Find the equation of the sphere for which the line segment pq connecting p(4,2,1) and q(5,-1,3) is the diameter

The coefficient of x4 in the Taylor series expansion of the given function is 0.

To find the coefficient of x4 in the Taylor series expansion of the function f(x) = 8 ln(9 + 3x2), we need to compute the fourth derivative of f(x) and evaluate it at x = 0.

The Taylor series expansion for a function centered at the origin is given by:

f(x) = f(0) + f'(0)x + f''(0)x2/2! + f'''(0)x3/3! + f''''(0)x4/4! + ...

In this case, we have:

f'''(x) = 48x/(9 + 3x2)

Evaluating f'''(x) at x = 0 gives:

f'''(0) = 0/9 = 0

Therefore, the coefficient of x4 in the Taylor series expansion centered at the origin for the function f(x) = 8 ln(9 + 3x2) is 0.

Answer:

The solutions are 1.275 and -6.275

Step-by-step explanation:

Given

x^2 = –5x + 8

First, put all terms in the left side of the equal sign, as follows:

x^2 + 5x - 8 = 0

Then, use the quadratic formula with a = 1 (the coefficient of the quadratic term), b = 5 (the coefficient of the linear term) and c = -8 (the independent term).

[tex]x = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)}[/tex]

[tex]x = \frac{-5 \pm \sqrt{5^2 - 4(1)(-8)}}{2(1)}[/tex]

[tex]x = \frac{-5 \pm \sqrt{57}}{2}[/tex]

[tex]x_1 = \frac{-5 + \sqrt{57}}{2}[/tex]

[tex]x_1 = \frac{-5 + 7.55}{2}[/tex]

[tex]x_1 = 1.275[/tex]

[tex]x_2 = \frac{-5 - \sqrt{57}}{2}[/tex]

[tex]x_2 = \frac{-5 - 7.55}{2}[/tex]

[tex]x_2 = -6.275 [/tex]

Final answer:

To seat 24 people at picnic tables that each seat 6, you divide 24 by 6, which equals 4 tables needed.

Explanation:

The question is asking how many picnic tables are needed to seat 24 people, if each table seats 6 people. This is a division problem where we need to divide the total number of people by the number of seats at a single table. You divide 24 (the total number of people) by 6 (the number of seats at one table) to find out the number of tables needed.

Here is the calculation: 24 \/ 6 = 4. Therefore, you would need 4 picnic tables to seat 24 people, assuming each person takes one seat and that there are no empty seats.

Answer: It’s A.

Step-by-step explanation:

for a p e x

Nick can spend a total of 13 minutes washing his car at the self-service car wash with his $10 budget, accounting for both the initial charge and the additional cost per minute after the first 5 minutes.

Nick is planning to use a self-service car wash that charges $4 for the initial 5 minutes and an additional $0.75 for each minute after that. With a budget of $10, he wants to calculate the number of minutes (m) he can spend washing his car. The cost for m minutes is given by the equation:

Total Cost = Initial Charge + (Additional Charge per minute * Number of extra minutes)

First, subtract the initial charge from the total amount Nick has:

$10 - $4 = $6

This is the amount remaining for the additional minutes. Next, divide this by the additional charge per minute:

$6 / $0.75 per minute = 8 minutes

Therefore, Nick can spend 8 minutes washing his car after the initial 5 minutes, for a total of 13 minutes.

Answer:

y = 24x3 - 1

Step-by-step explanation:

None needed YW

Answer:

33.9

Step-by-step explanation

I got 100% on my test and just wanted everyone to know that it is correct.

Answer:

True

Step-by-step explanation:

Answer:

-8/3

Step-by-step explanation:

i took the test on edg

The total number of positive integers between 100 and 999 inclusive that are divisible by 3 or 4 is 450.

The problem is looking for positive integers between 100 and 999 inclusive, that are divisible by three or four. First, we find out how many numbers between 100 and 999 are divisible by 3 by using the formula: (Last Numbers - First Number) divided by the number you are dividing + 1. Hence, [tex](999 - 102) / 3 + 1 = 300.[/tex] Similarly, for numbers divisible by 4: (996 - 100) / 4 + 1 = 225. However, we must subtract out the numbers that are counted twice because they are divisible by both 3 and 4 (i.e., divisible by 12). To find this, we do [tex](996 - 108) / 12 + 1 = 75.[/tex]

In conclusion, we add the numbers divisible by 3 and those divisible by 4 and subtract the ones that are divisible by both (12). Hence, the total number of positive integers between 100 and 999 inclusive that are divisible by 3 or 4 is [tex]300 + 225 - 75 = 450.[/tex]

https://brainly.com/question/13978375

#SPJ11

For this case we have that by definition, a variable is a symbol that can be replaced or that takes a numerical value in an equation or expression, mathematical in general.

Then we have the following options:

A) [tex]8 + 6[/tex]

It is a sum of two real numbers. There are no variables.

B)[tex]4d-2[/tex]

In this case the variable is "d"

C) [tex]7r-15 = 6[/tex]

In this equation, the variable is represented by "r"

D) [tex]11 + 14 = 25[/tex]

It is a sum of two real numbers. There are no variables.

Answer:

A) There are no variables

B) "d"

C) "r"

D) There are no variables

Answer:

its a ik it

Step-by-step explanation:

You would need to deposit approximately $20,701.27 today if this is the only money you save for the purpose of buying a car in 4 years, considering an expected annual interest rate of 11.5%.

We have,

To determine how much you need to deposit today, we can use the concept of present value (PV).

The present value represents the current value of a future cash flow, accounting for the time value of money and the expected interest rate.

In this case, you want to have $31,664 in cash in 4 years, and you expect to earn an annual interest rate of 11.5%.

Let's calculate the present value using the following formula:

[tex]PV = FV / (1 + r)^n[/tex]

where PV is the present value, FV is the future value, r is the interest rate per period, and n is the number of periods.

Plugging in the values, we have:

[tex]PV = $31,664 / (1 + 0.115)^4[/tex]

Calculating this equation, we find:

[tex]PV = $31,664 / (1.115)^4[/tex]

= $31,664 / 1.530749

PV ≈ $20,701.27

Therefore,

You would need to deposit approximately $20,701.27 today if this is the only money you save for the purpose of buying a car in 4 years, considering an expected annual interest rate of 11.5%.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ2

Answer:

  A, D, E

Step-by-step explanation:

Squaring both sides of the inequality, we get

  x < 25 . . . . . with the restriction x ≥ 0

The listed numbers that are in the range [0, 25) are 1, 18, 24.

Answer:

Given equation,

3|x| > 6 -----(1)

∵ [tex]\frac{1}{3}>0[/tex]

Thus, multiplying both sides of inequality (1) by [tex]\frac{1}{3}[/tex]

We get,

[tex]|x| > 2[/tex]

⇒ 2 < x or 2 < - x  

⇒ 2 < x or -2 > x   (when a > b where a > 0, b > 0, If c < 0  ⇒ ac < bc),

⇒ (2, ∞ ) ∪ (-∞, -2)

By plotting the above interval in the number line we can get the graph of the given equation ( shown below )

Answer:

what the other person said

Step-by-step explanation:

The length of the diagonal BD is 3 centimeters.

A parallelogram is a quadrilateral where each pair of parallel sides have the same length and can be form by two congruent triangles which share the same side (diagonal).

Perimeter equations for the parallelogram are the following:

[tex]AB + BD + AD = 8\,cm[/tex] (1)

[tex]2\cdot AB + 2\cdot AD = 10\,cm[/tex] (2)

Where:

By (2) we have the following conclusion:

[tex]AB + AD = 5\,cm[/tex]

And we find the length of the diagonal BD by (1):

[tex]5\,cm + BD = 8\,cm[/tex]

[tex]BD = 3\,cm[/tex]

The length of the diagonal BD is 3 centimeters. [tex]\blacksquare[/tex]

To learn more on parallelograms, we kindly invite to check this verified question: https://brainly.com/question/1563728

The Part A cross section will be rectangle and Part B cross section will be triangle .

A rectangular pyramid is a 3-D object with a base shaped like a rectangle and triangle-shaped faces or sides that correspond to each side of the base. Like the other types of pyramids, a rectangular pyramid also has a point on top of the base of the pyramid that is joined together by bringing the top of all the sides which is known as the apx. A rectangular pyramid has a total of 5 faces, 5 vertices, and 8 edges and is of two types a right pyramid or an oblique pyramid.  

According to the question

Part A: A cross section of the rectangular pyramid is cut with a plane parallel to the base.

When we cut a cross section parallel to base of the rectangular pyramid which have rectangular base

The cross section will always be a rectangle.  

Part B: If a cross section of the rectangular pyramid is cut perpendicular to the base, passing through the top vertex .

When we cut a cross section perpendicular to the base, passing through the top vertex of the rectangular pyramid

The cross section will always be a Triangle.  

As the lateral face of a rectangular pyramid  is a triangle, so a cross section that passes through the top vertex and the base is also a triangle.

Hence , The Part A cross section will be rectangle and Part B cross section will be triangle .

To know more about rectangular pyramid  here:

https://brainly.com/question/21308574

#SPJ2