Answer:
-216
Step-by-step explanation:
[tex]-6^3\\-6*-6*-6 = -216[/tex]
how do you find the value of f(-5) for the function
f(x)=3x^2-2x+5
Answer: 90
Step-by-step explanation:
f(x) = 3x^2-2x+5
f(-5) = 3 x (-5)^2 - 2(-5) + 5
f(-5) = 3 x (-5)^2 - 2(-5) + 5
f(-5) = (3x25) +10 + 5
f(-5) = 75 + 15
f(-5) = 90
To find the value of f(-5) for the given function , we just need to put the value of x ( which is -5) in the given function. Let's do it!
[tex] \purple{\frak{\implies f(x) = 3x^2-2x+5}} \\ [/tex]
[tex] \sf \implies f(-5) = 3 \times (-5)^2 - 2(-5) + 5 \\ [/tex]
[tex] \sf \implies f(-5) = 3 \times (-5)^2 - 2(-5) + 5 \\ [/tex]
[tex] \sf \implies f(-5) = (3\times 25) +10 + 5 \\ [/tex]
[tex] \sf \implies f(-5) = 75 + 10+5\\ [/tex]
[tex] \purple{\frak{ \implies f(-5) = 90} }\\ [/tex]
Henceforth, the value of the function is 90.2x² + 1 = 5x
A.
X =
B. X=
C.
X =
D. X =
-1+√39
5-√17
4
-1-√39
5+√√17
4
Answer: x= (5+√17)/(4) AND x=(5-√17)/(4)
Step-by-step explanation:
You subtract 5x to put it on the other side, so it's 2x^2-5x+1 and then use the quadratic formula. Hope this helps.
determine whether an observational study or an experimental study is used. a study was done on two groups of algebra students. group was given tutoring and study skills advice. group was not given any additional help. after weeks, the students took a test. the results of the two groups were compared.
This is an experimental study.
This study demonstrates an experimental design, as the intervention (tutoring and study skills advice) was used to examine the impact it had on the test scores.
An experimental study is used to examine the effects of an intervention or treatment on a group of participants. In this case, the study involved two groups of algebra students, one of which was given additional help in the form of tutoring and study skills advice while the other was not. After a few weeks, the students took a test and the results of the two groups were compared. This study demonstrates an experimental design, as the intervention (tutoring and study skills advice) was used to examine the impact it had on the test scores.
This study demonstrates an experimental design, as the intervention (tutoring and study skills advice) was used to examine the impact it had on the test scores.
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Eddy's plum weighs 3.042 ounces. Desta's plum weighs 3.24 ounces. Whose plum weighs more? How can you tell?
Answer:desta's plum
Step-by-step explanation:
Desta's plum weighs 0.198 ounces more than Eddy’s plum.
Given that, Eddy’s plum weighs 3.042 ounces Desta's plum weighs 3.24 ounces.
We need to find whose plum weighs more.
How to subtract decimal numbers?
Subtracting decimals is similar to the usual subtraction of whole numbers. We just need to place the decimal numbers, one below the other, according to their place values along with the decimal point. In some cases the two given numbers are different. If needed, we change the given decimal fractions to like decimal fractions to make the subtraction easier. Two decimals are called decimal fractions if they have an equal number of decimal places.
Now, the weight of Desta's plum-the weight of Eddy’s plum=3.24-3.042
=0.198 ounce
Hence, Desta's plum weighs 0.198 ounces more than Eddy’s plum.
Vickie sells cupcakes for $4.00 each at her bakery. Supplies to make one cupcake cost $0.20. She spent $256 on new equipment to make the cupcakes.
Complete the inequality to represent the least number of cupcakes, xx, Vickie must sell in order to make a profit. Then, complete the sentence to make a true statement.
Vickie must sell at least 64 cupcakes in order to make a profit.
The break-even point theoryThe inequality to represent the least number of cupcakes Vickie must sell in order to make a profit is 4x > 256 + 20, where x is the number of cupcakes she must sell.To make this a true statement, Vickie must sell at least 65 cupcakes to make a profit since 4x > 256 + 20 is equivalent to x > 65.In order to make a profit, Vickie must sell at least 65 cupcakes.The equation 4x > 256 + 20 can be used to represent this, where x is the number of cupcakes she must sell.Each cupcake costs $4.00 to make and sell, and supplies to make one cost $0.20. She spent $256 on new equipment to make the cupcakes.For Vickie to make a profit, she must sell at least 65 cupcakes in order to cover the cost of supplies, equipment, and make a profit.The inequality to represent the least number of cupcakes Vickie must sell in order to make a profit is: 4x - 0.2x ≥ 256.To learn more about the break-even point theory refer to:
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4. Alfonso surveyed several students in his school. He asked them to give the grade that they are in and the number of pets they have at home. The results are shown in the table below.
Survey Results
Grade
5
6
2
1
4
2
4
1
4
3
17
5
Number of
Pets
0
4
2
3
5
1
2
2
0
5
2
Find the correlation coefficient for the data. Round to the nearest hundredth
Answer:
0.35
Step-by-step explanation:
To find the correlation coefficient, we can use the formula:
r = (n * Σ(x * y) - Σx * Σy) / √((n * Σx^2 - (Σx)^2) * (n * Σy^2 - (Σy)^2))
where n is the number of data points, x is the grade, y is the number of pets, Σx is the sum of grades, and Σy is the sum of the number of pets.
To use this formula, we first need to find the sum of the grades and the sum of the number of pets from the data in the table.
Grade Number of Pets
5 0
6 4
2 2
1 3
4 5
2 1
4 2
1 2
4 0
3 5
17 2
sum of grades = 5+6+2+1+4+2+4+1+4+3+17+5 = 49
sum of number of pets = 0+4+2+3+5+1+2+2+0+5+2 = 26
Now we can substitute these values into the formula along with n = 12, the number of data points in the table:
r = (12 * (50 + 64 + 22 + 13 + 45 + 21 + 42 + 12 + 40 + 35 + 172 + 52) - (49*26)) / √((12 * (5^2 + 6^2 + 2^2 + 1^2 + 4^2 + 2^2 + 4^2 + 1^2 + 4^2 + 3^2 + 17^2 + 5^2) - 49^2) * (12 * (0^2 + 4^2 + 2^2 + 3^2 + 5^2 + 1^2 + 2^2 + 2^2 + 0^2 + 5^2 + 2^2) - 26^2))
Which after some calculation give us r=0.35,
So the correlation coefficient for the data is approximately 0.35.
At a grocery store, a bag of string cheese containing 24 pieces of cheese sells for $6.96. What is the price for a box containing 36 pieces of cheese using the same unit rate?
The price for a box containing 36 pieces of cheese will be sold for $10.44
What is unit rate?A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.
Given that, a bag of string cheese containing 24 pieces of cheese sells for $6.96, we need to find the price for a box containing 36 pieces of cheese using the same unit rate,
Since, 24 pieces are sold for = $6.96
Therefore,
1 piece will be sold for = 6.96 / 24 = $0.29
Therefore,
36 pieces of cheese will be sold = 0.29 x 36 = $10.44
Hence, the price for a box containing 36 pieces of cheese will be sold for $10.44
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answer how many feet per day
Based on the graph, the average number of feet per day is 0.25 per day.
How to calculate the average in this case?To calculate the average using the information of the graph, let's identify the highest and lowest number:
Highest number: 200
Lowest number: 75
Now let's find the average: 200 +75 /2 = 125
This means that on average there was a change of 125 feet during the 400 days
Now using this number, let's find the average daily change:
Average = average change/number of days
125/ 400 = 2.5 feet per day
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The number of assaults in a city is depicted in two different graphs below.
Step 1 of 2: How many times as many assaults were there actually in Year 5 compared to Year 1? Round your answer to 2 decimal places.
1) There were 1.26 times as many assaults in Year 5 compared to Year 1
2) Graph B best represents the data.
What is Graph?
A graph is a structure that resembles a set of items in discrete mathematics, more specifically in graph theory, in which some pairs of the objects are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.
Given that;
The data is most accurately depicted in bar graph B.
It allows for the following data observations:
In year 1, there were 235 assaults.
Year 1 saw 265 assaults, Year 2 saw 250 attacks, Year 1 saw 280 assaults, Year 1 saw 295 assaults, and Year 2 saw 260 assaults.
1)In the first year, there were 235 assaults, and by the fifth year, there were 295 assaults.
ratio = year5/year1 = 295/235 =1.26
Hence , there were 1.26 times as many assaults in Year 5 compared to Year 1
2) The total number of data points falls between 200 and 300.
Therefore, graph A, whose output value ranges from 0 to 300, is not truly necessary.
Graph B, on the other hand, uses the right range and has a step size of 10, which is also fairly accurate.
Therefore, Graph B best depicts the data.
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Write the equation for a parabola with a focus at (9, 0) and a directrix at y = -4.
y =
The equation for a parabola with a focus at (9, 0) and a directrix at y = -4 is y = (x - 9)^2 - 4.
What is parabola?Parabola is a type of curve that is symmetrical around a line called the directrix. It is an important conic section and is described by a quadratic equation.
This equation is derived from the equation for a parabola in standard form, which is y = a(x - h)^2 + k.
To find the equation for the parabola, we need to determine the values of a, h, and k. The focus of the parabola is (9, 0), so h = 9. The directrix of the parabola is y = -4, so k = -4. The value of a can be determined by the distance between the focus and the directrix, which is 4. So a = 1/4.
Putting these values together, we get y = (x - 9)^2 - 4.
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Which of the following statements is not true concerning angle measure?O The square of any side of a triangle is equal to the sum of the squares of the remaining 2 sides, minus twice the produce of the 2 remaining sides and the cos of angle between them
O Two angles in standard position are coterminal if they have the same terminal side
O The length of the leg opposite either of the pi/4 angles of a special pi/4, pi/4, pi/2 right triangle with a hypotenuse of square root of 2 is equal to 1.O The angle in standard position formed by rotating the terminal side of angle one complete counterclockwise rotation has a radian measure of pi radians
The angle in standard position formed by rotating the terminal side of angle one complete counterclockwise rotation has a radian measure of pi radians
What is concerning angle measure?Using a protractor, angles are measured in degrees (°). A measuring tool called a protractor is used to compute or draw angles in terms of degrees. As seen in the illustration below, for instance, the black arrow, when measured with a protractor, points to 100°, crossing 90°. As a result, the angle has a 100° measurement. A protractor is the most practical tool for measuring angles. The vertex of the angle you are measuring should be the protractor's midway. Align the protractor's zero line with one side of the angle (line with the number 0). The angle is the number of degrees at which the other side of the scale crosses.The angle created by rotating the terminal side of angle one completely counterclockwise has a radian measure of pi radians when it is in standard position.
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in exercises 19\[dash]22, determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system.
19.For the matrix to be the augmented matrix of a consistent linear system, the determinant of the coefficient matrix (1 h 4) must not be equal to zero. Therefore, h cannot be equal to -4. So, the value(s) of h that make the matrix a consistent linear system is any value other than -4.
20.For the matrix to be the augmented matrix of a consistent linear system, the determinant of the coefficient matrix (6 8 4) must not be equal to zero. Therefore, h does not affect the consistency of the system. The matrix is always consistent, regardless of the value of h.
21.For the matrix to be the augmented matrix of a consistent linear system, the determinant of the coefficient matrix (1 -4 3) must not be equal to zero. Therefore, h does not affect the consistency of the system. The matrix is always consistent, regardless of the value of h.
22.For the matrix to be the augmented matrix of a consistent linear system, the determinant of the coefficient matrix (2 -3 -6) must not be equal to zero. Therefore, h does not affect the consistency of the system. The matrix is always consistent, regardless of the value of h.
In summary, in all four cases, h does not affect the consistency of the system, so the matrix is always consistent regardless of the value of h.
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The gestation period of horses is 336 days is blank percent longer than the gestation period of dogs 65 days
The gestation period of horses is 417% longer than the gestation period of cats.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
We have been asked to find percentage change of the gestation period of horses and cats.
First of all we will find difference between our two numbers.
Difference= 336-65
=271
Now we will find percentage of our difference with respect to gestation period of cats.
Percentage change = 271/65*100
=416.92
Therefore, gestation period of horses is 417% longer than the gestation period of cats.
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what is the recursive formula for -1, -6, -36, -216
The recursive formula for the sequence is -1, -6, -36, -216
is -1[tex](-6)^{n-1}[/tex].
What is a geometric sequence?A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.
Example:
2, 4, 8, 16 is a geometric sequence.
We have,
-1, -6, -36, -216 is a geometric sequence.
The first term is -1,
The common ratio.
= -6/-1
= 6
Now,
The nth term of a geometric sequence is a[tex]r^{n-1}[/tex].
So,
= -1[tex](-6)^{n-1}[/tex]
Thus,
The recursive formula is -1[tex](-6)^{n-1}[/tex].
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Select the reason that justifies the step.
The correct justification to each box. The answer is 2(y − 5) + 4 = 4 given.
What is meant by box ?
A box is a type of container used to hold or convey its contents. The sides of most boxes are flat, parallel, and rectangular. Boxes come in all sizes and can be used for everything from functional to ornamental purposes.Boxes can be built from a wide range of materials, including strong ones like wood and metal and weaker ones like corrugated fiberboard and paperboard. Boxes made of corrugated metal are frequently used as shipping containers.Although rectangular prisms are the shape that boxes most frequently take, other shapes are also possible. Informally, rectangular prisms are frequently referred to as "boxes."To the complete questions is;
Drag the correct justification to each box.
2(y−5)+4=4
2y−10+4=4 []
2y−6=4 []
2y=10 []
y=5 []
2y − 10 + 4 = 4 Distributive Property
2y − 6 = 4 Addition
2y = 10 Addition Property of Equality
y = 5 Division Property of Equality
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A random sample of 100 adults aged 18 years or older were given a list of ice cream flavors and were asked to list which flavors they liked. The responses are given below. Chocolate 45 Strawberry 42 Vanilla 23 Mocha 19 Which of the following graphs would be most appropriate for visually displaying the results? Pie Chart Frequency Bar Graph Relative Frequency Bar Graph
The most appropriate graph to visualize the information is a PIE CHART. The frequency bar graph makes an independent bar of each fruit each, while it is ideal, it is not easy to identify the total or percentage of each.
Both charts could be used to make a display of the information given.
The frequency bar graph makes an independent bar of each fruit each, while it is ideal, it is not easy to identify the total or percentage of each.
The pie chart could be used to represent a whole of the 100 fruits as a single circle and divides the circle into parts based on the number of fruit belonging to each type including their respective percentages.
Also, since the number of fruits/types are just 5, using a pie chart gives a more accurate and readable visual representation of the information.
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The tables show the monthly costs for two different Internet service providers.
What will be the difference in the cost of the two plans after 18 months?
The difference in the cost of the two plans after 18 months will be 240. The solution has been obtained using linear equations.
What is a linear equation?
A linear equation is one that has the highest degree of 1 possible. This indicates that there are no variables in a linear equation with exponents greater than 1. Such an equation on the graph, forms a straight line.
According to the table, the companies increase the cost by equal amount every month.
So, the linear equations for both the companies come out to be,
Company A: y=40+35x
Company B: y=10+50x
Therefore, after 18 months cost of both the companies will be
Company A:
y=40+35(18)
y=40+630
y=670
Company B:
y=10+50(18)
y=10+900
y=910
The difference in the cost of the two plans after 18 months will be
910-670= 240
Hence, the difference in the cost of the two plans after 18 months will be 240.
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3xsquared minus 5 equals negative 5x minus 3
Answer:
x = 1/3 and x = -2
Step-by-step explanation:
3x² - 5 = -5x - 3
turn this into a quadratic equation by adding -5x and -3 to the other side
3x² + 5x - 2 = 0
factor:
(3x-1)(x+2) = 0
3x-1 = 0
x = 1/3 AND
x+2 = 0
x = -2
The solutions of the quadratic equation:
3x² - 5 = -5x - 3
are:
x = 1/3
x = -2
How to solve the quadratic equation?Here we want to solve this quadratic equation:
3x² - 5 = -5x - 3
We can move all the terms to the left side to get:
3x² - 5 + 5x + 3 = 0
3x² +5x - 2 = 0
The solutions are given by the quadratic formula:
[tex]x = \frac{-5 \pm \sqrt{5^2 - 4*3*(-2)} }{2*3} \\\\x = \frac{-5 \pm7 }{6}[/tex]
Then the two solutions are:
x = (-5 + 7)/6 = 1/3
x = (-5 - 7)/6 = -2
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NO LINKS!!!
Lin is trying to convince Andre that all circles are similar. Help her write a valid justification for why all circles are similar.
All circles are similar because their shape is same but sizes vary.
What are Similar Figures?Similar figures are those figures which have the same shape, but sizes are different.
To prove the given statement, consider two circles C and C' with radius r and r' respectively.
r can be greater than or less than r'.
Circle C can be dilated to a certain value to get the circle C'.
The shape of both the circles remain same.
But the size is different.
This is the case for any arbitrary circles.
Hence all circles are similar.
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suppose you want to make a visualization that shows how many students bought certain quantities of candy from the vending machine during the month of september. of the choices below, which chart would best convey this information to the person looking at the graph?
In the given situation the best way for the viewer to comprehend this information is through the graph's histogram.
What is the Histogram?The distribution of numerical data is roughly depicted by a histogram.
Karl Pearson was the person who first coined the phrase.
The first stage in creating a histogram is to "bin" (or "bucket") the range of values, divide it into a series of intervals, and then count the number of values that fall into each interval.
The bins are often defined as a series of discrete intervals that don't overlap.
The bins (intervals) must be close together and frequently, though not always, have the same size.
The graph's histogram would help the viewer understand this information the best.
Therefore, in the given situation the best way for the viewer to comprehend this information is through the graph's histogram.
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Correct question:
Suppose you want to make a visualization that shows how many students bought certain quantities of candy from the vending machine during the month of September. What chart would best convey this information to the person looking at the graph?
1. How many feet long is the space Mr. Hamilton wants to fill with pictures?
2. Convert this length to inches.
3. How many pictures will Mr. Hamilton use? Explain how you found your answer
4. How would your answer change if the pictures were 10 inches wide? Explain
The 9.75 ft wide wall and the 5.75 feet window in the center, through the use of unit conversion
1. The space to fill 4 feet
2. 4 feet = 48 inches
3. 8 pictures
4. Tne new number of pictures with 10 inches width is 4 pictures
Whart is unit conversion?Unit conversion is the expression of the same quantity, using different a different unit of measurement
Part of the question obtained from a similar question includes;
The width of the wall Mr. Hamilton decorates with pictures = 9.75 ft
The width of the window at the center of the wall = 5 3/4 feet = 5.75 ft
Location of the window = The center of the wall
Location Mr. Hamilton will fill with the pictures = Left and right sides of the window
The width of each pictiure of a president = 6 inches
1. The length of the space Mr. Hamilton wants to fill with pictures = 9.75 ft - 5.75 ft = 4 ft.
2. The unit convertion factor from feet to cm is;1 ft = 12 inches
Therefore, 4 feet = 4 ft × 12 inches/ft = 48 inches
3. The number of pictures Mr. Hamilton will use, n, is therefore;
n = 48 inches/(6 inches/picture) = 8 pictures
The number of pictures Mr. Hamilton can use for decorating by placing pictures of presidents on the wall is 8 pictures
4. The responses to the questions if the dimensions of the picture are 10 inches are;
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Which of the following represents a sum from the expression given?
3(14x^2+9x)-22
Answer:
Your answer is 42x^2+27x-22
Step-by-step explanation:
Hope this helps :)
The function is defined below. Find all values of that are NOT in the domain of g. g(x)=x^2+13+40 / x^2-9
Answer:
g(x)=x-2/x^2-9
If there is more than one value, separate them with commas.
Step-by-step explanation:
From the top of the Ferris wheel, the angle of depression of your friend on the ground is 61. If your friend is standing 30 feet from the foot of the ride, how tall is the Ferris wheel?
The Ferris wheel is 16.63 feet tall.
What is Angle of Depression?Angle of depression is the angle which is between a horizontal line and the line of sight which is pointed downwards.
We have a triangle formed here by the information given.
Angle of depression between the Ferris wheel and the friend on the ground = 61°
Distance of friend from the foot of the Ferris wheel = 30 feet
We have to calculate the height of Ferris wheel.
Let x be the required height.
tan 61 = 30 / x
x = 30 / tan 61
x = 30 / 1.804
x = 16.63 feet
Hence the height of the Ferris wheel is 16.63 feet.
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Zachary purchased a computer for $1,400 on a payment plan. Five months afyer he purchased the computer, his balance was $625. seven months after he purchased the computer, his balance was $315. what is the equationt that models the balance y after x months?
Answer:
y=-140x I think so
Step-by-step explanation:
The cost of a school banquet is $70 plus 13 for each person attending? Write an expression that models the problem
Answer: Cost = $70 + ($13)(n)
Step-by-step explanation: As we can see that the cost of the banquet is 70$ and for each person attending there will be a 13$ extra so as to model this problem, let's from an expression. The expression that models the problem can be written as -
Cost = $70 + ($13)(n)
In this expression 'n' will be the number of people attending the banquet at that time.
In this expression the 'x' will be the number of people attending the banquet. 'y' will be the cost of the banquet. y-intercept will be 70$, which is actually the cost of the banquet and the slope will be 13$ which is the cost for each person that will be attending.
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
10.58
Step-by-step explanation:
here we need to find out the value of x by Pythagoras theorem. By Pythagoras theorem in q right angled triangle the sum of squares of base and perpendicular is equal to the square of hypotenuse. so ,
h² = p² + b²
Now here ,
p = 12h = 16 b = x = ?on using Pythagoras theorem,
h² = p² + b²
16² = 12² + x²
256 = 144 + x²
x² = 256 -144
x² = 112
x = √112
x ≈ 10.58 [ required answer]
and we are done!
-Rishabh
Anna is a teacher at an elementary school. She purchased 63 tickets to take the first-grade children and some parents on a field trip to the zoo. She purchased
children's tickets for $7 each and adult tickets for $20 each. She spent a total of $571. How many of each ticket did she buy?
Answer:
Anna the teacher bought 54 child tickets and 19 adult tickets
Step-by-step explanation:
Match the differential equations with the solution graphs labeled I-IV. Give reasons for your choices.
I 9-1-013a.gif II 9-1-013b.gif
III 9-1-013c.gif IV 9-1-013d.gif
(a)
y' = 1 + x2 + y2
y' = 1 + x2 + y2 ? (? < ? > = )1 and y' ? ? (1 ? 0 -1 -? )as x ? ?.
The only curve satisfying these conditions is labeled ? (I II III IV) .
(b)
y' = xe?x2 ? y2
y' = xe?x2 ? y2 ?( > ? ? = <) 0 if x > 0 and y' ? (? = > < ?) 0 if x < 0.
The only curve with ---Select---( negative positive horizontal vertical) tangent slopes with
x < 0
and ---Select--- positive negative horizontal vertical tangent slopes when
x > 0
is labeled ? (I II III IV) .
(c) y' =
1
1 + ex2 + y2
y' =
1
1 + ex2 + y2
? ? = ? > < 0 and y' ? ? (-? ? 1 0 -1 )as x ? ?. The only curve satisfying these conditions is labeled ?( I II III IV) .
(d)
y' = sin(xy) cos(xy)
y' = sin(xy) cos(xy) ? (> ? < ? )= 0 if y = 0,
which is the solution graph labeled ?( I II III IV) .
The solution graphs for the differential equations y' = 1 + x2 + y2, y' = xe?x2 ? y2, y' = 1/(1 + ex2 + y2), and y' = sin(xy) cos(xy) are labeled I, II, III, and IV respectively. The slope of the graphs when x is less than 0 and greater than 0, as well as the horizontal tangent line when y is equal to 0, are used to determine the correct graph for each equation.
Match the differential equations with the solution graphs labeled I-IV. Give reasons for your choices.
I 9-1-013a.gif II 9-1-013b.gif
III 9-1-013c.gif IV 9-1-013d.gif
(a)
y' = 1 + x2 + y2
y' = 1 + x2 + y2 ? (? < ? > = )1 and y' ? ? (1 ? 0 -1 -? )as x ? ?.
The only curve satisfying these conditions is labeled ? (I II III IV) .
(b)
y' = xe?x2 ? y2
y' = xe?x2 ? y2 ?( > ? ? = <) 0 if x > 0 and y' ? (? = > < ?) 0 if x < 0.
The only curve with ---Select---( negative positive horizontal vertical) tangent slopes with
x < 0
and ---Select--- positive negative horizontal vertical tangent slopes when
x > 0
is labeled ? (I II III IV) .
(c) y' =
1
1 + ex2 + y2
y' =
1
1 + ex2 + y2
? ? = ? > < 0 and y' ? ? (-? ? 1 0 -1 )as x ? ?. The only curve satisfying these conditions is labeled ?( I II III IV) .
(d)
y' = sin(xy) cos(xy)
y' = sin(xy) cos(xy) ? (> ? < ? )= 0 if y = 0,
which is the solution graph labeled ?( I II III IV) .
a) I
b) IV
c) II
d) III
a) The differential equation is y' = 1 + x2 + y2, which has a positive slope when x is less than 0 and a negative slope when x is greater than 0. The only graph with these conditions is labeled I.
b) The differential equation is y' = xe?x2 ? y2, which has negative tangent slopes when x is less than 0 and positive tangent slopes when x is greater than 0. The only graph with these conditions is labeled IV.
c) The differential equation is y' = 1/(1 + ex2 + y2), which has a negative slope when x is less than 0 and a positive slope when x is greater than 0. The only graph with these conditions is labeled II.
d) The differential equation is y' = sin(xy) cos(xy), which has a horizontal tangent line when y is equal to 0. The only graph with this condition is labeled III.
The solution graphs for the differential equations y' = 1 + x2 + y2, y' = xe?x2 ? y2, y' = 1/(1 + ex2 + y2), and y' = sin(xy) cos(xy) are labeled I, II, III, and IV respectively. The slope of the graphs when x is less than 0 and greater than 0, as well as the horizontal tangent line when y is equal to 0, are used to determine the correct graph for each equation.
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of all the circular cones of slant height 8cm, find the dimensions of the cone of the largest volume
Surface area overall of a cone is A = L + B = πrs + πr2 = πr(s + r) = πr(r + √(r2 + h2))
What is meant by cone?Any two known variables will be used in this online calculator to determine the various properties of a right circular cone. This shape is described as "circular" and is therefore a pyramid with a circular cross section. When something is said to be "correct," it indicates that the cone's vertex is directly above the base. When used alone, the word "cone" frequently refers to a right circular cone. Note that although units are supplied for convenience, they have no bearing on the calculations. The units, like ft, ft2, or ft3, are there to indicate the order of the results.The typical cone formulas are listed below. Calculations are based on the manipulation of these common formulas through algebra.Volume of a cone:
V = (1/3)πr2h
Cone's slant height:
s = √(r2 + h2)
Lateral surface area of a cone:
L = πrs = πr√(r2 + h2)
Cone (circle) base surface area:
B = πr2
Total surface area of a cone:
A = L + B = πrs + πr2 = πr(s + r) = πr(r + √(r2 + h2))
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