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3 years ago

11

A two congruent sides of an isosceles triangle each measure 3b^2 + 2 centimeters the third side measure 4b-5 centimeters what is

the perimeter in centimeters of this triangle????

1 answer:

REY [17]3 years ago

3 0

You need to add (3b^2+2)+(3b^2+2)+(4b-5). This should equal to 6b^2+4b-1.

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Find a particular solution to the nonhomogeneous differential equation y??+4y?+5y=?10x+e^(?x).

Firdavs [7]

Answer:

A) Particular solution:

$2x+\frac{1}{2}e^{-x}-\frac{8}{5}$

B) Homogeneous solution:

$y_{h}=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))$

C) The most general solution is

$y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+2x+\frac{1}{2}e^{-x}-\frac{8}{5}$

Step-by-step explanation:

Given non homogeneous ODE is

$y''+4y'+5y=10x+e^{-x}---(1)$

To find homogeneous solution:

$D^{2}+4D+5=0\\D^{2}+4D+4-4+5=0\\\\(D+2)^{2}=-1\\D+2=\pm iD=-2 \pm i\\y_{h}=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))---(2)$

To find particular solution:

$y_{p}=Ax+B+Ce^{-x}\\\\y'_{p}=A-Ce^{-x}\\y''_{p}=Ce^{-x}\\$

Substituting $y_{p},y'_{p},y''_{p}$ in (1)

$y''_{p}+4y'_{p}+5y_{p}=10x+e^{-x}\\Ce^{-x}+4(A-Ce^{-x})+5(Ax+B+Ce^{-x})=10x+e^{-x}\\$

Equating the coefficients

$5Ax+2Ce^{-x}+4A+5B=10x+e^{-x}\\5A=10\\A=2\\4A+5B=0\\B=-\frac{4A}{5}B=-\frac{8}{5}2C=1\\C=\frac{1}{2}\\So,\\y_{p}=2x+\frac{1}{2}e^{-x}-\frac{8}{5}---(3)\\$

The general solution is

$y=y_{h}+y_{p}$

from (2) ad (3)

$y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+2x+\frac{1}{2}e^{-x}-\frac{8}{5}$

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2 years ago

On a horizontal number line, numbers are what

Vikentia [17]

Answer:

to the right of zero if postive if negative left

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2 years ago

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Zoya asked the students of her class their baseball scores and recorded the scores in the table shown below: Baseball Scores Sco

nlexa [21]

Answer:

4.06

Step-by-step explanation:

Given :

Scores Number of students

0 1

1 2

2 5

3 3

4 6

5 7

6 9

To Find: Mean

Solution:

Mean = $\frac{\text{Sum of all scores}}{\text{number of students}}$

Mean = $\frac{0 \times 1+1\times 2+2\times 5+3\times 3+4\times 6+5\times 7+6\times 9}{1+2+5+3+6+7+9}$

Mean = $\frac{134}{33}$

Mean = $4.06$

Hence, The Mean of baseball score is 4.06 .

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2 years ago

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What is science??ㅤㅤㅤㅤㅤ

Darina [25.2K]

Answer:

the study in which observations are made, experiments are done and logical conclusions are drawn in order to understand the principles of nature.

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2 years ago

Dmitry_Shevchenko [17]

Answer: Option (D) Add the exponents and keep the same base. Then find the reciprocal and change the sign of the exponent.

Explanation:

Given expression:

$(2^3)(2^{-4})$

<em>Step-1: </em>Add the exponents and keep the same base by using $x^a*x^b = x^{a+b}$ property.

$(2^3)(2^{-4}) = 2^{(3+(-4))} = 2^{-1}$

Step-2: The reciprocal of $2^{-1}$ is $\frac{1}{2^{-1}}$ , which is $2^1$

Step-3: The exponent of $2^1$ is +1; therefore, change the sign of exponent. The end expression will now become:

$2^{-1}$

Hence, the correct option is (D) Add the exponents and keep the same base. Then find the reciprocal and change the sign of the exponent.

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3 years ago

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