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postnew [5]
3 years ago
6

Find the length of the side of the square if the number of square meters in its area is 1.5 times the number of meters in its pe

rimeter
Mathematics
1 answer:
Alinara [238K]3 years ago
8 0

a - a length of side of square

The area: A = a²

The perimeter: P = 4a

The equation:

a^2=1.5\cdot4a\\\\a^2=6a\ \ \ \ |-6a\\\\a^2-6a=0\\\\a(a-6)=0\iff a=0\ \vee\ a-6=0\\\\\boxed{a=6}

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Please show me how to solve for Xsquared - 21.75X = -15.75. I have the solution but do not know how to solve it.
Andreas93 [3]
x^2-21.75x=-15.75 \\
x^2-21.75x+15.75=0

Use the quadratic formula:
x^2-21.75x+15.75=0 \\ \\
a=1 \\ b=-21.75 \\ c=15.75 \\ b^2-4ac=(-21.75)^2-4 \times 1 \times 15.75=473.0625-63=410.0625 \\ \\
x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}=\frac{-(-21.75) \pm \sqrt{410.0625}}{2 \times 1}=\frac{21.75 \pm 20.25}{2} \\
x=\frac{21.75-20.25}{2} \ \lor \ x=\frac{21.75+20.25}{2} \\
x=\frac{1.5}{2} \ \lor \ x=\frac{42}{2} \\
x=\frac{15}{20} \ \lor \ x=21 \\
x=\frac{3}{4} \ \lor \ x=21 \\
\boxed{x=\frac{3}{4} \hbox{ or } x=21}
3 0
3 years ago
Complete the Steps to Solve for x.<br><br> -0.57x+0.27x =8.1
IgorLugansk [536]

Answer:

x=-27

Step-by-step explanation:

-0.57x+0.27x = 8.1

-0.3x = 8.1

x = -8.1/0.3

x = -27

6 0
3 years ago
Read 2 more answers
Read this E[2X^2 â€" Y].
djyliett [7]

Looks like a badly encoded/decoded symbol. It's supposed to be a minus sign, so you're asked to find the expectation of 2<em>X </em>² - <em>Y</em>.

If you don't know how <em>X</em> or <em>Y</em> are distributed, but you know E[<em>X</em> ²] and E[<em>Y</em>], then it's as simple as distributing the expectation over the sum:

E[2<em>X </em>² - <em>Y</em>] = 2 E[<em>X </em>²] - E[<em>Y</em>]

Or, if you're given the expectation and variance of <em>X</em>, you have

Var[<em>X</em>] = E[<em>X</em> ²] - E[<em>X</em>]²

→   E[2<em>X </em>² - <em>Y</em>] = 2 (Var[<em>X</em>] + E[<em>X</em>]²) - E[<em>Y</em>]

Otherwise, you may be given the density function, or joint density, in which case you can determine the expectations by computing an integral or sum.

6 0
3 years ago
True or false variable is a letter used in place of a number
VikaD [51]
Answer: TRUE!


Variables ARE letters used in place of numbers absolutely
5 0
3 years ago
(a) By inspection, find a particular solution of y'' + 2y = 14. yp(x) = (b) By inspection, find a particular solution of y'' + 2
SOVA2 [1]

Answer:

(a) The particular solution, y_p is 7

(b) y_p is -4x

(c) y_p is -4x + 7

(d) y_p is 8x + (7/2)

Step-by-step explanation:

To find a particular solution to a differential equation by inspection - is to assume a trial function that looks like the nonhomogeneous part of the differential equation.

(a) Given y'' + 2y = 14.

Because the nonhomogeneus part of the differential equation, 14 is a constant, our trial function will be a constant too.

Let A be our trial function:

We need our trial differential equation y''_p + 2y_p = 14

Now, we differentiate y_p = A twice, to obtain y'_p and y''_p that will be substituted into the differential equation.

y'_p = 0

y''_p = 0

Substitution into the trial differential equation, we have.

0 + 2A = 14

A = 6/2 = 7

Therefore, the particular solution, y_p = A is 7

(b) y'' + 2y = −8x

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = -8x

2Ax + 2B = -8x

By inspection,

2B = 0 => B = 0

2A = -8 => A = -8/2 = -4

The particular solution y_p = Ax + B

is -4x

(c) y'' + 2y = −8x + 14

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = -8x + 14

2Ax + 2B = -8x + 14

By inspection,

2B = 14 => B = 14/2 = 7

2A = -8 => A = -8/2 = -4

The particular solution y_p = Ax + B

is -4x + 7

(d) Find a particular solution of y'' + 2y = 16x + 7

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = 16x + 7

2Ax + 2B = 16x + 7

By inspection,

2B = 7 => B = 7/2

2A = 16 => A = 16/2 = 8

The particular solution y_p = Ax + B

is 8x + (7/2)

8 0
3 years ago
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