I just need the equation please.

The value of the given differentiation f'(1).f'(1)=1024/1089 if f(x)+x²[f(x)]⁴=18.

To ascertain the instantaneous rate of change of a function dependent on one of its variables, differentiation is applied. The most common example is velocity, which is the rate at which a distance changes with respect to time.

The derivative of a function of a real variable in mathematics is used to assess a function's sensitivity to change with respect to a change in its argument. The derivative is a key mathematics tool.

The slope of the tangent line to the graph of a single-variable function at a specific input value is referred to as the derivative if the function exists at that point. The tangent line is the most accurate linear approximation of the function close to that input value.

Given,

f(x)+x²[f(x)]⁴=18

Now, by differentiating on both sides, we get:

f'(x)+2x[f(x)]⁴+4x²[f(x)]³f'(x)=0

f'(x)[1+4x²[f(x)]³]=-2x[f(x)]⁴

f'(x)= (-2x[f(x)]⁴)/[1+4x²[f(x)]³]

Given,

f(1)=2

Let x=1 then,

f'(1)=(-2(1)[f(1)]⁴)/[1+4x²[f(1)]³]

f'(1)=(-2×2⁴)/(1+4×2³)

f'(1)=-32/33

f'(1).f'(1)=(-32/33)(-32/33)

=1024/1089

Therefore, the value of the given differentiation f'(1).f'(1)=1024/1089 if f(x)+x²[f(x)]⁴=18.

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Given that Point T is on line segment SU, T is collinear with S and U, and the numerical length of SU is 24.

Since Point T is on line segment SU, then S, T, and U are collinear.

Collinear points refers to the points that lies on the same straight line.

IF S, T, and U are collinear, then the sum of the numerical length of ST and the numerical length of TU is equal to the numerical length of SU.

ST + TU = SU

Given:

ST = 3x + 2

TU = 3x + 4

SU = 5x + 9

Substitute the expressions in the equation and solve for x.

ST + TU = SU

3x + 2 + 3x + 4 = 5x + 9

3x + 3x - 5x = 9 - 2 - 4

x = 3

Substitute the value of x in the expression for SU.

SU = 5x + 9

SU = 5(3) + 9

SU = 24

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Answer:

B

Step-by-step explanation:

Commutative means that you change the order of an operation. So in this case, the 7 is written on the left of the brackets on the left side of the equation and on the right side of the brackets on the right side of the equation.

You are multiplying not adding. That makes A incorrect.

You have not removed the brackets so the answer is not C.

It's not addition so it's not D.

B

The absolute value of x minus one is equal to two. Therefore, x must be either one greater than two (x = 3) or one less than two (x = 1).

One less than x results in a value of two in absolute terms. As a result, x minus 1 has an absolute value of 2, which is a positive number. The separation of an integer from zero is its absolute value. As a result, x minus 1 is two units from zero in absolute terms. As x minus one has an absolute value of two, its real value must either be two or a negative two. That is to say, x must either be one more than two (x = 3) or one less than two (x = 1).In order to confirm this, let's look at a few examples. If x = 3, then |x - 1| = |2 - 1| = |1| = 1 which is not equal to two. Therefore, x = 3 is not the answer we are looking for. On the other hand, if x = 1, then |x - 1| = |1 - 1| = |0| = 0 which is not equal to two. Therefore, x = 1 is also not the answer we are looking for. The only two possible solutions for the equation |x - 1| = 2 are x = 3 and x = 1. Therefore, the result of |x - 1| = 2 is that x must be either one greater than two (x = 3) or one less than two (x = 1)

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Work Shown:

The diagram shows that JK = 12 and GF = 2.5*(JK) = 2.5*12 = 30

The midsegment HL will be the average of the two lengths it is parallel to.

We'll add up the values and then cut the result in half

HL = (JK+GF)/2

HL = (12+30)/2

HL = 42/2

HL = 21

There are two types of classifications for triangles, Classification according to internal angles and Classification according to the length of its sides.

A geometrical shape with three vertices, angles and sides, whose sum of internal angles is 180° is considered as a triangle.

Classification of triangles :-

There are two ways to classify triangles,

1) Based on the Angle :-

a) Acute Angled Triangle :- A triangle that has all three angles less than 90° is an acute angle triangle.

b) Right-Angled Triangle :- A triangle that has one angle that measures exactly 90° is a right-angle triangle.

c) Oblique Angled Triangle :- A triangle that has one angle that measures more than 90° is an obtuse angle triangle.

2) Based on the Sides :-

a) Scalene Angled Triangle :- A triangle that has all three sides of different lengths is a scalene triangle.

b) Isosceles Angled Triangle :- A triangle that has two sides of the same length and the third side of a different length is an isosceles triangle.

c) Equilateral Angled triangle :- A triangle that has all three sides of the same length is an equilateral triangle.

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The given problem can be represented with the help of Venn diagrams. Since 5 of the total 32 students neither swim nor play softball, there are 27 students who either swim or play softball or do both.

Here is the diagram for the given data:We can represent the values for each category as:A = Number of students who swim onlyB = Number of students who play softball onlyC = Number of students who swim and play softball bothD = Number of students who do neitherSwim | Play Softball | TotalNumber of Students (A) | |Number of Students (C) | |Number of Students (B) | |Number of Students (D) | |Total | |We have been given that 22 students swim and 20 students play softball. Let us start filling up the table using the given data:Swim | Play Softball | TotalNumber of Students (A) | |Number of Students (C) | |Number of Students (B) | |Number of Students (D) | 5Total | |27So, we can say that the values that complete the table are:A = 12B = 10C = ?D = 5C can be found out using the fact that the total number of students who either swim or play softball is 27.A + B + C = 27Substituting the values of A and B, we get12 + 10 + C = 27C = 5 + 27 - 12 - 10C = 10Therefore, the complete table is:Swim | Play Softball | TotalNumber of Students (A) | 12 |Number of Students (C) | 10 |Number of Students (B) | 10 |Number of Students (D) | 5Total | 32 |In total, there are 12 students who swim only, 10 students who play softball only, 10 students who do both, and 5 students who do neither.

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Answer:

-7 is in our domain.

0 is in our domain

7 is not in our domain.

Step-by-step explanation:

So we have the rational function:

\(f(x)=\frac{x}{x-7}\)

The domain restrictions of rational functions are the zeros of the denominator.  In other words, the domain of rational functions are always all real numbers except for the zeros of the denominator.

So, solve for the denominator by setting it to 0:

\(x-7=0\)

Add 7 to both sides:

\(x=7\)

So, our domain is all real numbers except for 7.

(When x=7, we have 7/0, which is undefined.)

Therefore:

-7 is in our domain.

0 is in our domain

7 is not in our domain.

Answer:

the picture has it all!

whatever equals zero is not the domain and whatever doesnt equal zero is the domain!

hope i helped :)

Answer:

Supplementary!

Answer:

Complementary I believe.

correct me if I’m wrong

if not adjacent

Answer:

..D).... x = 8..

Step-by-step explanation:

..x = 8..

Answer:

\( {p}^{2} - 13p - 30 \\ \\ {p}^{2} - 15p - 2p - 30 \\ \\ p(p - 15) + 2(p - 15) \\ \\ (p + 2)(p - 15)\)

# Jerry Don is here#

Answer:

\(\displaystyle [p + 2][p - 15]\)

Explanation:

Find two quantities that when differed to 13, they also multiply to 30. Those will be 2 and 15. The TINIER quantity gets the plus sign because the B-value is −13, therefore 15 gets the minus sign, leaving 2 with the plus sign.

I am joyous to assist you at any time.

The equation is: G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

The formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

From the graph, we see that:

y-intercept = 15 gallons

Now, the slope is gotten from the formula:

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (10 - 5)/(4 - 8)

Slope = -⁵/₄

Thus, equation is:

G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

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Answer:

2 hours

Step-by-step explanation:

if jasmine took the same amount of time as Paula and Paula took 2 hours that means Jasmine also took 2 hours

Answer:

Initial speed is 32 m/s

At uniform speed, acceleration is 0, (a = 0).

When speed reduced, (v - u) = 2.78 ms-¹, t = 1800 sec, s = 60 ,000 metres.

From first equation of motion:

\({ \boxed{ \bf{v = u + at}}} \\ { \tt{(v - u) = at}}\)

substitute:

\({ \tt{2.78 = (a \times 1800)}} \\ { \tt{acceleration = 0.0015 \: {ms}^{ - 2} }}\)

from second equation of motion:

\({ \boxed{ \bf{s = ut + \frac{1}{2} a {t}^{2} }}}\)

substitute:

\({ \tt{60000 = 1800u + ( \frac{1}{2} \times 0.0015 \times {1800}^{2}) }} \\ { \tt{1800u = 57570}} \\ { \tt{u = 32 \: m {s}^{ - 1} }}\)

Answer:

=42

Step-by-step explanation:

first find half of 28

=14

now you add that to 28

28+14 =

= 42

Answer:

Distributive Property

Step-by-step explanation:

If we have an equation where we multiply something in parentheses by a certain term, then we can apply the distributive property to simplify it.

In this case: \(5(x-7)=55\)

We can multiply \(x-7\) by 5 to simplify this equation - this is the distributive property.

\(5x - 35 = 55\)

So the property used to write the equation in Step 2 was the distributive property.

Hope this helped!

Answer:

the answer is didrtbutive

Step-by-step explanation:

hope it helps.

have a good day:)

Answer:

(a)\(20+(-9)+8+(-7)\)

(b)\(4x+(-7y)+(-5z)+6\)

Step-by-step explanation:

We are required to write an equivalent expression that uses only addition for each of the given term.

Note that the product of + and - is always -.

Therefore:

(a)20−9+8−7

\(20-9+8-7 \\=20+(-9)+8+(-7)\)

(b)4x−7y−5z+6

\(4x-7y-5z+6\\=4x+(-7y)+(-5z)+6\)

The equation typically used for modeling population growth is the logistic growth equation.

To provide a comprehensive answer, I would need the specific equation you are referring to in relation to population dynamics. The equation typically used for modeling population growth is the logistic growth equation, which is commonly written as:

dP/dt = rP(1 - P/K),

where:

dP/dt represents the rate of change of the population over time,

r is the intrinsic growth rate of the population,

P is the population size at a given time,

K is the carrying capacity, which represents the maximum population size that can be sustained by the environment.

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Answer:

55

Step-by-step explanation:

Z[√3] is a subset of the real numbers R, formed by combining integers (a, b ∈ Z) with the irrational number √3. It is closed under addition, subtraction, and multiplication. The arithmetic operations for elements in Z[√3] are:

1. Addition: (a1 + b1√3) + (a2 + b2√3) = (a1 + a2) + (b1 + b2)√3.
2. Subtraction: (a1 + b1√3) - (a2 + b2√3) = (a1 - a2) + (b1 - b2)√3.
3. Multiplication: (a1 + b1√3)·(a2 + b2√3) = (a1·a2 + 3b1·b2) + (a1b2 + a2b1)√3.

Z is the set of all integers, including negative and positive numbers. Z[√3] is a set formed by adding the square root of 3 to the set of integers. It includes numbers of the form a + b√3, where a and b are integers.

Z[√3] is closed under addition, subtraction, and multiplication when the operations are performed using the expressions given in terms of the two components associated with every number in the set. For example, when adding two numbers in Z[√3], we add the real and imaginary components separately. The same applies to subtraction and multiplication.

An example of a number in Z[√3] is 99999 + 222222√3. This number satisfies the criteria of being expressed as a sum of an integer and a multiple of the square root of 3.

Overall, Z[√3] is a set of numbers that includes all integers plus multiples of the square root of 3. It behaves like a normal set of numbers under arithmetic operations, as long as the expressions provided are used.

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According one-way ANOVA, the test is false.

In the given question,

When comparing three or more populations means within a set of quantitative data that is categorized according to one​ factor/treatment, a​ one-way ANOVA is appropriate. It is also appropriate in this​ situation, however, to compare two means at a time using multiple independent two sample​ t-tests. We have to check whether this is true or​ false.

We firstly learn about one-way ANOVA

"One-Way ANOVA, also known as "analysis of variance," examines the means of two or more independent groups to see if there is statistical support for the notion that the related population means are statistically substantially different."

According to the given method it is inappropriate to compare two means at a time using multiple independent two sample​ t-tests. It will create multiple testing problem and error.

So using one way ANOVA test when comparing three or more populations means within a set of quantitative data that is categorized according to one​ factor/treatment and compare two means at a time using multiple independent two sample​ t-tests is false.

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Answer: bigger number = 60 smaller= 15

Step-by-step explanation:

x-y=45

let y represent the smaller number

y= 75 / 5= 15

therefore x (bigger number) = 15+45=60

Answer: The farmer has 1377 sheeps.

Step-by-step explanation:

Farmer loses sheeps due to drought = 32½% of 2400

32½% of 2400

= 65 × 2400 × 1

2100

After cutting it will be,

65×12

=780

Number of sheeps that are left with him = 2400 - 780

=1620

After that,

The farmer loses due to sickness = 15% of 1620

15% of 1620

= 15 × 1620

100

After cutting it will be,

3 × 81

= 243

Total amount of sheeps that the farmer loses = 780 + 243

= 1023

Now the number of sheeps he has is 2400-1023

= 1377

Answer:

A

Step-by-step explanation:

\(\frac{2}{5} = \frac{4}{10} \\.3=\frac{3}{10} \\5\frac{3}{10} -\frac{4}{10} =4\frac{9}{10}\)

Correct option for sets of numbers with sufficient for the calculation is;

(3) p(A = 1), p(B = 1 | A = 1), p(C = 1 | A = 1)

A more detailed explanation of the answer.

(a) In order to calculate p(A = 1 | B = 1, C = 1), we need to find the joint probability p(A = 1, B = 1, C = 1) and divide it by p(B = 1, C = 1). To find the joint probability, we can use the following formula:

p(A = 1, B = 1, C = 1) = p(A = 1) * p(B = 1 | A = 1) * p(C = 1 | A = 1, B = 1)

Based on this formula, we can see that none of the given sets are sufficient for the calculation.

(b) Now that we know p(B | A, C) = p(B | A), the joint probability formula becomes:

p(A = 1, B = 1, C = 1) = p(A = 1) * p(B = 1 | A = 1) * p(C = 1 | A = 1)

In this case, set (3) is sufficient for the calculation:

(3) p(A = 1), p(B = 1 | A = 1), p(C = 1 | A = 1)

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Answer:

Step-by-step explanation:

Let the price for children and adults package be represented with x and y respectively.

For the first week the sum of the package will be as follows:

3x+8y = 126

For the two weeks after:

6x+4y= 108

So, we will be having two equations

3x+8y = 126..... (1)

6x+4y= 108.......(2)

These are simultaneous equations

From equation 1

3x+8y = 126

3x = 126-8y

X = 126-8y/3 ............. (3)

Put equation 3 into 2

6 ( 126-8y)/3 +4y = 108

756-48y/3 +4y = 108

756-48y+12y/3 = 108

Cross multiplying

756-48y+12y= 108×3

756-48y+ 12y = 324

Collecting like terms

756-324 = 48y-12y

432= 36y

Divide both sides by 36

432/36 = 36y/36

y= 12

Substituting y into equation 1

3x+8= 126

3x+96=126

3x= 126-96

3x= 30

Divide both sides by 3

3x/3 = 30/3

x = 10

Hence for each of the packages for children and adults. It will be 10 and 12 respectively.

Answer:

Step-by-step explanation:

Area of a rectangle = (l*b)

= (2x+5)(x+y+2)

= 2x*x + 2x*y + 2x*2 + 5*x + 5*y + 5*2

= 2x^2+2xy+9x+5y+10

Hope you understood!!

Answer:

2x² + 2xy + 9x + 5y + 10 units²

Step-by-step explanation:

The formula for area of rectangle is Length x Base.

We need to expand the given equation.

(2x + 5) (x + y + 2)

First, multiplying 2x with x, y & 2, we get,

2x² + 2xy + 4x. ------ (1)

Now, multiplying 5 with x, y & 2, we get,

5x + 5y + 10. ------- (2)

Adding 1 and 2,

=> 2x² + 2xy + 4x + 5x + 5y + 10

=> 2x² + 2xy + 9x + 5y + 10 units²

Hope it helps :)