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3 years ago

9

The velocity of a skydiver t seconds after jumping is given by V(t)= 80(1-e^-.2t). After how many seconds is the velocity 120 ft

/sec?

1 answer:

Ad libitum [116K]3 years ago

6 0

Answer:

∞

Step-by-step explanation:

The equation describes a velocity curve that has an asymptote of 80 ft/s. The skydiver will <em>never</em> have a velocity of 120 ft/s.

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Find the dimensions of the rectangle with largest area that can be inscribed in an equilateral triangle with sides of 1 unit, if

prohojiy [21]

<span>Maximum area = sqrt(3)/8 Let's first express the width of the triangle as a function of it's height. If you draw an equilateral triangle, then a rectangle using one of the triangles edges as the base, you'll see that there's 4 regions created. They are the rectangle, a smaller equilateral triangle above the rectangle, and 2 right triangles with one leg being the height of the rectangle and the other 2 angles being 30 and 60 degrees. Let's call the short leg of that triangle b. And that makes the width of the rectangle equal to 1 minus twice b. So we have w = 1 - 2b b = h/sqrt(3) So w = 1 - 2*h/sqrt(3) The area of the rectangle is A = hw A = h(1 - 2*h/sqrt(3)) A = h*1 - h*2*h/sqrt(3) A = h - 2h^2/sqrt(3) We now have a quadratic equation where A = -2/sqrt(3), b = 1, and c=0. We can solve the problem by using a bit of calculus and calculating the first derivative, then solving for 0. But since this is a simple quadratic, we could also take advantage that a parabola is symmetrical and that the maximum value will be the midpoint between it's roots. So let's use the quadratic formula and solve it that way. The 2 roots are 0, and 1.5/sqrt(3). The midpoint is (0 + 1.5/sqrt(3))/2 = 1.5/sqrt(3) / 2 = 0.75/sqrt(3) So the desired height is 0.75/sqrt(3). Now let's calculate the width: w = 1 - 2*h/sqrt(3) w = 1 - 2* 0.75/sqrt(3) /sqrt(3) w = 1 - 2* 0.75/3 w = 1 - 1.5/3 w = 1 - 0.5 w = 0.5 The area is A = hw A = 0.75/sqrt(3) * 0.5 A = 0.375/sqrt(3) Now as I said earlier, we could use the first derivative. Let's do that as well and see what happens. A = h - 2h^2/sqrt(3) A' = 1h^0 - 4h/sqrt(3) A' = 1 - 4h/sqrt(3) Now solve for 0. A' = 1 - 4h/sqrt(3) 0 = 1 - 4h/sqrt(3) 4h/sqrt(3) = 1 4h = sqrt(3) h = sqrt(3)/4 w = 1 - 2*(sqrt(3)/4)/sqrt(3) w = 1 - 2/4 w = 1 -1/2 w = 1/2 A = wh A = 1/2 * sqrt(3)/4 A = sqrt(3)/8 And the other method got us 0.375/sqrt(3). Are they the same? Let's see. 0.375/sqrt(3) Multiply top and bottom by sqrt(3) 0.375*sqrt(3)/3 Multiply top and bottom by 8 3*sqrt(3)/24 Divide top and bottom by 3 sqrt(3)/8 Yep, they're the same. And since sqrt(3)/8 looks so much nicer than 0.375/sqrt(3), let's use that as the answer.</span>

7 0

3 years ago

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Help me..<br> I’m stuck

vlabodo [156]

There would be enough room because if you do 60 times .375 (3 over 8) it would equal out to 22.5

5 0

3 years ago

PLEASEEE HELP ME WHAT IS THE ANSWER!!

blagie [28]

Answer:

Number 3 is correct.

129.19m

Step-by-step explanation:

You might be wondering how did I got 32⁰, well, that's because they are alternate angles.

Now, we're trying to find the opposite side of the triangle.

Using the laws,

we got cos32⁰=x/243.8

243.8cos32⁰=x

129.19⁰

Mark me as Brian list?

3 0

3 years ago

Here are the shopping times (in minutes) of ten shoppers at a local grocery store.

d1i1m1o1n [39]

The frequency which is to filled in the table is 3,1,2,4.

Given shopping time of ten shopkeeper: 36,20,32,18,20,33,28,34,37,23.

We have to complete the frequency in the table. Frequency of something is the number of times that number is coming.

Shopping time is given as 36,20,32,18,20,33,28,34,37,23.

Intervals for which frequency is given is 18 to 22, 23 to 27, 28 to 32, 33 to 37.

Numbers in the range 18 to 22=18,20,23 therefore 3

Numbers in the range 23 to 27=23 therefore 1

Numbers in the range 28 to 32=32 , 28 therefore 2

Numbers in the range 33 to 37=36, 33, 37, 34 therefore 4.

Hence the frequency which is to filled are 3,1,2,4.

Learn more about frequency at brainly.com/question/254161

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2 years ago

Please only responded if you can help

MAVERICK [17]

Answer:

for the first picture:

1. 1

2. 0.8

3. 0.4

for the second picture:

2,256

srry if i needed to show the steps

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3 years ago

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