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myrzilka [38]
3 years ago
8

Hey guys if i can get some pointers on how to do this that would be great ive been stuck on this problem for over an hour my not

es arent helping me and no one in the household understands it any help would be greatly appreciated.
(a)
Determine the difference of outputs of any two inputs that are 1 unit apart.
Show your work.
(b)
Determine the difference of outputs of any two inputs that are 2 units apart.
Show your work.
(c)
Determine the difference of outputs of any two inputs that
are 3 units apart.
Show your work.
(d)
What do you notice about the ratios of the differences in the outputs to the input intervals? Explain
your answer

Mathematics
1 answer:
leva [86]3 years ago
5 0

Answer:

  • a) 3
  • b) 6
  • c) 9
  • d) the outputs are 3 times as far apart as the inputs

Step-by-step explanation:

(a) "x" in considered to be the input to the function f(x). The variable(s) in parentheses as part of the function name are the inputs. The function value itself is the output.

That is, for an input (x-value) of 0, the output (f(0)) is 5. For an input of 1, the output (f(1)) is 8. These input values (0 and 1) are 1 unit apart: 1 - 0 = 1. The corresponding output values are 3 units apart: 8 - 5 = 3.

(b) Inputs -1 and 1 are 2 units apart (1-(-1)=2). The corresponding output values, 2 and 8, are 6 units apart. (8-2=6)

(c) Inputs 0 and 3 are 3 units apart. The corresponding output values, 5 and 14, are 9 units apart.

(d) The ratio of output differences to input differences can be seen to be ...

... 3/1 = 6/2 = 9/3 = 3

Output differences are 3 times input differences.

_____

<em>Comment on the problem</em>

These ratios are constant everywhere, so the function is considered to be "linear." The ratio is the "slope" of the line you see when the function is graphed.

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You have climbed to the top of a tall tree. When you get to the top, you use your clinometer to discover that the angle between
GuDViN [60]

Answer:

F. 34.64 m

Step-by-step explanation:

The measurements given in the question are;

The angle (of depression) given by the clinometer, θ = 30°

The horizontal distance of the lunchbox from the tree, d = 20 meters

The height (how tall) of the tree = Required

Let the height of the tree be assumed to be perpendicular to the ground, noting that the horizontal distance from the lunchbox to the tree is a straight line, let <em>l</em> represent the line of sight from the top of the tree to the lunchbox, and let <em>h </em>represent the height of the tree we have;

The line of sight to the lunchbox, <em>l</em>, the height of the tree, <em>h</em>, and the horizontal distance of the lunchbox from the base of the tree form a right triangle

The height of the tree is the adjacent leg to the given angle by the clinometer

Using trigonometric ratios, we have;

tan(30°) = d/h

∴ tan(30°) = (20 m)/h

h = (20 m)/tan(30°) ≈ 34.64m

The height of the tree, h ≈ 36.64 m.

5 0
3 years ago
What is the​ solution? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice 35- x
Anna11 [10]
You can multiply both sides of the equation by 12 to remove the fractions.

12(35 - x/4) = 12(x/3)

420 - 12x/4 = 12x/3

420 - 3x = 4x

Add 3x to both sides:

420 = 7x

Divide 7 to both sides:

x = 60
8 0
3 years ago
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The inflation rate on gas is 13%. If the price of
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Step-by-step explanation:

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3 years ago
Suppose f(x, y) is a differentiable function of x and y and let g(r, s) = f (2rs, 8s − 2r). Use
worty [1.4K]

By the chain rule,

\dfrac{\partial g}{\partial r} = \dfrac{\partial f}{\partial r} \\\\ ~~~~~ = \dfrac{\partial f}{\partial x} \dfrac{\partial x}{\partial r} + \dfrac{\partial f}{\partial y} \dfrac{\partial y}{\partial r} \\\\ ~~~~~ = 2 s \dfrac{\partial f}{\partial x} - 2 \dfrac{\partial f}{\partial y}

where x(r,s)=2rs and y(r,s)=8s-2r.

If r=2 and s=1, then

x = 2\cdot2\cdot1 = 4

y=8\cdot1-2\cdot2 = 4

so that

g_r(2,1) = 2\cdot1 f_x(4,4) - 2 f_y(4,4) = 2\cdot2-2\cdot3 = \boxed{-2}

5 0
1 year ago
How much do i need to get to 500 so rite now I have 423 and I need 500
Elza [17]

Answer:

77

Step-by-step explanation:

just do 500-423

4 0
3 years ago
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