The tangent planes to the surface are described by the equation "6x + 12y + 48z - 210 = 0" (3, 4, 3).
In this instance, the equation yields the parametrized surface "r(t) = (t², [tex]t^3[/tex], [tex]t^4[/tex]). On the surface, the issue that interests us is (3, 4, 3).
We may use the partial derivative concept to obtain the second derivative of the surface at points (3, 4, 3). Regardless of whether a change in the parameterization approaches zero, the time derivative of the parameter value of a variable serves as the upper estimate of the differentiating quotient.
[(r(3 + h) - r(3)) / h] as h approaches 0
For the x-coordinate of the surface, this limit is given by
[((3 + h)² - 3²) / h] as h approaches 0
which simplifies to
[(9 + 6h + h² - 9) / h] as h approaches 0
which simplifies to
[6h + h²] as h approaches 0
Since h is approaching 0, h2 is approaching it faster than h. As h approaches 0, the limit changes from 0 to 6, and the number of h2 decreases relative to the value of 6h.
Thus, the partial derivative of the x-coordinate of the surface concerning the time at the coordinates (3, 4, 3) is 6.
As a result, the vector is the normal vector to the ground at the location (3, 4, 3). (6, 12, 48). 6x + 12y + 48z + d = 0 is the equation of the tangent planes to the ground at this position.
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What is 5-kilometers / 400 meters
Answer: 12.5 meters!
Step-by-step explanation:
1km = 1000 meters
So 5km = 5000 meters
So take 5000 divided by 400 = 12.5 meters
Answer:
12.5 is the answer for this question
Can we use standard deviation on a curve that is not normal
Answer:Use it as it is or fit non-normal distribution
Step-by-step explanation:
the coefficient of determination resulting from a particular regression analysis was 0.85. what was the correlation coefficient, assuming a positive linear relationship? group of answer choices -0.5 0.922 0.5 there is insufficient information to answer the question.
The coefficient of determination resulting from a particular regression analysis was 0.85. Then, the correlation coefficient, assuming a positive linear relationship is 0.922.
The coefficient of determination, denoted R2 or r2 and pronounced "R-squared," is the proportion of predictable variation in the dependent variable from the independent variables.
R2 has several definitions, sometimes the same. One class of such cases involves simple linear regression where r2 is used instead of R2. If only one bin is included, r2 is simply the square of the sample correlation coefficient (that is, r) between the observed outcome and the observed prediction. If additional regressors are included, R2 is the square of the multiple correlation coefficient. In both cases, the coefficient of determination is usually between 0 and 1.
Regression analysis consists of a dependent variable (often called the "outcome" or "response" variable, or "label" in machine learning parlance) and one or more independent variables (often called "predictors"). ). ', 'covariate', 'explanatory variable' or 'feature'). The most common form of regression analysis is linear regression, which finds the best fit line (or more complex linear combination) to the data according to mathematical criteria. For example, the ordinary least-squares method computes a unique line (or hyperplane) that minimizes the sum of squared differences between the true data and that line (or hyperplane). For certain mathematical reasons (see linear regression), researchers can estimate the conditional expected value (or population mean) of the dependent variable given that the independent variable takes on a particular set of values . Less common forms of regression use slightly different techniques to estimate alternative site parameters (such as quantile regression and requirement analysis, or conditional expectations on a broader collection of nonlinear models. estimating values (such as nonparametric regression). Regression analysis is primarily used for two conceptually distinct purposes.
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assume there are 5 red balls, 6 blue balls, and 4 green balls. if the balls are removed from the box one at a time, in how many different orders can the balls be removed assuming two balls of the same type are indistinguishable?
The number of ways that we can remove the balls one at a time from the box is 1307674368000
Given,
The number of balls in a box;
5 red balls
6 blue balls
4 green balls
We have to find the number of ways the balls can removed from the box one at a time;
Here,
Order is indistinguishable, so combination can be followed;
Combination formula;
ⁿCr = n! / r1(n - r)!
Here,
Total number of balls in the box = 5 + 4 + 6 = 15 balls
Then.
¹⁵C₁₅ = 15! / 15! (15 - 15)! = 15! = 1307674368000
That is,
We can remove the balls one at a time from the box in 1307674368000 ways.
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i need help asap please! 100 points
f(-2) = 254 , meaning if the company sells shirts -2 , they would make a profit of 254 dollars. This interpretation is true in the context of the problem.
f(12) = 266 , meaning if the company sells shirts 12 , they would make a profit of 266 dollars. This interpretation is true in the context of the problem.
f(17.5) = 270.25, meaning if the company sells shirts 17.5 , they would make a profit of 270.25 dollars. This interpretation is true in the context of the problem.
Based on the observations above, it is clear that an appropriate domain for the function is x ≥ - 2.
How to calculate Functions and values?Functions and values given the function that represents elevation, in feet, of Jayden hikes expressed as:
f(x)=(x+2)²+250.
If the domain value of the function is -4, then;
f(-4)=(-4+2)²+250
f(-4) = 4 + 250
f(-4) = 254
f(-4) = 254 means If Jayden hikes 4 miles to the south, his elevation would be 254 feet. This interpretation is true in the context of the problem
If the domain value of the function is -4, then;
f(2)=(2+2)²+250
f(2) = 16 + 250
f(2) = 266
f(2) = 266 means If Jayden hikes 2 miles to the north, his elevation would be 266 feet. This interpretation is true in the context of the problem
If the domain value of the function is 2.5, then;
f(2.5)=(2.5+2)²+250
f(2.5) = 20.25 + 250
f(2.5) = 270.25
f(2.5) = 270.25 means If Jayden hikes 2.5 miles to the north, his elevation would be 270.25 feet. This interpretation is true in the context of the problem
Determining the domain
The domain exist for the value of (x+2)² ≥ 0
x + 2 ≥ 0
x ≥ - 2
Based on the observation above, it is clear that an appropriate domain of the function is x ≥ - 2
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What’s the value of x?
Answer:
a value that is not yet known
find the difference. (7x-6 2/3) - (-3x + 4 3/4)
10x-61/12 is the difference of (7x-[tex]6\frac{2}{3}[/tex]) - (-3x + [tex]4\frac{3}{4}[/tex]).
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is (7x-[tex]6\frac{2}{3}[/tex]) - (-3x + [tex]4\frac{3}{4}[/tex])
7x-[tex]6\frac{2}{3}[/tex]+3x- [tex]4\frac{3}{4}[/tex]
7x-20/3+3x-19/4
Add the variable terms and constant terms.
10x-20/3-19/4
The LCM of 3 and 4 is 12/
10x-4-57/12
10x-61/12
Hence, 10x-61/12 is the difference of (7x-[tex]6\frac{2}{3}[/tex]) - (-3x + [tex]4\frac{3}{4}[/tex]).
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Consider an ideal gas at 27.0 degrees Celsius and 1.00atmosphere pressure. Imagine the molecules to be uniformly spaced,with each molecule at the center of a small cube. What is thelength Lof an edge of each small cube if adjacent cubes touch but don'toverlap?
The length L of an edge of each small cube if adjacent cubes touch but don't overlap is 3.45 nm.
The formula to be used for calculation is -
PV = Nkt, where P is pressure, V is volume, N is number of molecules, k is Boltzmann constant and T is temperature in Kelvin.
T = 273 + 27
Performing addition on Right Hand Side of the equation
T = 300 K
P = 101325 Pa
k = 1.38 × [tex] {10}^{-23} [/tex] J/K
Now finding the volume
V = (1 × 1.38 × [tex] {10}^{-23} [/tex] × 300)/101325
Performing multiplication and division on Right Hand Side of the equation
V = 4.09 × [tex] {10}^{-3} [/tex] m³
As we know, V = L³
So, L = [tex] {V}^{1/3} [/tex]
Keep the value of volume
L = [tex] { (4.09/1000) }^{1/3} [/tex]
Performing calculations
L = 3.45 × [tex] {10}^{-9} [/tex] m
Hence, length is 3.45 nm.
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If 75% of a number is 24, what is 50% of the number? A. 64 B. 16 C. 12 D. 9
Answer:
16
Step-by-step explanation:
a teach selects 77 students from her class of 2727 students. how many ways are there for her to select the students if the chosen students
888030 ways are there for teachers to select the students.
What is the combination?
A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.
Here, we have
A teacher selects 7 students from her class of 27 students.
We have to find how many ways are there for her to select the students of the chosen students.
The order of selecting the students does not matter here so the number of ways to select 7 students from the class of 27 to work together on a project is:
C(27,7) = 27!/(7!*(27-2)! = 888030
Hence, 888030 ways are there for teachers to select the students.
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Solve the system by substitution.
y = -2x + 16
y = 2x
Answer: y = 8 , x = 4
Step-by-step explanation:
gosh darn i haven done this since algebra 1 !!
since both equations equal y, we can make them equal to each other since y = y
-2x +16 = 2x (im just gonna simplify without all the extra steps sorry)
x = 4 (this is the first answer)
now we can plug in x to find y
y = 2(4)
y = 8 (second answer)
im sorry if the grammar is horrid its 3 am
What is slope simple answer?
The slope is the measure of the steepness and direction of a line. You can predict whether lines in a coordinate plane are parallel, perpendicular, or none by finding the slope of the lines.
There are two distinct points on any line that can be used to calculate its slope. Between two distinct points on a line, the slope formula calculates the ratio of vertical and horizontal changes. In mathematics, the slope is calculated as the ratio of the rise to the run, or as the rise divided by the run. The slope is a measure of how steep a line is in a coordinate plane.
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rachel needs to identify the domain for the function {(-1,5) , (2, 3), (33, 6), (32, 7)}. what answer should she get?
The domain for the given function is {-1, 2, 33, 32}.
A function's or relation's domain is the set of all possible independent values that the relation can take. It is the sum of all possible inputs.
A function's or relation's range is the set of all possible dependent values that the relation can produce from the domain values. It is the sum of all possible outputs.
When dealing with sets of ordered pairs, we simply divide the pairs into x- and y-coordinates. The domain is formed by the x-coordinates, which are independent values. The y-coordinates are the dependent values, i.e. they define the range.The domain in the set of ordered pairs {(a,b); (c,d); (e,f); (g,h)} is the set of the first number in each pair (those are the x-coordinates): {a,c,e,g}. The range is the set of all the pairs with the second number (the y-coordinates): {b,d,f,h}.
Given,
The set of ordered pair = {(-1,5) , (2,3), (33,6), (32,7)}
then,
the Domain = {-1, 2, 33, 32}
Range = {5, 3, 6, 7}
Thus, the domain for the given function is {-1, 2, 33, 32}
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Write the coordinates for the center of the hyperbola: (x-2)^2/36 - (y+1)^2/64 = 1
The reasoning above makes it very evident that the hyperbola's coordinate is (8, -1)
How does hyperbola work?The hyperbola is open upward and downward because the expression 'y' has a positive leading coefficient. In comparison to the usual equation, the hyperbola's center is found to be at (2, -1) and its 'a' point, 6, and 'b' point is 8. A smooth curve that lies in a plane and is classified as a hyperbola in mathematics by either its geometric characteristics or by equations for which it is the solution set. Two parts of a hyperbola, referred to as connected components or branches, are mirror reflections of one another and resemble two infinite bows.
Given,
((x-2)²/36)-((y+1)²/64)=1
We know that the standard form of a parabola is:
((x-k)²/a²)-((y-h)²/b²)=1
Center for the given hyperbola is (2, -1)
And a=6, b=8
And the coordinates for the center of the hyperbola are x=8, y= -1
Therefore, (x, y)=(8, -1)
The reasoning above makes it very evident that the hyperbola's coordinate is
(8, -1)
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Which statement is TRUE for f(x)= x³+4x²+x-6?
( x - 1 ) is the factor of f(x) as remainder is 0
What is Polynomial ?A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.
According to the given information
The given polynomial is
f(x) = [tex]x^{3} + 4x^{2} +x -6[/tex]
According to the remainder theorem
( x - 1 ) will be the factor of f(x) , if f(1) is zero
So
= [tex]1^{3} + 4(1)^{2} + 1 -6[/tex]
= 1+4+1-6
= 6-6
= 0
So
( x - 1 ) is the factor of f(x) as remainder is 0
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sarah used 2.5 cups of cheese in a dish that serves 10 people. what constant of proportionality relates the number of servings to cups of cheese?
The constant of proportionality that relates the number of servings to cups of cheese is 0.25.
According to the question,
Sarah used 2.5 cups of cheese in a dish that serves 10 people, this can be written as :
let the c be the cups of cheese : c = 2.5 cups of cheese
let n be the number of the people that is been served
Then the equation can be written as :
c ∝ n
then we can bring in the proportionality constant sign as ;
then c = kn
then we can introduce the given figures into the equation as ;
=> 2.5=k (10)
the we can determine the value of the constant as :
=> k=2.5/10 = 0.25
Hence, constant of proportionality relates the number of servings to cups of cheese is 0.25
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50 points please help me
think sometimes prob 4x5 i don't know
a family of four went out to dinner. the cost of their meal was $75.99. Tax on the meal is 6.75% and they left a 19% tip on the cost of the meal. what is the total amount they will pay
The total amount they will pay would be $95.557
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
Given that the cost of their meal was $75.99. Tax on the meal is 6.75% and they left a 19% tip on the cost of the meal.
Cost of meal = $75.99
The tax amount = 6.75% of 75.99
= ( 6.75/100 ) x 75.99
= $5.129
Tip amount = 19% of 75.99
= (19/100) x 75.99
= $14.438
Thus, the Total amount they will pay
= $75.99 + $5.129 + $14.438 = $95.557
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2.8+1.36 divided by 4-2.7
Answer:
0.44
Step-by-step explanation:
type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. while making oatmeal cookies, angela needs to add 12 cup of milk to her dough. however, she has only a 14-cup measuring cup. how many times does she need to fill the measuring cup to pour 12 cup of milk? the number of times angela needs to fill the 14-cup measuring cup to pour 12 cup of milk is
Therefore , Angela needs to fill this cup 6/7 times.
What is fraction ?A fraction represents a component of a whole or, more generally, any number of equal parts. As in one-half, eight-fifths, and three-quarters, a fraction in conversational English denotes the number of components of a specific size.
Here,
To her dough, Angela needs to add 12 cups of milk. She only has a measuring cup that holds 14 cups.
Thus, the number of times angela needs to fill cup are = 12/14 times
thus ,
=> 12/14 =6/7
Therefore , Angela needs to fill this cup 6/7 times.
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I need help understanding number 3, please help!
Answer:
Step-by-step explanation:
It's asking you to find the measures for all the angles.
For example, angle 1 would be 59° because it is equal to the angle across from it.
Angle 2 would equal 31° because it's a supplement angle to 59° and so on
Find the demand function for the marginal revenue function. recall that if no items are sold, the revenue is 0.
R′(x)=0.06x2−0.05x+138
The required demand function for the marginal revenue function is P = 0.02x² - 0.025x.
What is demand function for the marginal revenue function?Marginal Revenue is the revenue that is gained from the sale of an additional unit. It is the revenue that a company can generate for each additional unit sold; there is a marginal cost attached to it, which must be accounted for.
According to question:The marginal revenue function, find the demand capability is P = 0.02x² - 0.025x + 138 when R'(x) = 0.06x² - 0.05x + 138 .
Considering that,
We need to find for the peripheral income capability, find the interest capability.
Recollect that the pay is zero assuming no things are sold:
R'(x) = 0.06x² - 0.05x + 138
p(x) is what.
That's what we know,
MR = dTR/dx = 0.06x² - 0.05x + 138
Incorporating the marginal revenue function , we get complete income capability,
MR = TR
= (0.06x²⁺¹)/(2+1) - (0.05x¹⁺¹)/(1+1) + 138x
= (0.06x³)/3 - (0.05x²)/2 + 138 x
TR = 0.02 x³ - 0.025 x² + 138 x
TR = (P)(Q) = (P)(x) = 0.02 x³ - 0.025 x² + 138 x
P = ( 0.02 x³ - 0.025 x² + 138 x)/x
P = 0.02x² - 0.025x + 138
In this manner, The marginal revenue function, find the interest capability is P = 0.02x² - 0.025x + 138 when R'(x) = 0.06x² - 0.05x + 138 .
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What is the radius of a circle whose equation is x2 y2 â 10x 6y 18 0 2 units 4 units 8 units 16 units?
The radius of the circle having the equation x² + y² - 10x + 6y + 18 = 0 is 4 units , the correct option is (b) .
In the question ,
it is given that ,
the circle is having equation ⇒ x² + y² - 10x + 6y + 18 = 0 ,
we know that ,
general equation of circle is ⇒ x² + y² + 2fx + 2gy + c = 0 ;
So , radius of circle is calculated using the below formula ,
radius [tex]=[/tex] √(f² + g² - c)
On comparing, given equation of circle with general equation of circle ,
we get , the values of f = -5 and g = 3 .
So after substituting values of f , g and c in radius formula ,
we get ,
radius = √(25 + 9 - 18)
= √(34 - 18)
= √16 = 4 .
Therefore , the given circle has radius = 4 units .
The given question is incomplete , the complete question is
What is the radius of a circle whose equation is x² + y² - 10x + 6y + 18 = 0 ?
(a) 2 units
(b) 4 units
(c) 8 units
(d) 16 units
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Please help asap
Triangle ABC has the following angle measures:
m∠A = (x + 6)°, m∠B = (3x − 15)°, m∠C = (5x + 36)°
What is m∠C?
17°
23°
36°
121°
Answer:
121°
Step-by-step explanation:
x + 6 + 3x -15 + 5x + 36 = 180
9x + 27= 180
9x = 180 - 27
9x = 153
9/9 x = 153/9
x = 17
mC = 5·17 + 36
85 + 36
121°
What is the inverse of the function f (x)=19/x^3
Answer:
Below
Step-by-step explanation:
y = 19/x^3 <===== solve for 'x'
x = cube rt (19/y) < ====now switch the x and y's
y = cube rt ( 19/x)
Answer: f^-1(x) = 19^3/x
Step-by-step explanation:
Given that : f(x) = y = 19/x^3
x^3 = 19/y
y = (19)^3/x = f^-1(x)
Maya uses 14 blue tiles and 10 white tiles to design section of an outdoor patio. Which ratio compares the number of blue tiles to the total number of tiles in the section
Answer:9 : 20
Step-by-step explanation:
graph equation of y = 3.5x after a translation 2 units up. what are the pairs?
The given equation after a translation by 2 units upwards is y = 3.5x + 2.
What is the rule for translation?The rules for translating an equation in both vertical and horizontal directions are:
The equation of the graph is y = f(x). Then its translation along the vertical direction is either upwards or downwards.The equations after upward and downward translations are y = f(x) + m and y = f(x) - m.When the translation is along the horizontal direction (i.e., left or right), the equations after the left and right translations are y = f(x+m) and y = f(x - m).Calculation:The given equation is y = 3.5x
The equation after translation by 2 units upward is obtained by using the rule we have y = f(x) + m.
⇒ y = 3.5x + 2
The graphs for the given equation and the translated equation are shown in the graph below.
For the pair that show translation in both equations, substituting x = 0, we get
y = 3.5x ⇒ y = 3.5(0) = 0; So, the point is (0,0)
and
y = 3.5x + 2 ⇒ y = 3.5(0) +2 = y = 2; So, the point (0,2)
Therefore, the required pair is (0,0) and (0,2).
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What is a split sentence in grammar?
Answer:
A split infinitive is a common grammatical mistake that can be hard for writers to spot. Many people think they are not a big deal, but they can often have a major impact on your writing and make it hard for a reader to understand what you have to say.
Step-by-step explanation:
Take, for example, this sentence:
I like to on a hot day eat a lot of ice cream.
Did you have to read it twice to be clear what it was saying? I know I did. But let's make just a little adjustment:
On a hot day, I like to eat a lot of ice cream.
Look at this set of data:
3, 7, 4, 6, 3, 5, 9, 40, 6, 3
What is the mode?
6
4
2
3
5
Answer:
mode = 3
Step-by-step explanation:
the mode is the value that occurs most often in the data set
3, 7, 4, 6, 3, 5, 9, 40, 6, 3
the value 3 occurs most often , 3 times
then mode of data set = 3
Find missing side with trigometry
The measure of the perpendicular of the right-angle triangle will be 16.728 units.
What is trigonometry?Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
The sine of the angle is the ratio of perpendicular to the hypotenuse.
sin θ = Perpendicular / Hypotenuse
The angle is 42° and the measure of Hypotenuse is 25. Then the measure of the side 'x' will be given as,
sin θ = Perpendicular / Hypotenuse
sin 42° = Perpendicular / 25
Perpendicular = 25 x sin 42°
Perpendicular = 16.728
The measure of the perpendicular of the right-angle triangle will be 16.728 units.
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