Linear equation for the relationship between flour and milk cups
y = 4x,
where x is number of milk cups
y is number of flour cups
What is linear equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.
A recipe requires 1 cup of milk for every 4 cups of flour.
Ratio between milk(x) and flour(y)
x/y = 1/4
y = 4x
where x number of cups of milk
y is number of cups of flour
Hence, y = 4x is the linear equation that defines the relationship.
Learn more about linear equation here:
https://brainly.com/question/29739212
#SPJ1
Chantelle works at Mattresses R Us. She had $60,000 in sales and made $1200 in commission. What percent commission does she get?
Jamie spent a total of $11.60 on 5 identical pens and a ruler. A ruler cost $1.30 less than a pen. How much did each pen cost?
Answer: $2.15
Step-by-step explanation: Let x represent the price of a pen.
5x + (x - 1.30) = 11.60
6x - 1.30 = 11.60
6x = 12.90
x = 2.15
What does "as a multiple of a power of 10" mean?
Answer:
When we multiply by a power of 10 (such as 10, 100, 1000, 10000, etc.), the number of digit zeros in the power of 10 is the number of places we move the decimal point to the right.
Check here for more information on this topic: www.khanacademy.org
Step-by-step explanation:
Find x, PLEASEE HELPP PLEASE
the angle bisector theorem formula yields the value x=10.
What is the angle bisector theorem's formula?The angle bisector theorem states that RU/RT=US/ST or a/b = x/y. A line or ray known as an angle bisector divides an angle in a triangle into two identically sized parts.
What guidelines apply to bisectors?The geometry concept known as the angle bisector theorem examines the ratios of the two segments that a line that bisects the opposing angle splits a triangle's side into. It contrasts their relative lengths with the ratios of the other two sides of the triangle.
Side ratio: RU/RT=US/ST
3x/40 = x+2/16
6x=5x +10
x=10
To know more about angle bisector theorem visit:-
https://brainly.com/question/8022146
#SPJ1
deep thought granola is 25% nuts and dried fruit. oat dream granola is 10% nuts and dried fruit. how much of deep thought and how much of oat dream should be mixed to form 20 lb of granola that is 19% nuts and dried fruit?
Let's call the amount of Deep Thought granola mixed "x" (in pounds). The amount of Oat Dream granola mixed would then be 20 - x (in pounds).
We know that Deep Thought granola is 25% nuts and dried fruit and Oat Dream granola is 10% nuts and dried fruit. We also know that the desired mix of 20 pounds of granola should be 19% nuts and dried fruit.
Therefore, we can set up the following equation to find the amount of Deep Thought and Oat Dream granola to be mixed:
0.25x + 0.10(20 - x) = 0.19 * 20
Expanding the right side of the equation and solving for x, we get:
0.25x + 2 - 0.1x = 3.8
0.15x = 1.8
x = 12
So, we would mix 12 pounds of Deep Thought granola and 8 pounds of Oat Dream granola to get 20 pounds of granola that is 19% nuts and dried fruit.
To know more about
To know more about Linear equation
https://brainly.com/question/2030026
#SPJ4
Use calculus to find the area of the triangle with the given vertices: (0,0) (2.8) (5,6)
The area of the triangle with the given vertices is 6.6.
The formula for finding the area of a triangle given its vertices is A = 1/2 abs(x1y2 + x2y3 + x3y1 - x2y1 - x3y2 - x1y3). To calculate the area of the given triangle, we substitute the coordinates of each vertex into the formula. First we find the three cross-products: x1y2 = 0 * 6 = 0, x2y3 = 2.8 * 6 = 16.8, and x3y1 = 5 * 0 = 0. Then, we find the two products of the y-coordinates: x2y1 = 2.8 * 0 = 0, and x3y2 = 5 * 6 = 30. Lastly, we find the product of the x-coordinates: x1y3 = 0 * 6 = 0. Adding all these up, we get 0 + 16.8 + 0 - 0 - 30 - 0 = -13.2. We then take the absolute value of the result, abs(-13.2) = 13.2. Finally, we multiply the result by 1/2 to get the area of the triangle, A = 1/2 abs(-13.2) = 1/2 * 13.2 = 6.6. Therefore, the area of the triangle with the given vertices is 6.6.
Learn more about area of a triangle here:
https://brainly.com/question/29133099
#SPJ4
find the lateral surface area of the cylinder used to play for for pie and round to the nearest whole number
Answer:
Step-by-step explanation:
10π cm * 12 cm = 120π cm² ≈ 377 cm²
Organize each of the following equations to express P as a function of Q. Q as a function of P P as a function of Q Q = 20 - P P = 20 - Q Q = 12 - 3P P=4-10 8Q = 18 - 2P
The following equations are organized for P as a function of Q
1) P = 20-8Q
2) p = [tex]\dfrac{12-Q}{3}[/tex]
3) p = 9 - 4Q
What is function?A function in mathematics is, technically speaking, a relation between a set of inputs and a set of potential outputs, where each input is related to exactly one output. Examples of functions in mathematics typically range from integers to integers or from real numbers to real numbers.
Additionally, it is a relation or a process that links each element x of a set X to the codomain of the function and to a single element y of a different set Y (typically the same set).
1) Q = 20-P
Q + P = 20
P = 20-Q
2) Q=12-3P
Q +3P = 12
3P = 12-Q
p = [tex]\dfrac{12-Q}{3}[/tex]
P = 4 - 1/3Q
3) 8Q = 18 -2p
8Q + 2p = 18
2p = 18 - 8Q
p = [tex]\dfrac{18-8Q}{2}[/tex]
p = 9 - 4Q
Learn more about function
https://brainly.com/question/12431044
#SPJ4
Complete question:
what is the answer to my i have struggle to get this problem
Answer:
X = 17
Step-by-step explanation:
Since M = N then,
(3x - 22) = (2x-5)
What we can do next is get the X's on one side and the numbers on the other side of the equal sign
Let's subtract 2x from both sides
3x - 2x is just X, so
X - 22 = -5
Now we can add 22 to both sides. -5+22 = 17
X = 17
Plug in 17 to make sure
(3x - 22) = 3(17)-22 = 51-22 = 29
(2x-5) = 2(17)-5 = 34 - 5 = 29
Add or Subtract the following equation
The solution for the given expression [tex]\frac{x^{2} + y^{2} }{x^{3} + y^{3} } - \frac{1}{x + y}[/tex] will be [tex]\frac{xy}{x^{3} + y^{3} }[/tex].
What is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given an expression [tex]\frac{x^{2} + y^{2} }{x^{3} + y^{3} } - \frac{1}{x + y}[/tex]
We will solve this equation using the simplification methods,
Since,
a³ + b³ = (a +b)(a² +b² - ab)
From this formula;
=> [tex]\frac{x^{2} + y^{2} }{x^{3} + y^{3} } - \frac{1}{x + y}[/tex]
=> [tex]\frac{x^{2} + y^{2} }{(x + y)(x^{2} + y^{2} - xy) } - \frac{1}{x + y}[/tex]
taking 1/(x +y) common,
=> 1/(x +y) { (x² + y²)/(x² +y² - xy) - 1}
=> 1/(x +y) { xy/(x² +y² - xy)}
=> xy/(x³ +y³)
Therefore, [tex]\frac{xy}{x^{3} + y^{3} }[/tex] will be the simplified form of the given Equation.
Learn more about expression here:
https://brainly.com/question/23246712
#SPJ1
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.
The correct two expressions have the same solution are,
⇒ 230p - 1010 = 650p - 400 - p
⇒ 23p - 101 = 65p - 40 - 0.1p
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ 2.3p - 10.1 = 6.5p - 4 - 0.01p
Now, We can simplify as;
⇒ 2.3p - 10.1 = 6.5p - 4 - 0.01p
Multiply by 10 both side,
⇒ 23p - 101 = 65p - 40 - 0.1p
And, ⇒ 2.3p - 10.1 = 6.5p - 4 - 0.01p
Multiply by 100 both side,
⇒ 230p - 1010 = 650p - 400 - p
Thus, The correct two expressions have the same solution are,
⇒ 230p - 1010 = 650p - 400 - p
⇒ 23p - 101 = 65p - 40 - 0.1p
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
The complete question is this;
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
for what value of θ is | r | a maximum if r = sinθ and 0 < θ < π?
The value of θ for which | r | has maximum value if r = sinθ is θ = π/2.
Given r = sinθ and the range of θ is 0 < θ < π
If 0 < θ < π the range of sinθ is:
0 ≤ sinθ ≤ 1
So, in 0 < θ < π, the maximum value of sinθ is 1 and this value occurs at θ = π/2.
Now, we are asked to determine the value θ for which | r | is maximum and it is also given that r = sinθ and we have already found out that the maximum of sinθ in 0 < θ < π is 1.
Therefore, the maximum value of | r | is 1 and this value occurs at θ = π/2.
To learn more about maximum value here:
brainly.com/question/14316282
#SPJ4
Natan Nave bought a home with a 13% adjustable rate mortgage for 20 years. He paid $11. 72 monthly per thousand on his original loan. At the end of 4 years he owes the bank $75,000. Now that interest rates have gone down to 10%, the bank will renew the mortgage at this rate or Natan can pay $75,000. Natan decides to renew and will pay $9. 66 monthly per thousand on this loan.
What is the amount of the old monthly payment and the new monthly payment? What is the percent of decrease in his new monthly payment? You can ignore the small amount of principal that has been paid
The amount of the old monthly payment = $879
The amount of the new monthly payment = $724.5
Then the small amount of principal that has been paid = -17.57%
Given that,
Natan Nave bought a home with a 13% adjustable rate mortgage for 20 years.
He paid $11. 72 monthly per thousand on his original loan.
At the end of 4 years he owes the bank $75,000.
Now that interest rates have gone down to 10%
The bank will renew the mortgage at this rate or Natan can pay $75,000.
Natan decides to renew and will pay $9. 66 monthly per thousand on this loan.
Per thousand value = 75000/1000 = 75
What was the old monthly payment,
$[tex]11.72*75[/tex] = $879
What is the new monthly payment,
$[tex]9.66*75[/tex] = $724.5
What is the percent decrease in his monthly payment (to the nearest tenth),
= [tex](\frac{9.66}{11.72} )-1 *100[/tex]
= -17.57%
Therefore,
The amount of the old monthly payment = $879
The amount of the new monthly payment = $724.5
Then the small amount of principal that has been paid = -17.57%
To learn more about Amount of Payment problems visit :
brainly.com/question/3492278
#SPJ4
in a change from f/1.4 to f/8 how many times does this change in aperture multiply the amount of light?
The amount of light that passes through a camera lens is determined by the aperture, which is the size of the opening in the lens that lets light in. changing from f/1.4 to f/8 reduces the amount of light that can pass through the lens by a factor of 32.49,
How many times does this change in aperture multiply the amount of light?The size of the aperture is expressed as an f-number, and the lower the f-number, the larger the aperture and the more light that can pass through.When you change from an aperture of f/1.4 to f/8, you're effectively decreasing the size of the aperture by a factor of 8/1.4, or about 5.7 times. As a result, the amount of light that can pass through the lens will be reduced by the square of this factor, or approximately 32.49 times.To put it simply, changing from f/1.4 to f/8 reduces the amount of light that can pass through the lens by a factor of 32.49, meaning less light reaches the camera's sensor and you need to compensate by using a slower shutter speed or higher ISO value.To learn more about Aperture refer:
brainly.com/question/1771913
#SPJ4
Find the function value given the function f(x) = |x|3
f(0)
f(-3)
f(3)
f(-10)
f(a-3)
f(ah)
The values are 0,27,27,1000 and dependent values.
A function is a mathematical rule that assigns a unique output to each input value. The input values are called the independent variables, and the output values are called the dependent variables. The relationship between the input and output values is defined by a mathematical expression or a set of instructions.
f(0) = |0|^3 = 0^3 = 0
f(-3) = |-3|^3 = 3^3 = 27
f(3) = |3|^3 = 3^3 = 27
f(-10) = |-10|^3 = 10^3 = 1000
f(a-3) = |a-3|^3 = (a-3)^3 if a >= 3, and -(a-3)^3 if a < 3
f(ah) = |ah|^3 = (ah)^3 if h >= 0, and -(ah)^3 if h < 0
So, depending on the values of a and h, the value of f(a-3) and f(ah) will change. For example, if a = 5 and h = -1, then f(a-3) = f(2) = |2|^3 = 8 and f(ah) = f(-5) = |-5|^3 = 125.
Therefore, The values are 0,27,27,1000 and dependent values.
To learn more about functions,
Visit; brainly.com/question/12431044
#SPJ4
The values are 0,27,27,1000 and dependent values.
A function is a mathematical rule that assigns a unique output to each input value. The input values are called the independent variables, and the output values are called the dependent variables. The relationship between the input and output values is defined by a mathematical expression or a set of instructions.
f(0) = |0|³= 0³ = 0
f(-3) = |-3|³ = 3³ = 27
f(3) = |3|³ = 3³ = 27
f(-10) = |-10|³ = 10³ = 1000
f(a-3) = |a-3|³ = (a-3)³ if a >= 3, and -(a-3)³ if a < 3
f(ah) = |ah|³ = (ah)³ if h >= 0, and -(ah)³ if h < 0
So, depending on the values of a and h, the value of f(a-3) and f(ah) will change. For example, if a = 5 and h = -1, then f(a-3) = f(2) = |2|³ = 8 and f(ah) = f(-5) = |-5|³ = 125.
Therefore, The values are 0,27,27,1000 and dependent values.
To learn more about functions,
brainly.com/question/12431044
#SPJ4
Answer sheet. 1. Samantha is y years old now. What is Samantha's age if her age 5 years from now is 17? 2. Aki is g centimeter tall. Pierre's height is 4 less than thrice the height of Aki. The difference between Aki's height when subtracted from Pierre's height wil result to 240 centimeters. How tall is Aki? 3. In three years, the price of a new model of an S6 - model phone will be six more than twice its current price. If the projected price of the new S6 phon is p 40,000. 0. What is its current price? 4. Benjie is 6 years old. Ruel is 5 years more than thrice Benjie's age. How ol is Ruel? 5. Five friends share a box of pencils. Each receives 4 pencils. Find the num of pencils in the box,
To Calculate the Sum or Difference : x = 12
How to find the Equation?When two or more numbers or terms are added together, the total is the outcome or answer.
Consequently, the sum is a method of assembling objects.
The process of combining two or more numbers to create a new result or total is known as the sum, to put it another way.
Where Samantha's age at the moment is y and her age in five years is a. In light of the fact that she will turn 17 in 5 years, she is currently 12 years old. Consequently, y in this situation equals 12.
In summary, a = age in 5 years, and y = age right now (12)
Based on the given condition, Write :
x = 17 - 5
Calculate the Sum or Difference : x = 12
x = 12.
To Learn more About Sum or Difference Refer To:
https://brainly.com/question/24170327
#SPJ4
A scatter plot is shown on the coordinate plane.
Which two points would a line of fit go through to best fit the data?
(3, 6) and (7, 3)
(3, 7) and (9, 1)
(1, 9) and (10, 1)
(1, 7) and (2, 5)
The two points that would line of fit go through to best fit the data is (1, 9) and (10, 1).
What is Scatterplots?Scatterplots are the plotting of set of points on a vertical axis and an horizontal axis. The shows the correlation extent between the numbers of the observed quantities.
Given a scatterplot.
There are 10 points which are marked in the scatterplot.
We have to identify the points which are closely related to the general trend of the line.
Those points will be best passing through the line of best fit.
Here the graph will be negative, since the values on the vertical line are decreasing with the increase in the values on horizontal.
Hence the two points are (1, 9) and (10, 1).
Hence the two points are (1, 9) and (10, 1).
Learn more about Scatterplots here :
https://brainly.com/question/29366075
#SPJ2
A gymnast joined a yoga studio to improve his flexibility and balance. He pays a monthly fee and a fee per class he attends. The equation y = 10 + 20x represents the amount the gymnast pays for his membership to the yoga studio per month for a certain number of classes.
Which graph represents this situation?
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 20 through the point 1 comma 30
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 20 through the point 1 comma 10
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point 1 comma 30
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point one half comma zero
The graph of y = 10 + 20x that represents the situation is shown in the attachment.
What is the Graph of a Linear Equation?A graph of a linear equation is a straight line on a coordinate plane that represents all the solutions to the equation. A linear equation can be written in the form of y = mx + b, where m is the slope of the line and b is the y-intercept.
The slope and y-intercept determine the position and direction of the line on the coordinate plane. Points on the line satisfy the equation, and any x and y values that satisfy the equation can be plotted on the graph to form the line. The graph of a linear equation can be used to visualize relationships between variables and to make predictions about the values of the variables based on the line.
Thus, the equation y = 10 + 20x will have a graph that has a y-intercept of 10 and a slope of 20. The graph is shown below.
Learn more about the graph of linear equation on:
https://brainly.com/question/14323743
#SPJ1
Answer:
what the person above said pls give the brainliest
Step-by-step explanation:
In a trivia game, Colleen had 260 points at the end of her first five turns.
On her next five turns, she lost 170 points. Which expression shows how to
find how many points Colleen had after ten turns?
Colleen had 90 points after ten turns, which was calculated by subtracting 170 from her initial 260 points.
The expression to find how many points Colleen had after her ten turns is 260 - 170 = 90. This expression can be written mathematically as P = 260 - 170, where P is the total points after ten turns. To solve this equation, we first subtract 170 from 260. This yields a total of 90 points, which is the number of points Colleen had after her ten turns. The calculation can be summarized as follows:
P = 260 – 170
P = 90
Therefore, after ten turns,Colleen had 90 points after ten turns, which was calculated by subtracting 170 from her initial 260 points.
Learn more about ten turns here:
https://brainly.com/question/556451
#SPJ4
A credit card holder has an outstanding balance on four different credit cards. Which method of paying off the credit card will take the longest period of time? Making fixed payments each month Paying the minimum balance each month Snowballing payments according to the highest interest rate Snowballing payments according to the lowest balance
Paying only the minimum balance each month will take the longest period of time to pay off the credit card debt.
What is interest?Simple interest is defined as the percentage of earnings on the lending for a period of time.
Paying only the minimum balance each month will take the longest period of time to pay off the credit card debt. This method is often referred to as "minimum payment plan." By making only the minimum payment each month, the credit card holder will pay mostly interest, and very little of the principal balance. This will result in a longer period of time to pay off the debt, as the outstanding balance will only decrease slowly each month.
In contrast, making fixed payments each month, regardless of the minimum payment, will result in paying off the debt more quickly. Snowballing payments according to the highest interest rate or the lowest balance will also help pay off the debt more quickly, as these methods prioritize paying off the credit cards with the highest interest rate or the lowest balance first.
Learn more about interest here:
https://brainly.com/question/20406888
#SPJ1
choose the phrase that correctly completes the statement. if r(x) is a rational function in simplest form where the degree of the numerator is 2 and the degree of the denominator is 2, then
Answer: this is the basic d
Step-by-step explanation idf k man comletely honest, i just searched that shi up and i saw that so yeah...
There must be at least one x-value that makes the function undefined if r(x) is a rational function.
If r(x) is a rational function in simplest form where the degree of the numerator is 2 and the degree of the denominator is 2, then it is possible for the function to be undefined for some values of x.
A rational function is defined as the quotient of two polynomials, and when the degree of the numerator is equal to the degree of the denominator, it is possible for the denominator to equal zero for some values of x, which would make the function undefined for those values.
This means that there must be at least one x-value that makes the function undefined. To determine these x-values, we need to find the zeros of the denominator and set the denominator equal to zero, then solve for x.
The x-values that make the denominator equal to zero are known as the vertical asymptotes of the function, and they are the x-values for which the function is undefined.
To know more about rational function click on the link below:
https://brainly.com/question/20850120#
#SPJ11
Solve equation by using the quadratic formula.
15 x squared + 13 x = 0
a.
x = negative StartFraction 13 Over 15 EndFraction, 0
c.
x = StartFraction 13 Over 15 EndFraction, 0
b.
x = 0
d.
x = plus-or-minus StartFraction 13 Over 15 EndFraction
The solution is Option A.
The value of the equation is x = -13/15 and x = 0
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
15x² + 13x = 0 be equation (1)
On simplifying the equation , we get
Subtracting 13x on both sides of the equation , we get
15x² = -13x
Divide by x on both sides of the equation , we get
15x = -13
Divide by 15 on both sides of the equation , we get
x = - ( 13/15 )
So , when x = 0
0 = 0
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
x = -13 ± √ ( 169 - 4 ( 15 ) ( 0 ) ) / 2 ( 15 )
x = -13 ± √ ( 169 - 0 ) / 30
x = ( -13 ± 13 ) / 30
So , we have 2 solutions to x ,
x = ( -13 - 13 ) / 30
x = -26 / 30
x = -13/15
And , x = ( -13 + 13 ) / 30
x = 0/30
x = 0
Hence , the solutions to the equation is x = -( 13/15 ) and x = 0
To learn more about quadratic equations click :
https://brainly.com/question/25652857
#SPJ1
need help fast Select the correct answer.
Consider the function f(x) = 7x and the function g(x), which is given below.
G(X) = 1/3 x F(X) = 1/3 x 7^X
How will the graph of g(x) differ from the graph of f(x)?
A.
The graph of g(x) is the graph of f(x) vertically compressed by a factor of three.
B.
The graph of g(x) is the graph of f(x) vertically stretched by a factor of three.
C.
The graph of g(x) is the graph of f(x) vertically compressed by a factor of 1/3.
D.
The graph of g(x) is the graph of f(x) vertically stretched by a factor of 1/3.
The correct statement regarding the transformation and the difference of functions f(x) and g(x) is given as follows:
A.
The graph of g(x) is the graph of f(x) vertically compressed by a factor of three.
How to describe the transformation?The parent function for this problem is given as follows:
f(x) = 7^x.
The transformed function for this problem is given as follows:
g(x) = f(x)/3 = (1/3) x 7^x.
The only transformation is a multiplication by the constant 1/3. As the constant has an absolute value less than 1, the graph of g(x) is a vertical compression of the graph of f(x) by a factor of 3.
More can be learned about transformations at https://brainly.com/question/29209050
#SPJ1
Find parametric equations for the line that is tangent to the given curve at the given parameter value. r(t) = (2t^2) i + (3t + 4) j + (2t^3) k, t = t_0 = 3 What is the standard parameterization for the tangent line? x= y= z =
The standard parameterization for the tangent line :
x = 12t + 18 , y = 3t + 13 , z = 54t + 54
parametric equation, a type of equation that employs an independent variable called a parameter (often denoted by t) and in which dependent variables are defined as continuous functions of the parameter and are not dependent on another existing variable.
as given,
r(t) = (2t^2) i + (3t + 4) j + (2t^3) k, t = t₀ = 3
so, [tex]x = 2t^{2}, y = 3t + 4 , z = 2t^{3}[/tex]
[tex]\frac{dx}{dt} = 4t, y=3, z=6t^{2}[/tex]
r'(t) = <4t, 3, [tex]6t^{2}[/tex]>
and at t =3,
r'(t=3) = <12, 3, 54>
we have to find the tangent line to the curve at t=3,
x = 18, y = 13, z = 54
for t=3, (x, y, z) = (18, 13, 54)
finally,
x = 12t + 18
y = 3t + 13
z = 54t + 54
Thus, the standard parameterization for the tangent line :
x = 12t + 18 , y = 3t + 13 , z = 54t + 54
To learn more about parametric equations visit : brainly.com/question/29168942
#SPJ4
The standard parameterization for the line tangent to the curve is
x=12t+18 , y=3t+9 , z=54t+54
In parameterization the variables are independent variables , whereas continuous functions are dependent variables , that is it is dependent on another functions. The given curve is r(t)=(2t^2)i+(3t+4)j+(2t^3)k and given t=t0=3
Given , r(t)=(2t^2)i+(3t+4)j+(2t^3)k
r'(t)=(4t)i+3j+(6t^2)k
and also given t=t0=3
r(t=t0=3) => (18 , 9 , 54)
r'(t=t0=3) => (12 , 3 , 54)
The standard parameterization for the tangent line can be given by using r(t) and r'(t) . so by that we came to know the required standard parameterization.
x=12t+18
y=3t+9
z=54t+54
Therefore, the about mentioned x, y, z are the standard parameterization for the tangent line of given curve.
Learn more about parameterization here:
https://brainly.com/question/13566905
#SPJ4
consider a normal distribution with a mean of 10 and standard deviation of 25. what’s the z score for the value of 35?
A normal distribution with a mean of 10 and standard deviation of 25, the z score for the value of 35 is 1.
A mean = 10
Standard Deviation = 25
We have to determine the z score for the value of 35. So X = 35.
The relationship between a value and a set of values' mean is described by the statistical measurement known as the Z-score. Standard deviations from the mean are used to measure Z-score. A Z-score of 0 indicates that the data point's value is equal to the mean score.
The formula is:
Z = (X - mean)/Standard Deviation
Now putting the values
Z = (35 - 10)/25
Z = 25/25
Z = 1
To learn more about z score link is here
brainly.com/question/15016913
#SPJ4
What can we say about the relationship between the correlation r and the slope b of the least-squares line for the same set of data? O both r and b always have values between -1 and 1 O b is always larger than r O r is always larger than b O the slope b is always equal to the square of the correlation O r and b are both positive or both negative
Answer: r and b are both positive or both negative
Reason:
The correlation coefficient r is between -1 and 1
[tex]-1 \le r \le 1[/tex]
If r = -1, then we have perfect negative correlation. All points are on the same straight line that goes downhill as you move to the right. This slope is negative. If -1 < r < 0, then we still have negative slope but the points aren't all on the same line.
If r = 1, then the slope is positive. The regression line moves upward as you move to the right. All points are on this line. If 0 < r < 1, then the points aren't on the same line but we have a positive slope.
If r = 0, then we have no linear correlation at all. Either the points are randomly scattered or they fall on a curve (eg: parabola).
In short:
negative correlation goes with negative slopepositive correlation goes with positive slopeA regular pentagon is centere about the orgin and has a vertex at (0, 4). Which transformation maps the pentagon to itself?.
A clockwise rotation of 144° about the origin will map the pentagon onto itself. Option(c) is the correct answer.
The number of sides (n) of the pentagon is:
n =5
The pentagon will not be plotted onto itself when reflected across the x-axis because the pentagon has 5 sides (an odd number of sides).
To draw the pentagon onto itself, the pentagon has to be rotated.
The angle of rotation is:
θ [tex]= \frac{360}{n}[/tex]
θ [tex]=\frac{360}{5} = 72[/tex]
Other possible angles of rotation must be multiple of 72. i.e.
θ= 72, 144, 216, 288...
Hence, a clockwise rotation of 144° about the origin will map the pentagon onto itself.
Read more about the pentagon:
https://brainly.com/question/11759904
#SPJ4
The complete question is:
A regular pentagon is centered about the origin and has a vertex at (0, 4). Which transformation maps the pentagon to itself?
a. A reflection across line m
b. A reflection across the x-axis
c) A clockwise rotation of 144 degrees about the origin
For what value of c is the function f (x) = c x=-5; 4 x=1; x^2-25 / (x+5)(x-7) otherwise continous at x = -5?
The required function is continuous at x = -5 when c = 4.
Explain about continuity of the function.If it is possible to draw the curve without encountering any breaks, the function is considered to be continuous in the interval. If every point in the interval satisfies the function, the function is said to be continuous.
According to question:For the function to be continuous at x = -5, the value of the function f(-5) must be equal to the value of c. That is,
f(-5) = c
Since f(x) = 4 when x = 1, we have
f(-5) = 4
Therefore,
c = 4
So the function is continuous at x = -5 when c = 4.
To know more about continuity of the function visit:
brainly.com/question/21447009
#SPJ4
Find a polynomial p(t) of degree 6 which has a zero of multiplicity 2 at t = 1 and a zero of multiplicity 3 at
t = 2, and also satisfying: p(0) = 2 and p`(0) = 1. What is the other root of p(t)?
The polynomial that satisfies the conditions is: p(t) = (1/4)(t - 1)² (t - 2)³
This polynomial has a root of multiplicity 2 at t = 1 and a root of multiplicity 3 at t = 2, and also satisfies p(0) = 2 and p'(0) = 1.
The other root of p(t) can be found by factoring the polynomial further, but since the degree of the polynomial is 6, it will have 3 additional roots, which can be found using various mathematical methods such as the Rational Root Theorem or numerical methods.
Polynomials are mathematical expressions that involve variables raised to a power and are combined using addition and subtraction operations. The degree of a polynomial is the highest power of the variable in the expression.
A zero of a polynomial is a value of the variable for which the polynomial evaluates to zero. The multiplicity of a zero is the number of times the factor (t - zero) appears in the polynomial's factorization.
Given the conditions that the polynomial p(t) has a zero of multiplicity 2 at t = 1 and a zero of multiplicity 3 at t = 2, we can write p(t) as the product of factors (t - 1)² and (t - 2)³:
p(t) = a(t - 1)² (t - 2)³
where a is some constant. To find the value of a, we use the fact that p(0) = 2 and p'(0) = 1. We evaluate p(0) and p'(0) using the polynomial expression above, then solve for a.
First, we find p(0):
p(0) = a(0 - 1)² (0 - 2)³ = a(-1)² (-2)³ = a * 8
Next, we find p'(0):
p'(t) = 2a(t - 1)(t - 2)³ + a(t - 1)² * 3(t - 2)²
p'(0) = 2a(-1)(-2)³ + a(-1)² * 3(-2)² = 16a + 12a = 28a
Now that we have expressions for p(0) and p'(0), we can solve for a:
p(0) = a * 8 = 2 => a = 1/4
p'(0) = 28a = 1 => 28 * 1/4 = 1
So the polynomial that satisfies the conditions is:
p(t) = (1/4)(t - 1)² (t - 2)³
Here you can learn more about Polynomials
https://brainly.com/question/11536910#
#SPJ11
An artist designs a rectangular quilt piece with different types of ribbon that go from the corner to the center of the quilt. The dimensions of the rectangle are AB = 12 inches and BC = 18 inches. Find the length of BX to the nearest tenth. (Be careful and don't round until the last step. )
The center is called rectangle point X. The distance from the corner of the rectangle to the center (BX) can be found using the Pythagorean theorem is 21.74 to the nearest tenth be 21.7.
Length of BX in QuiltThe Pythagorean theorem defined that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the right triangle is constructed by sides AB, BC, and BX, with BX being the hypotenuse. So, we can apply the Pythagorean theorem as follows:
BX² = AB² + BC²
Plugging in the values for AB and BC:
BX²= 12² + 18²
BX² = 144 + 324
BX² = 468
Finally, taking the square root of both sides gives us the length of BX:
BX = √(468)
BX = 21.74 to the nearest tenth = 21.7
The description above involves finding the length of the diagonal of a rectangle that goes from one corner of the rectangle to its center. This length is similar to as BX in the definition. To find BX, the Pythagorean theorem is used.
The Pythagorean theorem defined that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the right triangle is constructed by sides AB, BC, and BX, with BX being the hypotenuse.
By substituting the values of AB and BC, the equation BX² = AB² + BC² can be solved to find the length of BX. Finally, taking the square root of the solution gives the length of BX to the nearest tenth.
Learn more about Length of BX in Quilt here:
https://brainly.com/question/30266367
#SPJ4