Identify each expression and value that represents the area under the curve y= x^2+4 on the interval [-3, 2].
Answers
The area is given exactly by the definite integral,
[tex]\displaystyle\int_{-3}^2(x^2+4)\,\mathrm dx=\left(\frac{x^3}3+5x\right)\bigg|_{-3}^2=\frac{95}3\approx31.67[/tex]
We can write this as a Riemann sum, i.e. the infinite sum of rectangular areas:
• Split up the integration interval into n equally-spaced subintervals, each with length (2 - (-3))/n = 5/n - - this will be the width of each rectangle. The intervals would then be
[-3, -3 + 5/n], [-3 + 5/n, -3 + 10/n], …, [-3 + 5(n - 1)/n, 2]
• Over each subinterval, take the function value at some point x * to be the height.
Then the area is given by
[tex]\displaystyle\lim_{n\to\infty}\sum_{k=1}^nf(x^*)\Delta x_k=\lim_{n\to\infty}\sum_{k=1}^nf(x^*)\frac5n[/tex]
Now, if we take x * to be the left endpoint of each subinterval, we have
x * = -3 + 5(k - 1)/n → f (x *) = (-3 + 5(k - 1)/n)² + 4
If we instead take x * to be the right endpoint, then
x * = -3 + 5k/n → f (x *) = (-3 + 5k/n)² + 4
So as a Riemann sum, the area is represented by
[tex]\displaystyle\lim_{n\to\infty}\sum_{k=1}^n\left(\left(-3+\frac{5k}n\right)^2+4\right)\frac5n[/tex]
and if you expand the summand, this is the same as
[tex]\displaystyle\lim_{n\to\infty}\sum_{k=1}^n\left(13-\frac{30k}n+\frac{25k^2}{n^2}\right)\frac5n=\lim_{n\to\infty}\sum_{k=1}^n\left(\frac{65}n-\frac{150k}{n^2}+\frac{125k^2}{n^3}\right)[/tex]
So from the given choices, the correct ones are
• row 1, column 1
• row 2, column 2
• row 4, column 2
Answer:
Step-by-step explanation:
Related Questions
how to solve:
-25/j = 5
Answers
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer: -5
Explanation:
First -25/j = 5
-25 = 5j
-25/5 = 5j / 5
-5 = j
I hope this helped!
<!> Brainliest is appreciated! <!>
- Zack Slocum
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
I have 2 congruent, parallel, rectangular bases.
Answers
Answer:
The 3D figure formed is a Cuboid.
Answer:
The figure with 2 congruent, parallel, rectangular bases is a cuboid.
Abduls average speed is 40 mph in heavy traffic and his average speed is 50 mph in light traffic if he was in heavy traffic 1 hour and light traffic for 3 hours how far did Abdul travel
A. 90
B. 270
C. 190
D. 55
Answers
Answer:
c
Step-by-step explanation:
1 hour in heavy traffic = 40 miles
3 hours in light traffic = 50*3 = 150 miles
150+40 = 190 miles travelled
Megan's text messaging plan costs $5 for the first 700 messages and 30¢ for each additional text message. If she owes $63.20 for text messaging in the month of January, how many text messages did she send that month?
Answers
Answer:
Fixed cost $14 -350 messages
variable $ 0.25 each message i think
Step-by-step explanation:
58.20/.30=194
So she sent 700+194 for a total of 894 texts
Write the equation for the function g(x), which can be described as a
vertical shift 13 units up from the function f(x) = In x –1
Answers
Answer:
Step-by-step explanation:
When you shift up or down, the function gets added to or subtracted from the expression on the right of the y value. Put in simpler language, for this question, the equation becomes.
g(x) = f(x) + 13
And the solution is
g(x) = ln(x) - 1 + 13
g(x) = ln(x) + 12
Quadrilateral ABCD is similar to quadrilateral EFGH. Find the measure of side EF
Answers
Answer:
EF = 6.6
Step-by-step explanation:
Since ABCD is similar to EFGH, then EH is similar to AD. So, we can solve by first dividing 12 by 2 (EH by AD). The quotient of this is 6. This tells us that quadrilateral EFGH is 6 times larger than quadrilateral ABCD, since they are similar. So, with this and the measurement of AB (which is similar to EF), we can now solve for EF. We simply multiply 1.1 (the measurement of AB) by 6 (how many times larger EFGH is compared to ABCD). The product of this is 6.6, our final answer.
i need help w this plz thanks
Answers
Answer:
x = 4√7
y = 8√7
Step-by-step explanation:
Reference angle = 60°
Opposite = 4√21
Hypotenuse = y
Adjacent = x
To find x, apply TOA
Tan 60 = Opp/Adj
Tan 60 = (4√21)/x
x * Tan 60 = 4√21
x = (4√21)/Tan 60
x = (4√21)/√3 (tan 60 = √3)
Rationalize
x = (4√21*√3)/√3*√3
x = (4√63)/3
x = (4*3√7)/3
x = 4√7
To find y, apply SOH:
Sin 60 = Opp/Hyp
Sin 60 = (4√21)/y
y*Sin 60 = 4√21
y = 4√21/sin 60
y = (4√21)/(√3/2)
y = ✓(4√21 × 2/√3)
y = (8√21)/√3
y = 8√7
independent compound event definition
Answers
Answer:
Independent events occur when the outcome of one event does not affect the outcome of the second event. Rolling a four has no effect on tossing a head. To find the probability of two independent events, multiply the probability of the first event by the probability of the second event.
Other answer:
A compound event is the combination of two or more simple events (with two or more outcomes). Compound Probabilities (with more than one outcome (desired result) within a trial ): • The probability of rolling an even number less than 5 on a die. (
What is the z-score for the student with five siblings?
In a statistics class, students were asked how many
siblings they have. Their responses are shown.
2,3,1,3,5, 3, 3, 3, 6, 3,5, 0,3
0 -1.19
0-1.10
1.10
O 1.19
Subnat
Save and Exit
Tutoring Help
Answers
Answer:
C
Step-by-step explanation:
Answer: 1.19
Step-by-step explanation:
find the perimeter of the figure
Answers
Answer:
Step-by-step explanation:
You sign up for karate classes. The classes cost $80 per
month
Write an equation for the number of dollars, d, that
you pay for your karate classes if you take classes for
m months.
Complete the table for the missing values of d.
d
1
80
2
3
4
320
Answers
Answer:
m* = d**
1 = $80
2 = $160
3 = $240
4 = $320
*months
**Dollars ($)
Step-by-step explanation:
If it costs 80 per month then you times 80 by the number of months you want to work out. For example, you want to work out the cost of going to karate class for 3 months, and it costs $80 per month. Then you do $80 × 3 = $240.
The list price of an item is $550 and it is chain discount by 50%
less 10% less 20%. How much is the discount?
$352
$198
$440
$110
Answers
Answer:
$352
Step-by-step explanation:
first discount = 550 : 2 = $275
Second discount:
10 : 100 = x : 275
x = (2750/100) = $27,50
275 - 27,50 = $247,50
third discount
20 : 100 = x: 247,50
x = (247.50*20)/100 = $49,50
247,50 - 49,50 = $198 (final price)
total discount = 550 - 198 = $352
The two figures are similar. Find the ratios
(red to blue) of the perimeters and of the
areas. Write the ratios as fractions in
simplest form.
(100 points)
Answers
Answer:
1/5 to 1/5
Step-by-step explanation:
Can somone please help me this is due in 10 minutes please
Answers
Answer:
I believe that the answer is C
Which graph represents the function f(x)= 2x-1/x1?
Answers
Who’s smart at math?
Answers
Answer:
a
Step-by-step explanation:
times 4
Answer:
C. 35 to 49 Minutes
Step-by-step explanation:
ASAPPP! An arrow is shot into the air. A function representing the relationship between the number of
seconds it is in the air, t, and the height of the arrow in feet, h, is given by the equation below.
What is the initial height of the arrow?
h(t) = -16t^2+ 128t + 1.5
Answers
Answer:
The initial height of the arrow is 1.5 feet above the ground.
Step-by-step explanation:
Let be the height of the arrow be represented by the function [tex]h(t) = -16\cdot t^{2}+128\cdot t + 1.5[/tex], where [tex]h(t)[/tex] is the current height of the arrow, measured in feet, and [tex]t[/tex], is the time, measured in seconds.
Mathematically speaking, the initial height is the value of [tex]h[/tex] evaluated at [tex]t = 0\,s[/tex]. That is:
[tex]h(0) = -16\cdot (0)^{2}+128\cdot (0) + 1.5[/tex]
[tex]h(0) = 1.5\,ft[/tex]
The initial height of the arrow is 1.5 feet above the ground.
how to get the answer.
how to get the 1.2762815625?
I know it says to multiple, but how to multiple to get that number?
thanks
Answers
9514 1404 393
Answer:
1.05 × 1.05 × 1.05 × 1.05 × 1.05 = 1.2762815625
Step-by-step explanation:
An exponent indicates how many times the base is a factor in the product. That is, 1.05 to the 5th power means ...
1.05⁵ = 1.05 × 1.05 × 1.05 × 1.05 × 1.05
This multiplication expression is evaluated in the usual way.
= 1.1025 × 1.05 × 1.05 × 1.05
= 1.157625 × 1.05 × 1.05
= 1.21550625 × 1.05
= 1.2762815625
__
All scientific and graphing calculators have a button for computing the power of a number. On my calculator its label is [tex]\displaystyle \boxed{y^x}[/tex]. The particulars of the function of this button can be found in the manual for your calculator.
For on-line calculators, such as the go.ogle calculator, or the Desmos graphing calculator, the caret (^) is used to signify an exponent. (See the input line in the first attachment for an example.)
Plzz help will mark brainleast
Answers
Name all pairs
complementary angles
Answers
Answer:
See Explanation
Step-by-step explanation:
Require
All complementary angles
The image is blur and the texts are unreadable. However, the following explanation will assist you
To determine a pair of complementary angles, then both angles must add up to 90.
For instance: 50 and 40; 72 and 18, 10 and 80 etc.
So, all you need to do is select all pairs of angles that add up to 90 in the given image.
Take for instance:
[tex]\angle ABC = 50[/tex] and [tex]\angle BDE = 40[/tex] -- assumed values
This means that, you will select [tex]\angle ABC\ \&\ \angle BDE[/tex] as a pair
What is
-2.3 -
(4.5 – 3)?
2.3
1.3
10.3
-3.3
Answers
Answer:
-3.8
Step-by-step explanation:
-2.3 - 1.5 = -3.8
The area of the triangle below is 38.28 square meters. What is the length of the base?
Answers
Answer:
8.8 m
Step-by-step explanation:
Area of triangle = [tex]\frac{1}{2} bh[/tex]
38.28 = [tex]\frac{1}{2}[/tex] * b * 8.7
b = 38.28 * 2 / 8.7
b = 8.8 m
It takes at 45 minutes to complete his science homework. It takes him 2/3 as long to complete his math homework. How long does it take to complete his math homework
Answers
PLEASE HELP FAST GEOMERTY
Answers
Answer:
26
Step-by-step explanation:
125+29=154
180-154=26
Michelle opened an interest-bearing savings account. She deposited $8,750 into the account. If the account earns 1.3% interest, what will be Michelle’s balance after two years?
Answers
Answer:
$8977.50
Step-by-step explanation:
Diagram is shown below.
6
a. What the relationship between Z BEC and Z BAC?
b. What the measure of ZBEC ?
c. What the measure of BDC ?
Answers
Answer:
A) ∠BEC is one-half of ∠BAC
B) ∠BEC = 60°
C) ∠BDC = 120°
Step-by-step explanation:
C) arc BDC = 120°
arc BEC = 360° - 120° = 240°
∠BDC = 1/2(240°) = 120°
blue monkeys are swimming with 20 red and 30 black the total is 1000 how many are blue monkeys.
Answers
Answer:
950 Blue monkeys
Step-by-step explanation:
1000-20= 980-30= 950 blue monkeys
What is
-2.3 -
(4.5 – 3)?
2.3
1.3
10.3
-3.3
Answers
Answer:
-3.3
Step-by-step explanation:
I had to take a second look because the image and the description wasn't the same, but after simplifying the value, i got -3.3
Can you put a number for I can know which question you answered?
Answers
Answer:
The first one is y= 2
The second is y=4
The third one is y=4
The last one is y=2
Step-by-step explanation:
The easiest way to solve these types of problems is to Subsititute.
1) Givens: x=1; y=2x
Substitute
y=2
2) givens: x=2 y=2x
Substitute
y=4
3) Givens: x=-4; y=-2x-4
Substitute
y=4
4) givens: x=-3; y-2x-4
Substitute
y=2
Hope this helped :)
Answer:
1.) y=2
2.) y=4
3.) y=4
4.) y=-2
Step-by-step explanation:
1.) y=2x Multiply 1*2. y=2
2.) do the same thing. 2*2. y=4.
3.) plug in the x value and do order of operations. y= 2(-4)-4. y=4.
4.) plug in your values again. y= -2(-3)-4. y= -2.
hope this helps!!
Which point is a solution to y is less than or equal to 4x + 5?
Answers
Answer:(0,-2)
Step-by-step explanation: