The outside diameter of a pipe is 5 and 7/32 inches. The walls of the pipe are 5/32 inches thick. What is the inside diameter?

The value of y'' will be (- 5x/y² - 25x⁴/2y⁵).

What is implicit differentiation?

In implicit differentiation, we differentiate each side of an equation with two variables by treating one of the variable as a function of other.

Given that;

The equation is;

5x³ + 2y³ = 1

Now, Apply implicit differentiation rule we get;

5x³ + 2y³ = 1

After differentiation;

15x² + 6y² dy/dx = 0

dy/dx = - 15x² / 6y²

dy/dx = -5x²/2y²

Again differentiation;

d²y/dx² = -5/2 (y² × 2x - x² × 2y dy/dx) / y⁴

d²y/dx² = -5/2 (2xy² - 2x²y dy/dx) / y⁴

Substitute value of dy/dx;

d²y/dx² = - 5/2 (2xy² - 2x²y × -5x²/2y²) / y⁴

d²y/dx² = - 5/2 (2xy² + 5x⁴/y) / y⁴

d²y/dx² = - 5x/y² - 25x⁴/2y⁵

y'' = - 5x/y² - 25x⁴/2y⁵

Thus, The value of y'' will be (- 5x/y² - 25x⁴/2y⁵).

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1+3^2 = 1+9 = 10

10/5 = 2

2-6+2 = -4+2

 answer is -2

The number 720,808 in expanded form with exponents is written as:

[tex]\[ 7 \times 10^5 + 2 \times 10^4 + 8 \times 10^2 + 8 \times 10^0 \][/tex]

700,000  : [tex]7 \times 10^5 \\[/tex]

20,000  : [tex]2 \times 10^4 \\[/tex]

800  : [tex]8 \times 10^2 \\[/tex]

8  : [tex]8 \times 10^0[/tex]

[tex]\[ 7 \times 10^5 + 2 \times 10^4 + 8 \times 10^2 + 8 \times 10^0 \][/tex]

This representation helps in understanding the value of each digit based on its position in the number.

Shantel will need to study for 60 minutes more to complete her history review.

Shantel is studying history and after 20 minutes, she is [tex]\frac{1}{4}[/tex]  of the way done.

To determine how much longer she will study, we need to calculate how much time is needed to complete the remaining [tex]\frac{3}{4}[/tex] of her study time.

[tex]\frac{1}{4}[/tex] of the study done in 20 minutes means she will study for 4 * 20 = 80 minutes in total.

To find out how much longer she needs to study, subtract the time she has already studied (20 minutes) from the total study time (80 minutes): 80 - 20 = 60 minutes.

Therefore, Shantel will need to study for 60 minutes more to complete her history review.

Final answer:

To find the floor dimensions of a building that is 14 feet longer than it is wide with an area of 1715 sq ft, we solve the quadratic equation w * (w + 14) = 1715, resulting in w=100 feet and length l=114 feet.

Explanation:

The student is asked to find the length (l) and width (w) of a one-story building floor which is 14 feet longer than it is wide, with a total area of 1715 square feet. To solve this, we set up an equation where w represents the width and w + 14 feet represents the length. Since the area of a rectangle is length times width, the equation is w * (w + 14) = 1715.

After solving this quadratic equation, we find that w=100 feet which makes the length l = w + 14 = 114 feet. Therefore, the actual dimensions of the building are 114 ft by 100 feet.

Answer:

It will take 42 minutes.

Step-by-step explanation:

In order to solve this we first have to calulate how long will it take one person to paint one wall:

54/6=9minutes

That is between 4 people it will take 9 minutes to paint a wall, one person alone supposing they all work at the same rate will take 36 minutes.

Now we just multiply that by the number of walls to be painted:

36*7=252

And we divide that by the number of people painting:

252/6=42

So it will take 42 minutes to paint 7 walls with 6 people painting.

There are 12 possible choices for the player.

"It is a way of selecting items from a collection "

"[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]"

n! = n × (n - 1) × . . . × 2 × 1

For given question,

There are 3 doors and 4 curtains behind each door.

The number of possible ways of selecting a door from the 3 doors.

Using combination formula,

[tex]^3C_1=\frac{3!}{1!(3-1)!}\\\\ ^3C_1=\frac{3\times 2!}{2!}\\\\ ^3C_1=3[/tex]

The number of possible ways of selecting a curtain from the 4 curtains.

Using combination formula,

[tex]^4C_1=\frac{4!}{1!(4-1)!}\\\\ ^4C_1=\frac{4\times 3!}{3!}\\\\ ^3C_1=4[/tex]

So, the number of choices for the player to pick a door and then pick a curtain behind the door :

[tex]^3C_1\times ^4C_1\\\\=3\times 4\\\\=12[/tex]

Therefore, there are 12 possible choices for the player.

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The number of attendance on Thursday would be 9,315.

Given that,

During a 5-day training at your department, the number of visitors tripled each day.

Here, the training started on a Monday with 345 attendees.

Hence, the number of visitors on Tuesday is 3 times with 345 attendees.

That is, On Tuesday;

Number of attendees = 345 x 3

                                     = 1,035

On Wednesday;

Number of attendees = 1,035 x 3

                                     = 3,105

On Thursday;

Number of attendees = 3,105 x 3

                                     = 9,315

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Answer:

Common ratio for the sequence is 3

Step-by-step explanation:

Given sequence is

5, 15, 45, 135,.....

To find out common ratio, divide the second number by the first number

[tex]\frac{15}{5} =3[/tex]

[tex]\frac{45}{15} =3[/tex]

[tex]\frac{135}{45} =3[/tex]

we got 3 that is our common ratio 3

Common ratio for the sequence is 3