Can you pls help me 15 point you will earn???

To find the limit of the given expression as x approaches 0, we will use l'Hospital's Rule because the expression is in the indeterminate form 0/0. The given expression is: lim (x→0) [(√(1 + 9x) - √(1 - 2x))/x]

First, let's find the derivative of the numerator and denominator with respect to x. Numerator's derivative: d/dx [√(1 + 9x) - √(1 - 2x)] = (9/2) * (1/√(1 + 9x)) - (2/2) * (1/√(1 - 2x)) Denominator's derivative: d/dx [x] = 1

Now, apply l'Hospital's Rule and find the limit of the derivative: lim (x→0) [(9/2) * (1/√(1 + 9x)) - (2/2) * (1/√(1 - 2x))]

As x approaches 0: = (9/2) * (1/√(1 + 9*0)) - (2/2) * (1/√(1 - 2*0)) = (9/2) * (1/√1) - (2/2) * (1/√1) = (9/2) - (2/2) = (9 - 2)/2 = 7/2

So the limit of the given expression as x approaches 0 is 7/2.

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The excel statement to estimate the test average of these 4 grades is -

An average is the sum of many numbers divided by the total of numbers. It is also known as the arithmetic mean.

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Answer:

9.5 * 10^-2 mm

Step-by-step explanation:

To find the total thickness, we proceed to add the two thickness that we have

Mathematically, this will be;

0.025 mm + 7 * 10^-2 mm

7 * 10^-2 mm = 0.07

So we have;

0.025 mm + 0.07 mm = 0.095

In scientific notation, this is 9.5 * 10^-2 mm

Given function:y = √(1 – x³)We need to find dy/dx.As per the chain rule of differentiation, if y = f(u) and u = g(x), then the derivative of y with respect to x is given by dy/dx = dy/du * du/dx.

Now, let u = 1 – x³. Then, y = √u ⇒ y = u^(1/2).

dy/dx = dy/du * du/dxdy/du = 1/(2√u) = 1/(2√(1 – x³))du/dx = -3x²Therefore, dy/dx = dy/du * du/dx = 1/(2√(1 – x³)) * (-3x²) = (-3x²)/(2√(1 – x³)).

Therefore,  (A) 3(1 - x²)².Option (A) is the correct answer.

The given function is y = √(1 – x³) and we need to find dy/dx. As per the chain rule of differentiation, if y = f(u) and u = g(x), then the derivative of y with respect to x is given by dy/dx = dy/du * du/dx.

Let u = 1 – x³. Then, y = √u ⇒ y = u^(1/2).

We need to find dy/dx.dy/dx = dy/du * du/dxdy/du = 1/(2√u) = 1/(2√(1 – x³))du/dx = -3x².

Therefore, dy/dx = dy/du * du/dx = 1/(2√(1 – x³)) * (-3x²) = (-3x²)/(2√(1 – x³)).

Thus, dy/dx = (-3x²)/(2√(1 – x³)).Therefore, the correct option is (A) 3(1 - x²)².  

The derivative of the given function y = √(1 – x³) with respect to x is (-3x²)/(2√(1 – x³)) and the correct option is (A) 3(1 - x²)².

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Answer:

the answer is K for (2,-3)

17) \(x+2x+1+3x=\boxed{6x+1}\)

18) \(17-a+5a-1+4ab=\boxed{4ab+4a+16}\)

19) \(2(3y-5+y+2)=\boxed{8y-6}\)

20) \(k^2 +k+k^2 -9k+23+k^2 +k+2k^2 -17=\boxed{5k^2 -7k+6}\)

Translating words into algebraic expressions means taking words and replacing them with mathematical symbols to create an equation. For example, the expression "five more than a number" can be written as "x + 5" where "x" represents the number.

Translating words into algebraic expressions is a useful skill when solving math problems. It involves taking words and replacing them with mathematical symbols to create an equation. For example, the expression "five more than a number" can be written as "x + 5" where "x" represents the number. By translating words into an algebraic expression, it becomes easier to solve problems using the correct equations. It is important to remember to use the correct symbols and to be mindful of the order of operations when translating words into algebraic expressions. When done correctly, translating words into algebraic expressions can help to make complex math equations easier to understand and solve.

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The weight of the cable Dustin is using would be 58.67 pounds.

As per the given statement, Dustin is using a cable to lift heavy equipment.

His company has a table of the weights of various lengths of cable.

If Dustin needs to use 88 feet of cable, Pounds will this cable weigh:

Let us find the solution to the problem given in the question.

The length of the cable Dustin is using is 88 feet.

Using the table given by his company, the weight of the 88 feet long cable can be determined.

Using the terms given in the question, the solution is as follows:

Dustin needs to use 88 feet of cable, and the weight of this cable can be found from the table given by the company.

If we look at the table, it is evident that there is a weight of 2 pounds for every 3 feet of cable, so the weight of the 88 feet of cable Dustin is using would be:

Pounds of 3 feet of cable = 2 pounds of 3 feet of cable.

Pounds of 1 foot of cable = (2/3) pounds of 1 foot of cable

So, the weight of 88 feet of cable = (2/3) × 88 = 58.67 pounds.

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Question: Dustin is using cable to lift heavy equipment. his company has a table of the weights of various lengths of cable. if dustin needs to use 88 feet of cable, how many pounds will this cable weigh?

Length of cable in feet: 5 15 25 35

Weight of cable in pounds: 24.4 73.2 122.0 170.0

Step-by-step explanation:

37+9x+8=180( straight angle or linear pair)

9x=180-45

9x=135

x=15

The determinant of matrix A, det(A), is equal to -18.

To find the determinant of matrix A using the given information, we can apply the property that the determinant of a matrix is equal to the product of its eigenvalues.

Given that the eigenvalues of matrix A are λ1 = 1, λ2 = -2, λ3 = 3, and λ4 = -3, we can express the determinant of A as:

det(A) = λ1 * λ2 * λ3 * λ4

Plugging in the values of the eigenvalues:

det(A) = (1) * (-2) * (3) * (-3)

Now, let's simplify the exprecssion:

det(A) = -18

Therefore, the determinant of matrix A, det(A), is equal to -18.

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The work done by the force field F(x,y) = 2x/y i - x^2/y^2 j in moving an object from the point (-1,1) to (3,2) can be found by evaluating the line integral along the path connecting the two points. The line integral involves integrating the dot product of the force field and the path vector with respect to the path parameter.

To find the work done by the force field F(x,y) = 2x/y i - x^2/y^2 j in moving an object from the point (-1,1) to (3,2), we need to evaluate the line integral along the path connecting these two points.

Let's denote the path as C and parameterize it as r(t) = (x(t), y(t)), where t ranges from 0 to 1. We can express the path vector as dr = (dx, dy) = (dx/dt, dy/dt) dt.

The line integral can be written as:

Work = ∫ F · dr

where F is the force field F(x,y) = 2x/y i - x^2/y^2 j and dr is the path vector.

By substituting the expressions for F and dr, we have:

Work = ∫ (2x/y dx/dt - x^2/y^2 dy/dt) dt

To evaluate this line integral, we need to determine the parametric equations for x(t) and y(t) that describe the path connecting (-1,1) and (3,2). Once we have the parametric equations, we can calculate dx/dt and dy/dt, substitute them into the integral, and evaluate it over the interval [0,1].

The resulting value will be the work done by the force field in moving the object along the given path from (-1,1) to (3,2).

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Answer:

height = 20 cm

Step-by-step explanation:

the volume (V) of a cylinder is calculated as

V = πr²h ( r is the radius and h the height )

here r = 5 and V = 500π , then

π × 5² × h = 500π

25πh = 500π ( isolate h by dividing both sides by 25π )

h = \(\frac{500\pi }{25\pi }\) = 20 cm

The answer to the question is B.

Answer:

0.630

Step-by-step explanation:

Simply evaluating, we get v (0) = 1, v (0.31831) = 0.630, v (2) = 1.566. Thus, the minimum velocity over the interval [ 0, 2] is 0.630.

Step-by-step explanation:

Simply graph the two equations....the intersection of the two graphs is the solution

Answer:

40%

Step-by-step explanation:

1.50 - 0.90 = 0.60

0.60 cents are saved.

\(\frac{0.60}{1.50} = 0.4\)

0.4 = 40%

hope this helps :)

The type of probability in this case is conditional probability.

To find the percentage of workers surveyed who are likely to carpool to work each day.

Given that they are male, we need to calculate the proportion of male workers who carpool out of the total number of male workers surveyed.

From the survey, we know that out of the 200 downtown workers surveyed, there are 44 males who ride the train, 38 males who ride the bus, and 28 males who carpool.

Therefore, the total number of male workers surveyed is 44 + 38 + 28 = 110.

The percentage of male workers who carpool can be calculated as (28/110) * 100 = 25.45%.

So, approximately 25.45% of the workers surveyed are likely to carpool to work each day, given that they are male.

Therefore, the type of probability in this case is conditional probability, specifically the probability of carpooling given that the workers are male.

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Answer:

6z+25

Step-by-step explanation:

6(z+4)+1

=6z+24+1

=6z+25

Answer: 4+2

Step-by-step explanation:

z=1

6(4+1=5)+1=6

Answer:

The first step is false because the tub was not higher at 10:14 than at 10:01, The second box is true, because it is staying the same. The Third box is most likely true. The forth one is false , as there is a decline at 10:20 and the last one I am pretty sure is true also.

Answer:

(6a - 7b)(6a + 7b)

Step-by-step explanation:

Given

36a² - 49b² ← this is a difference of squares and factors in general as

a² - b² = (a - b)(a + b)

Thus

36a² - 49b²

= (6a)² - (7b)²

= (6a - 7b)(6a + 7b)

Answer:

The answer for question 3 is D, number 4 is C

Answer:

Optimisation Problem

Explanation:

Optimisation Problem is a mathematical economics, computer science problem - which finds the best solution from all feasible solutions (based on constraints & other aspects).

The problem might be in form of maximisation or minimisation. The bus system designing is based on minimizing walking distance. Thus is an optimisation problem.

Answer:

Option C. 154 cm²

Step-by-step explanation:

From the question given above, the following data were obtained:

Pi (π) = 22/7

Diameter (d) = 14 cm

Area (A) =?

Next, we shall determine the radius of the circle. This can be obtained as follow:

Diameter (d) = 14 cm

Radius (r) =?

r = d/2

r = 14/2

r = 7 cm

Finally, we shall determine the area of the circle as illustrated below:

Pi (π) = 22/7

Radius (r) = 7 cm

Area (A) =?

The area of a circle can be obtained by using the following formula:

A = πr²

A = 22/7 × 7²

A = 22/7 × 7 × 7

A = 22 × 7

A = 154 cm²

Thus, the area of the circle is 154 cm²

Answer:

area of circle=π(14/2)²=22/7 ×7²=22×7=154cm²

Answer:

7x8 is 56 plus four plus one equals 61

Step-by-step explanation:

Given:-

To find the resultant value of the sum of the equation.

The correct answer is option B) The graph of y = 1/2sin(x - π/2) is shifted units π /2 right from the graph of y = 1/2 sin x.

How do you describe a graph?

For most graphs, give a brief description including the title and axis labels, and mention trends not already described in the text. For simple charts, state the actual data points. For more complex charts, an ideal description would include the data in a table or list.

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There are 816 triangles that can be formed using diagonals from a common vertex of a 19-gon.

The number of available vertices that are not adjacent to the vertex in question is 18, and we have the freedom to pick three of them by selecting from a pool of 18C3 options. Nevertheless, as we disregard the order in which these vertices are selected, their sequence must be divided by 3!.

As such, the total count for possible triangles formed using diagonals originating at the same vertex in a 19-gon is:

The triangles that would be formed is given as  816 triangles

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The value of angle S is 53°

Exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of two remote interior angles.

With this theorem we can say that

7x+2 = 4x+13+19

collecting like terms

7x -4x = 13+19-2

3x = 30

divide both sides by 3

x = 30/3

x = 10

Since x = 10

angle S = 4x+13

angle S = 4(10) +13

= 40+13

= 53°

Therefore the measure of angle S is 53°

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