To draw and label EFGH, simply shift each vertex of ABCD by this translation vector (3, 4).
B. Tom rotated ABCD by 90º clockwise about the origin, O, to get the position of IJKL. To draw and label IJKL, rotate each vertex of ABCD 90º clockwise around the origin. This can be achieved by switching the x and y coordinates of each vertex and negating the new x value.
C. Tony placed a smaller car, MNOP, on the coordinate plane. MNOP is a dilation of ABCD with its center at the origin and a scale factor of -0.5. To draw and label MNOP, multiply the coordinates of each vertex of ABCD by the scale factor -0.5, keeping the origin as the center.
what is the number of cans that can be packed in a certain carton? (1) the interior volume of this carton is 2,304 cubic inches. (2) the exterior of each can is 6 inches high and has a diameter of 4 inches.
The number of cans that can be packed in a certain carton has correct statement as, Statements (1) and (2) together are not sufficient, option E.
Data sufficiency refers to evaluating and analysing a collection of data to see if it is sufficient to respond to a certain query. They are intended to assess the candidate's capacity to connect the dots between each question and arrive at a conclusion.
The size of each can is not revealed in statement 1 at all.
The size of the container is not disclosed in statement 2 at all.
We obtain two situations when we take into account both assertions. Case A: If the box is 1 x 1 x 2304 (inches) in size, then there are no cans that will fit within the carton.
Case B: If the box is 10 x 10 x 23.04 (inches) in size, then the carton can hold more than 0 cans.
The combined statements are insufficient because we lack clarity in our ability to respond to the target inquiry.
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Complete question:
What is the number of cans that can be packed in a certain carton?
(1) The interior volume of this carton is 2, 304 cubic inches.
(2) The exterior of each can is 6 inches high and has a diameter of 4 inches.
A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
C. Both statements together are sufficient, but neither statement alone is sufficient.
D. Each statement alone is sufficient.
E. Statements (1) and (2) together are not sufficient.
The dean of students at a large college is interested in learning about their opinions regarding the percentage of
first-year students who should be given parking privileges in the main lot. he sends out an email survey to all
students about this issue. a large number of first-year students reply but very few sophomores, juniors, and seniors
reply. based on the responses he receives, he constructs a 90% confidence interval for the true proportion of
students who believe first-year students should be given parking privileges in the main lot to be (0.71, 0.79). which
of the following may have an impact on the confidence interval, but is not accounted for by the margin of error?
o response bias
o nonresponse bias
o sampling variation
o undercoverage bias
mark this and retum
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The potential factor that may have an impact on the confidence interval, but is not accounted for by the margin of error, is nonresponse bias.
The dean of students received a large number of responses from first-year students but very few from sophomores, juniors, and seniors. Nonresponse bias occurs when some individuals chosen for a sample do not respond to a survey or study. In this case, the dean of students may not have received a representative sample of the opinions of all students, which could lead to an overestimation or underestimation of the true proportion of students who believe first-year students should be given parking privileges in the main lot.
The margin of error is the amount of random sampling error in a survey's results. It reflects the level of precision in the survey's results and decreases as the sample size increases. However, nonresponse bias is a systematic error that is not accounted for by the margin of error, as it may lead to a biased sample and inaccurate results. To minimize nonresponse bias, the dean of students could have used techniques such as follow-up emails or incentives to encourage a higher response rate from all student groups.
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A cone has a radius of 3 inches and a slant height of 12 inches.
What is the exact surface area of a similar cone whose radius is 9 inches?
The surface area of the similar cone is 415.8 in²
What is surface area of a cone?A cone is a shape formed by using a set of line segments or the lines which connects a common point, called the apex or vertex.
The surface area of a cone is expressed as;
SA = πr( r+l) where r is the radius and l is the slant height.
The slant height of the original cone =
l= √h²+r²
l = √12²+3²
l = √144+9
l = √153
l = 12.4 in
SA= 3π( 3+12.4)
SA = 3 × 15.4
SA = 46.2 in²
The surface area of similar cone with radius 9 inches is calculated by;
(3/9)² = 46.2/x
= 9/81 = 46.2/x
x = 46.2 × 81/9
x = 415.8in²
Therefore the surface area of the similar cone is 415.8 in³
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1. A company is testing a new energy drink. Volunteers are asked to rate their energy one hour
after consuming a beverage. Unknown to them, some volunteers are given the real energy
drink and some are given a placebo-a drink that looks and tastes the same, but does not have
the energy-producing ingredients. Show your work using the following list of random digits to
assign each participant listed either the real drink or the placebo.
We can assign each participant the real drink or placebo by assigning a drink based on the next random digit.
How to assign to the real and placebo ?One method for assigning participants their drink is to utilize a basic rule predicated on the oddness or evenness of specific digits. In this scenario, you may reserve “odd” numbers strictly for real drinks and “even” numbers exclusively for placebos.
To execute this procedure, we will begin at the left-hand side of our precomputed list of randomized digits and work to identify the subsequent digit in order to assign each participant with their corresponding drink:
Abby - Real (6)Barry - Placebo (9)Callie - Real (4)Dion - Placebo (2)Ernie - Real (9)Falco - Placebo (8)Garrett - Real (6)Hallie - Placebo (1)Indigo - Real (1)Jaylene - Real (6)How to assign numbers to each division ?Assign numbers to each of the houses in every subdivision, ranging from 1 through to 100. Utilize an online random number generator or a table containing random numbers within the range of 1 and 100 to construct a list of such randomly generated figures.
Choose the initial 20 unique figures from said list for both subdivisions selectively. Proceed with visiting those particular homes denoted by these chosen numbers, then examine and test their water sources accordingly.
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The base of a solid is the region in the first quadrant between the graph of y=2x
and the x-axis for 0≤x≤1. For the solid, each cross section perpendicular to the x-axis is a quarter circle with the corresponding circle’s center on the x-axis and one radius in the xy-plane. What is the volume of the solid?
The volume of the solid is A. [tex]\pi/3[/tex]
What is the volume of a solid?The volume of a solid in geometry signifies the space it occupies inside a three-dimensional area. It denotes how much content can fill up its inner region, and as usual, measured in units like cubic feet, meters, or centimeters.
Finding the measurement formula varies from shape to shape but commonly involves multiplying width, height, and length. Given that many sectors rely on this term, such as engineering, architecture, and physics, understanding the concept of the volume of a solid weighs significantly.
If we take a cross-section of (x,y)perpendicular to the x-axis, with width dx, now the cross-section is a quarter circle with radius y.
Thus, the volume of the cross-section, since y = 2x becomes: [tex]\pi x^2 dx[/tex]
Now, the volume of the solid when integrated becomes: [tex]\frac{\pi }{3}[/tex]
Option A is correct.
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Two containers are mathematically similar.
Their volumes are 54cm3
and 128 cm3
.
The height of the smaller container is 4.5cm.
Calculate the height of the larger container
Answer: 6cm
Step-by-step explanation: VF=(SF)^3
let x be the height of the larger container
VF1/VF2=(SF1/SF2)^3
54/128=(4.5/X)^3
rearrange to find x
x=cube root of (4.5^3*128)/54
x=6cm
What is the value of 6x-5y?
The value of 6x-5y = -31
The given equations are 2x-y=-7 -eq (1)
& 4x=-3y+16 -eq (2)
Multiplying eq (1) with 2 and rearranging to get equation as follows
(2x-y=-7)*2
4x-2y=-14 -eq (3)
Now, subtracting eq (3) from eq (2) to get y.
(4x+3y=16) - (4x-2y=-14)
5y=30
y=5
Substituting y=5 in eq (1) to get x.
2x-5=-7
x=-1
Now to determine 6x-5y substitute obtained values of x & y.
6*(-1)-5(5)=-31
Hence the value of 6x-5y=-31.
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An egg is dropped from the roof of a building. The distance it falls varies directly with the square of the time it falls. It takes 1/2 second for the egg to fall eight feet, how long will it take the egg to fall 200 feet?
What does K equal? And how many seconds?
Answer:
16 seconds
Step-by-step explanation:
A restaurant in Richmond, BC, lists the prices on its menus in fractions of a dollar. Three friends have lunch at the restaurant. Each of 3 friends orders a veggie mushroom cheddar burger for 11 % ( , with a glass of water to drink.
What was the total bill be fore taxes, in fractions of a dollar?
If each of the 3 friends orders a veggie mushroom cheddar burger for 11%, the cost of each burger would be:
11% of $1.00 = $0.11
Since the prices are listed in fractions of a dollar, we can express the cost of each burger as 11/100 of a dollar.
So, the total cost of 3 veggie mushroom cheddar burgers would be:
3 x 11/100 = 33/100 = $0.33
Assuming that the glass of water is free, the total bill before taxes would be $0.33 for the 3 burgers. However, it's important to note that this calculation is based on the assumption that the prices are listed in fractions of a dollar, which may not be the case. If the prices are listed in a different unit, the calculation would need to be adjusted accordingly.
The coach recorded the time it took 14 students to run a mile. The times are as follows: 9:23, 8:15, 9:23, 9:01, 6:55, 7:20, 9:14, 6:21, 7:12, 7:34, 6:10, 9:15, 9:18. Use the data set to complete the frequency table. Then use the table to make a histogram
The histogram for the frequency table is illustrated below.
To create the frequency table, we need to count how many times each time appears in the data set. The time 9:23 appears twice, so we would put a frequency of 2 in the row corresponding to 9:23. We do this for each time in the data set.
Here is the completed frequency table:
Time Frequency
6:10 1
6:21 1
6:55 1
7:12 1
7:20 1
7:34 1
8:15 1
9:01 1
9:14 1
9:15 1
9:18 1
9:23 2
As you can see, each time appears only once or twice in the data set. This tells us that there is no dominant time that most students ran the mile in.
To create the histogram, we'll draw a bar above each time on the x-axis with a height equal to the frequency of that time. For example, there are two times of 9:23, so we'll draw a bar above 9:23 with a height of 2.
As you can see, the histogram shows a relatively even distribution of times. The most common times are around 9 minutes, but there are also several times below 8 minutes and one time below 7 minutes.
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1. bona drives tor 3 hours at 44mph. clare drives 144 mies in 4 hours. how
for would bena travel if she drove for 3 hours at the same speed os
claire
2. janet and andrew leave their home at the same time. janet has 60
milles to travel and drives at 40 mph. andrew have 80 miles to travel
and also drives at 40 mph
a) how long does janets journey take?
(b) how much longer does andrew spend driving than janeta
1) Bona can drive 108 miles if she drove for 3 hour at the same speed as Claire.
2) Janet would take 1.5 hour to complete the journey and Andrew spend half hour more driving than Janet.
1) Bona speed is 44mph
Time taken by Bona is 3 hour
distance travelled by Claire is 144 miles
Time taken by Claire is 4 hour
Claire's speed = distance / time
Claire's speed = 144/4
Claire's speed = 36 mph
Distance travelled by Bona = speed × time
Distance travelled by Bona = 36 × 3
Distance travelled by Bona = 108 miles
2) Janet distance = 60 miles
Janet speed = 40 mph
Time taken by Janet = distance / speed
Time taken by Janet = 60/40
Time taken by Janet = 1.5 hour
Janet would take 1.5 hour to complete the journey
Andrew distance = 80 miles
Andrew speed = 40 mph
Time taken by Andrew = distance / speed
Time taken by Andrew = 80/40
Time taken by Andrew= 2 hour
Andrew spend half hour more driving than Janet.
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which rule explains why these triangles are congruent
Answer:
It's ASA, AAS,
Step-by-step explanation:
AAS- If two angles and a non-included side in one triangle are congruent to two angles and the corresponding non-included side in another triangle, then the triangles are congruent.
ASA-The ASA criterion for triangle congruence states that if two triangles have two pairs of congruent angles and the common side of the angles in one triangle is congruent to the corresponding side in the other triangle, then the triangles are congruent.
I need help Plssplss
Answer: 9.33
Step-by-step explanation: if you add them up, it's 9.33
Qn in attachment
.
..
Answer: d
Step-by-step explanation:
Answer:
pls mrk me brainliest
Step-by-step explanation:
(￣(ｴ)￣)ﾉ
If Kawan paints the visible outside
surfaces of his shed, what is the
total surface area that he paints?
3 ft
5
8 ft
8ft
8ft
A. 256 ft²
B. 286 ft²
C. 360 ft²
D. 444 ft²
If kawan paints the visible outside faces of her shed, she paints two rectangle faces and two triangle faces then the total surface area that she paints is 88ft².
The area of a triangle of altitude h and base b is given by;
A = 0.5bh
Therefore the area of one triangle face ;
At = 0.5 × 8 × 5
At = 20ft²
Area of a rectangle of length l and breadth b is;
A = lb
Therefore the area of a rectangle face;
Ar = 8 × 3
Ar = 24ft²
We have 2 triangle faces and 2 rectangle face, therefore total surface area as;
A = 2At + 2Ar
A = 2×20 + 2×24
A = 40 + 48
A = 88ft²
Therefore the answer is; 88ft².
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Answer the following questions regarding convergence of series. It is possible that the correct answer would be "cannot be determined". (a) Suppse that sum Ak is a convergent series with known sum L Bk a convergent series with known
k=1
sum M. If L < M, does this guarantee that ax < bx for all k > 1? If not, provide a counter example.
L < M, as 1 < 1.25.
a_2 = 1/4 > 1/8 = b_2, which shows that a_k < b_k is not guaranteed for all k > 1.
(a) Given two convergent series Σa_k (with sum L) and Σb_k (with sum M) where k=1 to ∞, and L < M, we are asked if a_k < b_k for all k > 1. The answer is no, this is not guaranteed.
Counter example:
Consider the following two convergent series:
Series A: Σa_k, where a_1 = 1/2, a_2 = 1/4, a_3 = 1/8, ... (a geometric series with a common ratio of 1/2)
Series B: Σb_k, where b_1 = 1, b_2 = 1/8, b_3 = 1/16, ... (a geometric series with a common ratio of 1/2 starting from the second term)
Sum L for Series A:
L = a_1 / (1 - (1/2)) = 1
Sum M for Series B:
M = b_1 + (b_2 / (1 - (1/2))) = 1 + 1/4 = 1.25
In this case, L < M, as 1 < 1.25. However, a_2 = 1/4 > 1/8 = b_2, which shows that a_k < b_k is not guaranteed for all k > 1.
Learn more about common ratio.
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