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2 years ago

Rudolph can fly 5 miles in 12 seconds. At that rate, how many miles can he fly per minute?

Mathematics

1 answer:

AleksandrR [38]2 years ago

7 0

Answer:

25 mpm

Step-by-step explanation:

60 devided by 12 = 5

5 times 5 = 25 mpm

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Need to pass this semester so please help

Aleks04 [339]

The correct answer is X= 14°

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2 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

2 years ago

The radiuses of two intersecting circles are 17 and 39. The distance between their centers is 44. Find the length of their commo

antoniya [11.8K]

Answer:

If x is the distance from centre fo the circle, with radius 25cm, to its intersection point with the common chord, x²+24²=25² =>x=7cm.

Distance from this intersecting point to the centre of the other circle=39–7=32cm

Ratio of the sides of the right triangle thus formed is 24:32=3:4. Since 3:4:5 is the basic pythagorean triplet, the radius of the other circle=5*24/3=40cm.

Aliter: radius of the other circle=√32²+24²= 40cm.

<h2>please mark me as brainalist</h2>

3 0

1 year ago

Bob’s Burger Place made 11 burgers with onions and 7 burgers without onions. What is the ratio of the number of burgers without

Anika [276]

Answer:

7:11

Step-by-step explanation:

There is no way to simplify the ratio.

7 0

2 years ago

Read 2 more answers

INFINITE SERIES

snow_lady [41]

Do you have to show ur work?

7 0

2 years ago