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3 years ago

3/4 - 2/7 = ? pls help me because I can get grounded

Mathematics

1 answer:

Leona [35]3 years ago

7 0

Answer:

1/7

Step-by-step explanation:

&&5_4_&&&&&&&&&&&&&---

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Use variation of parameters to find a general solution to the differential equation given that the functions y1 and y2 are linea

Aleks [24]

Recall that variation of parameters is used to solve second-order ODEs of the form

y''(t) + p(t) y'(t) + q(t) y(t) = f(t)

so the first thing you need to do is divide both sides of your equation by t :

y'' + (2t - 1)/t y' - 2/t y = 7t

You're looking for a solution of the form

$y=y_1u_1+y_2u_2$

where

$u_1(t)=\displaystyle-\int\frac{y_2(t)f(t)}{W(y_1,y_2)}\,\mathrm dt$

$u_2(t)=\displaystyle\int\frac{y_1(t)f(t)}{W(y_1,y_2)}\,\mathrm dt$

and W denotes the Wronskian determinant.

Compute the Wronskian:

$W(y_1,y_2) = W\left(2t-1,e^{-2t}\right) = \begin{vmatrix}2t-1&e^{-2t}\\2&-2e^{-2t}\end{vmatrix} = -4te^{-2t}$

Then

$u_1=\displaystyle-\int\frac{7te^{-2t}}{-4te^{-2t}}\,\mathrm dt=\frac74\int\mathrm dt = \frac74t$

$u_2=\displaystyle\int\frac{7t(2t-1)}{-4te^{-2t}}\,\mathrm dt=-\frac74\int(2t-1)e^{2t}\,\mathrm dt=-\frac74(t-1)e^{2t}$

The general solution to the ODE is

$y = C_1(2t-1) + C_2e^{-2t} + \dfrac74t(2t-1) - \dfrac74(t-1)e^{2t}e^{-2t}$

which simplifies somewhat to

$\boxed{y = C_1(2t-1) + C_2e^{-2t} + \dfrac74(2t^2-2t+1)}$

4 0

2 years ago

In ΔLMN, the measure of ∠N=90°, NL = 6. 8 feet, and LM = 9. 4 feet. Find the measure of ∠L to the nearest tenth of a degree.

egoroff_w [7]

Answer:

Step-by-step explanation:
The above is a right angled triangle
So you take the longest side
9.4^2 - 6.8^2
88.36- 46.24
sqrt of 42.12
6.4899

To the nearest tenth of a degree = 6.56.5ft

5 0

2 years ago

Subtract. – 0.41 – 8.91 a. –9.32 b. –8.50 c. 8.50 d. 9.32

Free_Kalibri [48]

The answer is a -9.32

5 0

3 years ago

A bank account earns 2.5% interest per year. If the account starts with $500, approximately how many years will it take for the

belka [17]

Answer:

Step-by-step explanation:

Since we have an amount in the future of 750, we are going to use Future value formula; FV = PV (1+r)^t

where PV= Initial amount deposited

r= interest rate or discount rate

t = total duration of the investment

FV= 750

PV=500

r = 2.5% or 0.025 as a decimal

t = ?

Next, plug in the numbers into the formula;

750 = 500* (1+0.025)^t

divide both sides by 500;

750/500 = 1.025^t

Introduce ln on both sides

ln 1.5 = ln $1.025^{t}$

ln 1.5 = t ln 1.025

0.4054651 = 0.0246926 t

Divide both sides by 0.0246926 to solve for t;

0.4054651/0.0246926 = t

t = 16.42

Therefore it will take 16.42 years

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3 years ago

How do you put mixed fractions on a number line in decimal form?

Natalka [10]

Like you would put 0.5 or 1. or 1.5 as like 1/2 or 1/3 and you plot negatives first

5 0

3 years ago