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vampirchik [111]
3 years ago
13

Use the formula to evaluate the infinite series riund to the nearest hundredth if necessary 9+3+1+

Mathematics
1 answer:
VikaD [51]3 years ago
6 0
Sum to infinity  =  a1 / ( 1 - r)   (This is a geometric series  a1 = first term, r = common ratio)

Here r = 3/9  = 1/3 and a1 = 9 

So the answer is 9 / (1 - 1/3)  = 9 / 2/3 = 9 * 3/2 = 13.5 Answer
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Show that a discrete metric on a vector space X≠{0} cannot be obtained from a norm (the pair (X,d) is called the discrete metric
topjm [15]

You know that the discrete metric only takes values of 1 and 0. Now suppose it comes from some norm ||.||. Then for any α in the underlying field of your vector space and x,y∈X, you must have that

∥α(x−y)∥=|α|∥x−y∥.

But now ||x−y|| is a fixed number and I can make α arbitrarily large and consequently the discrete metric does not come from any norm on X.

Step-by-step explanation:

hope this helps

4 0
1 year ago
20 points to answer a estimate question
Keith_Richards [23]

Answer:

The total cost =  $714

Step-by-step explanation:

Given

  • Monitor cost = $287
  • Scanner cost = $58
  • Keyboard cost = $49
  • Printer cost = $320

The total cost can be determined by adding the costs of all the pieces of equipment.

Thus,

Total cost = Monitor cost + Scanner cost + Keyboard cost + Printer cost

                = $287 + $58 + $49 + $320

                = $714

Therefore, the total cost =  $714

4 0
2 years ago
What is the value of K?
Ksju [112]
Answer: The value of k for which one root of the quadratic equation kx2 - 14x + 8 = 0 is six times the other is k = 3.
Let's look into the solution step by step.

Explanation:

Given: A quadratic equation, kx2 - 14x + 8 = 0

Let the two zeros of the equation be α and β.

According to the given question, if one of the roots is α the other root will be 6α.

Thus, β = 6α

Hence, the two zeros are α and 6α.

We know that for a given quadratic equation ax2 + bx + c = 0

The sum of the zeros is expressed as,

α + β = - b / a

The product of the zeros is expressed as,

αβ = c / a

For the given quadratic equation kx2 - 14x + 8 = 0,

a = k, b = -14, c = 8

The sum of the zeros is:

α + 6α = 14 / k [Since the two zeros are α and 6α]

⇒ 7α = 14 / k

⇒ α = 2 / k --------------- (1)

The product of the zeros is:

⇒ α × 6α = 8 / k [Since the two zeros are α and 6α]

⇒ 6α 2 = 8 / k

⇒ 6 (2 / k)2 = 8 / k [From (1)]

⇒ 6 × (4 / k) = 8

⇒ k = 24 / 8

⇒ k = 3
6 0
2 years ago
Solve simultaneous equation <br> X-2y=1<br> 2x-y=2
Step2247 [10]

Answer: x=1,y=0

Step-by-step explanation:

X-2y=1.....equation 1

2x-y=2.....equation 2

X=1+2y.......equation 3

Substitute equation 3into 2

2(1+2y)-y=2

2+4y-y=2

2+3y=2

3y=2-2

3y=0

Y=0/3

Y=0

Substitute for y=0 in equation 1

X-2y=1

X-2(0)=1

X-0=1

X=1

X=1 & Y=0

7 0
2 years ago
Read 2 more answers
What is a gradient of a line
Dennis_Churaev [7]
(slope) The higher the gradient<span> of a graph at a point, the steeper the </span>line<span> is at that point.</span>
4 0
3 years ago
Read 2 more answers
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