a sphere with radius r and a cylinder with radius r and a height of r are shown below. how do the surface areas of these solid figures compare?
which statements are correct? check all that apply
A: the surface area of the sphere in terms of r is 4(pi)r^2 square units
B: the surface area of the cylinder in terms of r is 4(pi)r^2 square units
C: the surface area of the cylinder in terms of r is 6(pi)d^2 square units
D: the surface area of the cylinder and sphere are the same
E: the surface area of the cylinder and sphere are NOT the same
Answers
The correct statements are A and B, while C, D, and E are incorrect.
The correct statements are:
A: The surface area of the sphere in terms of r is 4(pi)r^2 square units. This is true. The formula for the surface area of a sphere is given by A = 4(pi)r^2, where r is the radius.
B: The surface area of the cylinder in terms of r is 4(pi)r^2 square units. This is true. The formula for the lateral surface area of a cylinder is given by A = 2(pi)rh, where r is the radius and h is the height. Since the height of the cylinder is also r, the formula simplifies to A = 2(pi)rh = 2(pi)r(r) = 2(pi)r^2. Additionally, the two circular bases of the cylinder also contribute to the surface area, each with an area of (pi)r^2. Therefore, the total surface area of the cylinder is A = 2(pi)r^2 + 2(pi)r^2 = 4(pi)r^2.
C: The surface area of the cylinder in terms of r is 6(pi)d^2 square units. This statement is incorrect. The formula provided is incorrect. The correct formula for the surface area of a cylinder is A = 2(pi)rh, not 6(pi)d^2.
D: The surface area of the cylinder and sphere are the same. This statement is incorrect. The surface areas of a cylinder and a sphere are different. The surface area of a sphere is given by A = 4(pi)r^2, while the surface area of a cylinder is given by A = 2(pi)r^2 + 2(pi)rh. The presence of the curved surface in the cylinder makes its surface area different from that of a sphere.
E: The surface area of the cylinder and sphere are NOT the same. This statement is correct. As mentioned above, the surface areas of a cylinder and a sphere are different, so they are not the same.
In summary, the correct statements are A and B, while C, D, and E are incorrect.
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Related Questions
there are 50 people in a coffee shop fourteen are tourist.what percent of people in the shop are tourist and non tourist
Answers
Answer:
tourist: 28%
non-tourist: 72%
Step-by-step explanation:
total: 50
tourists: 14
non-tourists:50 - 14 = 36
tourist percentage: 14/50 × 100% = 28%
non-tourist percentage: 36/50 × 100 = 72%
Determine the period.
NAV
8 10 12 14
3
2
1
-1
-2
-3
2
Answers
Answer:
7
Step-by-step explanation:
V looking shape has ends at 1 & 8
8 - 1 = 7
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A marble is rolling up an inclined plane. The distance (in cm) the marble has rolled after t seconds is given by s(t)=100t/t+1
a. What is the initial velocity of the marble?
b. How fast is the marble rolling at time 4 seconds?
c. At what time is the velocity 50 cm/s?
d. How fast is the marble rolling when it is 90 cm from its starting point?
e. Find and interpret lim s(t) t-> infinity and lim v(t) lim t-> infinity. Do you think this model is valid for large values of t?
Explain.
Answers
a. The initial velocity of the marble is 0 cm/s.
b. The marble is rolling at a speed of 80 cm/s at 4 seconds.
c. The velocity is 50 cm/s at approximately t = 2√2 - 1 seconds.
d. The marble is rolling at a speed of 90 cm/s when it is 90 cm from its starting point at t = 9 seconds.
e. lim s(t) as t approaches infinity is 100 cm and lim v(t) as t approaches infinity is 0 cm/s; the model may not be valid for large values of t as it assumes the marble is rolling up an inclined plane without considering other factors such as friction.
a. To find the initial velocity of the marble, we need to calculate the limit of the function s(t) as t approaches 0:
lim (t->0) s(t) = lim (t->0) (100t / (t + 1))
By substituting 0 into the expression, we get:
lim (t->0) (0 / (0 + 1)) = 0 / 1 = 0.
Therefore, the initial velocity of the marble is 0 cm/s.
b. To find the speed of the marble at time 4 seconds, we substitute t = 4 into the expression for s(t):
s(4) = 100(4) / (4 + 1) = 400 / 5 = 80 cm/s
The marble is rolling at a speed of 80 cm/s at 4 seconds.
c. To find the time at which the velocity is 50 cm/s, we set s'(t) (the derivative of s(t)) equal to 50 and solve for t:
s'(t) = 50
[tex](100 / (t + 1))^2 = 50[/tex]
100 / (t + 1) = ±√50
100 = ±√50(t + 1)
±√50(t + 1) = 100
t + 1 = 100 / ±√50
t + 1 = ±2√2
Since time cannot be negative, we take t + 1 = 2√2:
t = 2√2 - 1
The velocity is 50 cm/s at approximately t = 2√2 - 1 seconds.
d. To find the speed of the marble when it is 90 cm from its starting point, we need to solve the equation s(t) = 90 for t:
100t / (t + 1) = 90
100t = 90(t + 1)
100t = 90t + 90
10t = 90
t = 9
The marble is rolling at a speed of 90 cm/s when it is 90 cm from its starting point, which occurs at t = 9 seconds.
e. The limit of s(t) as t approaches infinity (lim s(t) as t->∞) is calculated by considering the dominant term in the numerator and denominator:
lim (t->∞) (100t / (t + 1))
≈ lim (t->∞) (100t / t)
= lim (t->∞) 100
= 100
Therefore, lim s(t) as t approaches infinity is 100 cm.
Similarly, the limit of v(t) (velocity) as t approaches infinity (lim v(t) as t->∞) can be found by taking the derivative of s(t) and evaluating the limit:
[tex]v(t) = s'(t) = 100 / (t + 1)^2[/tex]
lim (t->∞) v(t) = lim (t->∞) (100 / [tex](t + 1)^2)[/tex]
≈ lim (t->∞)[tex](100 / t^2)[/tex]
= lim (t->∞) [tex](100 / t^2)[/tex]
= 0.
The limit of v(t) as t approaches infinity is 0 cm/s.
As for the validity of the model for large values of t, it is important to note that the given model assumes that the marble is rolling up an inclined plane.
However, without further information about the nature of the inclined plane (e.g., its slope, frictional forces), it is difficult to determine the accuracy.
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Drag each shape and value to the correct location on the image. Not all labels will be used.
The tower has a base that is 24 meters wide. The height is shown for the separate sections of the tower.
What is an appropriate shape to model each section of the tower? What is an approximate surface area if each of those shapes?
Answers
The appropriate shape to model each section of the tower are the cone and the cylinder.
The approximate surface area of each shape would be =
For cone = 1,041.27m²
For cylinder = 3,543.72m².
How to calculate the surface area of each shape given above?The first shape is a cone and the formula for the surface area = A = πr(r+√h²+r²)
where;
Radius = 24/2 = 12
height = 10m
Area = 1,041.27m²
For cylinder:
A = 2πrh+2πr²
where:
r = 12m
h = 35m
A = 3,543.72m²
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Which of the following gives the correct range for the piecewise graph?
A coordinate plane with a segment going from the point negative 3 comma 2 to 0 comma 1 and another segment going from the point 0 comma 1 to 5 comma negative 4.
Answers
The correct range for the piecewise graph is [-4, 2].
To solve this problemWe need to find the minimum and maximum values of the y-coordinates.
The first segment goes from (-3, 2) to (0, 1), so the range for this segment is from 1 to 2.
The second segment goes from (0, 1) to (5, -4), so the range for this segment is from -4 to 1.
We must take into account the minimum and maximum values from each segments in order to determine the overall range. The minimum and highest values are -4 and 2, respectively.
Therefore, the correct range for the piecewise graph is [-4, 2].
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the base of a square pyramid is 229 meters long, each slant height is 186 meters. what is the surface area
Answers
Answer:
The total surface area is given by: base area + 4 * triangular face area
Substituting the values we calculated: 52441 + 4 * 10424.4 ≈ 91588.4 square meters.
Therefore, the surface area of the square pyramid is approximately 91588.4 square meters.
4 * triangular face area
Substituting the values we calculated: 52441 +
4 * 10424.4 ~ 91588.4 square meters.
Therefore, the surface area of the square pyramid is approximately 91588.4 square meters.
The value v of a tractor purchased for $13,000 and depreciated linearly at the rate of $1,300 per year is given by v= -1,300t+13,000, where t represents the number of years since the
purchase. Find the value of the tractor after (a) two years and (b) six years. When will the tractor have no value?
Answers
a) the value of the tractor after two years is $10,400.
b) the value of the tractor after six years is $5,200.
To find the value of the tractor after a certain number of years, we can substitute the value of t into the equation v = -1,300t + 13,000.
a) After two years:
Substituting t = 2 into the equation, we get:
v = -1,300(2) + 13,000
v = -2,600 + 13,000
v = 10,400
Therefore, the value of the tractor after two years is $10,400.
b) After six years:
Substituting t = 6 into the equation, we get:
v = -1,300(6) + 13,000
v = -7,800 + 13,000
v = 5,200
Therefore, the value of the tractor after six years is $5,200.
To find when the tractor will have no value, we need to find the value of t when v = 0. We can set the equation v = -1,300t + 13,000 equal to 0 and solve for t:
-1,300t + 13,000 = 0
-1,300t = -13,000
t = -13,000 / -1,300
t = 10
Therefore, the tractor will have no value after 10 years.
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find the value of x and the measure of angle axc
Answers
Answer:
x = 4
m<AXC = 150
Step-by-step explanation:
m<1 + m<2 = m<AXC
102 + 10x + 8 = 6(6x + 1)
10x + 110 = 36x + 6
26x = 104
x = 4
m<AXC = 6(6x + 1)
m<AXC = 6(24 + 1)
m<AXC = 150
Rewrite 9 2/7 as an improper fraction. 25/2 65/7 25/7 23/7 Rewrite 2 4/5 as an improper fraction. 10/4 13/5 14/5 22/5 Find the product of 9 2/7 and 2 4/5. Express your answer in simplest form. 26 130/5 910/35 15
Answers
Answer:
1. 9 2/7 = (63+2)/7 = 65/7
2. 2 4/5 = (10+4)/5 = 14/5
3. 65/7 * 14/5 = 910/35 = 26
What is the measure of angle jnk?
Answers
The hourly wage, the number of hours and the number of days Jaxon works indicates that the amount Jaxon gets paid is $192
What is the formula for calculating hourly wage?The formula for hourly wage can be presented as follows;
Hourly wage = Total earnings/Total hours worked
The question in the link is presented as follows;
Jaxon gets paid $6 an hour. He works for 8 hours each day for four days. How much will Jaxon get paid
The amount Jaxon gets paid per hour (his hourly wage) = $6
The number of hours he works each day = 8 hours
The number of days Jaxon works = Four days
The amount Jaxin gets paid = Hourly wage × Hours per day × Number of days
Therefore we get;
Amount he gets paid = $6 per hour × 8 hours/day × 4 days = $192
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Is the expression quadratic 3x+5y-2
Answers
No, the expression 3x + 5y - 2200 is not a quadratic expression.
A quadratic expression is an expression of the form ax² + bx + c, where a, b, and c are constants and x is a variable raised to the power of 2.
It is a second-degree polynomial, meaning that the highest power of the variable is 2.Quadratic expressions often have a graph that is a parabola.
"3x + 5y - 2" is a linear expression, not a quadratic expression.
In a quadratic expression, the highest power of the variable(s) is 2, whereas in this expression, the highest power is 1.
The expression 3x + 5y - 2200 is a linear expression since it does not contain a term with a variable raised to the power of 2.
It is a first-degree polynomial, meaning that the highest power of the variable is 1.
Linear expressions often have a graph that is a straight line.
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No. The expression, 3x + 5y - 2, is not quadratic.
What are quadratic expressions?The expression "3x+5y-2" is a linear expression, not quadratic.
Quadratic expressions contain a squared term, like "[tex]ax^2 + bx + c[/tex]." In the given expression, there are no squared terms, only linear terms with variables "x" and "y" raised to the power of 1.
The coefficients for "x" and "y" are 3 and 5, respectively, and there is a constant term of -2. Therefore, it represents a linear relationship between "x" and "y" rather than a quadratic one.
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If f(x)=/x-7 and g(x) - 4x - 8
which statement is true
1 is in the domain
1 isnt in the domain of f(0) g
ANSWERED: 1 is NOT in the domain.
Answers
The statement "1 is NOT in the domain" is true because for the function f(x), the expression x - 7 results in division by zero when x equals 1, which makes 1 not a valid input for the function.
To determine if a value is in the domain of a function, we need to consider any restrictions or limitations on the input values.
For the function f(x) = √(x - 7), the square root function is defined only for non-negative values.
Therefore, the expression (x - 7) inside the square root must be greater than or equal to zero. In other words, x - 7 ≥ 0.
Solving this inequality, we find x ≥ 7.
This means that any value of x that is greater than or equal to 7 is in the domain of f(x).
However, the statement is asking specifically about the value 1.
Since 1 is less than 7, it does not satisfy the inequality x ≥ 7 and is therefore not in the domain of f(x).
Similarly, for the function g(x) = 4x - 8, there are no restrictions on the domain.
Any real number can be substituted into the function, including the value 1.
Therefore, the statement "1 isn't in the domain of f(0) g" is not accurate.
It is true that 1 is not in the domain of f(x), but it is in the domain of g(x).
In summary, the correct statement is that "1 is not in the domain."
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A race car driver won a 200 mile race with a speed of 159.5 miles per hour. Find the driver's time.
Answers
Answer:
1.255 seconds
Step-by-step explanation:
We can use the formula:
time = distance ÷ speed
to find the driver's time. Here, the distance is 200 miles and the speed is 159.5 miles per hour. Substituting these values into the formula, we get:
time = 200 miles ÷ 159.5 miles per hour
time = 1.255 seconds
Simplify the expression by combining
like terms:
2y + 2 + 3y + 5
Enter the number that belongs in the green box.
[?]y + [ ]
Answers
2+5=7
Add them ,5y+7
1. A target is divided into 100 squares colored in dark blue, white, and light blue. Amber throws a beanbag that lands on the target.
co
9 25
dark blue
What is the probability that it will land on a dark blue square?
26
white
light blue
Answers
The probability of landing on the dark blue target is 2/5.
Finding probabilityProbability is the ratio of required to the total possible outcomes of an event.
The required outcome = dark blue= 25Total possible outcomes= entire sample Space = 100P(dark blue ) = 40/100
divide through by 20
P(dark blue ) = 2/5
Therefore, the probability of landing on target is 2/5
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Can someone help me with this question?
Answers
Answer: - 27
Step-by-step explanation:
Plug in for x = 3 and y = -6
I'll start with x to make it easier.
Plugging in x =3
[tex]\sqrt{x^4}[/tex]
Means that first we find x^4, and take the square root of that result.
1. Find x^4
x = 3
3^4 = 3 * 3 * 3 *3 = 81
2. Take the square root of x^4
Square root of 81 = 9
So [tex]\sqrt{x^4}[/tex] = 9
Plugging in y = -6
Let's move onto plugging in y, which appears in the expression as y²
y = -6
so y² = -6 * -6 = 36
Putting this together into the expression
[tex]\sqrt{x^4}[/tex] - y²
9 - 36 = -27
Is there a difference between shapes when plotting Uniform acceleration towards (+)directtion,Uniform acceleration towards (-)direction, Uniform deceleration towards (+) direction and Uniform deceleration towards (-) direction in displacement time graph
Answers
Yes, there is a difference in the shapes of the displacement-time graphs for uniform acceleration towards the positive direction, uniform acceleration towards the negative direction, uniform deceleration towards the positive direction, and uniform deceleration towards the negative direction.
Uniform acceleration towards the positive direction:
In this case, the object's velocity increases in the positive direction over time. The displacement-time graph will have a concave-upward shape, forming a curve that starts with a small slope and gradually becomes steeper as time progresses.
Uniform acceleration towards the negative direction:
Here, the object's velocity increases in the negative direction, meaning it accelerates in the opposite direction to its positive direction.
The displacement-time graph will have a concave-downward shape, forming a curve that starts with a steep slope and gradually becomes less steep as time progresses.
Uniform deceleration towards the positive direction:
In this scenario, the object's velocity decreases in the positive direction, but it still moves towards the positive direction.
The displacement-time graph will show a curve with a decreasing slope, forming a concave-downward shape, indicating that the object is slowing down.
Uniform deceleration towards the negative direction:
Here, the object's velocity decreases in the negative direction, opposing its initial direction.
The displacement-time graph will have a curve with a decreasing slope, forming a concave-upward shape, indicating that the object is slowing down but still moving in the negative direction.
In summary, the shapes of the displacement-time graphs differ based on the direction and type of acceleration (positive or negative) and whether the object is undergoing uniform acceleration or uniform deceleration. These differences can be observed through the concavity and slope of the graphs.
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6 minutes 20 seconds into seconds.
Answers
Answer:
380 seconds
Step-by-step explanation:
Convert 6 minutes to seconds by multiplying 6 times 60, because there are 60 seconds per minute.
6 x 60 = 360
Now add the 20 seconds.
360 + 20 = 380
6 minutes and 20 seconds are equal to 380 seconds.
A rocket is launched from 168 feet above the ground at the time t=0. The function that model thsi situation is given by h =-16t^2+96t+168 where t is the time in seconds and h is the height of the position of the rocket above the ground level in feet. what is the reasonable domain restriction for t in this context?
Answers
The domain for the time in this context is (0, 7.4)
What is an equation?An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.
Let h represent the height of the ball after spending t seconds. A ball is thrown straight up from the top of a building that is 168 ft high with an initial velocity of 96 ft/s.
Given the equation:
h(t) = -16t² + 96t + 168
The reasonable domain restriction for t, is when the height of the rocket is above the ground. Hence the domain for the time in this context is (0, 7.4)
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4) AD is a common internal tangent to circles B and C. Find the length of the radius
of circle B. Round to the nearest hundredth. (Hint: Prove that the two triangles
are similar and use proportions to find missing lengths.) (10 points)
I
B
E
6
D
Answers
Both triangles in the image are similar based on the AAA similarity theorem. The radius of the circle B is therefore calculated as: AB = 12.
What are similar triangles?Similar triangles are geometric figures that have the same shape but may differ in size. They have corresponding angles that are equal and corresponding sides that are in proportion to each other.
Since AD serves as a common tangent, angle BAE is equal to 90 degrees, which is also equal to angle CDE due to being opposite angles.
By the Angle-Angle-Angle (AAA) similarity criterion, triangles ABE and DCE are similar.
Therefore:
AB/EA = DC/ED
Substitute:
AB/18 = 4/6
Cross multiply:
AB = 18 * 4/6
AB = 12
Therefore, the radius of the circle B is: 12.
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What is the mixed number or the fraction?? Please help
Answers
explanation: since there are two whole rectangles, (12/12 for one rectangle) it would be 24/24. then, there are 9 mini squares on the third rectangle, so 9/12 would be the fraction for the third rectangle. but thats not all. we can simplify 24/24 to 2, then 9/12 to 3/4. add the two and 3/4 and you should get answer choice b.
Find the area of the parallelogram
Answers
The area of the parallelogram is 189 square units
How to determine the areaFirst, we have the determine the length of the base and height.
The distance between the lines x = 9 and f(x) = 9 + 2x is the height
We have that the line parallel to f(x) passes through (4, 11)
The equation in point-slope form is;
y - 11 = 2(x - 4
y = 2x + 3
Substitute x = 9 in the equation, y = 2x + 3.
y = 2(9) + 3 = 21
The points are then (9, 21) and (9, 0).
The distance between the y-axis and the line x = 9 is the base.
Base = 9 units.
The formula for calculating area of a parallelogram is given by ;
= base × height
= 9 × 21
= 189 square units.
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Part of the graph of the function f(x) = (x – 1)(x + 7) is shown below.
Which statements about the function are true? Select three options.
The vertex of the function is at (–4,–15).
The vertex of the function is at (–3,–16).
The graph is increasing on the interval x > –3.
The graph is positive only on the intervals where x < –7 and where
x > 1.
The graph is negative on the interval x < –4.
Answers
Answer:
The vertex of the function is at (–3,–16)
The graph is increasing on the interval x > –3
The graph is positive only on the intervals where x < –7 and where
x > 1.
Step-by-step explanation:
The graph of [tex]f(x)=(x-1)(x+7)[/tex] has clear zeroes at [tex]x=1[/tex] and [tex]x=-7[/tex], showing that [tex]f(x) > 0[/tex] when [tex]x < -7[/tex] and [tex]x > 1[/tex]. To determine where the vertex is, we can complete the square:
[tex]f(x)=(x-1)(x+7)\\y=x^2+6x-7\\y+16=x^2+6x-7+16\\y+16=x^2+6x+9\\y+16=(x+3)^2\\y=(x+3)^2-16[/tex]
So, we can see the vertex is (-3,-16), meaning that where [tex]x > -3[/tex], the function will be increasing on that interval
The average lifetime of a certain new cell phone is 6 years. The manufacturer will replace any cell phone failing within 2 years of the date of
purchase. The lifetime of these cell phones is known to follow an exponential distribution.
What is the probability that a phone will fail within 2 years of the date of purchase? (Round your answer to four decimal places.)
Answers
The probability that a cell phone will fail within 2 years is 0.4866.
To solve this problemThe average lifetime of the cell phone is 6 years, so the decay rate is 1 / 6 = 0.1667.
The probability that a phone will fail within 2 years is given by:
[tex]P(x < 2) = 1 - e^{-0.1667 * 2} = 1 - 0.5134 = 0.4866[/tex]
Rounded to four decimal places, the probability is 0.4866.
Therefore, the probability that a cell phone will fail within 2 years is 0.4866.
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2) Looking at your average from question 1, with an expected weight of 4 ounces, what is the % error in actual weights? (Assume you think the answer is 10%. Find 10% of 4 ounces to check to see if that answer is reasonable!) Do not round!
A) 17.5%
B) .128%
C) 10%
D) 0.175%
Answers
The calculated percentage error with the assumed answer of 10%
To find the percentage error in actual weights, we can use the formula:
Percentage Error = [(|Measured Value - Expected Value|) / Expected Value] * 100%
In this case, the expected weight is 4 ounces. Let's assume the measured value is 10% off from the expected value. So the measured value would be:
Measured Value = Expected Value + (10% of Expected Value)
= 4 ounces + (10/100) * 4 ounces
= 4 ounces + 0.4 ounces
= 4.4 ounces
Now we can calculate the percentage error:
Percentage Error = [(|4.4 ounces - 4 ounces|) / 4 ounces] * 100%
= [(0.4 ounces) / 4 ounces] * 100%
= (0.4/4) * 100%
= 0.1 * 100%
= 10%
Comparing the calculated percentage error with the assumed answer of 10%, we can see that they are the same.
The percentage error represents the deviation from the expected value as a percentage of the expected value itself. In this case, it indicates that the actual weights deviate by 10% from the expected weight of 4 ounces. The calculated percentage error with the assumed answer of 10%
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(12²-15+17)+16= what is the answer
Answers
162
Step-by-step explanation:
(12 square - 15 + 17) + 16
=(144 - 15 + 17) + 16
=146 + 16
=162
Jade decided to rent movies for a movie marathon over the weekend. The function g(x) represents the amount of money spent in dollars, where x is the number of movies. Does a possible solution of (6.5, $17.50) make sense for this function? Explain your answer.
Yes. The input and output are both feasible.
No. The input is not feasible.
No. The output is not feasible.
No. Neither the input nor output is feasible.
Answers
The output value is feasible. The input value is not feasible, the possible solution of (6.5, $17.50) does not make sense for this function. The correct answer is No. The input is not feasible.
Jade decided to rent movies for a movie marathon over the weekend.
The function g(x) represents the amount of money spent in dollars, where x is the number of movies.
The given function is g(x) which represents the amount of money spent in dollars, where x is the number of movies.
The solution given is (6.5, $17.50).
We need to find whether the solution makes sense for the given function or not.
The input is given as 6.5 and the output is given as $17.50.
This means that Jade rented 6.5 movies and spent $17.50 on renting those movies.
To check whether the solution makes sense or not, we need to see if the input and output values are feasible or not.
The input value 6.5 is not a feasible value because it is not possible to rent half a movie.
Jade can rent 6 movies or 7 movies but not 6.5 movies.
Therefore, the input value is not feasible.
On the other hand, the output value $17.50 is a feasible value because it is possible for Jade to spend $17.50 on renting 6 movies.
The output value is feasible.
Since the input value is not feasible, the possible solution of (6.5, $17.50) does not make sense for this function. The correct answer is No. The input is not feasible.
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What does 13 round to the nearest thousandth
Answers
What percent of 50 is 20?
Answers
Answer:
40% of 50 is 20
Step-by-step explanation:
[tex]50x=20\\x=\frac{20}{50}=0.4=40\%[/tex]
Answer: 20 is 40% of 50.
Step-by-step explanation:
We can simply divide 20/50
20/50 = 0.4
Now multiply it by 100 to get the percent: 0.4×100 = 40%
Hope this helps!
Find the third, fourth, and fifth terms of the sequence defined by
a1 = 1, a2 = 3,
and
an = (−1)nan − 1 + an − 2
for
n ≥ 3.
Answers
The third term (a3) of the sequence is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183. These values are obtained by applying the given formula recursively and substituting the previous terms accordingly. The calculations follow a specific pattern and are derived using the provided formula.
The sequence is defined by the following formula:
a1 = 1, a2 = 3,
and
an = (-1)nan - 1 + an - 2 for n ≥ 3.
To find the third term (a3), we substitute n = 3 into the formula:
a3 = (-1)(3)(a3 - 1) + a3 - 2.
Next, we simplify the equation:
a3 = -3(a2) + a1.
Since we know a1 = 1 and a2 = 3, we substitute these values into the equation:
a3 = -3(3) + 1.
Simplifying further:
a3 = -9 + 1.
Therefore, the third term (a3) is equal to -8.
To find the fourth term (a4), we substitute n = 4 into the formula:
a4 = (-1)(4)(a4 - 1) + a4 - 2.
Simplifying the equation:
a4 = -4(a3) + a2.
Since we know a2 = 3 and a3 = -8, we substitute these values into the equation:
a4 = -4(-8) + 3.
Simplifying further:
a4 = 32 + 3.
Therefore, the fourth term (a4) is equal to 35.
To find the fifth term (a5), we substitute n = 5 into the formula:
a5 = (-1)(5)(a5 - 1) + a5 - 2.
Simplifying the equation:
a5 = -5(a4) + a3.
Since we know a4 = 35 and a3 = -8, we substitute these values into the equation:
a5 = -5(35) + (-8).
Simplifying further:
a5 = -175 - 8.
Therefore, the fifth term (a5) is equal to -183.
In summary, the third term (a3) is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183.
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