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larisa [96]
3 years ago
6

Reduce the following lambda-calculus term to the normal form. Show all intermediate steps, with one beta reduction at a time. In

the reduction, assume that you are supplied with extra rules that allow you to reduce the multiplication of two natural numbers into the corresponding result.
(λf. λx. f (f x)) (λy. Y * 3) 2
Mathematics
1 answer:
QveST [7]3 years ago
4 0

Answer:

Step-by-step explanation:

Reduction to normal from using lambda-reduction:

The given lambda - calculus terms is, (λf. λx. f (f x)) (λy. Y * 3) 2

For the term, (λy. Y * 3) 2, we can substitute the value to the function.

Therefore, applying beta- reduction on "(λy. Y * 3) 2" will return 2*3= 6

So the term becomes,(λf. λx. f (f x)) 6

The first term, (λf. λx. f (f x)) takes a function and an argument, and substitute the argument in the function.

Here it is given that it is possible to substitute the resulting multiplication in the result.

Therefore by applying next level beta - reduction, the term becomes f(f(f(6)) (f x)) which is in normal form.

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What is the exact distance from (–1, 4) to (6, –2)? (4 points) units units units units
irina1246 [14]

Answer:

\sqrt{85}

Step-by-step explanation:

Calculate the distance d using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (6, - 2)

d = \sqrt{(6+1)^2+(-2-4)^2}

  = \sqrt{7^2+(-6)^2}

  = \sqrt{49+36}

  = \sqrt{85} ← exact distance

4 0
3 years ago
In a small town in the Himalayas, the average snowfall each month is 6 inches. July is the month with the lowest average snowfal
OLga [1]

The function that models the above behavior is given as:

f(x) = ACos(B(x + C)) + 6 ..... .......i

where x = 1 (that is January)

D (Average Snowfall) = 6.

Hence, the amplitude (A) is given as:
A = 6-1

= 5

<h3>What is a mathematical function?</h3>

A mathematical function is a function comprising of different variables that    represent different factors or events and the relationships between them.

<h3>
During what period is there more than 10 inches of snowfall?</h3><h3 />

Recall that in a year we have 12 months. Hence, P = 12

→ P = (2π) /.B → (2π)/B = 12 → B = π/6

Taking the values of A and B and plugging them in, we ahve:

F(x) = 5 cos (π/6(x + C)) + 6................ii

This means that in July, we'll have

x = 7 and f(x) = 1

Therefore,

1 = 5cos ((π/6) (7 + C) + 6 → 5 Cos  ((π/6) (7 + C) →  -5cos ((π/6) (7 + C)

= -1

→   ((π/6) (7 + C) = π

→ 7 + C = 6

→ C = -1

Taking equation ii, we have

F(x) = 5cos ((π6) (x -1)) + 6

F (x) > 10

Therefore

5cos ((π/6) (x-1) + 6 > 10

→  cos ((π/6) (x-1) + 6 > 4/5

→  (π/6) (x-1)  > Cos⁻¹ (4/5)

(π/6) (x-1)  < 0.6435 and

(π/6) (x-1)  > 5.6397

→ x < 2.23 and x > 11.77

The interpretation is that upwards of ten inches of snow fall in January, February, November, and December.

Learn more about functions at;
brainly.com/question/25638609
#SPJ1

3 0
2 years ago
Imogene invested $8,000 in a bank account that pays 8 percent simple interest at the end of each year. Her friend invested the s
Natali5045456 [20]

The right system of equations to describe the situation would be on the form:

x1 = 8000 + y1*t

and

x2 = 8000 + y2*t

where x1 and x2 represents the total money of Imogene and her friend respectively at the end of t years.

Now for the value of amount earned, y1 and y2:

y1=8000*0.08

y2=2000*√(t-2)

<span> </span>

5 0
3 years ago
Help please i need this done soon!! tysm!!
olga nikolaevna [1]

Answer:

70

Step-by-step explanation:

Opposite Angles are supplementary in cyclic quadratlerials.

3 0
3 years ago
Question 1<br> Solve: 25.6 - 5y + 15. 3
QveST [7]

Answer:

40.9 - 5y

Step-by-step explanation:

25.6 - 5y + 15.3

40.9 - 5y ## ^ combine like-terms

8 0
3 years ago
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