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Doss [256]
3 years ago
8

Find the 20th term from the last term of the AP:3,8,13,..., 253. ​

Mathematics
1 answer:
RoseWind [281]3 years ago
3 0

Answer:

158

Step-by-step explanation:

The sequence is 3, 8, 13, ..., 253.

Going backwards, it's 253, 248, 243, ..., 3.

First term is 253, common difference is -5.

The nth term is:

a = 253 − 5(n − 1)

The 20th term is:

a = 253 − 5(20 − 1)

a = 158

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Answer:

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3 years ago
You are a lifeguard and spot a drowning child 60 meters along the shore and 40 meters from the shore to the child. You run along
sukhopar [10]

Answer:

The lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

Step-by-step explanation:

This is a problem of optimization.

We have to minimize the time it takes for the lifeguard to reach the child.

The time can be calculated by dividing the distance by the speed for each section.

The distance in the shore and in the water depends on when the lifeguard gets in the water. We use the variable x to model this, as seen in the picture attached.

Then, the distance in the shore is d_b=x and the distance swimming can be calculated using the Pithagorean theorem:

d_s^2=(60-x)^2+40^2=60^2-120x+x^2+40^2=x^2-120x+5200\\\\d_s=\sqrt{x^2-120x+5200}

Then, the time (speed divided by distance) is:

t=d_b/v_b+d_s/v_s\\\\t=x/4+\sqrt{x^2-120x+5200}/1.1

To optimize this function we have to derive and equal to zero:

\dfrac{dt}{dx}=\dfrac{1}{4}+\dfrac{1}{1.1}(\dfrac{1}{2})\dfrac{2x-120}{\sqrt{x^2-120x+5200}} \\\\\\\dfrac{dt}{dx}=\dfrac{1}{4} +\dfrac{1}{1.1} \dfrac{x-60}{\sqrt{x^2-120x+5200}} =0\\\\\\  \dfrac{x-60}{\sqrt{x^2-120x+5200}} =\dfrac{1.1}{4}=\dfrac{2}{7}\\\\\\ x-60=\dfrac{2}{7}\sqrt{x^2-120x+5200}\\\\\\(x-60)^2=\dfrac{2^2}{7^2}(x^2-120x+5200)\\\\\\(x-60)^2=\dfrac{4}{49}[(x-60)^2+40^2]\\\\\\(1-4/49)(x-60)^2=4*40^2/49=6400/49\\\\(45/49)(x-60)^2=6400/49\\\\45(x-60)^2=6400\\\\

x

As d_b=x, the lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

7 0
3 years ago
The question is jimmy scores is in the bottom 25% of the scores, but he does not have the lowest score. What is one possible val
Mariulka [41]

Answer:

50% duhh

Step-by-step explanation:

25% is also a equation

4 0
2 years ago
Which of the following best describes the intersection of two planes? (Points : 5)
charle [14.2K]
<span>In geometry, planes are two-dimensional spaces which extend infinitely. If they do not intersect at all, they are considered parallel. However, if they do intersect, that intersection come in the form of an infinitely-extending collection of 1-dimensional points, which collectively form a line. As such, the answer is "line".</span>
4 0
3 years ago
(SUPER EASY ANSWER QUICK 30 POINTS!)
harina [27]

\frac{35}{4} feet below the surface

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= (3 + 5 ) + (\frac{1}{2} + \frac{1}{4})

= 8 + (\frac{2}{4} + \frac{1}{4})

= 8 + \frac{3}{4} = 8 \frac{3}{4} = \frac{35}{4}


3 0
3 years ago
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