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V125BC [204]
3 years ago
9

A roofing job take 6 workers 8 hours to complete. If the number of workers is inversely proportional to the time a job takes to

complete, write a model for the number of hours in terms of the number of workers. How long would it take 10 workers to do the same job?
Mathematics
1 answer:
Wewaii [24]3 years ago
7 0

its a long time before finishing

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Which point is on the circle centered at the origin with a radius of 5 units?
Aleonysh [2.5K]

Answer:

(2,√21)

Step-by-step explanation:

The circle centered at the origin has equation:

{x}^{2}  +  {y}^{2}  = 25

Any point that satisfies this equation lie on this circle.

When x=2, we substitute and solve for y.

{2}^{2}  +  {y}^{2}  = 25 \\ 4 +  {y}^{2}  = 25 \\  {y}^{2}  = 25 - 4 \\ {y}^{2}  = 21

Take square root to get:

y =  \pm \sqrt{21}

Therefore (2,-√21) and (2,√21) are on this circle.

From the options, (2,√21) is the correct answer

3 0
3 years ago
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How to solve these 3 problems
Bingel [31]

Answer:

  1. a. decay; b. growth; c. decay; d. neither
  2. r = 4; a = 1; y = 1·4^x
  3. a. an = 3(5^(n-1)); b. f(x) = (3/5)(5^x); c. exponential growth; d. y-intercept: 3/5; first term: 3.

Step-by-step explanation:

There are two kinds of exponential problems here.

  1. exponential functions of the form f(x) = a·b^x
  2. exponential sequences of the explicit form an = a1·r^(n-1)

The second problem gives you a table that suggests the sequence form, but it asks for the exponential function form. The third problem does something similar.

__

<h3>1.</h3>

In an exponential function of the form f(x) = a·b^x, the function grows if b>1 and decays if b<1. Using this check, we can easily answer ...

  a. 0.4 < 1 . . . decay

  b. 1.3 > 1 . . . growth

  c. 1/2 < 1 . . . decay

  d. 1 = 1 . . . neither growth nor decay; the function is constant: j(x) = 1.

__

<h3>2.</h3>

The value of x is given starting at 1, so we can consider this a geometric sequence. The common ratio is r = 16/4 = 4. The first term is a1 = 4, so the explicit formula for the sequence is ...

  an = 4·4^(n-1)

When this is expanded to get rid of the constant in the exponent, we have ...

  an = 4·(4^n)·(4^-1) = 1·4^n

We recognize this form as matching the functional form f(x) = a·r^x. The multiplier of the exponential factor is a=1. In summary, ...

  r = 4; a = 1; f(x) = 1·4^x

__

<h3>3.</h3>

The first term of this geometric sequence is a1 = 3. The common ratio is r = 15/3 = 5. Using the explicit formula, we have ...

 a. explicit form: an = 3·5^(n-1)

Using the method of question 2 to write the functional form, we find ...

  an = 3(5^n)(5^-1) = (3/5)(5^n)

  b. functional form: f(x) = (3/5)(5^x)

  c. function family: exponential growth functions

 d. y-intercept: (3/5) . . . . read this from the f(x) form

     1st term: the first term listed in the given sequence is 3

_____

<em>Additional comment</em>

The "y-intercept" of a sequence is irrelevant (undefined), as the sequence term numbering starts with 1, not 0. The domain of the explicit formula is <em>natural numbers</em>, which does not include 0.

Similarly, the "first term" of a function f(x) needs further definition. Here, we've answered the question by saying the first term is f(1). There is no conventional definition of a "first term" for a continuous function.

3 0
2 years ago
Swimming speed of salmon. The graph is showed below shows the influence of the temperature T on the maximum sustainable swimming
Doss [256]

Answer:

Here we have the relation between the speed of the salmon and the temperature.

a) the relation dS/dT tell us how the speed of the salmon changes as the temperature changes, and the units should be (if speed is m/s and temperature is in °C )

[dS/dT ] = [m/s*°C ].

b) I can not do a draw of the figure, but i can give a aproximation.

For T = 18°C, we can see that we are around the maximum of the curve, this means that around this point we will find the zero in the first derivate.

then S'(18) ≈ 0 m/s*°C

this means that around this point the changes are small.

for T = 10°C

Around this region, we can see almost a linear behavior.

so we can take a range of +-2°C

S(12°C) = 25m/s

S(8°C) = 20m/s

then the slope can be obtained using the relation:

S = (Y2 - Y1)/(X2 - X1) where this is the slope for the line that goes trough the pairs. (X1, Y1) and (X2, Y2)

S = (25 - 20)/(12 - 8) = 5/4

then we have that S´(10°C) ≈ 5/4 m/s*°C

Those two results are approximations, you may find better approximations by doing this with a ruler and drawing the tangents.

5 0
3 years ago
Karl needs to build a stage that has an area of 84 square feet. The length of the stage should be longer than the width. What ar
iragen [17]

Answer/Step-by-step explanation:

84 = L x w

84 = 84 x 1

84 = 42 x 2

84 = 28 x 3

84 = 21 x 4

84 = 14 x 6

84 = 12 x 7

5 0
3 years ago
Read 2 more answers
Help Link (little green guy on the left) defeat Ganon and save Zelda. Find the distance from Link to the Green Soldier so Link c
kenny6666 [7]

Answer:

5 Units.

Step-by-step explanation:

In the attached diagram, Link is at (0,1) and Ganon is at (4,4)

To find the distance between the two, we use the distance formulaDistance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

(x_1,y_1)=(0,1), (x_2,y_2)=(4,4)

Distance between Link and Ganon=\sqrt{(4-0)^2+(4-1)^2}

=\sqrt{4^2+3^2}\\=\sqrt{16+9}\\=\sqrt{25}

=5 Units

The distance between the two is 5 Units.

3 0
3 years ago
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