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AlexFokin [52]
3 years ago
8

(1 point) a bookshelf has space for exactly 13 books. in how many ways can the books be arranged on the bookshelf?

Mathematics
1 answer:
Andre45 [30]3 years ago
6 0
I believe the answer is <span>6,227,020,800</span>
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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
Pls help I’ll brainlest
lora16 [44]

Answer:

8

Step-by-step explanation:

Jeremiah bought x toy sets for $20 each and then a video game for $60. Jeremiah spent a total of $220. How may toy sets did he buy?

To find our answer, we can solve the equation:

20x + 60 = 220

        -60    -60

20x = 160

/20    /20

x = 8

Jeremiah bought 8 toy sets!

I hope this helps :)

5 0
2 years ago
White and black shapes are used in a game Some of the shapes are circles All the other shapes are squares The ratio of white to
nydimaria [60]
Is there a picture to this question??
5 0
3 years ago
Read 2 more answers
2-1= plz help me i need help
Alinara [238K]

Answer:

1 :)

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Rani deposited AED 12000 for 3 years at the rate of 5 percent per annum. Calculate the simple interest and amount at the end of
Luda [366]

Answer:

the principal and the amount is 1,800 and 13,800 respectively

Step-by-step explanation:

The computation of the simple interest and amount for the end of the 3rd year is shown below:

Simple interest is

= Principal × rate of interest × time period

= 12,000 × 5% × 3 years

= 1,800

Now the amount is

= 12,000 + 1,800

= 13,800

hence, the principal and the amount is 1,800 and 13,800 respectively

7 0
2 years ago
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