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Vlada [557]
2 years ago
12

Graph a linear function which has a rate of change equal to the average rate of change of function f on the interval [-1, 1]. Th

e linear function should pass through the point (1,-2).

Mathematics
1 answer:
fomenos2 years ago
4 0
<h2>Answer:</h2>

The linear function is given by:

       y=\dfrac{3}{2}x-\dfrac{7}{2}

<h2>Step-by-step explanation:</h2>

It is given that the rate of change of the linear function is equal to the average rate of change of function f on the interval [-1, 1].

The slope(m) or average rate of change of  the linear function will be:

m=\dfrac{f(1)-f(-1)}{1-(-1)}\\\\\\m=\dfrac{-2-(-5)}{1+1}\\\\\\m=\dfrac{-2+5}{2}\\\\\\m=\dfrac{3}{2}

and the linear function pass through (1,-2)

We know that the equation of a line with given slope m and passing through point (a,b) is given by:

Here (a,b)=(1,-2)

and m=\dfrac{3}{2}

Hence, the equation of linear function is:

y-(-2)=\dfrac{3}{2}\times (x-1)\\\\\\y+2=\dfrac{3}{2}x-\dfrac{3}{2}\\\\\\y=\dfrac{3}{2}x-\dfrac{3}{2}-2\\\\\\y=\dfrac{3}{2}x-\dfrac{7}{2}

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Step-by-step explanation:

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4 0
2 years ago
Find point G on AB such that the ratio of AG to GB is 3:2
Alexxx [7]

The point G on AB such that the ratio of AG to GB is 3:2 is; G(4.2, 2)

How to partition a Line segment?

The formula to partition a line segment in the ratio a:b is;

(x, y) = [(bx1 + ax2)/(a + b)], [(by1 + ay2)/(a + b)]

We want to find point G on AB such that the ratio of AG to GB is 3:2.

From the graph, the coordinates of the points A and B are;

A(3, 5) and B(5, 0)

Thus, coordinates of point G that divides the line AB in the ratio of 3:2 is;

G(x, y) = [(2 * 3 + 3 * 5)/(2 + 3)], [(2 * 5 + 3 * 0)/(2 + 3)]

G(x, y) = (21/5, 10/5)

G(x, y) = (4.2, 2)

Read more about Line segment partition at; brainly.com/question/17374569

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8 0
1 year ago
Reparametrize the curve with respect to arc length measured from the point where t = 0 in the direction of increasing t. (Enter
Alex Ar [27]

Answer:

I would need more information to help you

Step-by-step explanation:

7 0
3 years ago
Please help...<br> i rlly need help on this
melamori03 [73]

Answer:

3

Step-by-step explanation:

Since

3 : 2 = X : 2

Then we know

3/2 = X/2

Multiplying both sides by 2 cancels on the right

2 × (3/2) = (X/2) × 2

2 × (3/2) = X

Then solving for X

X = 2 × (3/2)

X = 3

Therefore

3 : 2 = 3 : 2

5 0
2 years ago
HELP PLEASE!!! I need help with 94 if you could show the steps that would be very helpful!
aksik [14]
A combination is an unordered arrangement of r distinct objects in a set of n objects. To find the number of permutations, we use the following equation:

n!/((n-r)!r!)

In this case, there could be 0, 1, 2, 3, 4, or all 5 cards discarded. There is only one possible combination each for 0 or 5 cards being discarded (either none of them or all of them). We will be the above equation to find the number of combination s for 1, 2, 3, and 4 discarded cards.

5!/((5-1)!1!) = 5!/(4!*1!) = (5*4*3*2*1)/(4*3*2*1*1) = 5

5!/((5-2)!2!) = 5!/(3!2!) = (5*4*3*2*1)/(3*2*1*2*1) = 10

5!/((5-3)!3!) = 5!/(2!3!) = (5*4*3*2*1)/(2*1*3*2*1) = 10

5!/((5-4)!4!) = 5!/(1!4!) = (5*4*3*2*1)/(1*4*3*2*1) = 5

Notice that discarding 1 or discarding 4 have the same number of combinations, as do discarding 2 or 3. This is being they are inverses of each other. That is, if we discard 2 cards there will be 3 left, or if we discard 3 there will be 2 left.

Now we add together the combinations

1 + 5 + 10 + 10 + 5 + 1 = 32 choices combinations to discard.

The answer is 32.

-------------------------------

Note: There is also an equation for permutations which is:

n!/(n-r)!

Notice it is very similar to combinations. The only difference is that a permutation is an ORDERED arrangement while a combination is UNORDERED.

We used combinations rather than permutations because the order of the cards does not matter in this case. For example, we could discard the ace of spades followed by the jack of diamonds, or we could discard the jack or diamonds followed by the ace of spades. These two instances are the same combination of cards but a different permutation. We do not care about the order.

I hope this helps! If you have any questions, let me know :)








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