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const2013 [10]
2 years ago
8

Write the given second order equation as its equivalent system of first order equations

Mathematics
1 answer:
Lilit [14]2 years ago
3 0

The second-order equation as its equivalent system of first-order equations is

\left[\begin{array}{ccc}u(1)\\\\v(1)\end{array}\right] = \left[\begin{array}{ccc}7.5\\\\9\end{array}\right]

An equivalent system that has the identical answer is known as an equivalent structure. Given a gadget of two equations, we can produce an equal system by way of replacing one equation by means of the sum of the 2 equations, or by way of changing an equation by means of a couple of of itself.

Systems of linear equations are equivalent if and handiest in the event that they have an equal set of solutions. In other phrases, two systems are equal if and only if each answer of one in all of them is likewise a solution of the opposite.

In the structures sciences, a machine equivalent system is the conduct of a parameter or thing of a machine in a way just like a parameter or component of a distinctive system. Similarity means that mathematically the parameters and additives will be indistinguishable from each different.

Taking v = u, we have:

u" + 4u' + 6u = 4sin(3t)

--> v' + 4v + 6u = 4sin(3t)

So the system of equations is:

u' = 0u + 1v

v' = -6u - 4v + 4sin(3t)

So we can write it as:

u(1) = 7.5

v(1) = u'(1) = 9

So the initial condition matrix is:

\left[\begin{array}{ccc}u(1)\\\\v(1)\end{array}\right] = \left[\begin{array}{ccc}7.5\\\\9\end{array}\right]

Learn  more about the equivalent system here brainly.com/question/14878855

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Solve for x and verify:3(x+3)-2(x-1)=5(x-5)
Gekata [30.6K]

Answer:

x=9

Step-by-step explanation:

Distribute:

3x+9-2x+2=5x-25

Combine like terms:

x+11=5x-25

Solve:

x-x+11=5x-x-25

11=4x-25

11+25=4x-25+25

36=4x

Divide by 9:

x=9.

Hope this helps :D

7 0
3 years ago
Read 2 more answers
Central Park is a rectangular-shaped park in the middle of New York City. The area of the park is 3.41 square kilometers.
dmitriy555 [2]

Answer:

4,262.50 m

842 acres

Step-by-step explanation:

Given that :

Park is rectangular in shape

Width of park = 800 m

Area of park = 3.41 km²

Width of park = 800 / 1000 = 0.8 km

Area of rectangle, A

A = l * w

l = Length ; w = width

3.41 = l * 0.8

3.41 = 0.8l

l = 3.41 / 0.8

l = 4.2625 km

Hence, length in meters :

4.2625 * 1000

= 4,262.50 m

B.)

1 km² is approximately 247 acres

3.41km² = 3.41 * 247

3.41 km² = 842.27

= 842 acres

6 0
2 years ago
If y + 7 = 9, what does y equal?<br> +
asambeis [7]
Y=2
If you subtract 9-7 you get the answer 2 which makes y=2.
7 0
2 years ago
A medical researcher wondered if there is a significant difference between the mean birth weight of boy and girl babies. Random
Yuliya22 [10]

Answer:

b) independent samples t-test

t=\frac{(5.92 -5.74)-(0)}{\sqrt{\frac{1.88^2}{5}}+\frac{1.81^2}{5}}=0.154  

p_v =2*P(t_{8}>0.154) =0.881  

So with the p value obtained and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (boys) is NOT significantly different than the mean for the group 2 (Girls).  

Step-by-step explanation:

The system of hypothesis on this case are:  

Null hypothesis: \mu_1 = \mu_2  

Alternative hypothesis: \mu_1 \neq \mu_2  

Or equivalently:  

Null hypothesis: \mu_1 - \mu_2 = 0  

Alternative hypothesis: \mu_1 -\mu_2\neq 0  

Our notation on this case :  

n_1 =5 represent the sample size for group 1  

n_2 =5 represent the sample size for group 2  

We can calculate the mean and deviation for eaach group with the following formulas:

\bar X= \frac{\sum_{i=1}^n X_i}{n}

s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}

\bar X_1 =5.92 represent the sample mean for the group 1  

\bar X_2 =5.74 represent the sample mean for the group 2  

s_1=1.88 represent the sample standard deviation for group 1  

s_2=1.81 represent the sample standard deviation for group 2  

If we see the alternative hypothesis we see that we are conducting a bilateral test and with independnet samples t test.

b) independent samples t-test

The statistic is given by this formula:  

t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{\sqrt{\frac{s^2_1}{n_1}}+\frac{S^2_2}{n_2}}  

And now we can calculate the statistic:  

t=\frac{(5.92 -5.74)-(0)}{\sqrt{\frac{1.88^2}{5}}+\frac{1.81^2}{5}}=0.154  

The degrees of freedom are given by:  

df=5+5-2=8

And now we can calculate the p value using the altenative hypothesis:  

p_v =2*P(t_{8}>0.154) =0.881  

So with the p value obtained and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (boys) is NOT significantly different than the mean for the group 2 (Girls).  

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