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White raven [17]
2 years ago
13

A set W of strings of symbols is defined recursively by 1. a, b, and c belong to W. 2. If x belongs to W, so does a(x)c. Which o

f the following strings belong to W ? a. a(b)c b. a(a(b)c)c c. a(abc)c d. a(a(a(a)c)c)c e. a(aacc)c
Mathematics
1 answer:
Vadim26 [7]2 years ago
8 0

Answer:

a. a(b)c  

b. a(a(b)c)c  

d. a(a(a(a)c)c)c          

Step-by-step explanation:

We are given the following in the question:

a,b,c \in W\\\text{If } x \in W \Rightarrow a(x)c \in W

a. a(b)c

It is given b belongs to W.

b \in W\\\Rightarrow a(b)c \in W

b. a(a(b)c)c

a(b)c \in W\\\Rightarrow a(a(b)c)c \in W

c. a(abc)c

a(abc)c does not belong to W because we cannot find x in W such that a(abc)c belongs to W.

d. a(a(a(a)c)c)c

a \in W\\\Rightarrow a(a)c \in W\\\Rightarrow a(a(a)c)c \in W\\\Rightarrow a(a(a(a)c)c)c

e. a(aacc)c

a(aacc)c does not belong to W because we cannot find x in W such that a(aacc)c belongs to W.

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Surface area of a rectangular prism if W = 6in L = 9in and H = 2in
Delicious77 [7]

Answer:

Step-by-step explanation:

Two faces are 6” by 9”. Two faces are 6” by 2”. Two faces are 9” by 2”.

Surface are = 2*6*9 + 2*6*2 + 2*9*2 = 108 + 24 + 36 = 168 square inches

4 0
3 years ago
the distance between california and mexico border is 100 miles less than thrice the distance between california and washington.
harina [27]

Answer: B. 3m-100

Step-by-step explanation:

3 0
1 year ago
Solve the system using substitution: x = -4y and x + 5y = 2<br> Please and thank you.
Novay_Z [31]

Answer:

x = - 8, y = 2

Step-by-step explanation:

x =  - 4y......(1) \\ x + 5y = 2....(2) \\ plug \: x =  - 4y \: in \: equation \: (2) \\  - 4y + 5y = 2 \\ y = 2 \\ plug \: y = 2 \: in \: equation \: (1) \\ x =  - 4(2) \\ x =  - 8\\

7 0
3 years ago
The graph h = −16t^2 + 25t + 5 models the height and time of a ball that was thrown off of a building where h is the height in f
Thepotemich [5.8K]

Answer:

part 1) 0.78 seconds

part 2) 1.74 seconds

Step-by-step explanation:

step 1

At about what time did the ball reach the maximum?

Let

h ----> the height of a ball in feet

t ---> the time in seconds

we have

h(t)=-16t^{2}+25t+5

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

so

The x-coordinate of the vertex represent the time when the ball reach the maximum

Find the vertex

Convert the equation in vertex form

Factor -16

h(t)=-16(t^{2}-\frac{25}{16}t)+5

Complete the square

h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+5+\frac{625}{64}

h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+\frac{945}{64}\\h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+\frac{945}{64}

Rewrite as perfect squares

h(t)=-16(t-\frac{25}{32})^{2}+\frac{945}{64}

The vertex is the point (\frac{25}{32},\frac{945}{64})

therefore

The time when the ball reach the maximum is 25/32 sec or 0.78 sec

step 2

At about what time did the ball reach the minimum?

we know that

The ball reach the minimum when the the ball reach the ground (h=0)

For h=0

0=-16(t-\frac{25}{32})^{2}+\frac{945}{64}

16(t-\frac{25}{32})^{2}=\frac{945}{64}

(t-\frac{25}{32})^{2}=\frac{945}{1,024}

square root both sides

(t-\frac{25}{32})=\pm\frac{\sqrt{945}}{32}

t=\pm\frac{\sqrt{945}}{32}+\frac{25}{32}

the positive value is

t=\frac{\sqrt{945}}{32}+\frac{25}{32}=1.74\ sec

8 0
3 years ago
What is the answer of equation 9x(30+7)=(9x30)+(9x7)
RSB [31]

(9x30) =270 (9x7)  =63


Distributive Property

5 0
3 years ago
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