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3 years ago

What is the integral of a square root? Please explain.

Mathematics

2 answers:

dolphi86 [110]3 years ago

6 0

Its not guaranteed to be same form.it could be any polynomial that can not be easily formed into squares .try one out!

IrinaK [193]3 years ago

5 0

If y = xⁿ

∫y dx = xⁿ⁺¹ / (n + 1) + C Provided n ≠ -1.

y = √x

y = x^(0.5)

∫y dx = x^(0.5+1) / (0.5 + 1) = x^(1.5) / 1.5 = x^(1.5) / (3/2)

∫y dx = (2/3) x^(1.5) + C.

∫y dx = (2/3) x^(3/2) + C.

∫y dx = (2/3)√x³ + C

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Please explain this answer ☹️

GuDViN [60]

Answer:

see explanation

Step-by-step explanation:

Note that cos315° = cos45° and sin315° = - sin45° and

cos45° = sin45° = $\frac{1}{\sqrt{2} }$ = $\frac{\sqrt{2} }{2}$

Hence

12(cos315° + isin315°)

= 12(cos45° - isin45°)

= 12( $\frac{\sqrt{2} }{2}$ - i $\frac{\sqrt{2} }{2}$ )

= 6 $\sqrt{2}$ - 6i $\sqrt{2}$

7 0

3 years ago

ABM Services paid a $4.15 annual dividend on a day it closed at a price of $54 per share. What

Leni [432]

Answer:

- 22719559.

Step-by-step explanation:

3 0

3 years ago

The length of a rectangle is 5 inches shorter than double its width. The perimeter of the rectangle is 192 inches. Write a two-s

alukav5142 [94]

Answer:

Step-by-step explanation:

Givens

Let the width = x

Let the length = x + 5

Equation

2w + 2W = P

Solution

2x + 2(x + 5) = 192 Remove the brackets <=== Answer

2x + 2x + 10 = 192 Combine like terms

4x + 10 = 192 Subtract 10 from both sides

4x = 192 - 10

4x = 182 Divide by 4

4x/4 = 182/4

x = 45.5

8 0

2 years ago

Part A: The area of a square is (16x2 − 8x + 1) square units. Determine the length of each side of the square by factoring the a

d1i1m1o1n [39]

Answer:

see below

Step-by-step explanation:

16x^2 − 8x + 1

(4x)^2 -8x +1

Factor

This is a perfect square trinomial

a^2 -2ab +b^2 = (a-b)(a-b)

(4x)^2 -8x +1 = (4x-1) (4x-1)

The area of a square is given by

A = s^2

(4x-1) ^2 = s^2

4x-1 = s

The side length is 4x-1

(81x^2 − 4y^2)

(9x)^2 - (2y)^2

This is the difference of squares

a^2 - b^2 = (a-b) (a+b)

(9x-2) (9x+2)

The area of a rectangle is

A = l*w

(81x^2 − 4y^2) = (9x-2) (9x+2)

The dimensions are (9x-2) (9x+2)

3 0

3 years ago

(7)(8)(9) Geometry Check Ans 7) s = 15 8) y = 64 x = 99 9) 96

Katyanochek1 [597]

Problem 7: Correct
Problem 8: Correct
Problem 9: Correct

The steps are below if you are curious

===========================================================================================

Problem 7

S = 180*(n-2)
2340 = 180*(n-2)
2340/180 = n-2
13 = n-2
n-2 = 13
n = 13+2
n = 15

I'm using n in place of lowercase s, but the idea is the same. If anything, it is better to use n for the number of sides since S already stands for the sum of the interior angles. I'm not sure why your teacher decided to swap things like that.

===========================================================================================

Problem 8

First find y
y+116 = 180
y+116-116 = 180-116
y = 64

which is then used to find x. The quadrilateral angles add up to 180*(n-2) = 180*(4-2) = 360 degrees
Add up the 4 angles, set the sum equal to 360, solve for x

x+y+125+72 = 360
x+64+125+72 = 360 ... substitution (plug in y = 64)
x+261 = 360
x+261-261 = 360-261
x = 99

===========================================================================================

Problem 9

With any polygon, the sum of the exterior angles is always 360 degrees

The first two exterior angles add to 264. The missing exterior angle is x
x+264 = 360
x+264-264 = 360-264
x = 96

6 0

3 years ago