Answer:
huh okay well hi
Step-by-step explanation:
may the force be with u :)
100 points!!!
Determine the solution to the system of equations graphed below and explain your reasoning in complete sentences.
The solution to the system of equations graphed below is,
⇒ (0, 1)
Since, We have to given that;
Two system of equations are,
⇒ g (x) = 3x + 2
⇒ f (x) = |x - 1| + 1
Here, The graph of both system of equation are shown in graph.
We know that;
In a graph, the solution of system of equation are represented by a intersection point of both graph.
Here, In the graph of system of equation,
Intersection point is,
⇒ (0, 1)
Hence, The solution to the system of equations graphed below is,
⇒ (0, 1)
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which of the following is not a true dilation?
A. The image and preimage have congruent angles
B. The image and preimage have proportional sides
C. The image and preimage are congruent
D. The image and preimage are similar
Answer:
umm i think it is B.
Step-by-step explanation:
fill in the missing number: 0,1,1,2,3,5,8,13,-,34,55
The missing number of the series is 21.
The given sequence appears to follow the pattern of the Fibonacci sequence, where each number is the sum of the two preceding numbers. The Fibonacci sequence starts with 0 and 1, and each subsequent number is obtained by adding the two previous numbers.
Using this pattern, we can determine the missing number in the sequence.
0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55
Looking at the pattern, we can see that the missing number is obtained by adding 8 and 13, which gives us 21.
Therefore, the completed sequence is:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55.
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The missing number in the sequence 0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55 is 21.
To find the missing number in the sequence 0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55, we can observe that each number is the sum of the two preceding numbers. This pattern is known as the Fibonacci sequence.
The Fibonacci sequence starts with 0 and 1. To generate the next number, we add the two preceding numbers: 0 + 1 = 1. Continuing this pattern, we get:
011235813213455Therefore, the missing number in the sequence is 21.
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what is the answer
?
In 2 hours, the train will cover 120 miles, in 4 hours, the train will cover 240 miles. The train covered 120 more miles in 4 hours than it did in 2 hours.
A certain paint is sold and bought 1 gallon cans in 1 quart cans. The gallon can cost $12 and the carton cost $5. How much do you save per gallon buying the larger can?
If the paint gallon cost $12 and carton cost is $5 , then the amount saved per gallon buying the larger can is $8 .
We know that 1 gallon is = 4 quarts. So , a one-gallon can is equal to four one-quart cans.
To buy one gallon of paint, we need to buy 4 one-quart cans.
Each one-quart can costs $5, so 4 one-quart cans will cost:
⇒ 4 × $5 = $20 ,
Now, the cost of one gallon of paint if it is bought in one one-gallon can.
⇒ One one-gallon can costs $12.
So , if we buy the larger one-gallon can, we will save:
⇒ $20 - $12 = $8
Therefore, We will save $8 per gallon buying the larger can.
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Find a positive angle less than 360° that is coterminal with the given angle.
- 215°
A positive angle less than 360° that is coterminal with - 215° is
Answer:
The positive angle less than 360° that is coterminal with -215° has a measure of 145°.
Step-by-step explanation:
From Geometry, we know that angles form a family of coterminal angles as function of number of revolutions done on original angle. We can represent the set of all coterminal angles by means of the following expression:
\(\theta_{c} = \theta_{o} + 360\cdot i\), \(i \in \mathbb{Z}\) (1)
Where:
\(\theta_{o}\) - Original angle, in sexagesimal degrees.
\(\theta_{c}\) - Coterminal angle, in sexagesimal degrees.
\(i\) - Coterminal angle index, no unit.
If we know that \(\theta_{o} = -215^{\circ}\) and \(i = 1\), then the coterminal angle that is less than 360° is:
\(\theta_{c} = -215^{\circ} + 360\cdot (1)\)
\(\theta_{c} = 145^{\circ}\)
The positive angle less than 360° that is coterminal with -215° has a measure of 145°.
A recipe for lasagne to feed 7 people calls for 1,4 bs of ground beef. How much ground beef would you need to make a batch to serve 11 people Instead?
If a recipe for lasagne to feed 7 people calls for 1.4 lbs of ground beef, you would need approximately 2.2 lbs of ground beef to make a batch to serve 11 people. To calculate the answer, use the concept of proportions.
The given information is that a recipe for lasagne to feed 7 people calls for 1.4 lbs of ground beef.
To calculate the answer, use the concept of proportions.
The proportion can be set up like this: 7 : 1.4 = 11 : x
Solve for x.x = (11 × 1.4) ÷ 7x = 2.2
Therefore, you would need approximately 2.2 lbs of ground beef to make a batch to serve 11 people.
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help me please
The roasting guide for a turkey suggests cooking for a total of 100
minutes plus an additional 8 minutes per pound.
question: How much time would it take to roast a 27
lb turkey?
Answer minutes
Answer:
i think its 316 ?
Step-by-step explanation:
27 x 8 = 216, then add that to the 100 minutes and you get 316 minutes
Please help with this question.
Thanks.
Answer:
10
Step-by-step explanation:
E = V + 1/2mv^2
700 = 300 + 1/2*8*v^2
400 = 4v^2
100 = v^2
v = 10
the cost of a computer repair is worked out using the formula C = 35 + 15h.
C represents the cost in dollars.
H is the time taken in hours.
use the formula to find the cost of repair that takes 3 hours.
Answer: C = 35 + 15 x 3 = 80
Step-by-step explanation:
15h = 15 x (h) = 15 x 3 = 45 + 35 = $80
C = (15 x 3) + 35 = 80
What are the MRSs? Determine if there is a diminishing MRS
a. U(x,y)=3x+y
b. U(x,y)=x.y
c. U(x,y)=x⋅y
d. U(x,y)=x2−y2
e. U(x,y)=x+yx.y 3.
Consider each of a. U(x,y)=x0.1y0.4 b. U(x,y)=min(αx,βy) c. U(x,y)=αx+βy calculate the following i. Demand curves for x and y ii. Indirect utility function iii. (Indirect) expenditure function iv. Show that the demand curve is homogeneous in degree zero in terms of income and prices
a. The MRS is constant (not diminishing) at 1/3.
U(x,y) = 3x + y
The MRS for this utility function can be found by taking the partial derivative of x concerning y:
MRS = ∂U/∂y / ∂U/∂x = 1 / 3
The MRS is constant (not diminishing) at 1/3.
b. The MRS is diminishing because as y increases, the MRS decreases.
U(x,y) = x * y
The MRS for this utility function can be found by taking the partial derivative of x concerning y:
MRS = ∂U/∂y / ∂U/∂x = 1 / y
The MRS is diminishing because as y increases, the MRS decreases.
c. The MRS is diminishing because as y increases, the MRS decreases.
U(x,y) = x * y
The MRS for this utility function can be found by taking the partial derivative of x concerning y:
MRS = ∂U/∂y / ∂U/∂x = 1 / y
Similar to the previous case, the MRS is diminishing because as y increases, the MRS decreases.
d. The MRS depends on the ratio of y to x and can vary.
U(x,y) = x^2 - y^2
The MRS for this utility function can be found by taking the partial derivative of x concerning y:
MRS = ∂U/∂y / ∂U/∂x = -2y / 2x = -y / x
The MRS depends on the ratio of y to x and can vary. It is not necessarily diminishing.
e. The MRS depends on the values of x and y and can vary.
U(x,y) = x + y / (x * y)
The MRS for this utility function can be found by taking the partial derivative of x concerning y:
MRS = ∂U/∂y / ∂U/∂x = -1 / (y^2) + 1 / (x^2 * y)
The MRS depends on the values of x and y and can vary. It is not necessarily diminishing.
Now let's move on to the second part of the question:
For parts a, b, and c, we need more specific information about the utility functions, such as the values of α and β, to calculate the demand curves for x and y, the indirect utility function, and the expenditure function.
To show that the demand curve is homogeneous in degree zero in terms of income and prices, we need the specific functional form of the utility functions and information about the prices of x and y. Please provide the necessary details for parts A, b, and c to continue the analysis.
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Seved A store has the following demand figures for the last four years Help Year Demand 1 100 2 150 3 112 4 200 Given a demand forecast for year 2 of 100, a trend forecast for year 2 of 10, an alpha of 0.3, and a beta of 0.2, what is the demand forecast for year 5 using the double exponential smoothing method? Multiple Choice 125 134 100 104
The demand forecast for year 5 using the double exponential smoothing method is 134.
To calculate the demand forecast for year 5 using double exponential smoothing, we need to apply the following formula:
F_t+1 = F_t + (α * D_t) + (β * T_t)
Where:
F_t+1 is the forecast for the next period (year 5 in this case).
F_t is the forecast for the current period (year 2 in this case).
α is the smoothing factor for the level (given as 0.3).
D_t is the actual demand for the current period (year 2 in this case).
β is the smoothing factor for the trend (given as 0.2).
T_t is the trend forecast for the current period (year 2 in this case).
Given values:
F_t = 100 (demand forecast for year 2)
D_t = 100 (actual demand for year 2)
T_t = 10 (trend forecast for year 2)
α = 0.3 (smoothing factor for level)
β = 0.2 (smoothing factor for trend)
Let's calculate the demand forecast for year 5 step-by-step:
Calculate the level component for year 2:
L_t = F_t + (α * D_t) = 100 + (0.3 * 100) = 100 + 30 = 130
Calculate the trend component for year 2:
B_t = (β * (L_t - F_t)) / (1 - β) = (0.2 * (130 - 100)) / (1 - 0.2) = (0.2 * 30) / 0.8 = 6
Calculate the forecast for year 3:
F_t+1 = L_t + B_t = 130 + 6 = 136
Calculate the level component for year 3:
L_t+1 = F_t+1 + (α * D_t+1) = 136 + (0.3 * 150) = 136 + 45 = 181
Calculate the trend component for year 3:
B_t+1 = (β * (L_t+1 - F_t+1)) / (1 - β) = (0.2 * (181 - 136)) / (1 - 0.2) = (0.2 * 45) / 0.8 = 11.25
Calculate the forecast for year 4:
F_t+2 = L_t+1 + B_t+1 = 181 + 11.25 = 192.25
Calculate the level component for year 4:
L_t+2 = F_t+2 + (α * D_t+2) = 192.25 + (0.3 * 112) = 192.25 + 33.6 = 225.85
Calculate the trend component for year 4:
B_t+2 = (β * (L_t+2 - F_t+2)) / (1 - β) = (0.2 * (225.85 - 192.25)) / (1 - 0.2) = (0.2 * 33.6) / 0.8 = 8.4
Calculate the forecast for year 5:
F_t+3 = L_t+2 + B_t+2 = 225.85 + 8.4 = 234.25 ≈ 234 (rounded to the nearest whole number)
Therefore, the demand forecast for year 5 using double exponential smoothing is 234.
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KAYLA WALKS 3 2/5 MILES EACH DAY. HOW FAR WILL SHE WALK IN 7 DAYS?
Answer:
23.8 Miles in 7 days
Step-by-step explanation:
Answer:
In 7 days Kayla will walk 23 4/5 miles.
Step-by-step explanation:
3.4*7= 23.8 = 23 4/5
3 2/5 = 17/5 17/5*7= 119/5 = 23.8
What is the answer to
Graph y=−x−2.
this is the answer is -10 not sure tho
A cell phone company uses the equation C=$0.15t+$35.00 to determine the total cost, C, for a month of service based on the number of text messages, t. Identify the slope.
Slope is $0.15 of the equation of cost C=$0.15t+$35.00.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Given that A cell phone company uses the equation C=$0.15t+$35.00
C is the total cost for a month of service.
t is the number of text messages.
We have to find the slope of the equation.
slope is 0.15 and 35.00 is the y intercept of the equation given.
Hence, slope is $0.15 of the equation of cost C=$0.15t+$35.00.
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i need help making the sentence make sense
Answer:
first line is mode second line is 21
Guys pls help me!!!!!!!
Answer:
64 degrees
Step-by-step explanation:
since x is corresponding to 64, they are congruent.
Answer:
x = 64
Step-by-step explanation:
x and 64° are corresponding angles and are congruent , then
x = 64
can i have help with this please
Answer:
B) 7r² - r -1
Step-by-step explanation:
(3r² + 7r + 1) + (4r² - 8r - 2)
1. Remove unnecessary parentheses
3r² + 7r + 1 + 4r² - 8r - 2
2. Combine like terms (ex: r and -2r, n and 4n)
7r² - r -1
Therefore, the correct answer is B.
Hope this helps!
Answer: Heyaa! ~
Your Answer is... 7r²− r −1, Which is B.
Step-by-step explanation:
Subtract the numbers, And then combine like terms,
Solution: 7r²− r −1
Hopefully this helps you! ^
\(0.15 \times 0.3\)
2.1Simplifying Expressions: Problem 1 (1 point) Simplify the following expression. 6- 4(x - 5)-
The simplified expression is 26 - 4x.
To simplify the expression 6 - 4(x - 5), we can apply the distributive property and simplify the terms.
6 - 4(x - 5)
First, distribute -4 to the terms inside the parentheses:
6 - 4x + 20
Now, combine like terms:
(6 + 20) - 4x
Simplifying further:
26 - 4x
Therefore, the simplified expression is 26 - 4x.
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What are not exponential functions?.
It is not of exponential order for h(t) = et2. F is of exponential order and has order. F is piecewise continuous. No function's Laplace transform is possible. g(t) = eat, where t [0,.
Non-exponential form:
To represent a scientifically notated number as a non-exponential quantity: • Remove the exponential component of the number by moving the decimal point the same number of places as the exponent's value. The decimal is moved to the right by the same number if the exponent is positive.
Here are a few instances of functions other than exponential ones. y = 3 1 x as a result. n = 0 3 p as a result. Because y = ( 4) x. Since b = 1, y = 6 0 x.
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Select the correct answer. paula used these steps to solve an equation: step 1: step 2: step 3: step 4: step 5: between which two steps did paula use the division property of equality? a. steps 1 and 2 b. steps 2 and 3 c. steps 3 and 4 d. steps 4 and 5
In linear equations, x = 9.5 Paula use the division property of equality.
What is a formula for linear equations?
A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b). Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.The Division Property of Equality states that when both sides of an equation are divided by the same nonzero number, both sides remain equal.
That is, if a, b, and c are real numbers such that a = b and c ≠0, then
a/b = c/d
The equation was -6x = 57
To move to step 5, Paula had to divide both sides by the co-efficient of x (-6) in order to get the value of x. See below
-6x = 57 ( Divide both sides by -6)
-6x/6 = 57/-6
x = 9.5
Hence, we can conclude that the division property of equality.
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The complete question is -
Paula used these steps to solve an equation:
Step 1: -4(7 + 8) - 21 = 25
Step 2: -4r – 32 - 2x = 25
Step 3: -61 – 32 = 25
Step 4: -6x = 57
Step 5: x = -95
Between which two steps did Paula use the division property of equality?
three tanks a b and c are used to store oil
tank a contains n litres of oil tank b contains (n+150) litres of oil
tank c is empty
oil is pumped from tank a and from tank b into tank c so that all three tanks contain the same amount of oil
500 litres of oil are pumped from tank a into tank c
work out the value of n
The value of n is 1650 after oil is transferred from Tank A and Tank B to Tank C.
How to solve basic algebra word problems?It is given that initially,
Oil in tank A = n
Oil in tank B = n + 150
Oil in tank C = 0
Amount of oil transferred to tank C by tank A = 500 liters
Let us say 'x' amount of oil was transferred to tank C from tank B.
The amount of oil left in tank A after transferring 500 liters to tank C = n-500
Amount of oil left in tank B after transferring 'x' litres to tank C
= n + 150 - x
Amount of oil in tank C now = 500 + x
Since it is given that all three tanks contain the same amount of oil now. i.e. the new amount of oil in tank A = new amount of oil in tank B
n - 500 = n + 150 - x
x = 650
The new amount of oil in tank B = new amount of oil in tank C
n + 150 - x = 500 + x
n = 350 + 2x
Since x = 500
n = 350 + 2*650
n = 1650
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Work the problem for each card, look for the solution at the top of the next card. Use space and show all work
1. 12500 (1+r)^T
2. (18200)(3.25/100)(15)
Answer:Mathematics of Money:
Compound Interest Analysis With Applications
This site is a part of the JavaScript E-labs learning objects for decision making. Other JavaScript in this series are categorized under different areas of applications in the MENU section on this page.
Professor Hossein Arsham
Compound Interest: The future value (FV) of an investment of present value (PV) dollars earning interest at an annual rate of r compounded m times per year for a period of t years is:
FV = PV(1 + r/m)mt
or
FV = PV(1 + i)n
where i = r/m is the interest per compounding period and n = mt is the number of compounding periods.
One may solve for the present value PV to obtain:
PV = FV/(1 + r/m)mt
Numerical Example: For 4-year investment of $20,000 earning 8.5% per year, with interest re-invested each month, the future value is
FV = PV(1 + r/m)mt = 20,000(1 + 0.085/12)(12)(4) = $28,065.30
Notice that the interest earned is $28,065.30 - $20,000 = $8,065.30 -- considerably more than the corresponding simple interest.
Effective Interest Rate: If money is invested at an annual rate r, compounded m times per year, the effective interest rate is:
reff = (1 + r/m)m - 1.
This is the interest rate that would give the same yield if compounded only once per year. In this context r is also called the nominal rate, and is often denoted as rnom.
Numerical Example: A CD paying 9.8% compounded monthly has a nominal rate of rnom = 0.098, and an effective rate of:
r eff =(1 + rnom /m)m = (1 + 0.098/12)12 - 1 = 0.1025.
Thus, we get an effective interest rate of 10.25%, since the compounding makes the CD paying 9.8% compounded monthly really pay 10.25% interest over the course of the year.
Mortgage Payments Components: Let where P = principal, r = interest rate per period, n = number of periods, k = number of payments, R = monthly payment, and D = debt balance after K payments, then
R = P × r / [1 - (1 + r)-n]
and
D = P × (1 + r)k - R × [(1 + r)k - 1)/r]
Step-by-step explanation:
point $o$ is the center of an ellipse with major axis $\overline{ab}$ and minor axis $\overline{cd}.$ point $f$ is one focus of the ellipse. if $of
Given that $OF = 9$ and $OF' = 12,$ where $F$ and $F'$ are the foci of the ellipse, we can determine the lengths of the major and minor axes.
In an ellipse, the sum of the distances from any point on the ellipse to the two foci is constant. This property is expressed by the equation:
$$PF + PF' = 2a,$$
where $P$ is any point on the ellipse and $a$ is the semi-major axis. In our case, $P = O,$ and since $OF = 9$ and $OF' = 12,$ we have:
$$9 + 12 = 2a,$$
$$21 = 2a.$$
Therefore, the semi-major axis $a$ is equal to $\frac{21}{2} = 10.5.$
The distance between the center of the ellipse and each focus is given by $c,$ where $c$ is related to $a$ and the semi-minor axis $b$ by the equation:
$$c = \sqrt{a^2 - b^2}.$$
We can solve for $b$ using the distance to one focus:
$$c = \sqrt{a^2 - b^2},$$
$$c^2 = a^2 - b^2,$$
$$b^2 = a^2 - c^2,$$
$$b = \sqrt{a^2 - c^2}.$$
Substituting the known values:
$$b = \sqrt{10.5^2 - 9^2},$$
$$b = \sqrt{110.25 - 81},$$
$$b = \sqrt{29.25},$$
$$b \approx 5.408.$$
Therefore, the semi-minor axis $b$ is approximately $5.408.$
Finally, we can determine the lengths of the major and minor axes:
The major axis $\overline{AB}$ is twice the semi-major axis, so $\overline{AB} = 2a = 2(10.5) = 21.$
The minor axis $\overline{CD}$ is twice the semi-minor axis, so $\overline{CD} = 2b = 2(5.408) \approx 10.816.$
Therefore, the major axis $\overline{AB}$ is $21$ units long, and the minor axis $\overline{CD}$ is approximately $10.816$ units long.
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NEED HELP ASAP! NO LINKS PLEASE, WILL REPORT.
Segment Addition with Expressions.
Directions: K is between J and L. Solve for x
1. Let JK=15, KL=10, and JL=5x. x=____
Answer:
x=5
Step-by-step explanation:
set up the equation like this: JK+KL=JL
(15)+(10)=(5x)
calculate to find x!
x=5
Please someone help me im desperate
Find Tan0 , csc0, and cos0 where 0 is the angle shown in the figure. Give EXACT values, not decimal approximations.
Answer:
1. Tan θ = √11/5
2. Cosec θ = 6√11 /11
3. Cos θ = 5/6
Step-by-step explanation:
Let the side opposite to angle θ be y.
The value of y can be obtained by using the pythagoras theory as follow:
b² = 6² – 5²
b² = 36 – 25
b² = 11
Take the square root of both side.
b = √11
1. Determination of Tan θ
Tan θ =?
Opposite = √11
Adjacent = 5
Tan θ = Opposite /Adjacent
Tan θ = √11/5
2. Determination of Cosec θ.
We'll begin by calculating the Sine θ. This is illustrated below:
Sine θ =?
Opposite = √11
Hypothenus = 6
Sine θ = Opposite /Hypothenus
Sine θ = √11/6
Now, we shall determine Cosec θ as follow:
Cosec θ = 1/Sine θ
Sine θ = √11/6
Cosec θ = 1 ÷ √11/6
Cosec θ = 1 × 6/√11
Cosec θ = 6/√11
Rationalise the denominator
Cosec θ = 6/√11 × √11/√11
Cosec θ = 6√11 /11
3. Determination of Cos θ.
Cos θ =?
Adjacent = 5
Hypothenus = 6
Cos θ = Adjacent / Hypothenus
Cos θ = 5/6
Evaluate the Riemann Sum forf(x)=2x^2if0\leq x \leq 2with four equal subintervals using right-hand endpoints as the sample points.
\frac{15}{4}
\frac{7}{2}
\frac{15}{2}
15
\frac{30}{2}
Answer:
the Riemann Sum for $f(x)=2x^2$ with four equal subintervals using right-hand endpoints as the sample points is $\frac{15}{2}$.
Step-by-step explanation:
To evaluate the Riemann Sum for the function $f(x)=2x^2$ with four equal subintervals using right-hand endpoints as the sample points, we first need to determine the width of each subinterval. Since we have four subintervals to cover the interval $[0, 2]$, each subinterval has a width of $\Delta x = \frac{2-0}{4} = \frac{1}{2}$.
Next, we need to choose a sample point from each subinterval to evaluate the function. Since we are using right-hand endpoints as the sample points, we choose the endpoint of each subinterval as the sample point. The four subintervals are:
$[0, \frac{1}{2}]$, with sample point $x_1 = \frac{1}{2}$
$[\frac{1}{2}, 1]$, with sample point $x_2 = 1$
$[1, \frac{3}{2}]$, with sample point $x_3 = \frac{3}{2}$
$[\frac{3}{2}, 2]$, with sample point $x_4 = 2$
The Riemann Sum is then given by:
∑i=14f(xi)Δx=f(x1)Δx+f(x2)Δx+f(x3)Δx+f(x4)Δx=2(12)2⋅12+2(1)2⋅12+2(32)2⋅12+2(2)2⋅12=12+2+92+4=152i=1∑4f(xi)Δx=f(x1)Δx+f(x2)Δx+f(x3)Δx+f(x4)Δx=2(21)2⋅21+2(1)2⋅21+2(23)2⋅21+2(2)2⋅21=21+2+29+4=215
Therefore, the Riemann Sum for $f(x)=2x^2$ with four equal subintervals using right-hand endpoints as the sample points is $\frac{15}{2}$.
The Riemann Sum is 15/2 or 7.5.
To evaluate the Riemann Sum for the function f(x) = 2x^2 on the interval [0, 2] using 4 equal subintervals and right-hand endpoints, follow these steps:
1. Determine the width of each subinterval:
Δx = (b - a) / n = (2 - 0) / 4 = 0.5
2. Identify the right-hand endpoints of each subinterval:
x1 = 0.5, x2 = 1, x3 = 1.5, x4 = 2
3. Evaluate the function at each right-hand endpoint:
f(x1) = 2(0.5)^2 = 0.5
f(x2) = 2(1)^2 = 2
f(x3) = 2(1.5)^2 = 4.5
f(x4) = 2(2)^2 = 8
4. Calculate the Riemann Sum using these values:
Riemann Sum = Δx * (f(x1) + f(x2) + f(x3) + f(x4))
Riemann Sum = 0.5 * (0.5 + 2 + 4.5 + 8)
Riemann Sum = 0.5 * (15)
Riemann Sum = 7.5
The Riemann Sum for the given function using 4 equal subintervals and right-hand endpoints is 7.5, which is not among the provided options. However, the closest answer choice would be 15/2 or 7.5.
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a rectangle is measured to be 6.4 ± 0.2 cm by 8.3 ± 0.2 cm. a) calculate its area in square cm.
To calculate the area of the rectangle, we multiply its length by its width. Given that the length is measured to be 6.4 ± 0.2 cm and the width is measured to be 8.3 ± 0.2 cm, we can calculate the area as follows:
Length = 6.4 cm ± 0.2 cm
Width = 8.3 cm ± 0.2 cm
The maximum possible length is 6.6 cm (6.4 cm + 0.2 cm), and the minimum possible length is 6.2 cm (6.4 cm - 0.2 cm).
Similarly, the maximum possible width is 8.5 cm (8.3 cm + 0.2 cm), and the minimum possible width is 8.1 cm (8.3 cm - 0.2 cm).
Now, we can calculate the area of the rectangle using the maximum and minimum values:
Maximum area = Maximum length × Maximum width = 6.6 cm × 8.5 cm = 56.1 cm²
Minimum area = Minimum length × Minimum width = 6.2 cm × 8.1 cm = 50.22 cm²
Therefore, the area of the rectangle is within the range of 50.22 cm² to 56.1 cm².
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