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2 years ago

Evaluate it..........

Mathematics

1 answer:

trasher [3.6K]2 years ago

5 0

Answer:

the answer is $\frac{1}{41} (23x-2ln(5sinx+4cosx))$

Step-by-step explanation:

$\int {\frac{3sinx+2cosx}{5sinx+4cosx} } \, dx$

here,

a=3, b=2, c=5, d=4

$M=\frac{ac+bd}{c^2+d^2 }=\frac{3*5+2*4}{5^2+4^2}=\frac{23}{41}$

$N=\frac{bc-ad}{c^2+d^2 }=\frac{2*5-3*4}{5^2+4^2}=\frac{-2}{41}$

$\int {\frac{3sinx+2cosx}{5sinx+4cosx} } \, dx=\int{\frac{\frac{23}{41}(5sinx+4cosx)-\frac{2}{41}(5cosx-4sinx) }{5sinx+4cosx} }\,dx$

$=\frac{23}{41}\int\, dx -\frac{2}{41} \int{\frac{5cosx-4sinx}{5sinx+4cosx} }\, dx$

$=\frac{1}{41} (23x-2ln(5sinx+4cosx))$

pls mark it as the brainliest

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Find the general solution of the given higher-order differential equation. d3u dt3 + d2u dt2 − 2u = 0

STALIN [3.7K]

$\dfrac{\mathrm d^3u}{\mathrm dt^3}+\dfrac{\mathrm d^2u}{\mathrm dt^2}-2u=0$

This ODE has characteristic equation

$r^3+r^2-2=(r^3-r)+(r^2+r-2)=r(r^2-1)+(r+2)(r-1)$

$=(r(r+1)+(r+2))(r-1)=(r^2+2r+2)(r-1)=0$

which has roots at $r=1,-1\pm i$ . Then the characteristic solution to the ODE is

$u(t)=C_1e^t+C_2e^{(-1+i)t}+C_3e^{(-1-i)t}$

$\implies\boxed{u(t)=C_1e^t+C_2e^{-t}\cos t+C_3e^{-t}\sin t}$

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3 years ago

The test statistic of zequals2.32 is obtained when testing the claim that pgreater than0.3. a. Identify the hypothesis test as b

Sonja [21]

Answer:

a) We need to conduct a hypothesis in order to test the claim that the true proportion p is greatr than 0.3, so then the system of hypothesis are.:

Null hypothesis: $p \leq 0.3$

Alternative hypothesis: $p > 0.3$

Right tailed test

b) $p_v =P(z>2.32)=0.0102$

c) So the p value obtained was a very low value and using the significance level given $\alpha=0.1$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of interest is higher than 0.3

Step-by-step explanation:

Part a: Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion p is greatr than 0.3, so then the system of hypothesis are.:

Null hypothesis: $p \leq 0.3$

Alternative hypothesis: $p > 0.3$

Right tailed test

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

For this case the statistic is given by $z_{calc}= 2.32$

Part b: Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The next step would be calculate the p value for this test.

Since is a right tailed test the p value would be:

$p_v =P(z>2.32)=0.0102$

Part c

So the p value obtained was a very low value and using the significance level given $\alpha=0.1$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of interest is higher than 0.3

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3 years ago

Help me please!!!!!!!!!!!!!!!!!

Usimov [2.4K]

Answer:

Step-by-step explanation:

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3 years ago

The following graph shows a proportional relationship.

LenKa [72]

Answer:

Step-by-step explanation:

If we look at the graph this is an increasing graph where y increases with respect to x so in other words we can say that y is directly proportional to x.

$y\ \alpha\ x\\$

and when we remove the proportionality sign we replace it with an equal to sign and a constant. So it becomes ,

$y = kx\\$

now to find the Constant of proportionality which is k we can use any ordered pair(coordinate/point) from the graph,

Lets take ( 2 , 4) where 2 represents the value of x on the x-axis and 4 represents the value of y on the y-axis so now,

$y=kx\\(4)=k(2)\\4=2k\\4/2=k\\k=2\\$

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2 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

Evaluate it..........​

Evaluate it..........