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4 years ago

The area of a square is 49 cm. What is the length of one side

Mathematics

1 answer:

mestny [16]4 years ago

5 0

Actually, the area of the square is 49 cm^2.

The length of one side is sqrt(49 cm^2) = 7 cm (answer)

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Integration questions .

dlinn [17]

$\\\\\ \textbf{a)}\\\\~~~\displaystyle \int (6x- \sin 3x) ~ dx\\\\=6\displaystyle \int x ~ dx - \displaystyle \int \sin 3x ~ dx\\\\=6 \cdot \dfrac{x^2}2 - \dfrac 13 (- \cos 3x) +C~~~~~~~~~~~;\left[\displaystyle \int x^n~ dx = \dfrac{x^{n+1}}{n+1}+C,~~~n \neq -1\right]\\\\ =3x^2 +\dfrac{\cos 3x}3 +C~~~~~~~~~~~~~~~~~~~~;\left[\displaystyle \int \sin (mx) ~dx = -\dfrac 1m ~ (\cos mx)+C \right]\\$

$\textbf{b)}\\\\~~~~\displaystyle \int(3e^{-2x} +\cos (0.5 x)) dx\\\\=3\displaystyle \int e^{-2x} ~dx+ \displaystyle \int \cos(0.5 x) ~dx\\\\\\=-\dfrac 32 e^{-2x} + \dfrac 1{0.5} \sin (0.5 x) +C~~~~~~~~~~~~~~;\left[\displaystyle \int e^{mx}~dx = \dfrac 1m e^{mx} +C \right]\\\\\\=-\dfrac 32 e^{-2x} + 2 \sin(0.5 x) +C~~~~~~~~~~~~~~~~~;\left[\displaystyle \int \cos(mx)~ dx = \dfrac 1m \sin(mx) +C\right]\\\\\\=-1.5e^{-2x} +2\sin(0.5x) +C$

$\textbf{a)}\\\\y = \displaystyle \int \cos(x+5) ~ dx\\\\\text{Let,}\\\\~~~~~~~u = x+5\\\\\implies \dfrac{du}{dx} = 1+0~~~~~~;[\text{Differentiate both sides.}]\\\\\implies \dfrac{du}{dx} = 1\\\\\implies du = dx\\\\\text{Now,}\\\\y= \displaystyle \int \cos u ~ du\\\\~~~= \sin u +C\\\\~~~=\sin(x+5) + C$

$\textbf{b)}\\\\y = \displaystyle \int 2(5x-3)^4 dx\\\\\text{Let,}\\~~~~~~~~u = 5x-3\\\\\implies \dfrac{du}{dx} = 5~~~~~~~~~~;[\text{Differentiate both sides}]\\\\\implies dx = \dfrac{du}5\\\\\text{Now,}\\\\y = 2\cdot \dfrac 1 5 \displaystyle \int u^4 ~ du\\\\\\~~=\dfrac 25 \cdot \dfrac{u^{4+1}}{4+1} +C\\\\\\~~=\dfrac 25 \cdot \dfrac{u^5}5+C\\\\\\~~=\dfrac{2u^5}{25}+C\\\\\\~~=\dfrac{2(5x-3)^5}{25}+C$

$\textbf{a)}\\\\y = \displaystyle \int xe^{3x} dx\\\\\text{We know that,}\\\\ \displaystyle \int (uv) ~dx = u \displaystyle \int v ~ dx - \displaystyle \int \left[ \dfrac{du}{dx} \displaystyle \int ~ v ~ dx \right]~ dx\\\\\text{Let}, u =x~ \text{and}~ v=e^{3x} .\\\\y= \displaystyle \int xe^{3x} ~dx\\\\\\~~= x\displaystyle \int e^{3x} ~ dx - \displaystyle \int \left[\dfrac{d}{dx}(x) \displaystyle \int e^{3x}~ dx \right]~ dx\\\\\\$

$=x\displaystyle \int e^{3x}~ dx - \displaystyle \dfrac 13 \int \left(e^{3x} \right)~ dx\\\\\\=\dfrac{xe^{3x}}3 - \dfrac 13 \cdot \dfrac{ e^{3x}}3+C\\\\\\= \dfrac{xe^{3x}}{3}- \dfrac{e^{3x}}{9}+C\\\\\\=\dfrac{3xe^{3x}}{9}- \dfrac{e^{3x}}9 + C\\\\\\= \dfrac 19e^{3x}(3x-1)+C$

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8 0

2 years ago

What is the area of a triangle whose vertices are D(3, 3) , E(3, −1) , and F(−2, −5) What is the area of the rectangle?

RideAnS [48]

Answer:

The area of the triangle with the given vertices is 10 square units

Step-by-step explanation:

x y

D 3 3

E 3 -1

F -2 -5

D 3 3

Area: A=Abs [(xd ye + xe yf + xf yd) - (yd xe + ye xf + yf xd)] /2

Absolute value: Abs

A = Abs { [(3)(-1)+(3)(-5)+(-2)(3)] - [(3)(3)+(-1)(-2)+(-5)(3)] } / 2

A = Abs [ (-3-15-6)-(9+2-15) ] / 2

A = Abs [ (-24)-(-4) ] / 2

A = Abs ( -24+4) / 2

A = Abs (-20) / 2

A = 20 / 2

A = 10 square units

4 0

3 years ago

What is the LCM how do I find it

Nimfa-mama [501]

One of the quickest ways to find the LCM of two numbers is to use the prime factorization of each number and then the product of the least powers of the common prime factors will be the LCM of those numbers.

LCM-LOWEST COMMON MULTIPLE

6 0

3 years ago

select the irrational number? A)√9 B)√12 C)√16 D)√20 E)√25 (there should be more than one answer)

GenaCL600 [577]

The answers are:
__________________________
[B]: "√12 " ; AND:
__________________________
[D]: "<span>√20" .
__________________________
Note: "Irrational numbers" have decimals that are: 1) non-terminating; AND: 2) non-repeating.
__________________________
Consider the answer choices given; and consider the given information that there "should be no more than one answer.
__________________________________
Consider the following answer choices:
__________________________________
Choice A) "</span><span>√9" = 3 . Rule out this choice.
__________________________________
Choice C) "</span><span>√16" = 4 . Rule out this choice.
__________________________________
Choice E) "</span><span>√25" = 5. Rule out this choice.
_________________________________
We are left with 2 (two) remaining answer choices:
[B]: "</span>√12" ; and: [D]: "<span>√20" .
_________________________________
If there are more than one answer, then these two choices should be the correct answer. However, let us explore these two choices, using a calculator.
____________________________
[B]: </span>"√12" = 3.4641016151377546

[D]: "√20" = 4.4721359549995794
_________________________________
These two answer choices should the correct answers.

6 0

4 years ago

I need help please!!!!

frez [133]

Answer:

Step-by-step explanation:

Maybe A Emma, but how can we really know what Zhan, he could have any one of those in mind.. but not really figure it out with those straws :/

5 0

3 years ago