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3 years ago

What is the answer of this attachment:

Mathematics

1 answer:

Solnce55 [7]3 years ago

4 0

Answer:

(B) 2

Step-by-step explanation:

=> $\frac{\sqrt{32}+ \sqrt{48} }{\sqrt{8}+\sqrt{12} }$

=> $\frac{4\sqrt{2}+4\sqrt{3} }{2\sqrt{2}+2\sqrt{3} }$

=> $\frac{4(\sqrt{2}+\sqrt{3}) }{2(\sqrt{2}+\sqrt{3)} }$

Cancelling $\sqrt{2}+\sqrt{3}$

=> $\frac{4}{2}$

=> 2

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Inverse Function In Exercise,analytically show that the functions are inverse functions.Then use the graphing utility to show th

DanielleElmas [232]

Answer:

$g^{-1}(x)=f(x)=e^{\frac{x}{3}}$

Step-by-step explanation:

We have been given two functions as $g(x)=\text{ln}(x^3)$ and $f(x)=e^{\frac{x}{3}}$ . We are asked to show that both functions are inverse of each other algebraically and graphically.

Let us find inverse function of $g(x)=\text{ln}(x^3)$ as:

$y=\text{ln}(x^3)$

Interchange x and y values:

$x=\text{ln}(y^3)$

Using log property $\text{ln}(a^b)=b\cdot \text{ln}(a)$ , we will get:

$x=3\cdot \text{ln}(y)$

$\frac{x}{3}=\frac{3\cdot \text{ln}(y)}{3}$

$\frac{x}{3}=\text{ln}(y)$

Using log definition; If $\text{log}_a(b)=c$ , then $b=a^c$ , we will get:

$y=e^{\frac{x}{3}}$

$g^{-1}(x)=e^{\frac{x}{3}}$

Therefore, we can see that function $f(x)=e^{\frac{x}{3}}$ is inverse of function $g(x)=\text{ln}(x^3)$ .

We can see that both functions are symmetric about line $y=x$ , therefore, both functions are inverse of each other.

8 0

4 years ago

In 2015 the populations of City X and City Y were

Gnoma [55]

Answer:

160,000

Step-by-step explanation:

120,000 + 0.2(120,000)=120,000+24,000=144,000

144,000 were both populations in 2015.

x-0.1x = 144,000

0.9x=144,000

x=160,000

The Population of City Y in 2010 was 160,000

7 0

3 years ago

A data set lists earthquake depths. The summary statistics are

irinina [24]

Answer:

Step-by-step explanation:

The summary of the given statistics data include:

sample size n = 400

sample mean $\overline x$ = 6.86

standard deviation = 4.37

Level of significance ∝ = 0.01

Population Mean $\mu$ = 6.00

Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.

To start with the hypothesis;

The null and the alternative hypothesis can be computed as :

$H_o: \mu = 6.00 \\ \\ H_1 : \mu \neq 6.00$

The test statistics for this two tailed test can be computed as:

$z= \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt {n}}}$

$z= \dfrac{6.86 - 6.00}{\dfrac{4.37}{\sqrt {400}}}$

$z= \dfrac{0.86}{\dfrac{4.37}{20}}$

z = 3.936

degree of freedom = n - 1

degree of freedom = 400 - 1

degree of freedom = 399

At the level of significance ∝ = 0.01

P -value = 2 × (z < 3.936) since it is a two tailed test

P -value = 2 × ( 1 - P(z ≤ 3.936)

P -value = 2 × ( 1 -0.9999)

P -value = 2 × ( 0.0001)

P -value = 0.0002

Since the P-value is less than level of significance , we reject $H_o$ at level of significance 0.01

Conclusion: There is sufficient evidence to conclude that the original claim that the mean of the population of earthquake depths is 5.00 km.

7 0

3 years ago

Prove that T is one to one if and only if T carries linearly independent subsets of V onto linearly independent subsets of W.

balu736 [363]

Answer with Step-by-step explanation:

Suppose T is one-one

Let S be a linearly independent subset of V

We want to show that T(S) is linearly independent.

Suppose T(S) is linearly dependent.

Then there exist $v_1,v_2,...v_n\in S$ and some not all zero scalars $a_1,a_2,....a_n$ such that

$a_1T(v_1)+a_2T(v_2)+a_3T(v_3)+...+a_nT(v_n)=0$

T is linear therefore,

$T(a_1v_1+a_2v_2+..+a_nv_n)=0$

T is one-one therefore

N(T)=0

$a_v_1+....+a_nv_n=0$

S is linearly independent therefore,

$a_1=a_2=...a_n=0$

It is contradiction.Hence, T(S) is linearly independent.

Conversely, Suppose that T carries linearly independent subset of V onto linearly independent subsets of W.

Assume that T(x)=0 if the set x is linearly independent

Then, by assumption we conclude that {0} is linearly independent but {0} is linearly dependent.

It is contradiction .Hence, the set {x} is linearly dependent which implies that x=0

It means N(T)={0}.Therefore, T is one- one

4 0

3 years ago

How do I integrate trig functions

katrin [286]

Integrate sin(3x+1) with respect to x. Use the substitution method. Let u=3x+1 be y our substitution. Then du/dx = 3, and du = 3dx.

Then we have "integrate sin u with respect to u" . Here's where things are just a bit tricky at first. You have "integrate sin (3x+1) with respect to x." If u = 3x+1, then du/dx = 3 and du=3dx. But we don't have 3dx; we have only dx. Manipulate du=3dx as follows: du/3 = dx.

Then, "integral of sin (3x+1) dx" => "integral of sin u (du/3)"

and this is equivalent to (1/3) "integral of sin u du." We get:
(1/3)(-cos u) + c, or (-1/3)*cos u + c. Finally, subst. 3x+1 for du, obtaining

(-1/3)*cos(3x+1) + C (answer).

You should find the derivative of this as a check. If the result of your differentiation is sin(3x+1), your integral was correct. Otherwise, it's not.

Don't worry... this material becomes much easier once you've gotten the knack of it.

7 0

4 years ago