solve each equation using an array 3542 x 8 =

a. Trapezoidal Rule- 9.413607

b. Midpoint Rule-9.393861

c. Simpson's Rule -9.400407

a. We use n=8 for this integral, .Δt=4-0/8=0.5

Therefore the integral range is[0,0.5,1.0,1.5......3.0,3.5....4.0 ]

#For the Trapezoidal Rule:

[tex]\int\limits^a_b[/tex]∫(x)dx≈[tex]Tn=[/tex]Δr/2[∫([tex]x0[/tex])+2∫(x1)+....+∫(xn)]

=[tex]\int\limits^4_0[/tex][tex]In(2+ex[/tex])dx≈[tex]T8[/tex]

=0.5/2[[tex]In[/tex](2+[tex]e0.0[/tex])+2In(2+e0.5)+2In(2+e1.0)+....+2In(2+e3.5)+In(2+e4.0)]

=0.25[1.098612+2.588754+3.102889+3.737962+4.479090+5.304017+6.189846+7.117283+4.035976]

≈9.413607

Hence, the approximate integral value using Trapezoidal rule is 9.413607

b.For the Midpoint Rule, we calculate the integral as:

[tex]\int\limits^a_b[/tex]∫(x)dx≈[tex]Mn=[/tex]Δx[∫[tex](x1)[/tex]+∫([tex]x2)[/tex]........∫([tex]xn)}[/tex]

x1 is the midpoint of the ith interval.

From our interval ,[0,0.5,1.0,1.5....3.0,3.5,4.0]the applicable intervals are

[0.25,0.75,1.25,2.25,2.75,3.25,3.75]

We therefore have the integral value as:

=4/8[[tex]In[/tex](2+[tex]e0.25[/tex])+In(2+[tex]e0.72[/tex])+In(2+[tex]e1.25[/tex])+....+In(2+[tex]e1.75[/tex])+In(2+[tex]e2.25[/tex])[tex]In[/tex](2.75)+In(2+e0.5)+In(2+e1.0)]

Hence, the approximate integral value using the Midpoint Rule is 9.393861

c. For the Simpson's Rule, we calculate the integral rule as follows:

Hence, the approximate integral value using the Simpson's Rule is 9.400407

To learn more about trapezoidal rule refer to:

https://brainly.com/question/16996659

#SPJ4

The graph of the line with the slope of 4/3 and goes through the point (1,3) has been plotted

The slope of the line = 4/3

The line is passing through the point = (1,3)

Here we have to use the point slope form the line

The point slope form of the line = [tex](y-y_{1} )= m(x-x_{1})[/tex]

Where m is the slope of the line

[tex](x_{1},y_{1} )[/tex] is the coordinate of the point

Substitute the values in the equation

(y-3) = 4/3 (x-1)

y-3 = (4/3)x - 4/3

y = (4/3)x - 4/3 + 3

y = (4/3)x + 5/3

We got the slope intercept of the line.

Plot the graph using the slope intercept form of  the line

Hence, the graph of the line with the slope of 4/3 and goes through the point (1,3) has been plotted

Learn more about slope intercept form here

brainly.com/question/9682526

#SPJ1

Answer:

Go up 8 and right  2

8/2

Step-by-step explanation:

Step-by-step explanation:

We need to find the circumference of the equation.

One circle circumference is a circle full rotation.

[tex]c = \pi(d)[/tex]

[tex]d = 2r[/tex]

[tex]c = 2r\pi[/tex]

R is 14.

[tex]c = 28\pi[/tex]

We need a rotation 10times so

[tex]10 \times 28\pi = 280\pi[/tex]

The measure of the angle is 35°. The complement is 55° and the supplement is 145°.

Let's measure of the angle = x

Supplementary angle of x = 180° - x

Complementary angle of x = 90° - x

By the given condition

180° - x = 2(90° - x) + 35°

Find the measure of the angle

180° - x = 2(90° - x) + 35°

⇒ 180° - x = 180° - 2x + 35°

⇒ - x = - 2x + 35°

⇒ - x + 2x = 35°

⇒ x = 35°

The measure of the angle = 35

The complement will be:

= 90° - 35° = 55°

The supplement will be:

= 180° - 35° = 155°

The concept illustrates how angles are calculated.

Learn more about angles on:

https://brainly.com/question/25716982

#SPJ1

Answer: THE ANSWER IS 20/21

Step-by-step explanaTion:

Answer:

[tex]5\frac{1}{8}[/tex]

Step-by-step explanation:

[tex]=\frac{5}{2} +\frac{21}{8}[/tex]

[tex]=\frac{40+42}{16}[/tex]

[tex]=\frac{82}{16}[/tex]

[tex]=\frac{41}{8}[/tex]

[tex]=5\frac{1}{8}[/tex]

Hope this helps

Given the following equation:

Let's determine t at S = 9.

We get,

a = 1, b = -15 and c = 50

Apply the quadratic formula:

Therefore, the earliest month will be either the 5th or 10th month.

Among the given choices, only the 10th month is in the choices.

Therefore, the answer is CHOICE B : 10th

Answer:

Step-by-step explanation:

Find 5% of $79:

Answer:

Abdul must pay $ 3.95.

Step-by-step explanation:

Now we have to,

→ find the amount of tax he must pay.

Then the amount will be,

→ (79/100) × 5

→ 0.79 × 5 = $ 3.95

Hence, he must pay $ 3.95.

We will establish simple proportions. If [tex]16[/tex] miles takes [tex]20[/tex] minutes, how many minutes for [tex]12[/tex] miles?

That makes [tex]12[/tex] miles in [tex]15[/tex] minutes.

Answer:

B

Step-by-step explanation:

Fraction subtraction:

 [tex]\sf 6 \dfrac{3}{5}-(-2\dfrac{1}{5})=6\dfrac{3}{5}+2\dfrac{1}{5}[/tex]

Convert mixed fraction to improper fraction,

                    [tex]\sf = \dfrac{33}{5}+\dfrac{11}{5}[/tex]

Now, add.

                  [tex]\sf = \dfrac{33+11}{5}\\\\=\dfrac{44}{5}[/tex]

Covert improper fraction to mixed fraction.

                  [tex]\sf = 8\dfrac{4}{5}[/tex]

Answer: 2x^2 + 6x - 2

Step-by-step explanation:

4x - 3 - 2x^2 + 2x + 1 =

2x^2 + 6x - 2

Answer:C(x) = 2000+ 0.05 x

Step-by-step explanation: Cost (C) = fixed cost + (cost per pencil x number of pencils)

Since:

Fixed cost: $2000

Cost per pencil : $0.05

Replacing with the values given:

C(x) = 2000+ 0.05 x

Where x is the number of pencils manufactured.

Feel free to ask for more if needed or if you did not understand something.

The mystery number is y = 0.

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression. Numbers (constants), operations, variables, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Let's assume the mystery number to be y.

When we multiply it by 1, add 5, and finally subtract by 2 we obtain 3.

Using the statement we obtain the expression,

y × 1 + 5 - 2 = 3

y + 5 - 2 = 3

y + 3 = 3

Subtracting 3 from each side of the equation,

y + 3 - 3 = 3 - 3

y = 0

Hence the mystery number is 0.

Learn more about expression here:

brainly.com/question/1859113

#SPJ1

The simplest form of the graph is 3x + 0y = 0

And the values of A and B are 3 and 0 respectively.

The point which is plotted in the graph : (3, 0)

Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). Additionally, when resolving systems of two linear equations, this form is highly helpful.

The given general form of equation is Ax+By+C= 0

So as in this graph it is clearly visible that:

A= 3 and B= 0

Thus we can write it as 3x + 0y = 0

To know more about linear equations visit:

https://brainly.com/question/27664510

#SPJ13

The measurement that does not represent the dimension of the triangle is 15, 30 and 45cm

The measurement that does represent the dimension of the triangle is 4, 8 and 10 cm.

Two triangles are similar if the ratio of the side lengths of the triangle are equal.

The ratio of the length of the triangles are 6 cm : 12 cm : 15 cm

Express the ratio in its simplest form - 2 cm : 4 cm : 5 cm

Ratio of 12, 24 cm and 30cm in its simplest form - 2 : 4 : 5

Ratio of 10, 20 and 25cm in its simplest form - 2 : 4 : 5

Ratio of 18, 36, 45cm in its simplest form - 2 : 4 : 5

Ratio of 15, 30 and 45cm in its simplest form - 1 : 2 : 3

Ratio of 4, 8 and 10 in its simplest form - 2 : 4 : 5

To learn more about similar triangles, please check: https://brainly.com/question/10658464

#SPJ1

Answer:

k = -2.

Step-by-step explanation:

By the Factor Theorem, if x - 1 is a factor then p(1) = 0.

So, p(1) = (1)^2 + 1  + k = 0

k = -1 - 1

k = -2.

Step-by-step explanation:

Make the facts and then you can get the answer easily

The value of the function as x increases comes closer to 6 and at limit x→∝ the value is 6.

In mathematics, a limit is the value that such a function (or sequence) gains as the input (or index) gets closer to a particular value.

Given the function is  [tex]f(x) = 6-\frac{1}{x-4}[/tex]

Now we put the limit to the function as [tex]lim_{x\rightarrow \infty} f(x)[/tex]

Therefore :

[tex]lim_{x\rightarrow \infty} (6-\frac{1}{x-4})\\=lim_{x\rightarrow \infty} 6 - lim_{x\rightarrow \infty}\frac{1}{x-4}\\=6 - 0\\=6[/tex]

Hence the value of the function is 6.

To learn more about function visit:

https://brainly.com/question/12431044s

#SPJ1

Mean = Sum of points/ number of points

Median

The difference in the temperatures of the town is -37.4 degrees Fahrenheit.

The difference between two values refers to the result of a subtraction operation.

A subtraction operation has the following parts: minuend, subtrahend, and difference.

In this situation, the minuend is 26.2F while the subtrahend is -11.2F.

Thus, the difference results from subtracting -11.2F from 26.2F, which is -37.4F, showing that the temperature is reduced by -37.4F to reach -11.2F during the night.

Learn more about subtraction operation at https://brainly.com/question/28467694

#SPJ1

Answer:

Yes

Step-by-step explanation:

Because a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

Answer:

There could have been 5, 10, or 20 students at the party.If there were 5, each student got 4 cookies and 8 slices of pizza if there were 10, each student got 2 cookies and 4 slices of pizza if there were 20, each student got 1 cookie and 2 slices of pizza

Answer:

There is not sufficient evidence to support the conclusion that senators are average younger than 60.35

Step-by-step explanation:

Given a simple random sample, the size is 40 senators.

Since the relevant statistic is the sample mean, 60.35 years.

Calculate t as:

*Significance level is 0.05.

Area of 0.05, one-tail yields t=1.685.

Since t=4.82 does not fall in the critical region bounded, we fail to reject the null hypothesis.

There is not sufficient evidence to support the conclusion that senators are average younger than 60.35

Answer:

-32

Step-by-step explanation:

Answer:

-32

Step-by-step explanation:

45:3=15:3=5-37=-32

hope it helps

have a nice night with apples))

(tan x + cot x) sin x * cos x is 1

(tan x + cot x) sin x * cos x

= (tan x + 1 / tan x) sin x * cos x               because cot x = 1 / tan x

= (((tan x) ^2 + 1) / tan x) sin x * cos x             because (tan x) ^2 +1= (sec x) ^2

= (sin x / cos x) tan x

= tan x / tan x

= 1

The error interval of the area a of the shaded region

What is Error Interval?

Error intervals are the limits of accuracy when a number has been rounded or truncated. They are the range of possible values that a number could have been before it was rounded or truncated.

Given,

Area of the circle  = 67.1cm²

Area of the square  = 12.3cm²

According to the question:

The formula for the area of the shaded

region on the diagram is:

Area of the circle - Area of the square

Putting the value of Area of circle and Area of square

= 67.1cm² - 12.3cm²

= 54.8cm²

The Error interval of area a = 54.8 + 0.5   and 54.8 - 0.5

                                             = 54.85        and 54.75

Hence, Area of shaded region is 54.85< a < 54.75        

To learn more about Error Interval click on the link    

https://brainly.com/question/16744494

#SPJ9                          

The average length by which finger nails will grow in 12 months will be 60mm, considering that they grow by an average of 5mm every month.

As per the question statement, there is no information provided about the average monthly growth of fingernails, and we required to calculate the average length by which finger nails will grow in 12 months.
To solve this question, we assumed that, the fingernails grow by an average of 5mm every month.

Now, using the unitary method, we can form a series of Mathematical statements to solve this question, which goes as follows:

If the average monthly growth of fingernails is 5mm,

It means that, fingernails grow in 1 month, by an average of 5mm.

Therefore, they will grow in 12 months, by an average of (5 * 12) = 60mm.

To learn more about Average, click on the link below.

https://brainly.com/question/23857503

#SPJ1

1) Judging by the picture, which resembles a construction done with a compass with the same distance, therefore we can tell a regular polygon.

2) We can also trace some line segments then we'll have a:

Using linear regression, the function that best fits the data in the scatter-plot is given by:

f(x) = 1/2x + 1.

To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the context of the problem.

The scatter-plot in this problem contains these following points:

(-16, -7), (-9, -5), (-3, -3), (1, 2), (5, 4), (8, 3) and (14,6).

Inserting these points into a calculator, the equation is given by:

f(x) = 0.46835x + 1.

Approximating the slope to 1/2 considering the given options, the function is given by:

f(x) = 1/2x + 1.

More can be learned about linear regression at https://brainly.com/question/22992800

#SPJ1

Number of bags= 16

Bag weight= 1.8 pounds

Then, number of pounds is

= 16x 1.8 = 28.8 pounds of cherries