Answers
Answer:
[tex]Question 1\\1+i\\-1-i\\Question 2\\\\-1+i\\1-i[/tex]
Step-by-step explanation:
Complex Numbers:
Complex numbers can generally be expressed in the form: [tex]a+bi[/tex] where a and b are both real numbers, with the a part representing the real part of the complex number, and the bi representing the imaginary part.
We can also graph these numbers using the complex plane. The complex plane has the real axis where the x-axis would normally be, and the imaginary axis where the y-axis would normally be. So by this definition the "a" is what determines the horizontal position or the position on the real axis and the "b" is what determines the vertical position or the position on the imaginary axis.
I attached a diagram of the complex plane, and it's essentially the same as a normal graph, with a=x, and b=y.
Question 1:
So when a complex number lies above the real-axis, that means the imaginary part is greater than 0. When a complex numbers lies to the right of the imaginary axis, that means the real part is greater than 0.
This means we have the form: [tex]a+bi \text { where } a > 0 \text{ and } b > 0[/tex]. You can literally plug in any number for a and b, so long as it fits this. For example we can just do: [tex]1+i[/tex]
So when a complex number lies below the real-axis, that means the imaginary part is less than 0. when a complex numbers lies to the left of the imaginary axis, the real part is less than 0.
This means we have the form: [tex]a+bi \text { where } a < 0\text{ and }b < 0[/tex]. You can plug in any real number that lies within this restriction. An example would be:
[tex]-1-i[/tex]
Question 2:
Above real axis and to the left of the imaginary axis means: b>0 and a<0. So we can plug in any number into the standard form that fits this restriction. an example would be: [tex]-1+i[/tex]
Below real axis and to the right of the imaginary axis means: b<0 and a>0. So we can plug in any number into the standard form that fits this restriction. An example would be: [tex]1-i[/tex]
Related Questions
determine what type of model best fits the given situation: An Internet phone company presently provides service to 5,000 customers at a monthly rate of $20 per month. After a market survey, it was determined that for each $1 decrease in the monthly rate an increase of 500 new customers would result.
A. none of these
B. quadratic
C. linear
D. exponential
Answers
The option c is correct. The linear representation model is best for this situation out of the exponential, quadratic model.
According to the statement
we have given that:
Monthly Rate = $20, Number of customers = 5000
If there is a decrease of $1 in the monthly rate, the number of customers increase by 500.
And we have to find that The type of model that best fits the given situation.
So, according to the linear representation model
Monthly Rate = $20, Number of customers = 5000
Let us decrease the monthly rate by $1.
Monthly Rate = $20 - $1 = $19, Number of customers = 5000 + 500 = 5500
Let us decrease the monthly rate by $1 more.
Monthly Rate = $19 - $1 = $18, Number of customers = 5500 + 500 = 6000
Here, we can see that there is a linear change in the number of customers whenever there is decrease in the monthly rate.
We have 2 pair of values here,
x = 20, y = 5000
x = 19, y = 5500
Let us write the equation in slope intercept form:
y = mx + c
And Slope of a function is
m = y₂ - y₁ / x₂ - x₁
Then
m = 5500 - 5000 / 19 - 20
m = -500
So, the equation become
y = -500x +c
And find the value of by putting the values.
So, c = 15000
And the equation become
y = -500x + 15000.
According to this linear model is perfect for this situation.
So, The linear representation model is best for this situation.
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Find the output, y, when the input, x, is -5.
Answers
The output, y, when the input, x, is -5 is -2
How to determine the value of the output y?The input is given as:
-5
This means that
x = -5
This is so because x represents the input
From the graph, we have the following highlight
The line of the graph passes through the point x = -5
On the graph;
When x = -5, the value of y is -2
This means that the output, y, when the input, x, is -5 is -2
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Nuber 17 pls (question on quadratics)
Answers
Considering the equation of the parabola, the coefficients are given as follows: p = 5, q = -20, r = 19.
The graph is the one given at the side of the question.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
In this problem, the turning point is (2,-1), hence h = 2, k = -1, and the equation has the following format:
y = a(x - 2)² - 1
The curve passes through (3,4), that is, when x = 3, y = 4, and we use it to find a.
y = a(x - 2)² - 1
4 = a(3 - 2)² - 1
a = 5.
Hence the equation is:
y = 5(x - 2)² - 1
Placing it into standard form, we have that:
y = 5(x² - 4x + 4) - 1
y = 5x² - 20x + 19
Hence the coefficients are:
p = 5, q = -20, r = 19.
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please help me, i will give brainliest!! help me please
Answers
The answers are :
10) 25 : 24
11) 24 : 5
12) 36 : 5
13) 7 : 3
14) 15 : 1
Ratio = Number of event 1 : Number of event 2 (in same unit, if necessary)
10
Girls preferring orange juice : Boys preferring orange juice
50 : 48 (Divide by 2 on both sides)
25 : 24
11
Boys preferring orange juice : Boys preferring grapefruit juice
48 : 10 (Divide by 2 on both sides)
24 : 5
Remember :
1 minute = 60 seconds1 week = 7 days1 hour = 60 minutes12
3 minutes : 25 seconds
3 × 60 : 25 (Divide by 5 on both sides)
3 × 12 : 5
36 : 5
13
2 weeks : 6 days
2 × 7 : 6 (Divide by 2 on both sides)
7 : 3
14
5 hours : 20 minutes
5 × 60 : 20 (Divide by 20 on both sides)
5 × 3 : 1
15 : 1
john is constructing a satellite dish . The receiver is going to be located 15 inches above the vertex of the dish. The dish is going to be 84 inches wide. How deep will the dish be
Answers
The depth of the 84 inches wide satellite dish that has the receiver located 15 inches above the vertex is 29.4 inches.
How can the equations of a parabola be used to find the depth of the dish?The location of the receiver = 15 inches above the vertex
Width of the dish = 84 inches
The receiver of a satellite dish is normally located at the focus (focal point).
Taking the shape of the satellite dish as a parabola, and writing the equation of the parabola as x² = 4•a•y, we have;
Coordinates of the focus = (0, a)
Where;
a = The distance of the focus above the vertex
Therefore;
a = 15 inches
The dish is horizontally spaced equally about the vertex.
The farthest point horizontally from the vertex, X, of the dish corresponds to the furthest vertically from the vertex, which is the maximum depth or height, Y.
At the maximum height, from the vertex, Y, (farthest point, vertically from the vertex), we have;
X = 84 ÷ 2 = 42
Which gives;
42² = 4 × 15 × Y
Y = 42² ÷ (4 × 15) = 29.4
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Into how many equal parts can the same cake be cut if the cuts can only be made along the gridlines? cake can be cut into equal parts.
Answers
Into how many equal parts can the same cake be cut if the cuts can only be made along the gridlines, cake can be cut into 20 equal parts.
This is further explained below.
What are gridlines?Generally, In spreadsheet software, gridlines are the light gray lines that divide the cells, rows, and columns. Gridlines are often used to maintain track of data. Gridlines are widely used in popular spreadsheet programs like Spreadsheet.
In conclusion, If the cuts can only be done along the gridlines, the cake may be divided into 20 equal pieces when cutting along the lines.
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If a sum of money amounts to Rs. 2175 in 3 years and to Rs. 2625 in 5 years.Find the rate of interestsl
Answers
The rate of interest applied on the amount is 15%.
According to the statement
we have given that the sum of money amounts to Rs. 2175 in 3 years and to Rs. 2625 in 5 years.
And we have to find the rate of interest on this money.
So, For this purpose,
The given equation is:
Money in 3 years = 2175
Money in 5 years = 2625
Amount increased in 2 years = 2625-2175
Amount increased in 2 years = 450
And amount increased per year = 450/2
Amount increased per year = 225.
SI in 3 years=450/2 *3=Rs. 675
Principal amount= 2175-675=1500
so again,
R=(I*100)/(P*T)
R=15%
So, The rate of interest applied on the amount is 15%.
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1)Find the L.C.Mof the following set of numbers by prime factorization method:
a)6 and 9
b)16 and 24
c)24,48 and 64
2)Find L.C.M of the following set of numbers by division method:
a)6 and 15
b)25,30 and 75
Note: Answer must have proper explanation
Answers
Answer:
a) 18
b) 48
c) 192
a) 30
b) 150
Step-by-step explanation:
Answer:
1
a ) 18
b ) 48
c ) 144
2
a ) 30
b ) 150..
[tex]...[/tex]
Hey so I’m stuck on this. What is the solution to the equation 2= -8 -x?
Answers
Answer:
X = -10
Step-by-step explanation:
2 = -8 -X
2+X = -8
X = -10
Answer:
x = - 10
Step-by-step explanation:
Comment
The trick to any equation like this one is to get the numbers on one side and the term with an unknown on the other side. That way, your last step is to divide by the number in front of the letter into a number on the other side.
Solution
2 = - 8 - x Add 8 to both sides
2 + 8 = -8 + 8 - x Combine
10 = - x The number in front of x is - 1. Divide.
10/-1 = -x/-1
-10 =x
The letter usually has to be expressed as a number greater than 0. In other words x is positive for this question
In regression, the difference between the confidence interval and prediction interval formulas is ________
Answers
In regression, the difference between the confidence interval and the prediction interval formula is "The addition of 1 to the quantity under the radical sign i.e., standard error".
What are the formulas for the confidence interval and prediction interval?
The formula for the confidence interval is
[tex]y_h[/tex] ± [tex]t_{(1-\alpha /2,n-2)[/tex] × √(MSE([tex]\frac{1}{n}[/tex] + ([tex]x_h[/tex] - μ)²/∑([tex]x_i[/tex] - μ)²))
The formula for prediction interval is
Prediction interval = Sample estimate ± (t multiplier × standard error)
[tex]y_{new}[/tex] = [tex]y_h[/tex] ± [tex]t_{(1-\alpha /2,n-2)[/tex] × √(MSE(1 + [tex]\frac{1}{n}[/tex] + ([tex]x_h[/tex] - μ)²/∑([tex]x_i[/tex] - μ)²))
Where μ = x bar.
What is the difference between the confidence interval and the prediction interval?From the above, the prediction interval has one additional MSE term in the standard error calculation. But in the confidence interval, only one term is used.
So, the difference between them occurs in the standard error value.
The formula shows it by adding 1 to the quantity under the radical sign.
Thus, the difference is in the standard error.
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Puedes colorear el 20% del triangulo? Aqui tienes una pista
Answers
Find the area of quadrilateral abcd. [hint: the diagonal divides the quadrilateral into two triangles.]
Answers
The area of quadrilateral ABCD exists equivalent to the area of triangle ABD plus the area of triangle ADC
Heron's Formula exists a technique for estimating the area of a triangle when you know the lengths of all three sides.
Therefore, the total area of quadrilateral abcd exists 28.53 [tex]$$units^2[/tex].
How to find the area of quadrilateral abcd?Let a, b, and c be the lengths of the sides of a triangle.
The area is given by:
[tex]$$A = \sqrt{p(p-a)(p-b)(p-c)}[/tex]
where p exists half the perimeter
[tex]$p = \frac{a+b+c}{2}[/tex]
To estimate the area of triangle ABD
we have
a = AB = 2.89 units
b = BD = 8.59 units
c = DA = 8.6 units
To estimate the perimeter
[tex]$p = \frac{2.89+8.59+8.6}{2}[/tex]
= 10.4 units
To estimate the area
[tex]$A = \sqrt{10.04(10.04-2.89)(10.04-8.59)(10.04-8.6)}[/tex]
[tex]$A = \sqrt{10.04(7.15)(1.45)(1.44)}[/tex]
[tex]$A = \sqrt{149.89}[/tex]
A = 12.24 [tex]$$units^2[/tex]
To estimate the area of the triangle ADC
we have
a = AC = 4.3 units
b = AD = 8.6 units
c = DC = 7.58 units
To estimate the half perimeter p
[tex]$p = \frac{4.3+8.6+7.58}{2}[/tex]
= 10.24 units
To estimate the area
[tex]$A = \sqrt{10.24(10.24-4.3)(10.24-8.6)(10.24-7.58)}[/tex]
[tex]$A = \sqrt{10.24(5.94)(1.64)(2.66)}[/tex]
[tex]$A = \sqrt{265.35}[/tex]
A = 16.29 [tex]$$units^2[/tex]
To estimate the total area
A = 12.24+16.29 = 28.53 [tex]$$units^2[/tex].
Therefore, the total area of quadrilateral abcd exists 28.53 [tex]$$units^2[/tex].
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Simplify[tex](\frac{16}{81}x^{16}\right))^{\frac{1}{2}}[/tex]
Answers
Answer:
[tex]\sf \dfrac{4}{9}x^8[/tex]
Step-by-step explanation:
Law of exponents:[tex]\sf (a*b)^m = a^m *b^m\\\\(a^m)^n =a^{m*n}[/tex]
16 = 4 *4 = 4²
81 = 9 *9 = 9²
[tex]\sf\left (\dfrac{16}{81}x^{16}\right)^{\frac{1}{2}}= \left(\dfrac{4^2}{9^2}x^{16}\right)^{\frac{1}{2}}[/tex]
[tex]\sf =\dfrac{4^{2*\frac{1}{2}}}{9^{2*\frac{1}{2}}}*x^{16*\frac{1}{2}}\\\\=\dfrac{4}{9}x^8[/tex]
question down below about linear equations and grapghing.
Answers
The system of equations is -x + y = 4 and -2x + y = 0
How to create the system of linear equations?To do this, we make use of the following ordered pairs
(4, 8)
The above point represents April 2008.
Let the system of equations be
mx + ny = 4
2mx + ny = 0
Substitute (4, 8) for x and y in the above equations.
4m + 8n = 4
8m + 8n = 0
Subtract both equations
4m - 8m = 4
This gives
-4m = 4
Divide by 4
m = -1
Substitute m = -1 in 8m + 8n = 0
-8 + 8n = 0
This gives
8n = 8
Divide by 8
n = 1
So, the system of equations is -x + y = 4 and -2x + y = 0
The graph of the system of equationsThe system of equations is -x + y = 4 and -2x + y = 0
See attachment for the graph of the system of equation
Prove that the solution is (4, 8)The above is represented in the (a) part of this solution
Verify that the solution is (4, 8)
We have:
-x + y = 4 and -2x + y = 0
Substitute (4, 8) for x and y in the above equations.
-4 + 8 = 4 --- true
-2*4 + 8 = 0 --- true
Both equations are true
Hence, the system of equations have been verified
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What are the restricted values for x2−3x−2−4y⋅2x−2−xy2+2y2?
Answers
The restricted values in (x^2 - 3x - 2)/-4y * (2x - 2)/(-xy^2 + 2y^2) are x ≠2 and y ≠ 0
How to determine the restricted values for the function?The complete question is added as an attachment
The equation is given as:
(x^2 - 3x - 2)/-4y * (2x - 2)/(-xy^2 + 2y^2)
Set the products of the denominators to 0
-4y * (-xy^2 + 2y^2) = 0
Split the equation
-4y = 0 or (-xy^2 + 2y^2) = 0
Remove the bracket
-4y = 0 or -xy^2 + 2y^2 = 0
Divide both sides by -4 in -4y = 0
y = 0
Factor out y^2 in -xy^2 + 2y^2 = 0
y^2(-x + 2) = 0
This means that y^2 = 0 or -x + 2= 0
This gives y = 0 or -x + 2 = 0
Solve for x in -x + 2 = 0
x = 2
Hence, the restricted values in (x^2 - 3x - 2)/-4y * (2x - 2)/(-xy^2 + 2y^2) are x ≠2 and y ≠ 0
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B
23. Find the EXACT circumference of the circle
if AB = 2in and BC = 11in.
A
C
a. √117 in
b.
5√5π in
c.
35.1 in
d. 5√5 in
Answers
Answer:
C. 35.1
Step-by-step explanation:
First get the length of AC by using the Pythagorean Theorem, that ends up being about 11.18. Then you need to get the radius of the circle so you divide 11.18 by 2 and get 5.59. Then plug 5.59 for r into 2(pi)(r). 2(pi)(5.59) = 5.123
Answer:
Answer B is correct
Step-by-step explanation:
First, let us find the diameter (AC) of the circle using the Phythogerem theorem.
AC² = AB² + BC²
AC² = 2² + 11²
AC² = 4 + 121
AC² = 125
AC = √ 125
AC = 5√5
And now let us find the circumference of the circle.
C = π × d
C = π × 5√5
C = 5√5π in
A friend of mine believes that the average GPA at KSU is equal to 3.0. In order to test whether he/she is right, I collect some information from the data. Specifically, I use 100 KSU students to form a sample and find that their sample average GPA is equal to 3.3. In addition, suppose that I also know the population standard deviation of GPA at KSU is 1.5. I decide to use 0.05 as the level of significance for my hypothesis testing. Could you help me with Q1-Q10 below? Q1: What should be my null hypothesis? What should be my alternative hypothesis? Q2: Is this a lower-tailed, upper-tailed or two-tailed case? Q3: Show me how to calculate my test statistic.
Q4: If I use the critical value approach, explain how to derive my critical value(s). Q5: If I use the p-value approach, explain how to derive my p-value. Q6: If I use the confidence interval approach, show me how to derive the confidence interval. Q7: How to make my decision, if I use the critical value approach? Q8: How to make my decision, if I use the p-value approach? Q9: How to make my decision, if I use the confidence interval approach? Q10: Are the decisions in Q7, Q8, and Q9 the same?
Answers
The solution of the questions is given as
a)
The alternative hypothesis is that mu is equal to 3.0. ( the average GPA at KSU is not equal to 3.0)
b)
This is a case with two separate arguments. (This is a two-tailed case)
c)
Test Statistic is given by:
z= 2.00
d)
Critical values of Z come from the table and equal [tex]\pm[/tex]1.96.
e)
, p-value = 0.0455
f)
CI= (3.006, 3.594)
g)
Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.
h)
Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.
i) Conclusion: The evidence does not lend credence to the assertion that KSU's typical grade point average is equivalent to 3.0.
j)
The choices you choose in Questions 7, 8, and 9 are identical.
What is the null hypothesis?a)
The null hypothesis states that mu equals 3.0. ( the average GPA at KSU is equal to 3.0) (Claim)
The alternative hypothesis is that mu is equal to 3.0. ( the average GPA at KSU is not equal to 3.0)
b)
This is a case with two separate arguments.
c)
Test Statistic is given by:
[tex]z=\frac{\barx-u^0}{σ/Vn}\\\\z=33 - 3.0/1.5/V100[/tex]
z= 2.00
d)
[tex]\alpha = 0.05[/tex]
Critical values of Z come from the table and equal [tex]\pm[/tex]1.96.
e)
Z Score = 2.00
reading from table, p-value = 0.0455
f)
Confidence Interval:
[tex]CI= \barx \pm \frac{ZX\sigma }{\sqrt((n)}[/tex]
[tex]CI =3.3 \pm 1.96 x 1.5 / \sqrt{100}[/tex]
CI= (3.006, 3.594)
g)
The disparity is noteworthy given that the computed value of Z = 2.00 is higher than the crucial value of z = 1.96. Cast doubt on the null hypothesis.
Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.
h)
The difference may be considered statistically significant since the p-value of 0.0455 is lower than the alpha threshold of 0.05. Cast doubt on the null hypothesis.
Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.
i)
The difference is statistically significant since the value of 3.0 is not included in the confidence range (3.006 - 3.594). Cast doubt on the null hypothesis.
Conclusion: The evidence does not lend credence to the assertion that KSU's typical grade point average is equivalent to 3.0.
j)
The choices you choose in Questions 7, 8, and 9 are identical.
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Hazing has been reported all across america. What percentage of students say they have witnessed hazing and did not report it?.
Answers
percentage of students say they have witnessed hazing and did not report it are = 95%
What is Hazing?No matter how voluntarily a person is to take part, hazing, initiation or deposition are all actions that are demanded of someone when they join or participate in a group and which humiliate, degrade, abuse, or imperil them.
involves humiliating a person or group. involves making fun of someone or something. involves or includes the deliberate destruction of or removal of private or public property for the purpose of affiliation with, initiation into, or as a requirement for continuing membership in an organization.
What is an example of hazing?Paddling, beating, or other types of attack. Branding. consumption of disgusting substances or mixtures under duress or force.
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construct a quadrilateral
AB=6cm , BC = 5cm, AD = 4CM CD =7cm and BD = 6cm
Answers
If a quadrilateral exists as a parallelogram, then opposite sides exist congruent and parallel.
What is quadrilateral?
If a quadrilateral exists as a parallelogram, then opposite sides exist congruent and parallel.
Given: AB = 6cm , BC = 5cm, AD = 4cm, CD = 7cm and BD = 6cm
Draw a line AB with 6cm with A as the center draw an arc of radius 4 cm. And draw another arc of 6cm to cut the previous arc at D with B as the center draw an arc of radius 5cm. And with D draw another arc of 7cm to cut the previous arc at C. Join the lines of the quadrilateral.
Now ABCD exists as a required quadrilateral.
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Find the equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0).
Answers
The equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and
r(1, 1, 0) is x + y + z = 2 .
According to the question
Let the points
p(0, 1, 1) = (x1,y1,z1)
q(1, 0, 1)= (x2,y2,z2)
r(1, 1, 0)= (x3,y3,z3)
now,
The equation of the plane through the points
i.e
The formula of equation of a plane passing through three non collinear points
[tex]\left[\begin{array}{ccc}x-x1&y-y1&z-z1\\x2-x1&y2-y1&z2-z1\\x3-x1&y3-y1&z3-z1\end{array}\right] = 0[/tex]
by substituting the values in the formula of equation of a plane
[tex]\left[\begin{array}{ccc}x-0&y-1&z-1\\1-0&0-1&1-1\\1-0&1-1&0-1\end{array}\right] = 0[/tex]
[tex]\left[\begin{array}{ccc}x&y-1&z-1\\1&-1&0\\1&0&-1\end{array}\right] = 0[/tex]
x(1) - (y-1)(-1) + (z-1)(1) = 0
x + y - 1 + z - 1 = 0
x + y + z = 2
Hence, the equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2 .
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(50 POINTS PLEASE HELP!!!)
!!!THE QUESTION THAT I NEED TO BE ANSWERED IS THE PICTURE ATTACHED!!! BELOW IS JUST THE REQUIREMENTS AND EXAMPLE!!!
He has hired you as their new production manager. Your job is to look at four different figures and determine which would best suit the needs of the company for packaging the candy. You will choose one of the four options shown below. The candy is animal gummies. The package must hold between 80 and 100 cubic inches (roughly 5-7 cups of space). The cost of the plastic for the packaging is $0.004 per square inch. When finding cost you would multiply the Total Surface Area by $0.004.
For example:
Total Surface Area = 86 sq. in
Cost per sq in = $0.004
86 * .004 = .344 when rounded to nearest penny = $0.34
Your project should include the volume, total surface area, and materials cost for each figure given below, including the formulas you used and each step of your work. Be sure to find all measures for each figure, even if the figure does not meet the restraints that the company has given. Make sure to use the formulas given in your lessons, round your volume and area to the nearest hundredth, and round your cost to the nearest penny.
Answers
The figure in the question is a box with dimensions of 6 in. by 2 in. by 9 in., which gives;
Surface area of the packaging = 168 in.²Package volume = 108 in.³Cost of packaging = $0.672Which method can be used to provide the packaging estimates for the company?The dimensions of the box in the given figure are;
Length, L = 9 in.
Width, W = 2 in.
Height, H = 6 in.
The surface area, A, of a box is found using the following formula;
A = 2•L•W + 2•L•H + 2•H•W
Therefore;
A = 2×9×2 + 2×9×6 + 2×2×6 = 168
The surface area of the figure, A = 168 in.²The volume of a box, V, is calculated as follows;
V = L•W•HFor the given figure, therefore;
V = 9 × 2 × 6 = 108
The volume of the given figure, V = 108 in.³Cost of packaging per square inch, c = $0.004
Cost to package the figure, C, is therefore;
C = c × AWhich gives;
C = $0.004/in.² × 168 in.² = $0.672
Packaging cost, C = $0.672Learn more about working with formulas in mathematics here:
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find the surface area of composite figure. use 3.14 for π. round to the nearest tenth
Answers
Combining of the two cylinders gives a composite figure that has the surface area of a solid cylinder of radius 7 mm and height 6 mm, such that the surface area of the figure is approximately 571.5 mm².
Which method can be used to find the surface area of the figure?Radius of the inner cylinder, r = 3 mm
Radius of the outer cylinder, R = 7 mm
Height of the cylinders, h = 6 mm
Given that the inner cylinder exactly fits into the outer cylinder, we have;
The surface area of the composite figure is the surface area of the hollow outer cylinder + The area of the top and bottom of the inner cylinder.
Which gives;
The surface area of the composite figure, A, is the surface area of a solid cylinder, using the dimensions of the hollow outer cylinder.
A = 2•π•R² + 2•π•R•hWhich gives;
A = 2 × π × 7² + 2 × π × 7 × 6Where, π = 3.14, we have;
A = 2 × 3.14 × 7² + 2 × 3.14 × 7 × 6 ≈ 571.5
The surface area of the composite figure, A ≈ 571.5 mm²Learn more about the analyzing of composite figures here:
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The sum of three numbers is 134. The second number is 8 less than the first. The third number is 4 times the second. What are the numbers?
Answers
Answer:
29, 21, 84
Step-by-step explanation:
Let the first number be x.
The second number is x - 8.
The third number is 4(x - 8).
Their sum is 134.
x + (x - 8) + 4(x - 8) = 134
x + 5(x - 8) = 134
x + 5x - 40 = 134
6x = 174
x = 29
x - 8 = 29 - 8 = 21
4(x - 8) = 4(29 - 8) = 4(21) = 84
Which line does a better job capturing the trend of the data? Explain.
10
•
Graph A
10
10
00
6
-
2
O
●
N
●
4
20
●
Graph B
9
Answers
Answer:
B
Step-by-step explanation:
Line A mostly follows the trend of the higher points, entirely neglecting the existence of the lower points. Line b acknowledges the lower points and adjusts the line accordingly to be lower.
Find the most general antiderivative of the function. (check your answer by differentiation. use c for the constant of the antiderivative. ) f(x) = x(18x 4)
Answers
Answer:
Below in bold.
Step-by-step explanation:
f(x) = x(18x + 4)
f(x) = 18x^2 + 4x
Antiderivative = 18 * (x^2+1)/(2 + 1) -+4x(1+1) / (1+1) + C
= 18x^3 / 3 + 4x^2 / 2 + C
= 6x^3 + 2x^2 + C.
Checking by differentiating:
f'(x) = 6*3 x^(3-1) + 2*2x^(2-1)
= 18x^2 + 4x
= x(18 -+4)
Can someone help pls
Answers
Answer:
x = 0, x = 5
Step-by-step explanation:
x² - 5x = 0 ← factor out x from each term
x(x - 5) = 0
equate each factor to zero and solve for x
x = 0
x - 5 = 0 ⇒ x = 5
In 15 minutes Frankita created 15 drawings. In 30 minutes she created 17 drawings. In 45 minutes she created 20 drawings. In 60 minutes she created 24 drawings. If Frankita continues making drawings in the same pattern, how many total drawings will Frankita have created at the end of 90 minutes?
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In 90 minutes, she would have created 36 drawings.
How many total drawings will Frankita have created at the end of 90 minutes?The first step is to establish a pattern between time and the number of drawing that Frankita creates.
When the question is studied, it can be deduced that every 15 minutes the rate of increase in drawing is (previous drawing + (1 + rate of increase of previous drawing.
Drawing created in 30 minutes = 15 + 2 = 17
Drawing created in 45 minutes = 17 + ( 1 + 2) = 20
Drawing created in 60 minutes = 20 + (3 + 1 ) = 24
Drawing created in 75 minutes = 24 + (4 + 1) = 30
Drawing created in 90 minutes = 30 + (5 + 1) = 36
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The figure shows a square, a regular pentagon and a regular hexagon put together. What is the measure of ∠BAC
Answers
Answer:
42
Step-by-step explanation:
One angle of a regular pentagon = 108°
One angle of a regular hexagon = 120°.
One angle of a square = 90°
∴ ∠BAC = 360 – (108 + 20 + 90) 360 – 318 = 42°
This question is down below.
Answers
Answer:
Step-by-step explanation:
15 hope it help
Find the surface area of the composite figure.
4 cm
13 cm
3 cm
4 cm
SA =
12 cm
[?] cm²
5 cm
3 cm
Answers
With the help of the area formulae of rectangles and triangles and the concept of surface area, the surface area of the composite figure is equal to 276 square centimeters.
What is the surface area of a truncated prism?
The surface area of the truncated prism is the sum of the areas of its six faces, which are combinations of the areas of rectangles and right triangles. Then, we proceed to determine the surface area:
A = (12 cm) · (4 cm) + 2 · (3 cm) · (4 cm) + 2 · (12 cm) · (3 cm) + 2 · 0.5 · (12 cm) · (5 cm) + (5 cm) · (4 cm) + (13 cm) · (4 cm)
A = 48 cm² + 24 cm² + 72 cm² + 60 cm² + 20 cm² + 52 cm²
A = 276 cm²
With the help of the area formulae of rectangles and triangles and the concept of surface area, the surface area of the composite figure is equal to 276 square centimeters.
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