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Salsk061 [2.6K]
3 years ago
9

Suppose a deep sea driver dives from the surface to 248 feet below the surface. He then dives down 10 more feet. Use integers yo

represent this situation. Then find the driver' s present depth
Mathematics
1 answer:
Akimi4 [234]3 years ago
5 0

Answer:

Initial dive: - 248 (below the surface which represents '0')

Second dive: -10

Present depth -248 + -10 = -258 feet below the surface

Step-by-step explanation:

We can use negative integers to represent real-world scenarios such as in elevation and descent, bank account balances and temperatures.  In this case, because a diver is descending below the surface of the water, the surface of the water represents the '0' and going down into the water would be negative integers.  So, his initial dive is 248 down, or negative 248 (-248), he then dives down an additional 10 feet, or negative 10 (-10).  Since the second dive is in addition to his initial dive, we add the two integers together:

-248 + -10 = -258 feet

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There are 30 students in the class and 270 apples. if the apples are divided equally among the students, how many does each stud
Ede4ka [16]

Answer:

9

Step-by-step explanation:

270/30=9

7 0
3 years ago
Write an equation in slope intercept form of a line passing through the given point (8,5) m=3
Zepler [3.9K]

If m(slope)=3, you can start to set up the equation as y=3x+b.

Using y=3x+8, you can plug in the given point being (8,5).

y=5

x=8

5=(3*8)+b

5=24+b

b=-19

The equation would be y=3x-19

3 0
3 years ago
Which values are solutions to the inequality below? <br><br>Check all that apply.
zvonat [6]
+5 and -5 because you root 25 which gives you + 5 or - 5

6 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
Marion is 3 years more than 5 times as old as Paula. if p represents Paula's age, which expression represents Marion's age?
Alborosie
5p + 3

because its 5 times Paula's age with the additional 3 years tacked on to it
8 0
3 years ago
Read 2 more answers
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