The equation of the curve that passes through points (0,1), (1,8) is y = 1/9 (3x - 1)⁶ + 8/9
multiply dx on both sides, To shift it over. By doing this, we get
dy = 2 (kx - 1)⁵dx
Using integration, Integrate both sides in relation to dy and dx terms next.
dy = 2 (kx - 1)⁵dx
∫ dy = ∫ 2 (kx - 1)⁵dx
y = 2 ∫ (kx - 1)⁵dx
Here, a u-substitution is possible. Suppose u = kx-1, which results in du/dx = k, which becomes du = kdx and rearranges to dx = du/k. Consequently, the subsequent steps can look like, y = 2 ∫ (kx - 1)⁵dx
y = 2 ∫ u⁵ × du/k
y = 2/k ∫ u⁵ × du
y = 2/k ( 1/ 5 +1 u⁵⁺¹ + C )
y = 2/k ( 1/ 6 u⁶+ C )
y = 2/k ( 1/ 6 (kx - 1)⁶ + C )
Let's enter (x,y) = (0,1) and use a little algebra to find C. On the right, we'll see an equation in terms of k.
y = 2/k ( 1/ 6 (kx - 1)⁶ + C )
1 = 2/k ( 1/ 6 (k × 0 - 1)⁶ + C )
1 = 2/k ( 1/ 6 + C )
k = 2 ( 1/ 6 + C )
k = 1/3 + 2C
3k = 1 + 6C
6C = 3k - 1
C = (3k - 1) / 6
Let's now insert that C value along with (x,y) = (1,8). After that, calculate k to obtain a precise number.
y = 2/k ( 1/ 6 (kx - 1)⁶ + C )
8 = 2/k ( 1/ 6 (k × 1 - 1)⁶ + ( 3k - 1 )/6 )
Find the root of the function using a graphing calculator. The x intercept is 3 and k is the input x. This would get you, C = (3k - 1) / 6
C = (3 × 3 - 1) / 6
C = 8/6
C = 4/3
Therefore, y = 2/k ( 1/ 6 (kx - 1)⁶ + C )
y = 2/3 ( 1/ 6 (3x - 1)⁶ + 4/3 )
y = 1/9 (3x - 1) ⁶ + 8/9 , hence the final equation.
To learn more about integration click here
brainly.com/question/23567529
#SPJ4
The associative property states that when adding or multiplying three or more terms, you can group the terms in any order and still get the same answer. The expression must use only one operation. For example, 4 × 3 × 2 can be thought of as 4·(3 · 2), which is 4 · 6, or as (4 · 3) · 2, which is 12 · 2.
The associative property works with addition and multiplication, but not division and subtraction.
The associative property works with addition and multiplication, but not division and subtraction because the grouping of terms affects the result of the operation.
A mathematical concept known as the associative property governs the addition and multiplication of three or more terms. It claims that the way the phrases are grouped has no bearing on how the operation turns out.
This implies that the same result may be obtained by adding or multiplying three or more terms in any sequence. Nevertheless, division and subtraction are not covered by the associative property.
We should take a gander at the accompanying cases to show how expansion and increase are connected:
Example 1: Addition
(2 + 3) + 4 = 2 + (3 + 4)
5 + 4 = 2 + 7
9 = 9
Example 2: Multiplication
(2 × 3) × 4 = 2 × (3 × 4)
6 × 4 = 2 × 12
24 = 24
We can observe from both cases that the word grouping has no impact on the operation's outcome. The associative characteristic, therefore, applies to both addition and multiplication.
The associative characteristic, however, does not apply to division and subtraction. For instance:
(8 ÷ 4) ÷ 2 ≠ 8 ÷ (4 ÷ 2)
2 ÷ 2 ≠ 8 ÷ 2
1 ≠ 4
We can observe from this example that the term grouping has an impact on the operation's outcome. The associative property does not, therefore, apply to division.
The associative property does not also hold for subtraction. For instance:
(8 - 4) - 2 ≠ 8 - (4 - 2)
4 - 2 ≠ 8 - 2
2 ≠ 6
In this example, we can again see that the grouping of terms affects the result of the operation. Therefore, the associative property does not apply to subtraction.
Learn more about associative property at
https://brainly.com/question/30111262
#SPJ4
What is the answer for this I’m stuck
This is algebra
The simplest form of (m². m⁵. m⁻³ ) is m⁴
Exponent:Writing a number as the product of itself a number of times are known as an Exponent.
For example,
If 7 is multiplied by itself 3 times, i.e. 7 × 7 × 7. This can be represented as 7³. Where 7 is the base and 3 is the exponent.
If a is multiplied by itself b times, i.e. a × a × a...(b times). This can be represented as (aᵇ). Where 'a' is the base and 'b' is the exponent.
Here we have
The expression (m². m⁵. m⁻³ )
As we know, (aᵇ . aˣ. aᵃ) = aᵇ⁺ˣ⁺ᵃ
(m². m⁵. m⁻³ ) = m²⁺⁵⁻³ = m⁴
Therefore,
The simplest form of (m². m⁵. m⁻³ ) is m⁴
Learn more about Exponents at
brainly.com/question/29390053
#SPJ1
Solve number 10 in the image below.
The relationship between the rectangles ABCD and WXYZ is AB = WX.
What are rectangles?The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.
Given the rectangles ABCD and WXYZ, in a coordinate grid,
length of rectangle ABCD is parallel to the Y-axis and the length of rectangle WXYZ is parallel to the X-axis,
let us consider the scale of the grid to be 1 unit,
from graph,
AD = BC = 5 units
AB = DC = 3 units,
and for rectangle WXYZ,
XY = WZ = 5 units
WX = YZ = 3 units
so AB = WX
Hence option D is correct.
Learn more about rectangles;
https://brainly.com/question/29123947
#SPJ1
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 7, with tick marks every one unit up to 32. The graph is titled Tickets Sold for A Dance. The box extends from 15 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 8 and 31.
Which of the following is the appropriate measure of variability for the data, and what is its value?
The IQR is the best measure of variability, and it equals 13.
The IQR is the best measure of variability, and it equals 6.
The range is the best measure of variability, and it equals 13.
The range is the best measure of variability, and it equals 6.
The correct statement regarding the best measure of the variability is given as follows:
The IQR is the best measure of variability, and it equals 6.
What is the Interquartile Range of a data-set?The Interquartile Range (IQR) of a data-set represents the difference between the third quartile and the first quartile of the data-set.
As it is not affected by outliers, it is the best measure of variability of a data-set.
The quartiles for this problem are given as follows:
First quartile: Q1 = 15.Third quartile: Q3 = 21.Hence the IQR is obtained as follows:
IQR = 21 - 15
IQR = 6.
More can be learned about the interquaritle range of a data-set at https://brainly.com/question/12323764
#SPJ1
solid shapes are regular when all the faces are eaqual which 3d shapes is regular?
a) cylinder
b) cube
c) cuboid
A solid shape is considered to be regular if all of its faces are congruent, meaning they have the same shape and size. In the context of three-dimensional shapes, there are several examples of regular solid shapes, including the cylinder, cube, and cuboid.
A) Cylinder: A cylinder is a solid shape with two parallel, congruent circular bases connected by a lateral surface. All of the lateral faces of a cylinder are parallelograms, and the circular bases have the same shape and size, making the cylinder a regular solid shape.
B) Cube: A cube is a regular solid shape with six congruent square faces. All of the faces meet at right angles, and each face is parallel to the opposite face, making the cube a regular solid shape.
C) Cuboid: A cuboid is a solid shape with six rectangular faces. The opposite faces of a cuboid are congruent rectangles, and all of the faces meet at right angles, making the cuboid a regular solid shape.
In conclusion, the cube and the cuboid are regular solid shapes because all of their faces are congruent, while the cylinder is a regular solid shape because all of its lateral faces are congruent parallelograms and its bases have the same shape and size. These regular solid shapes are useful in geometry and provide a foundation for understanding the properties of more complex solid shapes.
To know more about solid shape: https://brainly.com/question/21173778
#SPJ4
Find the value of x. 117° 94°
Answer im not sure frl but its ok
Step-by-step explanation:
Answer: 7
Step-by-step explanation:
PLEASE HELP ASAP WILL GIVE BRAINLEST!
The value of the x is 228.57 units.
What is the angle bisector theorem?
The angle bisector theorem states that a triangle's angle divides the opposing side into two portions that are proportionate to one another.
We have given,
Triangle, Let's consider it ΔABC,
then,
Measures of Angles ∠B= 37, ∠C=32, and side AD = 82
To find x =?
In the triangle side AD is the bisector, it forms a new triangle ΔADC.
According to the angle bisector theorem, the angle bisector of a triangle divides the opposite side into two parts that are proportional to the other two sides of the triangle.
As per the Angle bisector theorem, the ratio of the line segment BD to DC equals the ratio of the length of the side AB to AC.
To find AB & AC:
sin θ = side opposite to angle θ / hypotenuse
cos θ = side adjacent to angle θ / hypotenuse
sin θ = AD / AB
sin 37 = 82 / AB
AB = 82/ sin 37
AB = 136.25
cos θ = BD / AB
cos θ = BD/136.25
BD = cos37 * 136.25
BD = 104.9
sin θ = AD / AC
sin32 = 82 / AC
AC = 149
cos32 = DC / AC
cos32 = DC / 149
DC = 123.67
So, x = BD + DC
x = 104.9 + 123.67
x = 228.57
Hence, the value of the x is 228.57 units.
To learn more about the angle bisector theorem visit,
https://brainly.com/question/9742008
#SPJ1
7/3a-8/5+4/15a perform the operation and simplify the resulting fraction
Answer:
13a-8/5 simplified
Find the solution of the differential equation that satisfies the given initial condition.
dy/dx = x/y, y(0) = -2
Refer to the attached image.
Exercise 13.2 Mark the following ordered pairs of points on a graph paper and join the points as required. A(0, 3), B(5, 8), C(9, 8), D(4, 3), E(9, 6), F(4, 1), G(0, 1) on a graph paper
The ordered pairs of points on a graph is added as an attachment
How to mark and join the ordered pairs of points on a graph?From the question, we have the following parameters that can be used in our computation:
The ordered pairs
The ordered pairs are represented as
A(0, 3), B(5, 8), C(9, 8), D(4, 3), E(9, 6), F(4, 1), G(0, 1)
Next, we create a plot of the ordered pairs
When this is done, we then connect the points
See attachment for the graph of the ordered pairs
Read more about graphs at
https://brainly.com/question/16749301
#SPJ1
Taffy twist candy company keeps the same ratio of pieces of strawberry candy to banana candy in their packs. The mega pack has 40 strawberry candies and 50 banana candies. The party pack has 20 strawberry candies.
How many banana candies are in the party pack?
Answer:
The party pack has 20 strawberry candies and 25 banana candies. To calculate this, divide the number of strawberry candies in the mega pack (40) by the total number of candies in the mega pack (90). This gives you a ratio of 4:5. For the party pack, divide the number of strawberry candies (20) by that same ratio (4:5) to find the number of banana candy pieces, which is 25.
Solve the following system of inequalities graphically on the set of axes below.
State the coordinates of a point in the solution set.
y≥-x+3
y > 2x - 6
The graph of the inequality is added as an attachment and a solution is (1, 5)
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
y ≥ -x + 3
y > 2x - 6
The above expression is an inequality that implies that:
The inequality is a linear inequality
Next, we plot the graph
One of the points in the shaded region is (1, 5)
See attachment for the graph of the inequality
Read more about inequality at
brainly.com/question/25275758
#SPJ1
The density of water is 1 gram per cubic centimeter. An object floats in the water if its density is less than water's density, and it sinks if its density is great than water's.
Suppose a ball with mass 90 grams is in the shape of a sphere with radius 4 centimeters. Will the ball sink or float in the water?
ROUND YOUR ANSWERS TO THE NEAREST HUNDRETH AND USE THE π BUTTON WHEN CALCULATING.
The sphere ball will not sink because it has a density of 0.34 g/cm³ which is lesser than density of water
What is density?Density is the substance's mass per unit of volume. The symbol most often used for density is ρ, although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume.
Density = mass/volume
volume of the sphere = 4/3 πr³
= 4/3 × 3.14 ×4³
= 803.84/3
= 267.95 cm³
Density of the sphere = 90/267.95
= 0.34 g/cm³( nearest hundredth)
Therefore the sphere will not sink because it's density is lesser than that of water.
learn more about density from
https://brainly.com/question/26364788
#SPJ1
The scatter plot shows the number of hours worked x and the earnings y (in dollars) of a food server
a. The server worked for about 2.5 hours to earn $35
b. the server earn $77 for 5 hours of work
c. the earnings will increase as the number of hours worked increases
How to find how much the server earn for 5 hours of workThis solved by tracing the information from the graph
Tracing the graph the information that coincides with earning $35 is about 2.5 hours
Tracing the graph the information that coincides with earning $77 is about 5 hours
The graph shows that increase in earning will lead to increase n hours of work
Learn more about linear graphs:
https://brainly.com/question/10634943
#SPJ1
yolonda has 7 more baseball cards than jeff. jeff has three times as many baseball cards as clara. all together, they have 21 baseball cards, how many does clara have?
As per the mentioned distribution of cards, Clara has 2 baseball cards.
Let the number of baseball cards with Clara be x. So, number of baseball cards with Jeff will be 3x. Now, the baseball cards that Yolonda has is (3x + 7). We know their sum is 21, therefore, forming the equation now -
x + 3x + 3x + 7 = 21
Performing addition on Left Hand Side of the equation
7x + 7 = 21
Dividing the whole equation by 7
x + 1 = 3
Rewriting and solving the equation for x
x = 3 - 1
Performing division on Right Hand Side of the equation
x = 2
The number of baseball cards with Clara are 2.
Learn more about expression -
https://brainly.com/question/1859113
#SPJ4
A mason needs to purchase mortar mix for a retaining wall consisting of 640 blocks. The guidelines for this mix suggest that 12 bags are required for every 100 blocks. Assuming that he cannot purchase part of a bag, how many bags will he need?
The mason will need 77 bags of mortar mix for the retaining wall.
What is purchase?Purchasing is the process a business or organization uses to acquire goods.
To find out how many bags of mortar mix the mason needs
we need to calculate the number of bags required for 640 blocks.
The guidelines suggest that 12 bags are required for every 100 blocks, so for 640 blocks, we need:
12 bags * (640 blocks / 100 blocks) = 12 * 6.4 = 76.8
Since the mason cannot purchase part of a bag, he will need to round up to the nearest whole number of bags. In this case, 77 bags will be required.
So, the mason will need 77 bags of mortar mix for the retaining wall.
Learn more about purchase here :brainly.com/question/29040864
#SPJ1
what is the tempature change of 15 to -9
Answer:
change in temperature = final - temperature
= -9°-15° = -24°C
The distance between two towns, A and B, is 100 km. Mr Jones drove from A to B at an average speed of v km/h. (a) Write down an expression, in terms of v, for the time, in hours, that he took to complete the journey from A to B. [1]
The expression giving the time that he took to complete the journey is given as follows:
t = 100/d.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:
v = d/t.
For this problem, the distance is given as follows:
d = 100 km.
Hence the expression to obtain the time needed is given as follows:
v = 100/t
vt = 100
t= 100/v.
More can be learned about the relation between velocity, distance and time at https://brainly.com/question/24316569
#SPJ1
a rectangle is meters long and meters wide. the area of the rectangle is square meters. the solution is
Multiplying the length and width together, we get 3m x 4m = 12m². This means that the area of the rectangle is 12 square meters.
Area = Length x Width
Area = 3m x 4m
Area = 12m²
To solve for the area of a rectangle, you will need to use the formula Area = Length x Width. In this example, the length of the rectangle is 3 meters and the width is 4 meters. To calculate the area of the rectangle, you will need to multiply the length and width together. 3m x 4m = 12m². Therefore, the area of the rectangle is 12 square meters.
The area of a rectangle is calculated by multiplying the length and width of the rectangle together. The formula used to calculate the area of a rectangle is Area = Length x Width. To put this formula into practice, lets use the example of a rectangle that is 3 meters long and 4 meters wide. Multiplying the length and width together, we get 3m x 4m = 12m². This means that the area of the rectangle is 12 square meters. This formula can be used for any rectangle, as long as the length and width are known. Knowing the area of a rectangle can be useful for many purposes, such as calculating the amount of paint or carpeting needed to cover the surface area of the rectangle.
learn more about area here
https://brainly.com/question/27683633
#SPJ4
Write the following as an algebraic equation . Use x as the unknown and use a sum. Sum of a number and its equivalent to 115.6
Answer:
x+1=115.6
Step-by-step explanation:
an unknown x
plus a number imagine 1
so x+1=115.6
Jahnay is following this recipe to make cakes. Jahnay uses 840 g of flour. How many cakes is Jahnay making? Recipe: Makes 1 Cake 150 g sugar 120 g butter 210 g flour 2 eggs
Answer:
To determine how many cakes Jahnay is making, we need to calculate the total weight of the ingredients for one cake and then divide the total amount of flour Jahnay is using by that amount.
First, let's calculate the total weight of ingredients for one cake:
150 g sugar + 120 g butter + 210 g flour + 2 eggs = 480 g
Next, let's divide the total amount of flour Jahnay is using by the total weight of ingredients for one cake:
840 g / 480 g = 1.75 cakes
So Jahnay is making 1.75 cakes.
I was wondering how you solve for x if you 2x=18?
Answer: the answer is 9
Step-by-step explanation:
simply divide 2 from both sides in order to cancel out the left side and isolate the variable. 18 divided by 2 is 9
find the geometric mean of 2 and 22
6.63324958071 is the mean of 2 and
Answer:
2 sqrt(11)
Step-by-step explanation:
To find the geometric mean of two numbers, take the square root
sqrt( 2*22)
sqrt(44)
sqrt(4*11)
2 sqrt(11)
Which of the following graphs are identical?
Answer:
[tex]\sqrt[3]{-x}[/tex] and [tex]-\sqrt[3]{x}[/tex]
Step-by-step explanation:
I inserted these functions into a graphing calculator and checked if they were identical or not
Answer:
First part is D and F
The Second part is A,C,D
Step-by-step explanation:
EDG 2023
part a: list three ways in which you can represent the expression, “for every 96 action/ adventure movies, there are 38 sci-fi movies to stream,” as a ratio. part b: explain why 96:38 is the same as 38:96
They both represent the same information - for every 96 action/ adventure movies, there are 38 sci-fi movies to stream. 96:38 and 38:96 are both equivalent ratios because they are inverse proportions of each other.
What is the inverse ?Inverse is the opposite of something. It can be used to describe the opposite of a mathematical operation, such as taking the reciprocal of a number, or the opposite of a logical statement, such as negating the statement. It can also be used to describe the opposite of an action, such as reversing a direction or undoing an action. Inverse can also be used to describe the opposite of an effect, such as the opposite of a physical reaction or the opposite of an emotional response. Inverse relationships can often be seen in nature, such as how a decrease in temperature results in an increase in pressure, or how an increase in the amount of light results in a decrease in the number of insects in a certain area.
a:
1. 96:38
2. 38:96
3. (96/38):1
b: 96:38 and 38:96 are both equivalent ratios because they are inverse proportions of each other. They both represent the same information - for every 96 action/adventure movies, there are 38 sci-fi movies to stream. The only difference is the order of the numbers, but the ratio remains the same.
To learn more about inverse
https://brainly.com/question/3831584
#SPJ1
A cubic function of the form u = a * x ^ 3 + b * x ^ 2 + cx + d yields the following table:
x y
oo
- 5
The coefficient a =
,and d= Box.
,b=
,C=
The value of the coefficients a, b, c, and constant d will be 0.50, 0, -1.50, and 1, respectively.
How to get polynomials with zeroes?Let a, b, c, and d are the zeroes of the polynomial and k be the leading corefficient. Then the polynomial is given as,
⇒ k(x - a)(x - b)(x - c)(x - d)
The degree of the polynomial will be greater than or equal to the number of zeroes.
From the graph, the zeroes are -2, 1, and 1. Then the polynomial is given as,
y = a(x + 2)(x − 1)²
The curve passes through (0, 1), then we have
1 = a(0 + 2)(0 − 1)²
1 = 2a
a = 1/2
a = 0.5
Then the polynomial is given as,
y = 0.50 (x + 2)(x − 1)²
y = 0.50 (x + 2)(x² + 1 - 2x)
y = 0.50 (x³ + 2x² + x + 2 - 2x² - 4x)
y = 0.50 (x³ - 3x + 2)
y = 0.50x³ - 1.5x + 1
Compare with standard equation, then we have
a = 0.50
b = 0
c = - 1.5
d = 1
The value of the coefficients a, b, c, and constant d will be 0.50, 0, -1.50, and 1, respectively.
More about the polynomial link is given below.
https://brainly.com/question/11536910
#SPJ1
The missing graph is attached below.
Hide Sample Answer
The area formula is A = 7². Substitute the values of r (3.5 inches) and TT (3.14) in the formula to find A:
A-3.14x (3.5)² square inches
A = 38.465 square inches.
The area of each light is about 38.465 square inches.
Part C
What is the total area of all three circular lights?
The total area of all three circle lights is:
115.395 square inches.
How do you find the area of a circle?The area of the circle formula helps measure the space occupied by a circular field or plot. Assuming you have land to the fence, the area formula will help you determine how much fencing you will need.
The area of a circle is the area occupied by the circle in the two-dimensional plane. It can be easily determined by the formula A = [tex]\pi r^{2}[/tex], (Pi r-square) where r is the radius of the circle. Area units are square units such as For example m², cm², etc.
The total area of all three circular lights can be calculated by multiplying the area of one light (38.465 square inches) by 3.
Total area = 3 x 38.465 square inches
Total area = 115.395 square inches.
To know more about area visit:
https://brainly.com/question/27683633
#SPJ1
A parabola opening up or down has vertex (0, 0) and passes through (12, 18). Write its equation in
vertex form.
Simplify any fractions.
Answer:
[tex]y=\dfrac{1}{8}x^2[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
Given that the vertex of the parabola is (0, 0):
h = 0k = 0Substitute the values of h and k into the formula:
[tex]y=a(x-0)^2+0[/tex]
[tex]y=ax^2[/tex]
Given that the parabola passes through the point (12, 18), substitute this into the equation and solve for a:
[tex]18=a(12)^2[/tex]
[tex]18=144a[/tex]
[tex]a=\dfrac{18}{144}[/tex]
[tex]a=\dfrac{1}{8}[/tex]
Therefore, the equation of the parabola in vertex form is:
[tex]y=\dfrac{1}{8}x^2[/tex]
Graphing Exponential Exponents Practice
Directions: Graph the function. Compare the graph to the graph of the parent function, identify the y-intercepts, asymptotes, domain, and range.
3) f(x)=[tex]\frac{4}{3}[/tex](6)^x
4)f(x)= -([tex]\frac{1}{3}[/tex])^x
The properties of the functions and the graphs are listed beloe
How to determine the features of the functionsFunction 3
Here, we have
f(x) = 4/3(6)^x
See attachment for the graph, where we have the following features
Domain = All set of real numbersRange: y >= 0y-intercepts = 4/3Asymptotes: y = 0Function 4
Here, we have
f(x) = -(1/3)^x
See attachment for the graph, where we have the following features
Domain = All set of real numbersRange: y < 0y-intercepts = -1Asymptotes: y = 0Read more about exponential function at
https://brainly.com/question/2456547
#SPJ1
Can someone please explain the answer with steps and formula I have a test tomorrow
Answer:
sorry but it not possible here i can explain on another platform