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podryga [215]
3 years ago
13

A hot air ballon went from an elevation of 6,669 feet to an elevation of 3,402 in 54 minutes. What was its rate of descent?

Mathematics
1 answer:
marysya [2.9K]3 years ago
4 0

Answer:

elevation refers to the height of the balloon. Descent refers to moving down, and rate of descent refers to how quickly the balloon moved down.

  In this case, we have a descent of 2,125 feet (initial height of 5,439 - ending height of 3,314). Since it took 34 minutes for the balloon to descend this distance, we divide the descent by the time (2,125/34). This gives us a rate of 62.5 feet per minute.

  That means that the balloon traveled downward 62.5 feet every minute. That's a fast moving balloon!

Step-by-step explanation:

hopefully this helps

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(1 point) If p(x) and (x) are arbitrary polynomials of degree at most 2, then the mapping =p(-1)q(-1) + p(070) +p(3)q(3) defines
Ainat [17]

If p(x) and q(x) are arbitrary polynomials of degree at most 2 then

||p||||q|| = 26(\sqrt{640}) and angle between p(x) and q(x) is 0.233.

Given that

<p,q> = p(-1)q(-1) + p(0) q(0) + p(3)q(3)

and p(x) = 2x²+ 6 , q(x)= 4x²-4x

then the values of p and q at x = -1,0,3 are given as;

x = -1,

p(-1) = 2(-1)² + 6 = 8   ,    q(-1) = 4(-1)² - 4(-1) = 8

x = 0,

p(0) = 2(0)² + 6 = 6   ,    q(0) = 4(0)² - 4(0) = 0

x = 3,

p(3) = 2(3)² + 6 = 24  ,  q(3) = 4(3)²- 4(3) = 24.

<p,q> = p(-1)q(-1) + p(0)q(0) + p(3)q(3)

         = (8)(8) + (6)(0) + 24(24)

         = 64 + 0 + 576

<p,q> = 640

Now we have to find ||p|| ||q||, for this we'll find ||p|| and ||q||

||p|| = \sqrt{ < p,p > }

     = \sqrt{8(8) + 6(6) + 24(24)}

     = \sqrt{676}

||p|| = 26

and

||q|| = \sqrt{ < q,q > }

      =\sqrt{8(8) + 0(0) + 24(24)}

||q||  =\sqrt{640}

∴||p||||q|| = 26(\sqrt{640\\)

Now we have to find angle between p(x) and q(x),

∴ α = cos⁻¹\frac{ < p,q > }{||p||||q||}

      = cos ⁻¹ \frac{640}{26(\sqrt{640}) }

      = cos ⁻¹ \frac{4\sqrt{10} }{13}

  α  = 13.34°

In radian

α = 0.233.

To know more about Inner product here

brainly.com/question/14185022

#SPJ4

5 0
1 year ago
There are 43 pine trees currently in the park. Park workers will plant more pine trees
Luden [163]

Answer:

20 pine trees

Step-by-step explanation:

No of pine trees today = 63

No of pine trees there = 43

So no of pine trees planted today= 63-43= 20

8 0
2 years ago
What is the numerator of the simplified sum?
sashaice [31]

Answer:

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Step-by-step explanation:

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To determine what the numerator would be, after simplifying both fractions, take the following steps:

Step 1: Factorise the denominator of the first fraction, x² + 3x + 2.

Thus,

x² + 2x + x + 2

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x(x + 2) +1(x + 2)

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We would now have the following as our new fractions to add together and simplify:

\frac{x}{(x + 1)(x + 2)} + \frac{3}{x + 1}

Step 2: find the highest common factor of the denominator of both fractions.

Highest common factor of (x + 1)(x + 2) and (x + 1) = (x + 1)(x + 2)

Step 3: To add both fractions, divide the highest common factor gotten in step 2 by each denominator, and then multiply the result by the numerator of each fraction.

Thus,

\frac{x}{(x + 1)(x + 2)} + \frac{3}{x + 1}

\frac{x + 3(x + 2)}{(x + 1)(x + 2)}

\frac{x + 3x + 6)}{(x + 1)(x + 2)}

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Therefore, the numerator of the simplified form sum of both fractions = 4x + 6

8 0
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Answer:

Step-by-step explanation:

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Answer:

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