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Mumz [18]
2 years ago
13

5!=5*4*3*2*1;6!=6*5*4*3*2*1 What is the value of 4^4/4!

Mathematics
1 answer:
german2 years ago
3 0

Answer:

\frac{32}{3}

Step-by-step explanation:

If 5! is equal to 5 × 4 × 3 × 2 × 1 and 6! is equal to 6 × 5 × 4 × 3 × 2 × 1, then 4! is equal to 4 × 3 × 2 × 1. Thus, 4! = 4 × 3 × 2 × 1, which can simplify to 24. 4! = 24.

4^{4} is basically 4 × 4 × 4 × 4, which can simplify to 256.

So,  \frac{4^{4}}{4!} = \frac{256}{24}.  \frac{256}{24} can simplify to \frac{32}{3}. Therefore,  \frac{4^{4}}{4!} = \frac{32}{3}.

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Adiya said that the first step to solving the quadratic equation x2 + 6 = 20x by completing the square was to divide 6 by 2, squ
Dahasolnce [82]

Answer: Adiya’s method is not correct. To form a perfect square trinomial, the constant must be isolated on one side of the equation. Also, the coefficient of the term with an exponent of 1 on the variable is used to find the constant in the perfect square trinomial. Adiya should first get the 20x term on the same side of the equation as x2. Then she would divide 20 by 2, square it, and add 100 to both sides.

7 0
3 years ago
Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y)=4x2 2y2; 3x
nevsk [136]

For given f(x, y) the extremum: (12, 24) which is the minimum.

For given question,

We have been given a function f(x) = 4x² + 2y² under the constraint 3x+3y= 108

We use the constraint to build the constraint function,

g(x, y) = 3x + 3y

We then take all the partial derivatives which will be needed for the Lagrange multiplier equations:

f_x=8x

f_y=4y

g_x=3

g_y=3

Setting up the Lagrange multiplier equations:

f_x=\lambda g_x

⇒ 8x = 3λ                                        .....................(1)

f_y=\lambda g_y

⇒ 4y = 3λ                                         ......................(2)

constraint: 3x + 3y = 108                .......................(3)

Taking (1) / (2), (assuming λ ≠ 0)

⇒ 8x/4y = 1

⇒ 2x = y

Substitute this value of y in equation (3),

⇒ 3x + 3y = 108

⇒ 3x + 3(2x) = 108

⇒ 3x + 6x = 108

⇒ 9x = 108

⇒ x = 12

⇒ y = 2 × 12

⇒ y = 24

So, the saddle point (critical point) is (12, 24)

Now we find the value of f(12, 24)

⇒ f(12, 24) = 4(12)² + 2(24)²

⇒ f(12, 24) = 576 + 1152

⇒ f(12, 24) = 1728                             ................(1)

Consider point (18,18)

At this point the value of function f(x, y) is,

⇒ f(18, 18) = 4(18)² + 2(18)²

⇒ f(18, 18) = 1296 + 648

⇒ f(18, 18) = 1944                            ..............(2)

From (1) and (2),

1728 < 1944

This means, given extremum (12, 24) is minimum.

Therefore, for given f(x, y) the extremum: (12, 24) which is the minimum.

Learn more about the extremum here:

brainly.com/question/17227640

#SPJ4

6 0
2 years ago
On her way home, Carrie must drive up a hill that has an incline of . If CarrieÍs vehicle stops at an elevation 0.25 miles highe
anzhelika [568]
She would drive up the hill C.2.87.The ovesiouse answer would have been c because if you do the math then it would give you 2.87.
8 0
3 years ago
Read 2 more answers
A curve has equation y=x^3_6x+1.at the point where x=2
lisov135 [29]

Answer:2^3=8

6.2=12

Y=8-12+1= -3

Step-by-step explanation:

6 0
3 years ago
WHAT IS X<br> PLEASE HELP 50 POINTS
Iteru [2.4K]

Answer:

x=52

Step-by-step explanation:

90+34

124

180 (sum of all interior angles) - 124

56

x+72+56=180 (straight line)

x+128=180

 -128  -128

x=52

*replace to verify*

52+72= 124

124+56= 180 (straight line)

4 0
2 years ago
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