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svetlana [45]
2 years ago
5

A bale of fabric is 189 metres long. If lengths of 15 metres, 36 metres and 29 metres are cut off, how much fabric is left?.

Mathematics
1 answer:
Xelga [282]2 years ago
5 0

Answer:

109 metres

Step-by-step explanation:

1. Do 15+36+29 which equals 80

2. Do 189-80 and u get 109

Hope this helps :3

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He floor of a moving van is 3 feet off of the ground. The ramp into the van makes a 12° angle with the ground. About how long is
soldier1979 [14.2K]

Given :

Hight of the van from the ground, h = 3 feet.

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To Find :

How long is the ramp.

Solution :

Let, length of ramp is l .

So, height of ramp in terms of length is given by :

h = l \times sin\ 12^o\\\\l = \dfrac{h}{sin \ 12^o}\\\\l = \dfrac{3}{sin \ 12^o}\\\\l = 14.429 \ feet

Hence, this is the required solution.

8 0
2 years ago
Add and write the result in the form a+bi. a. (4 + 2i) + (-6 - 7i)
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Answer:

- 2 - 5i

Step-by-step explanation:

Given

(4 + 2i) + (- 6 - 7i) ← remove the parenthesis

= 4 + 2i - 6 - 7i ← collect like terms

= - 2 - 5i

7 0
2 years ago
If two distinct lines intersect, which is NOT necessarily true?
Thepotemich [5.8K]

Answer:

Option (b) is the answer.

Step-by-step explanation:

If two distinct lines intersect

Then they are not parallel because parallel lines never intersect they go hand in hand

But since, we need to tell which is not true

So, option A is discarded.

Option (c) and (d) are also true hence, discarded.

Option (b) is correct that is the lines are perpendicular this is not true. hence, considered

Therefore, option (b) is the answer.

7 0
2 years ago
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Which shows the prime factorization of 80? Check all that apply. 2 × 4 × 10 2 × 2 × 2 × 2 × 5 24 × 5 2 × 5 × 8
TEA [102]

Answer:

The Prime Factorization of 80 is,  2 × 4 × 10, 2 × 2 × 2 × 2 × 5  and  2 × 4 × 10

Step-by-step explanation: They are correct, because they all equal 80. 2 × 4 × 10=80 and  2 × 4 × 10=80, and 2 × 2 × 2 × 2 × 5=80.

24 × 5=120, Therefore it's the only incorrect question.

4 0
3 years ago
Read 2 more answers
a) What is an alternating series? An alternating series is a whose terms are__________ . (b) Under what conditions does an alter
andriy [413]

Answer:

a) An alternating series is a whose terms are alternately positive and negative

b) An alternating series \sum_{n=1}^{\infty} a_n = \sum_{n=1}^{\infty} (-1)^{n-1} b_n where bn = |an|, converges if 0< b_{n+1} \leq b_n for all n, and \lim_{n \to \infty} b_n = 0

c) The error involved in using the partial sum sn as an approximation to the total sum s is the remainder Rn = s − sn and the size of the error is bn + 1

Step-by-step explanation:

<em>Part a</em>

An Alternating series is an infinite series given on these three possible general forms given by:

\sum_{n=0}^{\infty} (-1)^{n} b_n

\sum_{n=0}^{\infty} (-1)^{n+1} b_n

\sum_{n=0}^{\infty} (-1)^{n-1} b_n

For all a_n >0, \forall n

The initial counter can be n=0 or n =1. Based on the pattern of the series the signs of the general terms alternately positive and negative.

<em>Part b</em>

An alternating series \sum_{n=1}^{\infty} a_n = \sum_{n=1}^{\infty} (-1)^{n-1} b_n where bn = |an|  converges if 0< b_{n+1} \leq b_n for all n and \lim_{n \to \infty} b_n =0

Is necessary that limit when n tends to infinity for the nth term of bn converges to 0, because this is one of two conditions in order to an alternate series converges, the two conditions are given by the following theorem:

<em>Theorem (Alternating series test)</em>

If a sequence of positive terms {bn} is monotonically decreasing and

<em>\lim_{n \to \infty} b_n = 0<em>, then the alternating series \sum (-1)^{n-1} b_n converges if:</em></em>

<em>i) 0 \leq b_{n+1} \leq b_n \forall n</em>

<em>ii) \lim_{n \to \infty} b_n = 0</em>

then <em>\sum_{n=1}^{\infty}(-1)^{n-1} b_n  converges</em>

<em>Proof</em>

For this proof we just need to consider the sum for a subsequence of even partial sums. We will see that the subsequence is monotonically increasing. And by the monotonic sequence theorem the limit for this subsquence when we approach to infinity is a defined term, let's say, s. So then the we have a bound and then

|s_n -s| < \epsilon for all n, and that implies that the series converges to a value, s.

And this complete the proof.

<em>Part c</em>

An important term is the partial sum of a series and that is defined as the sum of the first n terms in the series

By definition the Remainder of a Series is The difference between the nth partial sum and the sum of a series, on this form:

Rn = s - sn

Where s_n represent the partial sum for the series and s the total for the sum.

Is important to notice that the size of the error is at most b_{n+1} by the following theorem:

<em>Theorem (Alternating series sum estimation)</em>

<em>If  \sum (-1)^{n-1} b_n  is the sum of an alternating series that satisfies</em>

<em>i) 0 \leq b_{n+1} \leq b_n \forall n</em>

<em>ii) \lim_{n \to \infty} b_n = 0</em>

Then then \mid s - s_n \mid \leq b_{n+1}

<em>Proof</em>

In the proof of the alternating series test, and we analyze the subsequence, s we will notice that are monotonically decreasing. So then based on this the sequence of partial sums sn oscillates around s so that the sum s always lies between any  two consecutive partial sums sn and sn+1.

\mid{s -s_n} \mid \leq \mid{s_{n+1} -s_n}\mid = b_{n+1}

And this complete the proof.

5 0
3 years ago
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