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3 years ago

Round to nearest ten 6811.09

Mathematics

2 answers:

goldfiish [28.3K]3 years ago

5 0

The answer is 6811.1

melisa1 [442]3 years ago

5 0

Answer:

6810

Step-by-step explanation:

round to nearest ten 6811.09

First we write the place value of given number

6811.09

9 is in hundredths place

1 is in once place

1 is in tens place

8 is in hundreds place

6 is in thousands place

we have 1 in once place that is less than 5 so we keep the numbers as it in tens place

6811.09 rounded to 6810

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3 years ago

Two solutions to y'' – 2y' – 35y = 0 are yı = e, Y2 = e -5t a) Find the Wronskian. W = 0 Preview b) Find the solution satisfying

pashok25 [27]

Answer:

a. $w(t)=-12e^{2t}$

b. $y(t)=-\frac{9}{2}e^{7t}-\frac{5}{2}e^{-5t}$

Step-by-step explanation:

We have a differential equation

y''-2 y'-35 y=0

Auxillary equation

$(D^2-2D-35)=0$

By factorization method we are finding the solution

$D^2-7D+5D-35=0$

$(D-7)(D+5)=0$

Substitute each factor equal to zero

D-7=0 and D+5=0

D=7 and D=-5

Therefore ,

General solution is

$y(x)=C_1e^{7t}+C_2e^{-5t}$

Let $y_1=e^{7t} \;and \;y_2=e^{-5t}$

We have to find Wronskian

$w(t)=\begin{vmatrix}y_1&y_2\\y'_1&y'_2\end{vmatrix}$

Substitute values then we get

$w(t)=\begin{vmatrix}e^{7t}&e^{-5t}\\7e^{7t}&-5e^{-5t}\end{vmatrix}$

$w(t)=-5e^{7t}\cdot e^{-5t}-7e^{7t}\cdot e^{-5t}=-5e^{7t-5t}-7e^[7t-5t}$

$w(t)=-5e^{2t}-7e^{2t}=-12e^{2t}$

a. $w(t)=-12e^{2t}$

We are given that y(0)=-7 and y'(0)=23

Substitute the value in general solution the we get

$y(0)=C_1+C_2$

$C_1+C_2=-7$ ....(equation I)

$y'(t)=7C_1e^{7t}-5C_2e^{-5t}$

$y'(0)=7C_1-5C_2$

$7C_1-5C_2=23$ ......(equation II)

Equation I is multiply by 5 then we subtract equation II from equation I

Using elimination method we eliminate $C_1$

Then we get $C_2=-\frac{5}{2}$

Substitute the value of $C_2$ in I equation then we get

$C_1-\frac{5}{2}=-7$

$C_1=-7+\frac{5}{2}=\frac{-14+5}{2}=-\frac{9}{2}$

Hence, the general solution is

b. $y(t)=-\frac{9}{2}e^{7t}-\frac{5}{2}e^{-5t}$

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3 years ago

Find the equation of the straight line parallel to 2y=3x-7 and passing though the point (0.5,-1)

scZoUnD [109]

2y=3x-7
y = 3/2x - 7/2
y = 1.5x - 3.5 so slope = 1.5
line parallel so it has same slope = 1.5

y +1 = 1.5(x - 0.5)
y + 1 = 1.5x - 0.75
y = 1.5x - 1.75

answer: equation y = 1.5x - 1.75

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3 years ago