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andrey2020 [161]
3 years ago
10

Find the derivative of the function using the definition of derivative.f(x) = mx + qf '(x) =

Mathematics
1 answer:
Natasha_Volkova [10]3 years ago
5 0

Answer:

a) f'(x) = m

b) x \in (-\infty, \infty)

c) x \in (-\infty, \infty)

Step-by-step explanation:

We are given the following in the question:

f(x) = mx + q

a) We have to find the derivative of the given function.

f'(x) = \dfrac{f(x+h)-f(x)}{h}\\\\= \dfrac{m(x+h)+q - mx - q}{h}\\\\f'(x) = \dfrac{mh}{h}\\\\f'(x) = m

b) Domain of f(x)

Domain is the collection of all values of x for which the function is defined.

Domain of f(x) is all real numbers.

x \in (-\infty, \infty)

c) Domain of f'(x)

Domain of f'(x) is all real numbers.

x \in (-\infty, \infty)

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A school pays $1,825 for 150 shirts. This includes the $25 flat-rate shipping cost. What equation models the total cost as a fun
likoan [24]

Answer:

c(t) = 25 +12 * t

where t is the number of shirts

Step-by-step explanation:

The total cost for the shirts  is the flat fee plus the cost per shirt times 150 shirts

total = fee + cost per shirt* shirts

1825 = 25 +c*150  

 where c is the cost per shirt

We need to determine the cost per shirt by subtracting 25 from each side

1825-25 = 150c

1800 =150c

Divide by 150 on each side

1800/150 =150c/150

12 =c

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We want to make the function in terms of cost per shirt

c(t) = 25 +12 * t

where t is the number of shirts

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3 years ago
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vesna_86 [32]

Answer:

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Step-by-step explanation:

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The following graph shows a proportional relationship.
LenKa [72]

Answer:

2

Step-by-step explanation:

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y\ \alpha\ x\\

and when we remove the proportionality sign we replace it with an equal to sign and a constant. So it becomes ,

y = kx\\

now to find the Constant of proportionality which is k we can use any ordered pair(coordinate/point) from the graph,

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4 0
2 years ago
4. Find the standard from of the equation of a hyperbola whose foci are (-1,2), (5,2) and its vertices are end points of the dia
Ad libitum [116K]

The <em>standard</em> form of the equation of the hyperbola that satisfies all conditions is (x - 2)²/4 - (y - 2)²/5 = 1 .

<h3>How to find the standard equation of a hyperbola</h3>

In this problem we must determine the equation of the hyperbola in its <em>standard</em> form from the coordinates of the foci and a <em>general</em> equation of a circle. Based on the location of the foci, we see that the axis of symmetry of the hyperbola is parallel to the x-axis. Besides, the center of the hyperbola is the midpoint of the line segment with the foci as endpoints:

(h, k) = 0.5 · (- 1, 2) + 0.5 · (5, 2)

(h, k) = (2, 2)

To determine whether it is possible that the vertices are endpoints of the diameter of the circle, we proceed to modify the <em>general</em> equation of the circle into its <em>standard</em> form.

If the vertices of the hyperbola are endpoints of the diameter of the circle, then the center of the circle must be the midpoint of the line segment. By algebra we find that:

x² + y² - 4 · x - 4 · y + 4= 0​

(x² - 4 · x + 4) + (y² - 4 · y + 4) = 4

(x - 2)² + (y - 2)² = 2²

The center of the circle is the midpoint of the line segment. Now we proceed to determine the vertices of the hyperbola:

V₁(x, y) = (0, 2), V₂(x, y) = (4, 2)

And the distance from the center to any of the vertices is 2 (<em>semi-major</em> distance, a) and the semi-minor distance is:

b = √(c² - a²)

b = √(3² - 2²)

b = √5

Therefore, the <em>standard</em> form of the equation of the hyperbola that satisfies all conditions is (x - 2)²/4 - (y - 2)²/5 = 1 .

To learn more on hyperbolae: brainly.com/question/27799190

#SPJ1

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1 year ago
What is 4 times 2 please I’m in need of an answer
MAXImum [283]
8 is the answer to your question
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