Finite approximation method of estimating the area under the curve of the
given function makes use of rectangular approximation of the area.
The correct responses are;
i) The estimated area using a lower sum with two rectangles of equal width is 1,715 square units.
ii) The estimated area using a lower sum with four rectangles of equal width is 3,001.25 square units.
iii) The estimated area using an upper sum with two rectangles of equal width is 8,575 square units.
iv) The estimated area using a upper sum with four rectangles of equal width is 6,431.25 square units.
Reasons:
The given function is f(x) = 5·x²
The given domain is x₀ to x₁₄
i) Estimate using lower sum with two rectangles of equal width;
[tex]Let \ \Delta x = \dfrac{14}{2} = 7 \ we \ get;[/tex]
f(0) = 0
f(7) = 5 × 7² = 245
A = 0 × 7 + 245 × 7 = 1,715
The estimated area using a lower sum with two rectangles of equal width
is 1,715 square units.
ii) Estimate using lower sum with four rectangles of equal width;
[tex]Let \ \Delta x = \dfrac{14}{4} = 3.5 \ we \ get;[/tex]
f(0) = 0
f(3.5) = 5 × 3.5² = 61.25
f(7) = 5 × 7² = 245
f(10.5) = 5 × 10.5² = 551.25
A = 0 × 3.5 + 61.25 × 3.5 + 245 × 3.5 + 551.25 × 3.5 = 3,001.25
The estimated area using a lower sum with four rectangles of equal width is 3,001.25 square units.
iii) Estimate using an upper sum with two rectangles of equal width;
[tex]Let \ \Delta x = \dfrac{14}{2} = 7 \ we \ get;[/tex]
f(7) = 5 × 7² = 245
f(14) = 5 × 14² = 980
A = 245 × 7 + 980 × 7 = 8575
The estimated area using an upper sum with two rectangles of equal width
is 8,575 square units.
iv) Estimate using an upper sum with four rectangles of equal width;
[tex]Let \ \Delta x = \dfrac{14}{4} = 3.5 \ we \ get;[/tex]
f(3.5) = 5 × 3.5² = 61.25
f(7) = 5 × 7² = 245
f(10.5) = 5 × 10.5² = 551.25
f(14) = 5 × 14² = 980
A = 61.25 × 3.5 + 245 × 3.5 + 551.25 × 3.5 + 980 × 3.5 = 6,431.25
The estimated area using a upper sum with four rectangles of equal width
is 6,431.25 square units.
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https://brainly.com/question/2264277
Fill in the blanks below, pelase.
Need help with number 2 and 3
Answer:
2. SSS ( Side-Side-Side)
There are 4 red balls and 6 black balls in a bag. Draw consecutively 3 balls with replacement. Find the probability when the first two balls drawn are black and the third ball drawn is red.
Answer:
[tex]\frac{1}{3} *\frac{1}{2} =\frac{1}{6}[/tex]
Step-by-step explanation:
So the first two balls are black, so the way to change the path is to take two out of six black balls over two out of ten balls, which is 1/3.
If the last one is red then the probability is that if you take one of the four red balls and you take one of the eight balls, you get 1/2.
So the total probability is 1/3 times 1/2 is 1/6.
I NEED HELP WITH THIS ASAP
Answer:
4
Step-by-step explanation:
( 5x - 6 ) and ( 3x + 2 ) are alternate interior angles.
Alternate interior angles are equal,
So,
5x - 6 = 3x + 2
5x - 3x = 2 + 6
2x = 8
x = 8 / 2
x = 4
how man1/3 are in 2 2/3
Answer:
that 8/3
Step-by-step explanation:
thats because it goes too 2 2/3
Please I need help I wasn’t at school today
A woman wishes to rent a house within 9 miles of her work. If she lives x miles from her work, her transportation cost will be cx dollars per year, while her rent will be 49c x 1 dollars per year, where c is a constant taking various situational factors into account. How far should she live from work to minimize her combined expenses for rent and transportation
Answer:
5 miles
Step-by-step explanation:
divide the 9 by 45 to get 6 subtract the 1 to get 4
Stefan's family raises honey bees and sells the honey at the farmers' market. To get ready for market day, Stefan fills 24 equal sized jars with honey. He brings a total of 16 cups of honey to sell at the farmers' market.
Answer:
Have you ever wondered how a tiny little insect like a bee could ever fill a jar of honey? If it were just down to one bee it would be a mighty task but the work is shared by many thousands of bees and is a great example of what can be achieved by a co-ordinated effort. Think of it in terms of humans creating something like a pyramid.
A jar of honey weighs 454 grammes and a bee can carry about 0.04 grammes of nectar. But nectar is only about 40% sugar and honey needs to be about 80% sugar so the bee actually only carries about 0.02 grammes of honey on each trip.
Step-by-step explanation:
The Student Council is selling raffle tickets to raise money for the Winter Dance. They have a total of 275 tickets to sell and are told they must sell at least 82% of them to raise enough money. How many do they need to sell?
Answer:
226
Step-by-step explanation:
To find the percentage of a given value, firstly convert to a decimal by dividing by 100:
82 ÷ 100 = 0.82
Now, multiply this decimal by the number of tickets:
275 x 0.82 = 225.5
Because you can't sell half a ticket, round up.
This means the total of tickets they need to sell is 226.
Hope this helps!
What is the equation of the line that passes through the point (-4, 2) and
has a slope of -2?
Answer:
y-2 = -2(x+4)
or
y = -2x-6
Step-by-step explanation:
We can use the point slope form of a line
y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line
y - 2 = -2(x- -4)
y-2 = -2(x+4)
If we want the equation in slope intercept form
Distribute
y-2 = -2x-8
Add 2 to each side
y-2+2 = -2x-8+2
y = -2x-6
Rationalise 10/√7-√2
[tex] \frac{10}{ \sqrt{7} - \sqrt{2} } \\ = \frac{10}{ \sqrt{7} - \sqrt{2} } \times \frac{ \sqrt{7} + \sqrt{2} }{ \sqrt{7} + \sqrt{2} } \\ = \frac{10( \sqrt{7} + \sqrt{2}) }{( \sqrt{7} - \sqrt{2} )( \sqrt{7} + \sqrt{2} )} \\ = \frac{10 \sqrt{7} + 10 \sqrt{2} }{( { \sqrt{7} )}^{2} - ( \sqrt{2} ) ^{2} } \\ = \frac{10( \sqrt{7} + \sqrt{2} )}{7 - 2} \\ = \frac{10( \sqrt{7} + \sqrt{2} ) }{5} \\ = 2( \sqrt{7} + \sqrt{2} ) \\ = 2 \sqrt{7} + 2 \sqrt{2} [/tex]
[tex]\frac{10}{\sqrt{7} } -\sqrt{2} =\frac{10\sqrt{7} -7\sqrt{2} }{7}[/tex]
( Decimal: [tex]2.36543...[/tex])
Steps:
1: Convert element to fraction.
[tex]\sqrt{2} =\frac{\sqrt{2}\sqrt{7} }{\sqrt{7} }[/tex]
[tex]=\frac{10}{\sqrt{7} } -\frac{\sqrt{2} \sqrt{7} }{\sqrt{7} }[/tex]
2: Since denominator are equal, combine the fractions.
[tex]\frac{a}{c}[/tex] ± [tex]\frac{b}{c} =\frac{a+b}{c}[/tex]
[tex]=\frac{10-\sqrt{2} \sqrt{7} }{\sqrt{7} }[/tex]
-----------------------
[tex]\sqrt{2} \sqrt{7} =\sqrt{14}[/tex]
[tex]=\frac{10-\sqrt{14} }{\sqrt{7} }[/tex]
Rationalize [tex]\frac{10-\sqrt{14} }{\sqrt{7} }[/tex] : [tex]\frac{10\sqrt{7} -7\sqrt{2} }{7}[/tex]
[tex]=\frac{10\sqrt{7}-7\sqrt{2} }7}[/tex]
(01.02 HC) A jar contains 0.85 liter of strawberry juice and 0.50 liter of mango juice. Celina poured 0.15 liter of watermelon juice into the jar. She then drank 0.30 liter of the mixture.
Part A: Write an expression to represent the total amount of juice left in the jar.
Part B: Simplify the expression and identify which property is used in each step.
Part A:
GIVEN: Strawberry Juice = [tex]0.85[/tex] liters, Mango Juice = [tex]0.50[/tex] liters, Watermelon Juice = [tex]0.15[/tex] liters, Drank Juice = [tex]0.30[/tex] liters.
-------------------------------------------------------------------------------------------
· Find the expression
In this case, all of them have to be combined to find the expression
Thus,
Expressions in these queries are arithmetical statements that may be defined by the operator, and the following discussion could indeed define a minimum of 2 terms containing the numbers or the variables, or both.
strawberry juice = 0.85 liter
mango juice = 0.50 liter
watermelon juice= 0.15 liter
drank juice = 0.30 liter
solution:
0.85+0.5+0.15 = 1.5
if she drank 0.3, remove it from 1.5, then 1.3
this expression would be : (0.85+0.5+0.15) - 0.3 = 1.2
please help me with this sum
Answer:
Step-by-step explanation:
2. 3 × 12 = 3 × 2 × 6 = 3 × 2 × 2 × 3
3. 4 × 9 = 2 × 2 × 3 × 3
4. 6 × 6 = 2 × 3 × 2 × 3
please give me a brainliest answer
Step-by-step explanation:
2. 36 = 3 × 12 = 3 × 2 × 6 = 3 × 2 × 2 × 3
3. 36 = 4 × 9 = 2 × 2 × 3 × 3
4. 36 = 6 × 6 = 2 × 3 × 2 × 3
DO NOW: What is the surface area of the cube? 4 in 4 in 4 in
Answer:
96 in^2.
Step-by-step explanation:
It has 6 surfaces each of area 4*4 = 16
Answer is 6*16 = 96.
The number of marbles each sister gets when m marbles are shared equally among four sisters x = m/4
Answer:
m/4
Step-by-step explanation:
Solve the following two problems using Calculus. Show all of your work on a separate sheet of paper, making clear how you arrived at all your solutions. Please be aware that you are using similar thinking for both of these problems, but you are solving for maximum area in Part A and minimum cost in Part B. Enjoy
A. If the materials for the fence cost $12 per foot, find the dimensions of the
corral for the largest possible area that can be enclosed with $2400 worth of fence.
B. If he only requires an area of 288 square feet for his vegetable garden, find the minimum cost of putting up this fence, if the cost per foot is $10. Indicate the dimensions of the garden that will minimize the cost.
9514 1404 393
Answer:
A. 50 ft square
B. 12√2 ft square
Step-by-step explanation:
These problems are basically the same, so have the same solution. The rectangle with maximum area for a given perimeter will have the same shape as the one with minimum perimeter for a given area.
We can find it generically. Let p represent the perimeter of a rectangular area with one side that measures x. The area will be ...
A = x(p/2 -x) = -x^2 +(p/2)x
The area will be maximized when dA/dx = 0:
dA/dx = -2x +p/2 = 0
p/2 = 2x . . . . . add 2x
x = p/4 . . . . . . divide by 2
The other dimension is ...
p/2 -x = p/2 -p/4 = p/4
The dimensions of the maximum area for perimeter p are ...
p/4 × p/4 . . . . . . . a square
__
A.$2400 worth of fence at $12 per foot is 2400/12 = 200 ft of fence. The largest possible area that can be enclosed will have dimensions of 200 ft/4 = 50 ft square:
50 ft × 50 ft
__
B.The perimeter of the garden will be at its shortest when the shape of the garden is square.
√(288 ft²) = 12√2 ft
The dimensions of the garden that will minimize the cost are ...
12√2 ft × 12√2 ft
Ben can paint 280 square feet in 12 minutes. How many square feet can he paint in 1 hour?
Answer:
1400 sq. ft
Step-by-step explanation:
60 min = 1 hour
280 sq. ft / 12 min = x / 60 min
x = 60 min * (280 sq. ft / 12 min)
minuets cancel out
x = 1400 sq. ft
In the equation x² + 18x + 81 = 0, the roots are?
Answer:
x = (-9)Step-by-step explanation:
x^2 + 18x + 81 = 0
x^2 + 9x + 9x + 81 = 0
x(x+9) + 9(x+9) = 0
(x + 9)(x + 9) = 0
(x + 9) = 0
x + 9 = 0
x = 0 - 9
x = -9Mary found a pair of boots that cost $60 sales tax is 7% what is the total price Mary will pay for the boots?
Answer:
2 Hola cómo estás mi amigo
Answer:
sale price SP= cost + sales tax
SP= 60 + 7% of 60
SP= 60+4.2
SP= $64.2
Find the probability that an observation randomly selected from the normal distribution is between 75 inches and 81 inches.
Answer:
Happy birthday to you
Nobody like you
U look like a an animal go back to the zoo
Step-by-step explanation:
HINDI PO NAKATAWA
solve the following inequality using the algebraic approach: 3x>-6
Answer:
x > -2
Step-by-step explanation:
3x>-6
Divide each side by 3
3x/3 > -6/3
x > -2
to the nearest 0.01cm3, what is the volume of this sphere?
Answer: Calculate the sphere volume, the volume of a spherical cap or of a hemisphere thanks to this sphere volume calculator.
How many solutions exist for the mixed-degree system graphed below?
Answer:
(c) part two is correct ans.
Step-by-step explanation:
mark me as a brainlist plz.
HELP ASAP PLSSS IM DESPERATE!!!! HELP IN 5MINS PLS!!!
Answer:
angle v and angle w,
angle x and angle y
(the first one)
Two bicyclist are 180 miles apart when they start racing towards each other. If their speeds are 14 mph and 16 mph respectively, how long will it be before they are twenty miles apart? I WILL MARK AS BRANLIEST IF YOU GOT THIS CORRECT!
Answer:
5 hours 20 minutes
Step-by-step explanation:
Distance traveled to be 20 miles apart
180 - 20 = 160 miles
Combined speed
14 + 16 = 30 mph
time = distance / speed
t = 160/30
t = 5 1/3 hours
t = 5 hours 20 minutes
Answer:
5 hours and 20 minutes
Step-by-step explanation:
it will take them 5 hours and 20 minutes.
A coin is tossed 10 times, find the probability of getting seven heads.
Answer:
7/10 or 70%
Step-by-step explanation:
because 10/10 is 100%-----> so 7/10----> 70%
64 is 20% of what number?
Answer:
320
Step-by-step explanation:
64 by 5 equals 320
Answer:
320
Step-by-step explanation:
Divide 64 by 0.2
.
Simplify: -8(13 – 5c + 12d)
a -104 – 5c + 12d
b -104 - 40c - 96d
c -104 -13c + 4d
d -104 + 40c – 96d
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Simplification ~
[tex] - 8(13 - 5c + 12d)[/tex][tex]( - 8 \times 13) + ( - 5c \times - 8) + ( - 8 \times 12d)[/tex][tex] - 104 + 40c - 96d[/tex]Correct choice is D
Simplify: -8(13 – 5c + 12d)
= −8 (13−5c+12d)
= (−8×13) + (−5c×−8) + (−8×12d)
= - 104 + 40c - 96d
Correct option is D
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Answered by:-Cutest Ghost (･◡･)▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪
Suppose that an airline overbooks seats on their flights. In particular, it sells 300 tickets for a flight when there are only 270 seats available. On average, we expect 15% of those with tickets to not show up. What is the probability that we will have enough seats for everyone who shows up
Using the normal approximation to the binomial, it is found that there is a 0.994 = 99.4% probability that we will have enough seats for everyone who shows up.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].In this problem:
15% do not show up, so 100 - 15 = 85% show up, which means that [tex]p = 0.85[/tex].300 tickets are sold, hence [tex]n = 300[/tex].The mean and the standard deviation are given by:
[tex]\mu = np = 300(0.85) = 255[/tex]
[tex]\sigma = \sqrt{np(1-p)} = \sqrt{300(0.85)(0.15)} = 6.185[/tex]
The probability that we will have enough seats for everyone who shows up is the probability of at most 270 people showing up, which, using continuity correction, is [tex]P(X \leq 270 + 0.5) = P(X \leq 270.5)[/tex], which is the p-value of Z when X = 270.5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{270.5 - 255}{6.185}[/tex]
[tex]Z = 2.51[/tex]
[tex]Z = 2.51[/tex] has a p-value of 0.994.
0.994 = 99.4% probability that we will have enough seats for everyone who shows up.
A similar problem is given at https://brainly.com/question/24261244
SOLVE ASAP!!!!! NO LINKS!!!!!!∛²³1 + 4 x -96
Answer:
All i got was 3√23+4x−96
Step-by-step explanation: