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nikdorinn [45]
2 years ago
10

Some values of the exponential function f (x ) are shown in the table, where m and n are real numbers.

Mathematics
1 answer:
olchik [2.2K]2 years ago
8 0

Answer:

-6

Step-by-step explanation:

bc m and m are real numbers.

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Answer:

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A company wishes to manufacture some boxes out of card. The boxes will have 6 sides (i.e. they covered at the top). They wish th
Serhud [2]

Answer:

The dimensions are, base b=\sqrt[3]{200}, depth d=\sqrt[3]{200} and height h=\sqrt[3]{200}.

Step-by-step explanation:

First we have to understand the problem, we have a box of unknown dimensions (base b, depth d and height h), and we want to optimize the used material in the box. We know the volume V we want, how we want to optimize the card used in the box we need to minimize the Area A of the box.

The equations are then, for Volume

V=200cm^3 = b.h.d

For Area

A=2.b.h+2.d.h+2.b.d

From the Volume equation we clear the variable b to get,

b=\frac{200}{d.h}

And we replace this value into the Area equation to get,

A=2.(\frac{200}{d.h} ).h+2.d.h+2.(\frac{200}{d.h} ).d

A=2.(\frac{200}{d} )+2.d.h+2.(\frac{200}{h} )

So, we have our function f(x,y)=A(d,h), which we have to minimize. We apply the first partial derivative and equalize to zero to know the optimum point of the function, getting

\frac{\partial A}{\partial d} =-\frac{400}{d^2}+2h=0

\frac{\partial A}{\partial h} =-\frac{400}{h^2}+2d=0

After solving the system of equations, we get that the optimum point value is d=\sqrt[3]{200} and  h=\sqrt[3]{200}, replacing this values into the equation of variable b we get b=\sqrt[3]{200}.

Now, we have to check with the hessian matrix if the value is a minimum,

The hessian matrix is defined as,

H=\left[\begin{array}{ccc}\frac{\partial^2 A}{\partial d^2} &\frac{\partial^2 A}{\partial d \partial h}\\\frac{\partial^2 A}{\partial h \partial d}&\frac{\partial^2 A}{\partial p^2}\end{array}\right]

we know that,

\frac{\partial^2 A}{\partial d^2}=\frac{\partial}{\partial d}(-\frac{400}{d^2}+2h )=\frac{800}{d^3}

\frac{\partial^2 A}{\partial h^2}=\frac{\partial}{\partial h}(-\frac{400}{h^2}+2d )=\frac{800}{h^3}

\frac{\partial^2 A}{\partial d \partial h}=\frac{\partial^2 A}{\partial h \partial d}=\frac{\partial}{\partial h}(-\frac{400}{d^2}+2h )=2

Then, our matrix is

H=\left[\begin{array}{ccc}4&2\\2&4\end{array}\right]

Now, we found the eigenvalues of the matrix as follow

det(H-\lambda I)=det(\left[\begin{array}{ccc}4-\lambda&2\\2&4-\lambda\end{array}\right] )=(4-\lambda)^2-4=0

Solving for\lambda, we get that the eigenvalues are:  \lambda_1=2 and \lambda_2=6, how both are positive the Hessian matrix is positive definite which means that the functionA(d,h) is minimum at that point.

4 0
3 years ago
An experimenter is randomly sampling 4 objects in order from among 43 objects. What is the total number of samples in the sample
Ivenika [448]

Answer:

10.75

Step-by-step explanation:

First you see how many times 4 can go into 4 in the tens place which is 1 .You multiply 4 times 1and you get 4 .Then you minus 4 from 4 and get

Then you bring down the 3 and see how many times 4 can go into 3 which is 0 .So you put a decimal point and bring down a 0.

See how many times 4 can go into 30,which will be 7 times.After , you multiply 7 times 4 and you get 28.Subtract 29 from 30 and you get 20.You bring down the 0 .

See how many times 4 can go into 20 which is 5.Mutiply 5 times 4 and get 20 then subtract 20 from 20.

Get a final quotient of 10.75.

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3 years ago
About 10% of the human population is left-handed. Suppose a researcher speculates that artists are more likely to be left-handed
nevsk [136]

Answer:

Given the information in the question;

a) The parameter of interest is the population of artists who are left-handed and its is 10% = (10/1000 = 0.10

b) The Null hypothesis and alternative hypothesis are;

<em>H₀ : p </em>= 0.10

<em>H₁ : p</em> > 0.10

c) The sample proportion is calculated as:

p = number of left handed artist / sample size

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d) To find the p-value, The researcher should calculate the probability that the sample proportion would be 0.13 or larger for a sample of size 200 if the population proportion is actually 0.10.

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leonid [27]

Answer:

H=25√3

Step-by-step explanation:

So you would use the 30°,60°,90° Triangle theorem to solve this problem

Since we are trying to find out the 60°, because the x is across from 60° we can assume that we are just going to plug in x√3.

Hopefully you understand, didn't really explain it that well...

6 0
3 years ago
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