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3 years ago

Please help!!!!!!!!....

Mathematics

1 answer:

serious [3.7K]3 years ago

4 0

Answer:

Area:12.5663706 Circumference: 12.5663706

Step-by-step explanation:

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Park city Utah gets 43.8inches of rain per year. Usually 45% of that amount falls in November. How much rain falls in those mont

aliina [53]

43.8 = 100%
43.8/100 = 0.438 = 1%
0.438 x 45 = 19.71 = 45%
19.71 inches of rain falls in November.

3 0

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

What is the degree of 12x4 - 8x + 4x2 - 3? A. 8 B. 4 C. 3 D. 12

Soloha48 [4]

In this problem, we are asked to determine the degree of the given expression 12X4 - 8X + 4X2 -3. To answer this, first, we need to arrange the mathematical expression in descending order with respect to its power such as the new arrangement will become 12x4 + 4x2 -8x -3. The degree is clearly visible and it is 4. Therefore, the answer to this problem is the letter "B" which is 4.

4 0

3 years ago

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Mr. Hollins determines that he gives away $800 each month. If he gives away 16% of his budget, then how much is his overall budg

Fynjy0 [20]

Answer:

5000 dollars

Step-by-step explanation:

Let his budget be x

16% of x is 800 dollars

.16 * x = 800

Divide each side by .16

.16x/.16 = 800/.16

x=5000

His budget is 5000 dollars

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2 years ago

What is the place value of 6 in 685

statuscvo [17]

Answer:

600 because it is in the hundreds place

Step-by-step explanation:

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3 years ago

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