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3 years ago

Use the equation of the water level of the river represented by the equation y=-4x + 170, where x represents the

Mathematics

2 answers:

vovangra [49]3 years ago

4 0

Answer:

(0,170) and (60,-70) and (5, 150)

Step-by-step explanation:

To see if a given point is on the line or not, you just have to enter the x value (first value in the parenthesis) and see if the function returns the correct y value (second number in the parenthesis).

f(x) = -4x + 170

(170,0) => -4 (170) + 170 = -680 + 170 = 510. NO, not equal to 0.

(0,170) => -4 (0) + 170 = 0 + 170 = 170. YES

(12, 126) => -4 (12) + 170= -48 + 170= 122. No, not equal to 126.

(50,30) => -4(50) + 170 = -200 + 170 = 130. No, not equal to 30.

(5, 150) => -4(5) + 170 = -20 + 170 = 150. YES

(60,-70) => -4(60) + 170 = -240 + 170 = -70. YES

Vedmedyk [2.9K]3 years ago

3 0

Answer:

(0,170) and (60,-70) and (5, 150)

Step-by-step explanation:

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I think I know this much so far for A (but I could be wrong):

Eduardwww [97]

Part A. You have the correct first and second derivative.

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Part B. You'll need to be more specific. What I would do is show how the quantity (-2x+1)^4 is always nonnegative. This is because x^4 = (x^2)^2 is always nonnegative. So (-2x+1)^4 >= 0. The coefficient -10a is either positive or negative depending on the value of 'a'. If a > 0, then -10a is negative. Making h ' (x) negative. So in this case, h(x) is monotonically decreasing always. On the flip side, if a < 0, then h ' (x) is monotonically increasing as h ' (x) is positive.

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Part C. What this is saying is basically "if we change 'a' and/or 'b', then the extrema will NOT change". So is that the case? Let's find out

To find the relative extrema, aka local extrema, we plug in h ' (x) = 0
h ' (x) = -10a(-2x+1)^4
0 = -10a(-2x+1)^4
so either
-10a = 0 or (-2x+1)^4 = 0
The first part is all we care about. Solving for 'a' gets us a = 0.
But there's a problem. It's clearly stated that 'a' is nonzero. So in any other case, the value of 'a' doesn't lead to altering the path in terms of finding the extrema. We'll focus on solving (-2x+1)^4 = 0 for x. Also, the parameter b is nowhere to be found in h ' (x) so that's out as well.

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3 years ago

What is the 100th term in the following sequence: 25, 36, 49, 64...

Mandarinka [93]

The sequence is given by (n+5)²
For n=100:
(100+5)² = 105² = 11025

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2 years ago

Given the function f(x)=6x-11, find f(-1/3).

Nadya [2.5K]

Answer:

-13

Step-by-step explanation:

(-1/3)*6 = -2

f(-1/3) = -2 -11

f(-1/3) = -13

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3 years ago

David brought a variety pack of delicious donuts for his daughters Amy & Anna. Amy ate 2/3 of the pack and Anna devoured 1/4

Naya [18.7K]

Answer:

Step-by-step explanation:

Let the total number of donuts in the pack be x.

Amy = 2/3x

Anna = 1/4x

David = 1

x - 2/3x - 1/4x = 1

Find common denominators for 2/3 and 1/4

The common denominator is 12

2/3 * 4/4 = 8/12

1/4 * 3/3 = 3/12

x - 8/12x - 3/12x = 1

x - 11/12x = 1

1/12x = 1

x = 12

You can always check

Amy = 8

Anna = 3

So David must equal to 1

Hope this helps :)

Have an awesome day!

6 0

2 years ago

Jeff bought a 5-gallon bucket of paint. He used 1.25 gallons to paint his bedroom, then he used two-thirds of the remaining pain

Rainbow [258]

Answer:

2.5 gallons

Step-by-step explanation:

5-1.25=3.75

3.75/3=1.25

1.25*2=2.50

4 0

3 years ago