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Licemer1 [7]
3 years ago
10

A sequence is defined to be An = n^2 + 2. What is the 5th term of this sequence?

Mathematics
1 answer:
STatiana [176]3 years ago
4 0

Answer:

27

Step-by-step explanation:

To find the fifth term substitute n = 5 into the rule, that is

A_{5} = 5² + 2 = 25 + 2 = 27

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Use the method of lagrange multipliers to find
Yanka [14]

Answer:

a) The function is: f(x, y) = x + y.

The constraint is: x*y = 196.

Remember that we must write the constraint as:

g(x, y) = x*y - 196 = 0

Then we have:

L(x, y, λ) = f(x, y) +  λ*g(x, y)

L(x, y,  λ) = x + y +  λ*(x*y - 196)

Now, let's compute the partial derivations, those must be zero.

dL/dx =  λ*y + 1

dL/dy =  λ*x + 1

dL/dλ = (x*y - 196)

Those must be equal to zero, then we have a system of equations:

λ*y + 1 = 0

λ*x + 1 = 0

(x*y - 196) = 0

Let's solve this, in the first equation we can isolate  λ to get:

λ = -1/y

Now we can replace this in the second equation and get;

-x/y + 1 = 0

Now let's isolate x.

x = y

Now we can replace this in the last equation, and we will get:

(x*x - 196) = 0

x^2 = 196

x = √196 = 14

then the minimum will be:

x + y = x + x = 14 + 14 = 28.

b) Now we have:

f(x) = x*y

g(x) = x + y - 196

Let's do the same as before:

L(x, y, λ) = f(x, y) +  λ*g(x, y)

L(x, y, λ) = x*y +  λ*(x + y - 196)

Now let's do the derivations:

dL/dx = y + λ

dL/dy = x + λ

dL/dλ = x + y - 196

Now we have the system of equations:

y + λ = 0

x + λ = 0

x + y - 196 = 0

To solve it, we can isolate lambda in the first equation to get:

λ = -y

Now we can replace this in the second equation:

x - y = 0

Now we can isolate x:

x = y

now we can replace that in the last equation

y + y - 196 = 0

2*y - 196 = 0

2*y = 196

y = 196/2 = 98

The maximum will be:

x*y = y*y = 98*98 = 9,604

6 0
2 years ago
Instructions:Select the correct answer. What is the nth term of the geometric sequence 4, 8, 16, 32, ... ?
Minchanka [31]
4, 8, 16, 32, 64, 128, 256, 512, 1,024.

1,024 is the ninth number in this geometric sequence.

Hope this helps!!
~Kiwi
7 0
3 years ago
If you rearrange the equation so w is the independent variable, then what is u?<br><br> -2u+6w=9
Serjik [45]

Answer:

u  = - ( 9-6w)/2

Step-by-step explanation:

to  evaluate for u in the expression -2u+6w=9 is simply to look for a way such that we would express u in terms of w and other variables.

solution

-2u+6w=9

-2u = 9 - 6w

divide both sides by the coefficient of u which is -2

-2u/u = 9 - 6w/-2

u  = - ( 9-6w)/2

therefore the value of u when rearranged in the equation -2u+6w=9 is evaluated to be equals to

u  = - ( 9-6w)/2

7 0
2 years ago
Help me ASAP please I don't understand it please help It is dued by TONIGHT
Sergeu [11.5K]

So, the first blank is for what kind of angle it is: acute, obtuse, reflex, straight, or right. The second blank is for what the measure of the angle is. You can find that out by looking at the protractor. It should tell you what the measure of the angle is. You can read the protractor by looking at the numbers. The numbers are the degrees of incline the angle measures, which is what you're looking for.

3 0
3 years ago
Wendy has 5 and 1 over 3 feet of ribbon. How many 2 over 3 foot pieces can Wendy cut from the 5 and 1 over 3 feet of ribbon? Sho
denis-greek [22]

Answer:

Your answer is 8

Step-by-step explanation:

First you have to convert the mixed number into an improper fraction. To do this, multiply the denominator by the whole number. Then add the numerator and put that answer in a fraction over the original. So it would be 3*5=15+1=16/3. So now that the denominators are the same, all you need to do is see how many times 2 goes into 16. 16/2 which is 8. Answer = 8

6 0
3 years ago
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