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3 years ago

Explain why there are restrictions on the domain of a sequence when the sequence is defined as a function.

2 answers:

7 0

The domain of any function is the set of x-values.

For a sequence written as a function, the domain is the set of term numbers. In a sequence, term numbers describe the position of each term in a sequence. We start a sequence with the first term (1), the second term (2), etc.

When we are counting positions, we do not count half positions or quarter positions; only whole positions are counted. It would make no sense to say "the first and a half term"; we go from first to second.

This means the domain of the sequence written as a function is restricted to the set of whole numbers.

katrin2010 [14]3 years ago

6 0

Answer: The domain of a sequence written as a function is restricted to the set of natural numbers.

Step-by-step explanation:

Domain of any function is the set of input values of independent variable to a function on which the output values of dependent variable depends.

If a sequence is written as a function, then the domain is the set of natural numbers because the term starts with first term then second then so on.

The number of terms can not be negative or rational.

Here natural numbers represents the position of each term in a sequence.

This means the domain of the sequence written as a function is restricted to the set of natural numbers.

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A straight slide in a playground design makes an isosceles triangle with the

julia-pushkina [17]

Answer:

Option D.

Step-by-step explanation:

First, the you need ti understand that the triangle is an isosceles right angled triangle. In other words, the base and height are equal in length. The third side is the slide. This is the longest side.
Next, we know that the formula for calculating the area of a right angled triangle is given by:

A = 1/2 (base × perpendicular height)

The perpendicular height is equal to the base. Let's say the base is <em>x</em>. It means that the height is also x, since height = base.
Therefore, the formula will be:

A = 1/2 (x.x)

=1/2 (x²)

32 = 1/2 (x²)

Multiplying both sides by 2 gives:

32×2 = x²

64 = x²

8 = x

To find the third side, we use the Pythagoras theorem:

C² = A² + B²

= 8² + 8²

= 128

C = √128

= 8√2

However, the answer will not be exact, so we multiply the length of the base and height by 2. This gives x = 16 (Length of base = length of height)

Repeating the steps above gives C = √ (16)² + (16)²

= √256

This corresponds to option D.

3 0

4 years ago

The slope of the tangent line to the curve x^3y+y^2-x^2=5 at the point (2,1) is

zheka24 [161]

Answer:

-4/5

Step-by-step explanation:

To find the slope of the tangent to the equation at any point we must differentiate the equation.

x^3y+y^2-x^2=5

3x^2y+x^3y'+2yy'-2x=0

Gather terms with y' on one side and terms without on opposing side.

x^3y'+2yy'=2x-3x^2y

Factor left side

y'(x^3+2y)=2x-3x^2y

Divide both sides by (x^3+2y)

y'=(2x-3x^2y)/(x^3+2y)

y' is the slope any tangent to the given equation at point (x,y).

Plug in (2,1):

y'=(2(2)-3(2)^2(1))/((2)^3+2(1))

Simplify:

y'=(4-12)/(8+2)

y'=-8/10

y'=-4/5

5 0

3 years ago

Help me plzzz what is x

Grace [21]

Answer:

24.56

Step-by-step explanation:

1.14x-5+5=23+5

1.14x=28

x is roughly equal to 24.56.

Hope this helps!

7 0

4 years ago

At a 20th high school reunion, all the classmates were asked the number of children they had. The probability of having a partic

finlep [7]

Answer:

a) We need to check two conditions:

1) $\sum_{i=1}^n P_i = 1$

$0.05+0.14+0.34+0.24+0.11+0.07+0.02+0.02+0.01= 1$

2) $P_i \geq 0 , \forall i=1,2,...,n$

So we satisfy the two conditions so then we have a probability distribution

b) $P(C \geq 1)$

And we can use the complement rule and we got:

$P(C \geq 1)= 1-P(C$

c) $P(C=0) = 0.05$

d) For this case we see that the result from part b use the probability calculated from part c using the complement rule.

Step-by-step explanation:

For this case we have the following probability distribution given:

C 0 1 2 3 4 5 6 7 8

P 0.05 0.14 0.34 0.24 0.11 0.07 0.02 0.02 0.01

And we assume the following questions:

a) Verify that this is a probability distribution

We need to check two conditions:

1) $\sum_{i=1}^n P_i = 1$

$0.05+0.14+0.34+0.24+0.11+0.07+0.02+0.02+0.01= 1$

2) $P_i \geq 0 , \forall i=1,2,...,n$

So we satisfy the two conditions so then we have a probability distribution

b) What is the probability one randonmly chosen classmate has at least one child

For this case we want this probability:

$P(C \geq 1)$

And we can use the complement rule and we got:

$P(C \geq 1)= 1-P(C$

c) What is the probability one randonmly chosen classmate has no children

For this case we want this probability:

$P(C=0) = 0.05$

d) Look at the answers for parts b and c and explain their relationship

For this case we see that the result from part b use the probability calculated from part c using the complement rule.

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3 years ago

Y+1=3/4(x+3) in general form pls??

Vikentia [17]

Answer:

Step-by-step explanation:

y+1 =(3/4)x+9/4

y=(3/4)x+1/4

7 0

3 years ago

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