What is the remainder of (6x^3)÷(x+2)

Answers

Answer 1

Answer: $6x^3:(x+2)\n\nw(x)=6x^3\ remainder\ of\ 6x^2:(x+2)\ equal\ w(-2)\n\nw(-2)=6\cdot(-2)^3=6\cdot(-8)=-48\leftarrow answer$

Answer:

The next value in the given pattern of digits and numbers is:

Step-by-step explanation:

Since, if we see the first pair:

1 I

Then we see that the alphabet I requires just one vertical line to get formed.

The next pair is:

2 L

Hence, from this we could claim that L is formed with the help of one vertical and one horizontal line.

The next pair is:

3 F

Again the alphabet F could be formed with the help of 3 lines one vertical and two horizontal line.

Hence, from the above three pairs we may infer that the next pair will be:

4 E

because E is formed with the help of four lines 1 vertical and three horizontal lines.

Final answer:

The next term in the sequence is 4U.

Explanation:

The given sequence seems to follow a pattern where the 1st term is the number itself, and the 2nd term is the last letter of the number. The 3rd term is the 1st letter of the next number, and so on.

Therefore, the next term in the sequence would be 4U.

Learn more about sequence here:

brainly.com/question/36944481

What is the problem of this solving?!

Answers

This question can be solved primarily by L'Hospital Rule and the Product Rule.

$y= \lim_(x \to 0) (x^2cos(x)-sin^2(x))/(x^4)$

I) Product Rule and L'Hospital Rule:

$y= \lim_(x \to 0) ([2xcos(x)-x^2sin(x)]-2sin(x)cos(x))/(4x^3)$

II) Product Rule and L'Hospital Rule:

$y= \lim_(x \to 0) ([-2xsin(x)+2cos(x)]-[2xsin(x)+x^2cos(x)]-[2cos^2(x)-2sin^2(x)])/(12x^2) \n y= \lim_(x \to 0) (2cos(x)-4xsin(x)-x^2cos(x)-2cos^2(x)+2sin^2(x))/(12x^2)$

III) Product Rule and L'Hospital Rule:

$]y= \alpha + \beta \n \n \alpha =\lim_(x \to 0) (-2sin(x)-[4sin(x)+4xcos(x)]-[2xcos(x)-x^2sin(x)])/(24x) \n \beta = \lim_(x \to 0) (4sin(x)cos(x)+4sin(x)cos(x))/(24x) \n \n y = \lim_(x \to 0) (-6sin(x)-4xcos(x)-2xcos(x)+x^2sin(x)+8sin(x)cos(x))/(24x)$

IV) Product Rule and L'Hospital Rule:

$y = \phi + \varphi \n \n \phi = \lim_(x \to 0) (-6cos(x)-[-4xsin(x)+4cos(x)]-[2cos(x)-2xsin(x)])/(24x) \n \varphi = \lim_(x \to 0) ([2xsin(x)+x^2cos(x)]+[8cos^2(x)-8sin(x)])/(24x)$

V) Using the Definition of Limit:

$y= (-6*1-4*1-2*1+8*1^2)/(24) \n y= (-4)/(24) \n \boxed {y= (-1)/(6) }$

The cost of parts on your automobile repair bill was $149. The cost for labor was $25Per hour. Write a linear equation giving the total cost C, in terms of t, the number of
Hours. C(t)

Answers

Answer:

C=149+25t

Step-by-step explanation:

Since the total cost is C you would set it all equal to C.

Then the one time cost for parts was 149 so you have to add that in.

And $25 per hour would be multiplied by t because t is the number of hours.

(15x-5)
35

Geometry set-up
Equation 35+(x-5)
X=
m/WIN

Answers

The given expression is (15x - 5) multiplied by 35. To simplify this expression, we can distribute the 35 to both terms inside the parentheses.

(15x - 5) * 35 = 15x * 35 - 5 * 35

Multiplying each term by 35:

= 525x - 175

Therefore, the simplified expression is 525x - 175.

Please note that the equation 35 + (x - 5) and the term m/WIN mentioned in your question seem unrelated to the given expression. If you have any further questions or need clarification, feel free to ask!Answer:

Step-by-step explanation:

An open box is to be constructed from a square piece of sheet metal by removing a square of side 6 feet from each corner and turning up the edges. If the box is to hold 864 cubic feet, what should be the dimensions of the sheet metal?

Answers

Answer:

24 feet

Step-by-step explanation:

We are given that an open box is to be constructed from a square piece of sheet metal by removing a square side 6 feet from each corner and turning up the edges.

We have to find the dimensions of the sheet metal

Let x feet be the side of square metal sheet

Length of box=x-12 feet (because 6 feet removed from each corner)

Width of box=x-12 feet

Height of box=6 feet

Volume of box=864 cubic feet

We know that volume of cuboid= $l* b* h$

Box is in cuboid shaped

Therefore, volume of box= $6(x-12)(x-12)$

$6(x^2-24x+144)=864$

$x^2-24x+144=(864)/(6)$

$x^2-24x+144=144$

$x^2-24x+144-144=0$

$x(x-24)=0$

Then , $x=0 , x-24=0$

$x=24$

x=0 is not possible because side of square metal sheet can not be zero

Therefore, x=24

All sides of square metal sheet are equal.

Hence, side of square metal sheet =24 feet

Final answer:

The original sheet of metal from which an open box holding 864 cubic feet is constructed by removing 6-foot squares from each corner and folding up the edges should be a square with a side length of 26 feet.

Explanation:

To answer your question about the open box constructed from a square piece of sheet metal, let's assume the original side length of the sheet metal is x feet. When squares of length 6 feet are removed from each corner and the edges are turned up, we're left with a box with length and width of (x - 2*6) feet and height of 6 feet.

Given that the volume of the box is 864 cubic feet, we set up this equation to find x:

(x - 12 feet)(x - 12 feet)*6 feet = 864 cubic feet.

Solving this equation gives us a value for x, which is the side length of the original square piece of sheet metal. Doing the math, we find x = 26 feet. So, the dimensions of the original sheet metal are 26 feet by 26 feet.