A calculus cheat sheet can be a helpful tool to assist you in studying and reviewing calculus concepts.
Here are some tips for how to use a calculus cheat sheet effectively:
1. Familiarize yourself with the content: Take the time to read through the entire cheat sheet to get a sense of what topics are covered and how the information is organized.
2. Use it as a study aid: A calculus cheat sheet can be a helpful study aid to review concepts and formulas before a test or exam. Work through practice problems and apply the concepts you have learned.
3. Keep it handy: Print out the cheat sheet or save it to your phone or computer so that you can refer to it whenever you need to.
4. Use it as a reference: As you work on calculus problems, use the cheat sheet to remind yourself of key concepts, formulas, and rules.
5. Customize it: You can create your own cheat sheet, which includes the formulas and concepts that you find most challenging. This will help you focus on the areas that you need to improve upon.
Remember that while a calculus cheat sheet can be a helpful tool, it is important to develop a deep understanding of calculus concepts through practice, problem-solving, and building intuition. The cheat sheet should be used as a supplement to your learning, not a replacement for it.
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Learn what an identity matrix is and about its role in matrix multiplication. ... How do you find the multiplicative inverse of a given matrix?
Answer:
See below
Step-by-step explanation:
[tex]I_1=[1],\, I_2=\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right],\,I_3=\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right],\,...[/tex] and so on are examples of identity matrices.
The multiplicative inverse of a 2x2 matrix is [tex]\displaystyle A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right][/tex] where ad-bc represents the determinant. Multiplying this with the original matrix will produce the identity matrix as described previously. Usually, you'll mostly deal with 2x2 matrices when it comes to this topic, but don't worry too much.
Show that the quadrilateral with the vertices $H(1,\ 9),\ J(4,\ 2),\ K(5,\ 2),\ L(8,\ 9)$H(1, 9), J(4, 2), K(5, 2), L(8, 9) is a trapezoid. Then decide whether it is isosceles.
The midpoints of the given quadrilateral, AB = CD and AD = BC, are equal.
What is meant by quadrilateral vertices?Vertices are the angular intersections of two sides or edges. The four vertices of a quadrilateral are A, B, C, and D. (iii)Angles. A quadrilateral's angle is the inclination between its two sides.A closed quadrilateral is a form of polygon with four sides, four vertices, and four angles. Four non-collinear points are joined to create it. Quadrilaterals' interior angles add up to a constant 360 degrees.A polygon's vertex is a point where the sides or edges of the object or two rays or line segments meet. Vertices is the plural of a vertex.Let P represent the quadrilateral's vertices (-4,2) Q (2,6): Let A, B, C, and D be the midpoints of P(-4,2) and Q. R(8,5) and S (9,-7) (2,6)
Consequently, A's coordinates are
[tex]$\left(\frac{-4+2}{2}, \frac{2+6}{2}\right)=\left(\frac{-2}{2}, \frac{8}{2}\right)=(-1,4)$[/tex]
Coordinates of B are
[tex]$\left(\frac{2+8}{2}, \frac{6+5}{2}\right)=\left(\frac{10}{2}, \frac{11}{2}\right)=\left(5, \frac{11}{2}\right)[/tex]
Coordinates of c are
[tex]$\left(\frac{8+9}{2}, \frac{5-7}{2}\right)=\left(\frac{17}{2}, \frac{-2}{2}\right)=\left(\frac{17}{2},-1\right)[/tex]
coordinates of D are [tex]$\left(\frac{9-4}{2}, \frac{7+2}{2}\right)=\left(\frac{5}{2}, \frac{-5}{2}\right)$[/tex]
Distance between A and B
[tex]$& d(A, B)=\sqrt{(-1-5)^2+\left(4-\frac{11}{2}\right)^2}=\sqrt{36+\frac{9}{4}}=\sqrt{\frac{153}{4}} \\[/tex]
Simplify,
[tex]$& d(C, D)=\sqrt{\left(\frac{17}{2}-\frac{5}{2}\right)^2+\left(-1+\frac{5}{2}\right)^2}=\sqrt{36+\frac{9}{4}}=\sqrt{\frac{153}{4}} \\[/tex]
Then,
[tex]$& d(A, D)=\sqrt{\left(-1-\frac{5}{2}\right)^2+\left(4+\frac{5}{2}\right)^2}=\sqrt{\frac{49}{4}+\frac{169}{4}}=\sqrt{\frac{218}{4}} \\[/tex]
We get,
[tex]$& d(B, C)=\sqrt{\left(5-\frac{17}{2}\right)^2+\left(\frac{11}{2}+1\right)^2}=\sqrt{\frac{49}{4}+\frac{169}{4}}=\sqrt{\frac{218}{4}}[/tex]
As a result, the given quadrilateral's midpoints, AB = CD and AD = BC, are equal.
It is a parallel gramme as a result.
The complete question is :
A quadrilateral has the vertices at the point (−4,2),(2,6),(8,5) and (9,−7). Show that the mid-point of the sides of this quadrilateral are the vertices of a parallelogram.
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Which statements are true about the median? Check all that apply.
1. Put the values in numerical order before trying to find the median.
2. Median is a number that is much lower or much higher than the rest of the numbers.
3. The median is always greatly impacted by outliers.
4. The median is the number in the middle of an ordered set of values.
5. The median must be calculated by finding the mean of the two middle points when
there is an even number of data points.
Determine the equation of the circle graphed below
The equation of the circle graphed is given as follows:
(x + 3)² + (y - 4)² = 41.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The center in this problem has the coordinates given as follows:
(-3,4).
Hence:
(x + 3)² + (y - 4)² = r².
x = -1 and y = 9 is a point on the circumference of the circle, hence the radius of the circle is obtained as follows:
r² = (-1 + 3)² + (9 - 4)²
r² = 41.
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Please help me I’ll give you the best rating nO lie Trust
The distance the cyclist travelled during the time are as follows;
4 meters, 18 m and 45 etc.
What is speed?Speed can be calculated as the ratio of distance traveled to the time taken
Distance = speed x time
Distance = 5 x 0.8
= 4 meters
Distance = 10 x 1.8
= 18 meters
Distance = 15 x 3
= 45 meters.
Here Segment shows as time is increasing, distance is also increasing. Which means the cyclist is moving forward at a speed.
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what is 3/4+1/2 answer
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{3}{4} + \dfrac{1}{2}}[/tex]
[tex]\mathsf{= \dfrac{3}{4} + \dfrac{1\times2}{2\times2}}[/tex]
[tex]\mathsf{= \dfrac{3}{4} + \dfrac{2}{4}}[/tex]
[tex]\mathsf{= \dfrac{3 + 2}{4 + 0}}[/tex]
[tex]\mathsf{= \dfrac{5}{4}}[/tex]
[tex]\mathsf{= 1 \dfrac{1}{4}}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{\dfrac{5}{4}\ or \ 1 \dfrac{1}{4}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Use the rules of equations and Inverse operations to solve the equation.
3x² = 48
04
0 +4
0 -4
0+2
Answer:
Below
Step-by-step explanation:
3 x^2 = 48 divide both sides of the equation by 3 to get
x^2 = 16 Now, sqrt both sides
x = + 4 or -4
The change in the number of students at a high school in Naples was the same from 2007 to 2013 as it was from 2013 to 2019.
Which type of function best models the data?
Answer: The type of function that best models the data would depend on the actual change in the number of students and the specific data points for each year. However, if the change in the number of students was the same for each time period, a linear function would be a good candidate for modeling the data. This function would have the form y = mx + b, where m represents the rate of change (the change in the number of students over a certain time period) and b is the y-intercept (the number of students at the starting year).
Step-by-step explanation:
Graph the angle -4pi/3 in standard position :)
The point (-0.5, 0.866) represents the angle -4pi/3 graphed on the unit circle.
What is the unit circle?For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].
The angle for this problem is given as follows:
-4pi/3.
Hence the sine and the cosine are given as follows:
sin(-4pi/3) = 0.866.cos(-4pi/3) = -0.5.Hence the point (-0.5, 0.866) represents the angle -4pi/3 graphed on the unit circle.
(the equation of the unit circle is x² + y² = 1).
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Write the word sentence as an inequality. Then solve the inequality.
225 is no less than 3/4 times a number w .
An inequality that represents this word sentence is.
The solution is
Answer:
Like the other solver, I believe they are correct because I arrived at the same solution:
3/4w <= 225
Multiplying both sides by 4/3 to isolate w:
w >= (225 * 4)/3
w >= 300
Solution is w >= 300. In order to meet the inequality, the value of w must be equal to or larger than 300.
Find two consecutive whole numbers that \sqrt(139) lies between.
Answer:
11 and 12
Step-by-step explanation:
11^2<139
but
12^2>139
therefore
it lies between 11 and 12
can you help me with this question
Answer:
No, Tony should have rounded up to 38.
Step-by-step explanation:
Tony solved the inequality correctly; however, he rounded incorrectly.
8c+200≥500
Subtract 200 from both sides
8c≥300
Divide each side by 8
c≥37.5
Tony cannot wash 37.5 cars, because in the context it is impossible to wash half of a car. We round the answer up because rounding down would give us a value less than $500 (the inequality is greater than or equal to).
Therefore, the answer is 38. Tony is incorrect.
Custom Castings, Inc. pays its employees on a piece-rate basis of $1.28 for each acceptable piece produced. What gross pay was earned by an employee whose production of 483 pieces included 9 pieces
that did not pass inspection?
Which one of these ordered pairs show a combination of 12 coins from the graph?
Which one of these ordered pairs show a combination of 12 coins from the graph?
(10, 2)
(5, 5)
(10, 5)
(10, 10)
The ordered pair that show a combination of 12 coins from the graph is (10, 2)
How to determine the ordered pairfrom the question, we have the following parameters that can be used in our computation:
The graph
The purple line represents the combination of 12 coine
Using the above as a guide, we have the following:
The equation is
x + y = 12
From the list of options, we have
(10, 2): 10 + 2 = 12
Hence, the ordered pair is (10, 2)
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Question Progress
Homework Progress
19/48 Marks
The circle shown has a radius of 4 cm.
Not drawn
to scale
What is the length of the diameter of the circle?
The length of the diameter of the circle is 8 cm.
What is Diameter?The diameter of a circle is the distance measured through its centre. The radius of a circle is the distance from the center to any point on the edge. The diameter is divided by the radius.
Given:
Radius = 4 cm
As, the radius is the point which starts from center and reach to point on the surface of the Circle.
and, the Diamter is the two times of the radius.
So, Diameter = 2 x radius
D= 2 x 4
diameter = 8 cm
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Assume that we have two events, A and B; that are mutually exclusive Assume further that we know P(A) = 0.30 and P(B) = 0.70. If an amount zero, enter "0". What is P(AnB)? What is P(AIB)? student in statistics argues that the concepts of mutually exclusive events and independent events are really the same_ and that if events are mutually exclusive they must be independent; Do You agree with this statement? Use the probability information in this problem to justify your answer. Select your answer because P(AIB) Select your answer P(A). What genera conclusion would You make about mutually exclusive and independent events given the results of this problem?
P(A∩B) = 0 (the probability of both events occurring is zero).
P(A|B) = 0.
No. The student's argument that mutually exclusive events are independent is incorrect.
How to find P(AnB) and P(AIB) of the event?If events A and B are mutually exclusive, then by definition they cannot occur at the same time.
Thus, P(A∩B) = 0 (the probability of both events occurring is zero).
Since events A and B are mutually exclusive, they cannot be independent. In fact, if two events are mutually exclusive, it means that the occurrence of one event precludes the occurrence of the other event, so they are completely dependent on each other.
To calculate P(A|B), we can use the formula:
P(A|B) = P(A∩B) / P(B)
Since P(A∩B) = 0 and P(B) = 0.70, we have:
P(A|B) = 0 / 0.70 = 0
This means that if we know event B has occurred (i.e., P(B) > 0), then the probability of event A occurring (i.e., P(A|B)) is zero. Therefore, events A and B are not independent.
The student's argument that mutually exclusive events are independent is incorrect. Mutually exclusive events are by definition dependent events.
In general, the concept of mutually exclusive events and the concept of independent events are not the same. Mutually exclusive events are dependent events, while independent events are events that do not depend on each other.
In this problem, the fact that events A and B are mutually exclusive means that they are dependent events, and this is reflected in the probability calculation for P(A|B), which is zero. Therefore, we can conclude that mutually exclusive events are not independent events.
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Independent Practice
Graph the following function. Then, write the domain and range.
f(x)=3*
*HINT: Make a table first
Based on the graph of this exponential function, the domain and range are as follows;
Domain = {-∞, ∞}.
Range = {0, ∞}.
What is a domain?In Mathematics, a domain is the set of all real numbers for which a particular function is defined.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-∞, ∞}.
Range = {0, ∞} or {y|y > 0}.
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please help
question 10!
The note Micah made for the test on right triangles is correct by the Pythagoras rule.
What is the Pythagoras rule?The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
so by Pythagoras rule we can write:
For the first right triangle;
(x/√2)² + (x/√2)² = x²...(1)
from the left hand side of equation (1): (x/√2)² + (x/√2)²
x²/2 + x²/2
2(x²)/2 = x² {the right hand side of equation (1)}
and for the second right triangle;
(x√3/2)² + (x/2)² = x²...(2)
from the left hand side of equation (2): (x√3/2)² + (x/2)²
x²(3)/4 + x²/4
3x²/4 + x²/4
(3x² + x²)/4
4x²/4 = x² {the right hand side of equation (2)}
Therefore by Pythagoras rule the note Micah made for the test on right triangles is correct
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A triangle has vertices on a coordinate grid at
J(-7,−7) K(−7,3) and L(−1,3)
What is the length, in units, of JK ?
The requried measure of length JK on the coordinate plane is 10 units.
The distance between two points on the coordinate plane can be evaluated by the distance formula as,
D = √((x₂ - x₁)^2 + (y₂ - y₁)²)
Here,
The coordinates of the two points J(-7, -7) and K(-7, 3) suggest that they lie on a vertical line, where the x-coordinate is constant (-7) and only the y-coordinate changes. The distance between these points is equal to the difference in their y-coordinates.
Therefore, the length of JK is,
JK = |y-coordinate of K - y-coordinate of J|
= |3 - (-7)| = |3 + 7| = 10
So, the length of JK is 10 units.
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Does someone mind helping me with this problem? Thanks!
By evaluating the linear equation we can see that the complete table is:
x| -4 -2 0 2 4
y| 17 13 9 5 1
How to compete the table?Here we have a linear function:
y = -2x + 9
And we want to complete the given table, to do so, we just need to evaluate the linear function in the given values of x.
if x = -2
y = -2*-2 + 9 = 4 + 9 = 13
if x = 0
y = -2*0 + 9 = 9
if x = 2
y = -2*2 + 9 = 5
if x = 4
y = -2*4 +9 = 1
Then the complete table is:
x| -4 -2 0 2 4
y| 17 13 9 5 1
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A standard volleyball court is in the shape of a rectangle. It has an area of 2100 square feet. If the length of the court is 22.4 feet, then what will be the height?
Answer: The height of the court is 93.75 feet.
Step-by-step explanation:
We know that the area of a rectangle is given by :-
Area = length x width/height (1)
Given : A standard-size volleyball court has an area of 2,100 square feet.
The length of the court is 22.4 feet.
To find : The width of the court.
According to (1) , we have
[tex]2100=22.4*height[/tex]
Then,
[tex]Height=\frac{2100}{22.4} =93.75[/tex]
Hence, the height of the court is 93.75 feet.
May i get some help Fast please
Mr. Fernandez deposits $60,000 into an account that pays 2.5% annual interest compounded quarterly. What will be the balance after 20 years? Round to the nearest cent
:Answer: $90000
i = prt (interest = principle x rate x time)
i = 60000 x 0.025 x 20
i = $30000 interest
b = p + i (balance = principle + interest)
b = 60000 + 30000
b = $90000 balance
55/135 in simplest form
Answer:
11/27
Step-by-step explanation:
55/135 (divide by 5)
11/27
A rectangle with side lengths y and z has perimeter 2y+2z. Elizabeth bought a rectangular painting of the seashore and wants to decorate the edges with sky-blue ribbon. The painting is 2 feet long and 1.5 feet wide.
What is the perimeter of the painting?
The perimeter of the painting 7 feet.
What is Perimeter?Perimeter is the distance around the edge of a shape. To find the perimeter by adding up the side lengths of various shapes.
Given:
A rectangle with side lengths y and z has perimeter 2y+2z.
Elizabeth bought a rectangular painting whose length = 2 ft and width = 1.5 ft.
So, the perimeter of the painting
= 2l+ 2w
= 2(2)+ 2(1.5)
= 4 + 3
= 7 feet
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What happens when a distribution is skewed to the right?
Answer:
Step-by-step explanation:
A distribution is said to be skewed to the right (also known as positively skewed) if it has a longer tail on the positive side of the mean or median, indicating that the majority of the data values are on the lower end and there are a few large values on the higher end. This results in a mean that is larger than the median.
In other words, the right skew occurs when the tail of the distribution is located to the right side of the peak, which pulls the mean to the right as well. The presence of outliers or extreme values on the right side of the distribution can cause right skew.
Right-skewed distributions are common in data sets that represent measurements or quantities that have a minimum value of zero or a natural lower limit, but can increase without bound, such as income, wealth, and height.
In summary, when a distribution is skewed to the right, it has a higher mean and lower median compared to a symmetrical distribution, and the majority of the data is concentrated on the left side.
Ruby says that a quadrilateral is a square if and only if it is a rectangle. Is this a true biconditional statement?.
The statement "a quadrilateral is a square if and only if it is a rectangle" made by Ruby is a true biconditional statement in mathematical terms.
A quadrilateral is a four-sided shape that can have different properties based on its sides and angles.
Ruby says that a quadrilateral is a square if and only if it is a rectangle. This statement can be written as:
(Q is a square) if and only if (Q is a rectangle)
To understand if this statement is a true biconditional statement, we need to examine the definition of a square and a rectangle and how they relate to each other.
A square is a type of quadrilateral where all four sides are equal in length and all four angles are equal (90 degrees). In other words, a square is a rectangle that has four equal sides.
A rectangle is a type of quadrilateral where all four angles are equal to 90 degrees. This means that the opposite sides are parallel and equal in length.
Based on the definitions, we can conclude that the statement "a quadrilateral is a square if and only if it is a rectangle" is a true biconditional statement.
This means that if a quadrilateral is a square, it is also a rectangle and vice versa. If a quadrilateral is not a square, it cannot be a rectangle.
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I need help with this please and thank you.
The standard form of the Polynomial would be [tex]x^{4}[/tex] -x³ /2 -8
What is polynomial?The term "polynomial" refers to a mathematical statement of one or more algebraic terms in which the variables are all of non-negative integer powers. Variables, fixed values, and exponents are all present in the terms. The degree 'n' standard form polynomial is Standard form is one method of expressing a polynomial.
We must consider each term's degree in order to write any polynomial in standard form.
Given the polynomial -8 -x³ /2 -xx³ with the highest degree comes first, followed by x raise to power 4, and then the constant, -8, comes last.
Thus, we would have:
[tex]x^{4}[/tex] -x³ /2 -8
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From 1995 to 2005, the tuition at a college increases by about 7% per year. If this trend continues......
a. Write an exponential growth function that models the tuition over time.
b. What will the tuition be in 2020?
c. What was the tuition be in 1995?
d. What was the tuition in 2011?
a) An exponential growth function that models the tuition which increased from 1995 to 2005 by 7% annually, is y = 8,000 (1.07)^t.
b) If the trend of annual increase in tuition continues, the tuition in 2020 will be $43,419.20.
c) The tuition in 1995 was $8,000.
d) If the trend of annual increase in tuition continues, the tuition in 2011 will be $23,617.28.
What is an exponential growth function?An exponential growth function is one of the two types of exponential functions.
The exponential growth function is marked by an increasing constant rate and modeled as f(x ) = a (1 + r)^x , where r is the growth rate.
The other exponential function is known as an exponential decay function because it shows a constant rate of decrease.
The tuition in 1995, y = $8,000
Annual increase = 7% = 0.07
Time from 1995 = t
Time from 1995 to 2020 = 25 years
Time from 1995 to 2011 = 16 years
Exponential function:y = 8,000 x (1 + 7%)^t
y = 8,000(1.07)^t
When t = 25 years, y = 8,000 x (1.07)^25 = 8,000 x 5.4274 = $43,419.20
When t = 16 years, y = 8,000 x (1.07)^16 = 8,000 x 2.95216 = $23,617.28
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Question Completion:Tuition in 1995 = $8,000
what is (fxg)(x)
f(x)=x^3-4x+2
g(x)=x^2+2
Answer: x^6+6x^4+8x^2+2
Step-by-step explanation:
Since g comes after f then you will take g's equation and plug it into the f equation so it would turn out to be if you plugged it in
(x^2+2)^3-4(x^2+2)+2 which would equal x^6+6x^4+8x^2+2
The freshman class at Arlington High school is made up of 480 female students. This represents 65% of the freshman class. How many total students are freshmen?
The number of freshmen that are students is 738
How to calculate the number of freshmen that are students?
Let y represent the number of students that are freshmen
The freshmen class is made up of 480 female students
This number represents 65% of the freshmen class
Therefore the total number of students that are freshmen can be calculated as follows
y × 65/100= 480
65y/100= 480
Cross multiply both sides
65y= 480 × 100
65y= 48000
y= 48000/65
y= 738.4
≅ 738
Hence 738 students are freshmen
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