Find x, y, and z such that x³+y³+z³=k, for each k from 1 to 100.
Answers
Answer:
x3+y3+z3=k with k is integer from 1 to 100
solution x=0 , y=0 and z=1 and k= 1
For K= 1 , we have the following solutions (x,y,x) = (1,0,0) ; or (0,1,0) ; or (0,0,1) ,
For k =1 also (9,-8,-6) or (9,-6,-8) or (-8,-6,9) or (-8,9,-6) or (-6,-8,9) or (-6,9,8)
And (-1,1,1) or (1,-1,1)
=>(x+y)3−3x2−3xy2+z3=k
=>(x+y+z)3−3(x+y)2.z−3(x+y).z2=k
=>(x+y+z)3−3(x+y)z[(x+y)−3z]=k
lety=αand z=β
=>x3=−α3−β3+k
For k= 2 we have (x,y,z) = (1,1,0) or (1,0,1) or (0,1,1)
Also for (x,y,z) = (7,-6,-5) or (7,-6,-5) or (-6,-5,7) or (-6,7,-5) or (-5,-6,7) or (-5,7,-6)
For k= 3 we have 1 solution : (x,y,z) = (1,1,1)
For k= 10 , we have the solutions (x,y,z) = (1,1,2) or (1,2,1) or (2,1,1)
For k= 9 we have the solutions (x,y,z) = (1,0,2) or (1,2,0) or (0,1,2) or (0,2,1) or (2,0,1) or (2,1,0)
For k= 8 we have (x,y,z) = ( 0,0,2) or (2,0,0) or (0,2,0)
For k= 17 => (x,y,z) = (1,2,2) or (2,1,2) or ( 2,2,1)
For k = 24 we have (x,y,z) = (2,2,2)
For k= 27 => (x,y,z) = (0,0,3) or (3,0,0) or (0,3,0)
for k= 28 => (x,y,z) = (1,0,3) or (1,3,0) or (1,3,0) or (1,0,3) or (3,0,1) or (3,1,0)
For k=29 => (x,y,z) = (1,1,3) or (1,3,1) or (3,1,1)
For k = 35 we have (x,y,z) = (0,2,3) or (0,3,2) or (3,0,2) or (3,2,0) or 2,0,3) or (2,3,0)
For k =36
we have also solution : x=1,y=2andz=3=>
13+23+33=1+8+27=36 with k= 36 , we have the following
we Have : (x, y,z) = (1, 2, 3) ; (3,2,1); (1,3,2) ; (2,1,3) ; (2,3,1), and (3,1,2)
For k= 43 we have (x,y,z) = (2,2,3) or (2,3,2) or (3,2,2)
For k = 44 we have ( 8,-7,-5) or (8,-5,-7) or (-5,-7,8) or ( -5,8,-7) or (-7,-5,8) or (-7,8,-5)
For k =54 => (x,y,z) = (13,-11,-7) ,
for k = 55 => (x,y,z) = (1,3,3) or (3,1,3) or (3,1,1)
and (x,y,z) = (10,-9,-6) or (10,-6,-9) or ( -6,10,-9) or (-6,-9,10) or (-9,10,-6) or (-9,-6,10)
For k = 62 => (x,y,z) = (3,3,2) or (2,3,3) or (3,2,3)
For k =64 => (x,y,z) = (0,0,4) or (0,4,0) or (4,0,0)
For k= 65 => (x,y,z) = (1,0,4) or (1,4,0) or (0,1,4) or (0,4,1) or (4,1,0) or (4,0,1)
For k= 66 => (x,y,z) = (1,1,4) or (1,4,1) or (4,1,1)
For k = 73 => (x,y,z) = (1,2,4) or (1,4,2) or (2,1,4) or (2,4,1) or (4,1,2) or (4,2,1)
For k= 80=> (x,y,z)= (2,2,4) or (2,4,2) or (4,2,2)
For k = 81 => (x,y,z) = (3,3,3)
For k = 90 => (x,y,z) = (11,-9,-6) or (11,-6,-9) or (-9,11,-6) or (-9,-6,11) or (-6,-9,11) or (-6,11,-9)
k = 99 => (x,y,z) = (4,3,2) or (4,2,3) or (2,3,4) or (2,4,3) or ( 3,2,4 ) or (3,4,2)
(x,y,z) = (5,-3,1) or (5,1,-3) or (-3,5,1) or (-3,1,5) or (1,-3,5) or (1,5,-3)
=> 5^3 + (-3)^3 +1 = 125 -27 +1 = 99 => for k = 99
For K = 92
6^3 + (-5)^3 +1 = 216 -125 +1 = 92
8^3 +(-7)^3
Step-by-step explanation:
Related Questions
find 30% of 70
please help
Answers
Answer:
21
Step-by-step explanation:
HA GODE
Billy bought Katie a present wrapped in this box. How much wrapping paper would He need to wrap the present in this box, PLEASE HELP! WILL MARK BRAINLIEST
Answers
Answer:
284mm²
Step-by-step explanation:
S.A.= 2(lw) + 2(lh)+ 2(wh)
2[12.6(8)] + 2[12.6(2)] + 2[8(2)]
201.6 + 50.4 + 32
S.A.= 284mm²
Answer:
B
Step-by-step explanation:
You need a top and bottom (same size)
You need a front and back (same size for them as well)
You need a left and right covering.
Top and bottom = 2 * 12.6 * 8 = 201.6
Left Right = 2 * 8 * 2 = 32.0
Front/Back= 2 * 2 * 12.6 = 50.4
Total 284
1- Finding angle measures between intersecting lines
NOTE: Angles not necessarily drawn to scale
x = ??
Answers
lcm of 2/5 and 5/18?
Answers
Answer:
10
Step-by-step explanation:
Which of the following statements is true for a function with equation f(x) = 5(3)x?
Answers
The graph has y-intercept (0,5) and increases with a constant ratio of 3.
What is the function?A function in mathematics is a connection between a set of inputs (sometimes referred to as the domain) and a set of outputs (also referred to as the range). Each input value is given a different output value.
The y-intercept lies at (0, 5) because the value of the function at x=0 is 530 = 5. The 'constant ratio' is 3, meaning that any increment of 1 in x causes the function value to grow by a factor of 3. (That serves as the exponential term's foundation.)
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Missing parts;
Which of the following statements is true for a function with equation f(x) = 5(3)*?
The graph has y-intercept (0,5) and increases with a constant ratio of 3.
The graph has y-intercept (0, 3) and decreases with a constant ratio of 3.
The graph has y-intercept (0, 3) and increases with a constant ratio of 5.
The graph has y-intercept (0,5) and decreases with a constant ratio of 3.
can sombody helpp me with this question pls
Answers
Answer:
The answer is B.
Step-by-step explanation:
Please answer who ever answers first and correct will get brainliest
Answers
Answer: Yes
Step-by-step explanation:
To test, we can see if 5^2 + 12^2 = 13^2.
As this holds true, this is a right triangle.
Answer:No
Step-by-step explanation: 5 squared x 12 squared does not equal 13 squared.
Which steps should be used to graph the equation below?
y – 4 = y - 4 = 1/3 (x+2)
Answers
After finding the slope and the coordinates for x and y-axis, you can plot the graph and follow the explanation part.
What is a graph?In math, graph science is the theory of geometric structures called graphs that are used to represent pairwise different objects. Vertices—also known as nodes or points—that are joined by edges make form a network in this sense.
Undirected graphs, where edges connect two vertices equally, and focused therapy, where edges connect two vertices unevenly, are distinguished.
As per the given information in the question
It is in point slope form, as may be seen.
y - y₁ = m(x - x₁)
The slope is m.
(x₁, y₁) is a point
Then,
y - 4=1/3(x - (-2))
Slope m is 1/3
Then, a point on the graph (-2, 4)
So, Initially, plot the point (-2, 4)
Then move 3 units to the right and 1 unit up, and draw a point connecting the two points.
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Eddie est discutiendo con Tana sobre las probabilidades de los distintos resultados al lanzar tres monedas. Decide lanzar una moneda de un centavo, una de cinco centavos y una de die centavos. ¿ Cuál es la probabilidad de que las tres monedas salgan cruz?
Answers
The probability of getting tails in the three coins would be 0.125 or 12.5%.
How to calculate the probability?To calculate the probability of an event happening, first, we need to identify the rate of the desired outcome versus the total possible outcomes. Moreover, to determine the total probability of two or more events happening we need to calculate the probability of each event and then multiply the results.
Probability of getting tails in any of the three coins:
1 / 2 = 0.5
Total probabilityy:
0.5 x 0.5 x 0.5 = 0.125 or 12.5%
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What mathematical term describes both 5. 3 and 8. 2 in the expression 5. 3x-8. 2y+11. 1?
Answers
Answer:
coefficients
Step-by-step explanation:
5.3 and 8.2 are coefficients since they are in front of an x and a y.
x and y are called variables.
any number on its own, ie without an x or y, is called a constant
Ms. Lauren Alexander, supply chain manager of ACR, Inc., is negotiating a contract to buy 25,000 units of a common component from a global supplier. Ms. Alexander conducted a thorough cost analysis on manufacturing the part in-house and determined that she would need $450,000 in capital equipment and incur a variable cost of $19.00 per unit to manufacture the part in-house. There is no fixed cost in purchasing the component from the supplier. What is the maximum purchase price per unit of component that Ms. Alexander should negotiate with her supplier?
Answers
The maximum purchase price per unit of the component that Ms. Alexander should negotiate with her supplier is $19.00, which is equal to the variable cost per unit to manufacture the part in-house.
In this scenario, Ms. Alexander needs to determine the maximum price per unit that she should be willing to pay the supplier for the component. She conducted a cost analysis and found that manufacturing the part in-house would require $450,000 in capital equipment and have a variable cost of $19.00 per unit.
Since there is no fixed cost associated with purchasing the component from the supplier, the maximum purchase price per unit should not exceed the variable cost per unit of manufacturing in-house. This ensures that the company does not incur additional costs by outsourcing the component.
Therefore, Ms. Alexander should negotiate a price with the supplier that is equal to or lower than the variable cost per unit, which is $19.00. By doing so, the company can avoid the initial capital investment and ongoing variable costs associated with in-house production, making it more cost-effective to purchase the component from the supplier.
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Can someone help me find m !!!
Answers
\( \qquad \qquad \huge \rm \underline{ \underline{ \Répondre}}\)
Since the two polygons are similar, ratio of their corresponding sides must be equal ~
\(\qquad \rm\dashrightarrow \: \dfrac{m}{28} = \dfrac{30}{40} \)
\(\qquad \rm\dashrightarrow \: \dfrac{m}{28} = \dfrac{3}{4} \)
\(\qquad \rm\dashrightarrow \: {m} = \dfrac{3}{4} \times 28\)
\(\qquad \rm\dashrightarrow \: {m} = {3}{} \times 7\)
\(\qquad \rm\dashrightarrow \: {m} = 21 \: \: units\)
Y=400(.99)^x is this growth or decay
Answers
Answer:
its decreasing. .........
The given function of the growth decay is decreasing.
We have given that,
Y=400(.99)^x
When does growth decay increase or decrease?
Exponential growth is a process that increases quantity over time. decreases over time, and is said to be undergoing exponential decay instead.
Therefore, The given function of the growth decay is decreasing.
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Milo's Ice Cream Factory sold more than 45 waffle cones yesterday. Which of the following inequalities represents the number of waffle cones Milo's Ice Cream Factory sold yesterday?
A.
x 45
D.
x < 46
Answers
Answer:
I believe the answer would be x<46
Answer:
I'm fairly sure that it would be D, or the final answer.
Step-by-step explanation:
Since he sold more than 45 waffle cones, x would not equal 45. This is why D is correct. Hope it helps!
Write the equation of the line PARALLEL to the line y = 4x - 9 that passes through the point (-2, 4)
*
y = -4x -4
y = -1/4x + 5/2
y = 4x + 12
Answers
The equation of the line parallel to the given line passes through the point (-2, 4) is, y = 4x + 12.
What is slope - intercept form of the line?
y = mx + b, where m denotes the slope and b the y-intercept, is how the line's equation is expressed in the slope-intercept form.
Consider, the given equation of line
y = 4x - 9
We have to find the equation of line that parallel to the given line.
The point is (-2, 4).
First we have to find the slope of the line.
Since, slope of the parallel line, is same as the slope of the given line.
Here, the slope of the given line is 4.
So, the slope of the parallel line is also 4.
Now, consider the point - slope form of the line
\(y-y_1=m(x-x_1)\)
Plug \((x_1, y_1) = (-2, 4), m = 4\)
\(y-4=4(x-(-2))\\y-4=4(x+2)\\y-4=4x+8\\y=4x+8+4\\y=4x+12\)
Hence, the equation of line parallel to the given line in slope-intercept form is y = 4x + 12.
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I have no clue how to do this math using the diagram: 3.) At this point, the plane started descending. As the plane turned, it’s altitude dropped from 3060 feet to 1650 feet above ground level. Calculate the angle of descent if the plane traveled 0.5 miles (c). (Note: the difference in altitude is 1390 feet)
Answers
Step-by-step explanation:
.5miles = 2640 ft
tan a = 2640/1390
a - angle of descent
a = 62.22
A student who is at the 40th percentile of first-year gpas is also likely to be at the 40th percentile of second-year gpas. true false
Answers
False. We would anticipate the second-year GPA to be slightly higher than the 40th percentile based on the regression impact.
How does your GPA translate?
Your grade point average (GPA) is calculated by dividing the total number of credits you have earned in high school by the sum of all of your course grades. The majority of colleges and secondary schools use a 4.0 scale to report grades.Given this,
A student who has a first-year GPA in the 40th percentile
is likely to have a second-year GPA in the same range.
The scatter plot is shaped like a football. ————— (False)
If the scatter diagram is shaped like a football, then all of the data points are drawn in a circle. As a result, the data does not fit well.
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The arc length x = True O False 4(3 + y)² on the interval [1, 4] is approximately 131 units.
Answers
The statement is false. The arc length of the curve defined by x = 4(3 + y)² on the interval [1, 4] is not approximately 131 units.
To find the arc length of a curve, we use the formula ∫ √(1 + (dx/dy)²) dy, where the integral is taken over the given interval.
In this case, the equation x = 4(3 + y)² represents a parabolic curve. By differentiating x with respect to y and substituting it into the arc length formula, we can calculate the exact arc length over the interval [1, 4].
However, it is clear that the arc length of the curve defined by x = 4(3 + y)² cannot be approximately 131 units, as this would require a specific calculation using the precise integral formula mentioned above.
Therefore, the statement is false, and without further calculations, we cannot determine the exact arc length of the given curve on the interval [1, 4].
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Which answer shows 0.00897 written in scientific notation?
0.897 x 10-2
8.97 x 10-3
8.97 x 10-2
8.97 x 20 3
Answers
Answer:A
Step-by-step explanation:
Consider the probability density function f(x) = 1/theta^2 xe^- x/theta, 0 lessthanorequalto x < infinity, 0 < theta < infinity Find the maximum likelihood estimator for theta.
Answers
To find the maximum likelihood estimator for theta, we need to first find the likelihood function by taking the product of the density function for each observation. Assuming we have n observations, the likelihood function is given by:
L(theta) = (1/theta^2) * Π[i=1 to n] (xi * e^(-xi/theta))
Taking the logarithm of the likelihood function and simplifying it, we get:
ln(L(theta)) = -2ln(theta) + Σ[i=1 to n] ln(xi) - Σ[i=1 to n] (xi/theta)
To find the maximum likelihood estimator for theta, we need to differentiate ln(L(theta)) with respect to theta and set it equal to zero. Solving for theta, we get:
θ = Σ[i=1 to n] xi / n
Therefore, the maximum likelihood estimator for theta is the sample mean of the n observations.
It is important to note that this estimator is unbiased and efficient, meaning that it has the smallest possible variance among all unbiased estimators. This makes it a desirable estimator for practical applications.
In conclusion, the maximum likelihood estimator for theta in the given probability density function is the sample mean of the n observations.
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question i like this girl but she keeps throwing me to the curve evertime we get close and just doesnt talk to me but gets with somebody else what does this mean?
Answers
Either she dosent want to admit that she likes you or she dosnt even like u
Answer:
well, she may have her walls up when you are around her. she is scared to hurt you so she just pushes you away instead. My suggestion would be to act like her friend and that every time you work your way closer pretend that its just like in the beginning aka keep pretending your just regular friends nothing more. Then when you notice her starting to open up a little more start working your way out of the friend zone.
Step-by-step explanation:
SOMEONE HELP ME PLEASE
Decide if the following scenario involves a permutation or combination. Then find the number of possibilities.
There are 50 applicants for two Systems Engineer positions at a local company.
Answers
Answer:
this is a combination problem... permutations would basically let you know
if you had to arrange all 50 applicants on tables for dinner , how many ways can they be seated...
in your case you have 50 items and you are CHOOSING 2 ...
you need the 50c2
Step-by-step explanation:
How do you convert categorical variables to dummy variables?
Answers
To convert categorical variables to dummy variables, follow these steps:
1. Identify the categorical variable(s) in your dataset that you wish to convert.
2. For each categorical variable, determine the number of unique categories (levels).
3. Create new binary variables (dummy variables) equal to the number of unique categories minus one for each categorical variable.
4. Assign a unique combination of 0s and 1s to represent each category within the new dummy variables. Typically, 1 indicates the presence of a category, while 0 indicates its absence.
5. Replace the original categorical variable(s) with the corresponding dummy variables in your dataset.
By converting categorical variables to dummy variables, you can use them in statistical analyses that require numerical data, such as regression models.
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24, which is 10% of the money they wanted to raise
Answers
Answer:
$2,000
Step-by-step explanation:
Let the amount of money they want to raise be $20,000.
We are going to look for 10% of $20000 as shown:
10% of 20,000 = 10/100 * 20,000
= 0.1 * 20,000
= 2,000
Hence the 10% of the money they want to raise is $2,000
Note the the money the amount of money they want to raise was assumed.
Find the particular solution of the differential equation that satisfies the initial condition(s). f?''(x) = sin(x), f?'(0) = 2, f(0) = 3
f(x)=
Answers
The particular solution of the differential equation is:
f(x) = -sin(x) + 3x + 3
To find the particular solution of the differential equation f''(x) = sin(x) that satisfies the initial conditions f'(0) = 2 and f(0) = 3, follow these steps:
1. Integrate f''(x) = sin(x) once with respect to x:
f'(x) = ∫sin(x) dx = -cos(x) + C₁
2. Use the initial condition f'(0) = 2 to find C₁:
2 = -cos(0) + C₁
C₁ = 3
So, f'(x) = -cos(x) + 3
3. Integrate f'(x) again with respect to x:
f(x) = ∫(-cos(x) + 3) dx = -sin(x) + 3x + C₂
4. Use the initial condition f(0) = 3 to find C₂:
3 = -sin(0) + 3(0) + C₂
C₂ = 3
So, the particular solution of the differential equation is:
f(x) = -sin(x) + 3x + 3
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Is (0, 0) a solution to the equation y = 4x?
Answers
Answer: Yes
Step-by-step explanation:
If you plug in (0,0) to the equation you get: 0=4(0)
which is 0=0
Therefore, (0,0) is is a solution to y=4x
Answer:
Yes
Step-by-step explanation:
You can quickly test this by plugging (0, 0) into the equation. Remember that the first point in a coordinate is x, and the second is y.
y = 4x
0 = 4(0)
0 = 0
AC is a diameter of OE, the area of the
circle is 289 units2, and AB = 16 units.
Find BC and mBC.
B
A
C
E. plssss hurry !!
Answers
The measure of arc BC is 720 times the measure of angle BAC.
Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).
To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:
AB * BC = AC * CE
16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)
Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:
Area = π * r^2
289 = π * r^2
r^2 = 289 / π
r = √(289 / π)
Now, we can substitute the known values into the equation for the product of the segments:
16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8
To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.
mBC = 0.5 * m(arc BC)
To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:
arc BC = (mBC / 0.5) * 360
arc BC = 720 * mBC
Therefore, the length of the arc BC equals 720 times the length of the angle BAC.
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Which values are areas of cross sections that are parallel to a face of this right rectangular prism?
480 square units
120 square units
80 square units
24 square units
Answers
The value is 24 square units is parallel to the face of the right rectangular prism.
We can see that the face of the given rectangular prism shows a width 4 and a height of 6. If we cut the figure at any point along the length 20, such that the cross-section is parallel to the face, the cross-section, which occurs at x length, will always have the same dimensions, which are 4 and 6.
So the area of the cross-section which is parallel to the face of the given rectangular prism is given by:
A = 6 × 4
A = 24
Thus, the value is 24 square units is parallel to the face of the right rectangular prism.
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A = 6 × 4
A = 24
Thus, the value is 24 square units is parallel to the face of the right rectangular prism.
(1 point) find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, have distinct digits :
Answers
The number of positive integers with exactly four decimal digits that is positive integers between 1000 and 9999 is 4536.
The positive integers between 1000 and 9999 inclusive have 4 digits.
The first digit cannot be zero because otherwise, it will become a digit integer.
So, the first digit can be filled in 9 ways.
The second digit can be filled by 9 different ways.
Because the second digit cannot be the same as that of the first digit but zero can be the second digit.
The third digit can be filled by 8 different ways.
The fourth digit can be filled in 7 different ways.
Number of four decimals digits = 9 * 9 * 8 * 7
= 81 * 8 * 7
= 81 * 56
= 4536 digits.
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Find the radius of convergence and the interval of convergence
for the following
series.
∑[infinity] (x − 2)n
nn n=1
Problem 2 Find the radius of convergence and the interval of convergence for the following series. [infinity] n=1 (x − 2)n nn
Answers
the radius of convergence is 1 and the interval of convergence is (1, 3) in terms of x-values.
To determine the radius of convergence, we can use the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1 as n approaches infinity, then the series converges. Applying the ratio test to the given series, we have:
lim(n->∞) |((x - 2)^(n+1)/(n+1)) / ((x - 2)^n/n)| < 1
Simplifying the expression, we get:
lim(n->∞) |(x - 2)n+1 / (n+1)(x - 2)^n| < 1
Taking the absolute value and rearranging, we have:
lim(n->∞) |x - 2| < 1
This implies that the series converges when |x - 2| < 1, which gives us the interval of convergence. The radius of convergence is the distance between the center of the series (x = 2) and the nearest point where the series diverges, which in this case is 1.
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