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marshall27 [118]
3 years ago
6

The distance between the two points (4,2) and (8,k) is 5 units. Find value(s)of k

Mathematics
1 answer:
Sliva [168]3 years ago
5 0
D^2 = (x2 - x1)^2 + (y2 - y1)^2
d^2 = (8 - 4)^2 + (k - 2)^2
d = 5 so
5^2 = 4^2 + k^2 - 4k + 4
25 = 16 + k^2 - 4k + 4
25 = 20 + k^2 - 4k
0 = k^2 - 4k - 5
0 = (k - 5)(k + 1)
k has 2 answers
k - 5 = 0
k = 5
k + 1 = 0
k = - 1

The two answers are
(8, 5) and (8, -1) <<<< answer
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You throw a ball up and its height h can be tracked using the equation h=2x^2-12x+20.
postnew [5]

<em><u>This problem seems to be wrong because no minimum point was found and no point of landing exists</u></em>

Answer:

1) There is no maximum height

2) The ball will never land

Step-by-step explanation:

<u>Derivatives</u>

Sometimes we need to find the maximum or minimum value of a function in a given interval. The derivative is a very handy tool for this task. We only have to compute the first derivative f' and have it equal to 0. That will give us the critical points.

Then, compute the second derivative f'' and evaluate the critical points in there. The criteria establish that

If f''(a) is positive, then x=a is a minimum

If f''(a) is negative, then x=a is a maximum

1)

The function provided in the question is

h(x)=2x^2-12x+20

Let's find the first derivative

h'(x)=4x-12

solving h'=0:

4x-12=0

x=3

Computing h''

h''(x)=4

It means that no matter the value of x, the second derivative is always positive, so x=3 is a minimum. The function doesn't have a local maximum or the ball will never reach a maximum height

2)

To find when will the ball land, we set h=0

2x^2-12x+20=0

Simplifying by 2

x^2-6x+10=0

Completing squares

x^2-6x+9+10-9=0

Factoring and rearranging

(x-3)^2=-1

There is no real value of x to solve the above equation, so the ball will never land.

This problem seems to be wrong because no minimum point was found and no point of landing exists

3 0
3 years ago
In a candy mix there are 4 green bars for every 3 red bars. How many red bars are there if there are 200 green bars
erastovalidia [21]

Answer:

Since there are 4 green bars for every 3 red bars and we are trying to find the number of red bars if there are 200 green bars, we can create the ratio:

4 x : 3 y

Where  x  is equal to the number of green bars and  y is the number of red bars.

We know the number of green bars is equal to 200, so we can divide it by 4, giving us:

200 /4=50

Then we can solve for  y , the number of red bars.

// Multiple y  by 50

3 ⋅ 50 = 150

So for every 4 green bars, there are 3 red bars.

For every 200 green bars, there are 150 red bars

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
In automobile mileage and gasoline-consumption testing, 13 automobiles were road tested for 300 miles in both city and highway d
Aloiza [94]

Answer:

A. No

City driving mean requires less miles than Highway driving mean.

B. No

City driving median requires less miles than Highway driving median.

C. No

City driving mode requires less miles than Highway driving mode

D.

The driving conditions in the City is better than the driving conditions in the Highway because all measures of centers are lesser than those of Highway.

Step-by-step explanation:

3 0
3 years ago
40,000 is 10 times as much as
Dimas [21]
40,000 is 10 times as much as 4,000
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Alecsey [184]
<h3>Answer:  Independent</h3>

For two events A and B, if the occurrence of either event in no way affects the probability of the occurrence of the other event, then the two events are considered to be <u>  independent  </u> events.

=========================================================

Explanation:

Consider the idea of flipping a coin and rolling a dice. If these actions are separate (i.e. they don't bump into each other), then one object won't affect the other. Hence, one probability won't change the other. We consider these events to be independent.

In contrast, let's say we're pulling out cards from a deck. If we don't put the first card back, then the future probabilities of other cards will change. This is considered dependent.

3 0
2 years ago
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