EASY 5 POINTS!!! You have a new pool and want to know its volume. The pool is 5 feet deep and has a radius of 7 feet. About how much water can the pool hold? Use 3.14 for pi.
Answers
Answer:
The volume of water that can be hold by the pool is approximately 770 cubic feet.
Step-by-step explanation:
To calculate it we have to use the volume formula for a cylinder. This is:
[tex]Volume=pi*r^{2}*h\\pi=3.14\\r=radius\\h=deep[/tex]
Solving the equation with the given values:
[tex]Volume=3.14*7^{2} *5\\Volume=769.3 cubic feet \\Aprox.Volume= 770 cubic feet[/tex]
The volume of water that can be hold by the pool is approximately 770 cubic feet.
Related Questions
In the diagram AB and AC are tangent to the circle. Find the length of the radius D.C.
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Otherwise, you need to give more information.
Answer:
D. 6 on e2020
Step-by-step explanation:
just took test
A company that packages cold cuts needs to transport the packaged meat to the supermarket.it will cost $1,200 to rent a truck,and it will cost an additional $100 for every 50 pounds transported.which equation represents the transport cost for every 50 pounds if cold cuts transported? The options are
A) y=1,200-100x
B) y= 1,200+100x
C) y=1,200x +100
D) y=100x-1,200
Answers
it to calculate the cost of $100 for every 50lbs, you would use 100x
then you need to add that to the 1200
so the equation would be y = 1200+100x
B is the correct answer
How often is the number of house representatives assigned to states reallocated? every 2 years every 6 years every 10 years never?
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The members of the executive branch are the president, vice president and the cabinet. The president holds all the power for this branch of the government and the other members report to the president. The legislative branch writes up and votes on laws. This is called legislation. The legislative branch also known as congress has two parts: the House of Representatives and the senate. Other powers of the congress include declaring war, confirming presidential appointments for groups like the Supreme Court and the cabinet and investigating power. According to Article 1, Section 2, Clause 1, the House of Representatives shall constitute members every 2 years by the people of the state.
martha and mary had 375 jelly beans in all. after mary ate 24 jelly beans and martha ate 1/7 of her jelly beans, they each had the same number of jelly beans left. how many jelly beans did each girl have at first?
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Let x = number of beans with Martha
Let y = number of beans with Mary
Since total beans is 375,
x + y = 375
Mary ate 24 beans, after this she must be having x - 24 beans
Similarly after eating 1/7y beans, mary must be having y - y/7 beans
Setting them equal to each other
x - 24 = y - y/7
Solving both equations gives x = 186, y = 189
Exactly 1/20 of the students in mr.perez's class has a bird. what percentage of his students has a bird.
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The difference between the squares of two numbers is 7. four times the square of the first number increased by the square of the second number is 73. find the numbers.
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a-b=7
4a+b=73
4(7+b)+b=73 5b=45 b=9
a=7+b = 7+9 = 16
Then
x^2=16, x=+-4
y^2=9, y=+-3
The difference between the squares of two numbers is 7. Four times the square of the first number increased by the square of the second number is 73. By formulating this information into equations, the numbers, thus, obtained are 3 and 4 or -3 and -4.
An equation is a combination of numbers, variables, functions, mathematical operations, etc. in a meaningful way. The equation comprises two or more expressions separated by the equality sign(=), indicating the equivalency.
Let the numbers be x and y, then according to the question,
[tex]x^2 - y^2 = 7[/tex] ...(i)
[tex]4x^2 + y^2 = 73[/tex] ...(ii)
Add both equations,
[tex](x^2 - y^2) + (4x^2 + y^2) = 7 + 73\\(x^2 + 4x^2) + (-y^2 +y^2) = 80\\5x^2 = 80\\x^2 = 16\\x = \pm4[/tex]
Put x = 4 in equation (i),
[tex]4^2 - y^2 = 7\\16 - y^2 = 7\\y^2 = 16-7\\y^2 = 9\\y = \pm3[/tex]
So, the numbers are 3 and 4 or -3 and -4.
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The points L(10,9) M(10,-5) N(-1,-5) and O(-1,9) form rectangle L M N O Which point is halfway between O and N.
A.) (-1,0)
B.) (-1,7)
C.) (-1,2)
D.) (2,-1)
Answers
Answer:
C.) (-1, 2)
Step-by-step explanation:
You can plot the points on a graph, or you can just find the midpoint:
midpoint = (O + N)/2 = ((-1, 9) +(-1, -5))/2 = (-1-1, 9-5)/2 = (-2, 4)/2
midpoint = (-1, 2)
A Square has sides that are the same length as the radius of a circle. If the circle has an area of 36π square units how many units long is the perimeter of the square?
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now side of a square (l)=radius (r)=6
perimeter of square=4l=6×4=24 units ans
Find the volume of this figure to the nearest whole number. Use 3.14 for pi. Please help me!!
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volume of square middle = 12 x 12 x 7 = 1008
if you put the 2 ends together it would be a cylinder so volume for that is:
3.14 x 6^2 x 7 = 791.28
1008 + 791.28 = 1799.28 round it off to 1800 mm^3
So D is the correct answer
Answer:
4th option is correct.
Step-by-step explanation:
Here in the given image, we can see that there can be 2 figures if separated. A cuboid with dimensions 12*12*7 and a cylinder with radius as 6 mm and height as 7 mm.
We will first find the volume of cuboid.
V = [tex]12\times12\times7[/tex] = 1008 cubic mm
Now, volume of cylinder is given as : [tex]\pi r^{2} h[/tex]
[tex]3.14\times6^{2}\times7[/tex] = 791.28 cubic mm
Now adding both the volumes to get the volume of complete figure:
V = [tex]1008+791.28=1799.28[/tex] cubic mm
Now this value is closest to option 4th : 1800 cubic mm.
Therefore, last option is true.
the point(-2,4) is on the line given by the equation below
A.y=x -4
B.y=x+4
C.y=2x
D.y=-2x
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the primary advantage of a stratified random sample is that it ____.
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Explanation:
It is sometimes practical to divide the population being surveyed into subpopulations before applying random sampling.on each subpopulation.
Doing so ensures that no subpopulations are under represented or over represented, thereby removing bias.
a rectangular floor is 18 feet long and 12 feet wide. what is the area of the floor in square yards
Answers
1 yard=3 feet
Divide 18 and 12 by 3
18/3=6
12/3=4
A=bh
A=4*6
A=24 yards ^2
hope this helps:)
please mark thanks and brainliest:)
1 yard = 3 feet
18/3 =6
12/3=4
6*4 = 24 square yards
The table shows the outputs y for different inputs x:
Input
(x) 3 7 11 15
Output
(y) 4 6 8 10
Part A: Do the data in this table represent a function? Justify your answer. (3 points)
Part B: Compare the data in the table with the relation f(x) = 5x – 21. Which relation has a greater value when x = 11? (2 points)
Part C: Using the relation in Part B, what is the value of x if f(x) = 99? (5 points)
(10 points)
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B. For the table, y is 8 when x is 11.
Plug in the value to determine the y value for the equation.
f(x)= 5(11)-21
f(x)= 55-21
f(x)= 34
Since 34>8, the value of the equation f(x) is greater when x=11.
C. 99=5x-21
120=5x
x=24
Final answer: 24
Answer:24
Step-by-step explanation:
Convert r =-72/12+6 sin theta to Cartesian form.
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[tex]r = \sqrt{x^2 + y^2} [/tex]
[tex]x = rcos \theta , y = rsin \theta[/tex]
Given equation is
[tex]r = \frac{-72}{12} + 6sin \theta [/tex]
We can simplify it as
[tex]r = -6 + 6sin \theta[/tex]
Now we can write it as
[tex]r^2 = -6r + 6rsin \theta[/tex]
Now we can use
[tex]r^2 = x^ 2+ y^2 , rsin \theta = y , r = \sqrt{x^2 + y^2} [/tex]
So equation we can write it as
[tex]x^2 + y^2 = -6 \sqrt{x^2 + y^2} + 6y [/tex]
[tex]x^2 + y^2 - 6y = -6 \sqrt{x^2 + y^2} [/tex]
On squaring both sides
[tex](x^2 + y^2 - 6y)^2 = (-6 \sqrt{x^2 + y^2})^2 [/tex]
[tex]x^4 + y^4 + 36y^2 +2x^2y^2 -12y^3 -12x^2y = 36(x^2 + y^2)[/tex]
[tex]x^4 + y^4 +36y^2 + 2x^2y^2 -12y^3 -12x^2y = 36x^2 + 36y^2[/tex]
[tex]x^4 + y^4 + 36y^2 +2x^2y^2 -12y^3-12x^2y - 36x^2 - 36y^2 = 0[/tex]
[tex]x^4 + y^4 -12y^3 + 2x^2y^2 - 12x^2y - 36x^2 = 0[/tex]
Answer:
The answer is b. [tex]4x^2+3y^2-24y-144=0[/tex]
Step-by-step explanation:
The equation is:
[tex]r=\frac{-72}{12+6\sin(\theta)}[/tex]
Cross multiply;:
[tex]r(12+6\sin(\theta)=-72[/tex]
Expand;:
[tex]12r+6r\sin(\theta)=-72[/tex]
Divide through by 6;:
[tex]2r+r\sin(\theta)=-12[/tex]
[tex]2r=-12-r\sin(\theta)[/tex]
Substitute;:
[tex]y=r\sin(\theta), r=\sqrt{x^2+y^2}[/tex]
[tex]2\sqrt{x^2+y^2}=-12-y[/tex]
Square both sides;:
[tex](2\sqrt{x^2+y^2})^2=(-12-y)^2[/tex]
[tex]4(x^2+y^2)=144+24y+y^2[/tex]
[tex]4x^2+4y^2=144+24y+y^2[/tex]
Simplify;:
[tex]4x^2+3y^2-24y-144=0[/tex]
A bag contains 6 poker chips, one is red and the other 5 are blue. you and a friend take turns selecting a chip at random from the bag. the first person to get the red chip is the winner. find the probability that you win if you go first and
Answers
first it's 1/6
second = 1/5
Third= 1/4
fourth= 1/3
Fifth = 1/2
And sixth is guaranteed
Final answer:
The probability that you win if you go first is calculated as a sum of an infinite geometric series considering the odds of drawing the red chip in the first or subsequent rounds and is found to be 1/2.
Explanation:
The probability that you win the game if you go first can be found by considering the possibilities of either drawing the red chip on your first turn or on subsequent turns after both you and your friend did not draw the red chip in the previous rounds. In the first round, you have a 1/6 chance of picking the red chip and winning immediately. If you don't draw the red chip, then your friend has a 1/5 chance of drawing it on their first turn, assuming you drew a blue chip.
If both of you fail to draw the red chip on the first turn, the situation repeats with you having another chance to win with the same odds as your first turn. Since this can go on indefinitely, the probability of you winning can be expressed as a geometric series:
P(you win) = 1/6 + (5/6)(4/5)(1/6) + (5/6)^2(4/5)^2(1/6) + ...
This series can be summed up using the formula for the sum of an infinite geometric series a/(1-r), where a is the first term of the series (1/6 in this case), and r is the common ratio ((5/6)(4/5)). The common ratio can be simplified to (4/6) or (2/3), and the sum of the series gives us the final probability. Therefore, the probability that you win the game if you go first is:
P(you win) = 1/6 / (1 - (2/3)) = 1/6 / (1/3) = 1/2.
What is the slope of a trend line that passes through the points (–3, 3) and (18, 26)?
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[tex] \frac{Y_2 - Y_1 }{X_2 - X_1} [/tex]
Then, substitute values into the formula.
[tex] \frac{26 - 3}{18 - (-3)} [/tex]
Then solve. You get the fraction, [tex] \frac{23}{21} [/tex]. That is your slope.
Answer:
C.) 23/21
Step-by-step explanation:
just took the test on edge
Which one of the following pairs of terms is composed of like terms? A. 2a, 2b B. –3x, +3y C. abc, cab D. 4mn, 3my
Answers
Answer:
Option C
Step-by-step explanation:
We have to find the pair of terms composed of like terms.
(A) 2a, 2b Unlike terms
(B) -3x, +3y Unlike terms
(C) abc, cab
As we know cumulative property of multiplication shows a×(b×c) = (a×b)c
Therefore, both the terms abc and cab are similar.
(D) 4mn, 3my Unlike terms
Option C is the answer.
a vendor has learned that, by pricing pretzels at $1.50 sales will reach 91 pretzels per day. raising the price to $2.25 will cause the sales to fall to 58 pretzels per day. Let y be the number of pretzels the vendor sells at x dollars each. Write a linear equation that models the number of pretzels sold per day when the price is x dollars each
Answers
We are given with two points so we can derive the equation using the two-point form.
That is,
y – y1 = ((y2 – y1)/(x2 – x1))(x – x1)
We may choose which among our derived coordinates will be 1 and 2. Substituting to the equation,
y – 91 = ((58 – 91)/(2.25 – 1.5))(x – 1.5)
y – 91 = -44(x – 1.5)
Simplifying further,
y – 91 = -44x + 66
y = -44x + 157
Thus, the equation above gives the number of pretzels that can be sold given the price.
To model the number of pretzels sold per day as a function of the price in dollars using a linear equation, calculate the slope of the line using two known points, and then use the slope and one point to find the y-intercept. The resulting linear equation is y = -44x + 157, where y represents the number of pretzels sold and x represents the price in dollars.
To write a linear equation that models the number of pretzels sold per day when the price is x dollars each, we can start with two given points that represent the sales and price data: (1.50, 91) and (2.25, 58).
Using these points, we can first find the slope of the demand line.
The formula for slope (m) is:
m = (y2 - y1) / (x2 - x1)
Plugging in our values, we get:
m = (58 - 91) / (2.25 - 1.50) = (-33) / (0.75) = -44
The slope of the demand function is -44. This means that for each dollar increase in price, 44 fewer pretzels are sold.
Next, we use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. To find the y-intercept, we can use one of the given points. Let's use (1.50, 91).
91 = (-44)(1.50) + b
b = 91 + 66
b = 157
The y-intercept, b, is 157. Knowing both m and b, we can now write the equation of the line:
y = -44x + 157
This equation models the number of pretzels sold, y, at a price of x dollars each.
Quadrilateral STWR is inscribed inside a circle as shown below. Write a proof showing that angles T and R are supplementary. Circle Q is shown with an inscribed quadrilateral labeled RSTW.
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Let m(R)=α degrees and m(T)=β degrees.
1.
Angle R, is an inscribed angle, intercepting the arc WTS.
This means that the measure of the arc WTS is double the measure of the angle R,
so m(arc WTS) = 2α degrees.
2.
Similarly,
Angle T, is an inscribed angle, intercepting the arc WRS. So
m(arc WRS) = 2β degrees.
3.
m(arc WTS)+m(arc WRS)=360° since these arcs cover the whole circle.
thus
2α+2β=360°
divide by 2:
α+β=180°
this means T and R are supplementary angles.
Answer:
Step-by-step explanation:
Arc STR measures twice the measure of angle R, and arc WRS measures twice the measure of angle T.
STR = 2 x ∠R and WRS = 2 x ∠T --- This is because of the Inscribed Angle Theorem
If the measure of arcs STR and WRS are added together, the total would be 360° since a full circle is made up of 360°.
So mSTR + mWRS = 360°
Substituting the angle measures of R and T in for the arcs, the equation becomes:
2 • ∠R + 2 • ∠T = 360°
Simplifying further:
2 • [∠R + ∠T] = 360°
∠R + ∠T = 360° / 2
∠R + ∠T = 180° - This proves that opposite angles of a quadrilateral inscribed in a circle are supplementary.
An electronic product contains 40 integrated circuits. the probability that any integrated circuit is defective is 0.01, and the integrated circuits are independent. the product operates only if there are no defective integrated circuits. what is the probability that the product operates?
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Final answer:
The probability that the product operates is 0.6706 or 67.06%.
Explanation:
To find the probability that the product operates, we need to find the probability that all 40 integrated circuits are not defective. Since the probability of any integrated circuit being defective is 0.01, the probability that a circuit is not defective is 1 - 0.01 = 0.99. Since the integrated circuits are independent, we can multiply the probabilities together:
P(product operates) = (0.99)⁴⁰ = 0.6706
Therefore, the probability that the product operates is 0.6706 or 67.06%.
Melissa is making clothes for her dolls. She has 78 yard of fabric. Each style shirt requires 2/7 of a yard of fabric. How many shirts can she make for her dolls?
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Mix 20ml per 500 ml of water what is ratio of the amount of insecticide to the amount of water
Answers
Answer:
1 : 25
Step-by-step explanation:
Mix 20 ml per 500 ml. of water the ratio is = 20 : 500
Or [tex]\frac{20}{500}[/tex] = [tex]\frac{1}{25}[/tex] = 1 : 25
1 ml insecticide per 25 ml of water.
The ratio of the amount of insecticide to the amount of water is 1 : 25
Fractions are written as the ratio of two integers. The ratio of the amount of insecticide to the amount of water is 1:25
Ratio and proportionsFractions are written as the ratio of two integers
From the given question, we have the following measurement:
20ml per 500 ml of water
Required
The ratio of the amount of insecticide to the amount of water
Ratio = 20ml/500ml
Ratio = 1/25 = 1:25
Hence the ratio of the amount of insecticide to the amount of water is 1:25
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Which graph represents the solutions to the inequality |2x − 4| less than or equal to 14?
A)number line with an open circle on negative 5, shading to the right and an open circle on 9, shading to the left
B) number line with a closed circle on negative 5, shading to the right and a closed circle on 9, shading to the left
C) number line with an open circle on negative 5, shading to the left and an open circle on 9, shading to the right
D) number line with a closed circle on negative 5, shading to the left and a closed circle on 9, shading to the right
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is okay you lease a car at $415 per month for 4 years estimate the total cost of the least
Answers
The total cost of the least is $19,920.
Here,
lease a car at $415 per month for 4 years.
We have to find the total cost of the least.
What is Multiplication?
Multiplication is the process of calculating the total of one number multiplied by another.
Now,
lease a car at $415 per month for 4 years.
1 years = 12 month
4 years = 4 x 12 = 48 months.
Hence, total cost of the least = $415 x 48
= $19,920
So, The total cost of the least is $19,920.
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What is the distance between the two points?
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[tex]\bf d=\sqrt{\left[ \frac{3}{8}-\frac{1}{8} \right]^2+\left[-\frac{4}{5}-\left( -\frac{9}{5} \right) \right]^2}\implies d=\sqrt{\left( \frac{3}{8}-\frac{1}{8} \right)^2+\left(-\frac{4}{5}+\frac{9}{5} \right)^2} \\\\\\ d=\sqrt{\left( \frac{2}{8}\right)^2+\left(\frac{5}{5} \right)^2}\implies d=\sqrt{\left( \frac{1}{4} \right)^2+\left( 1 \right)^2}\implies d=\sqrt{\frac{1^2}{4^2}+1}[/tex]
[tex]\bf d=\sqrt{\frac{1}{16}+1}\implies d=\sqrt{\cfrac{17}{16}}\implies d=\cfrac{\sqrt{17}}{\sqrt{16}}\implies d=\cfrac{\sqrt{17}}{4}[/tex]
AB = √[(x₂ - x₁)² + (y₂ - y₁)²]
A(1/8 , 9/5) and B(3/8 , - 4/5)
Plug in the related value:
AB = √[(3/8 - 1/8)² + ( - 4/5 - 9/5)²] = √(2729/400) (ALREADY SIMPLIFIED)
AB = distance = 2.61
Amy is doing a science experiment on how a certain bacterium reacts to an antibiotic. She has 3 dishes of identical bacterium samples with 17 bacteria in each dish. She gives an antibiotic to all of the bacteria in one dish. All of the treated bacteria died, and the bacteria in the other two dishes survived. Is there a sampling bias in the situation above? A. There is not enough information. B. Yes. The antibiotic may not work on the other bacteria. C. Yes. The bacteria in the other 2 dishes are different than the treated bacteria. D. No. All 3 dishes are filled with the same number of identical bacteria.
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I need help badly please help !!
Answers
Probability of blue die being even: 3/6, which simplifies to 1/2.
Compound probability:
1/2* 1/2= 1/4
Final answer: 1/4
If the slope of a straight line Is 0 and the y-intercept is -2, what is the equation of the line
Answers
it is simply y=-2
hoped I helped :)
You invest $9000 with a 6% interest rate compounded semiannually. After 9 yrs, how much money is in your account?
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Calculate M6 for f(x)=4⋅ln(x^2) over [1,2].
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According to this formula if we have to calculate [tex] \int\limits^a_b {f(x)} \, dx [/tex]
then we will divide the interval [a,b] into n subinterval of equal width.
Δx = [tex] \frac{b-a}{n} [/tex]
So we will denote each of interval as follows
[tex][x_0 , x_1] , [x_1, x_2], ................[x_{n-1} , x_n][/tex] where [tex]x_0 = a , x_n = b[/tex]
Then for each interval we will calculate midpoint.
So we can calculate definite integral as
[tex] \int\limits^a_b {f(x)} \, dx = \triangle x f(y_1) + \triangle x f(y_2)+ ...............+ \triangle x f(y_n)[/tex]
where [tex]y_1 , y_2 , ....................y_n [/tex] are midpoint of each interval.
So in given question we need to calculate [tex]M_6[/tex] . So we will divide our interval in 6 equal parts.
Given interval is [1,2]
[tex]\triangle x = \frac{2-1}{6} = \frac{1}{6} [/tex]
So we will denote 6 interval as follows
[tex][1 , \frac{7}{6}] , [ \frac{7}{6} , \frac{8}{6} ] , [ \frac{8}{6} , \frac{9}{6} ] , [ \frac{9}{6} , \frac{10}{6} ] , [ \frac{10}{6} , \frac{11}{6} ] , [ \frac{11}{6} , 2 ] [/tex]
Now midpoint of each interval is
[tex]y_1 = \frac{1+ \frac{7}{6} }{2} = \frac{13}{12} = 1.084[/tex]
[tex]y_2 = \frac{ \frac{7}{6} + \frac{8}{6} }{2} = \frac{15}{12} = 1.25[/tex]
[tex]y_3 = \frac{ \frac{8}{6} + \frac{9}{6} }{2} = \frac{17}{12} = 1.417[/tex]
[tex]y_4 = \frac{ \frac{9}{6} + \frac{10}{6} }{2} = \frac{19}{12} = 1.584[/tex]
[tex]y_5 = \frac{ \frac{10}{6} + \frac{11}{6} }{2} = \frac{21}{12} = 1.75[/tex]
[tex]y_6 = \frac{ \frac{11}{6} + \frac{12}{6} }{2} = \frac{23}{12} = 1.917[/tex]
So [tex]M_6[/tex] for the given function is
[tex]M_6 = \triangle x [f(y_1) + f(y_2) + f(y_3) + f(y_4) + f(y_5) + f(y_6) ][/tex]
[tex]= \frac{1}{6}[0.6452+1.7851+2.7883+3.6796+4.4769+5.4243][/tex]
[tex]= \frac{1}{6} * 18.7994 = 3.1333 [/tex]
So [tex]M_6 value for function is 3.1333[/tex]
To calculate M6 for f(x)=4⋅ln(x^2) over [1,2], differentiate the function to find f'(x). Integrate f'(x) over the given interval to find the area under the curve. Subtract the value of the integral at the lower limit from the value at the upper limit to get M6.
Explanation:To calculate M6 for the function f(x) = 4⋅ln(x^2) over the interval [1,2], follow these steps:
Differentiate the function to find f'(x).Integrate f'(x) over the given interval to find the area under the curve.Subtract the value of the integral at the lower limit from the value at the upper limit to get M6.In this case, since f(x) = 4⋅ln(x^2), we have f'(x) = 8/x. Integrate f'(x) from 1 to 2 to get M6.
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