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posledela
3 years ago
8

Analyze the diagram below and complete the instructions that follow.

Mathematics
2 answers:
makkiz [27]3 years ago
6 0

Answer:

D. x=7√3 , y=4√2

Step-by-step explanation:

<em>Step 1: Lets assume an imaginary line from A to B to make the triangle ABC( (refer to the attached image).</em>

AB = 4

BD = 3

<em>Step 2: Find the value of y by the sin formula.</em>

opposite = 4

adjacent = BC

hypotenuse = AC

sin (angle) = opposite/hypotenuse

sin (45) = 4/AC

√2/2 = 4/AC

AC = y = 4√2

<em>Step 3: Find the value of x</em>

Tan (45) = opposite/adjacent

1 = 4/CB

CB = 4

x = CB + BD

x = 4 + 3

x = 7

Therefore, the answer is D where x = 7 and y = 4√2

!!

ElenaW [278]3 years ago
6 0

Answer: its C. not d. i just took the test on edg and D was wrong

Step-by-step explanation:

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Opening Exercise
Jobisdone [24]

Answer:

100% of 180 = 180

25% of 180 = 45

-75% of 180 = -135

37.5% of 180 = 67.5

Step-by-step explanation:

I looked them up on an app so I hope its right!

4 0
2 years ago
Which of the following pairs of points both lie on the line whose equation is 3x-y=2?
zalisa [80]
Though you did not list the points, I can tell you how to solve for the question.

One way to tell if a point lies on a given line is to take the point and plug it into the equation. If the equation remains true, then the point lies on the line. For example:

If we have the point (1,1), we can plug in 1 for x and 1 for y and see if the equation is true:


3 0
3 years ago
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
Graph the function and its parent function on the calculator . Then describe the transformation.
Nuetrik [128]
“Vertical translation up” because the parents fuction which is the f(x) is equal to x^2
4 0
3 years ago
A cylinder has a radius of 10 inchunits s and a height of 6 inches. About what is it’s volume in cubic inches? Use 3.14
kotykmax [81]

Given: A cylinder with radius = 10 inches and height = 6 inches.

We have to determine the volume of the cylinder.

Volume of a cylinder with radius 'r' and height 'h' is given by the formula \pi r^2 h

Substituting the value of 'r' and 'h', we get

Volume = 3.14 \times (10)^2 \times 6

Volume = 314 \times 6

Volume = 1884 cubic inches.

Therefore, the volume of the cylinder is 1884 cubic inches.

4 0
3 years ago
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