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marin [14]
3 years ago
5

Given points A(3, -5) and B(19, -1), find the coordinates of point C that sit 3/8 of the way along line AB, closer to A than to

B.
Given points A(3, -5) and B(19, -1), find the coordinates of point C such that CB/AC = 1/7
Mathematics
1 answer:
jeka943 years ago
8 0

1) (9,-3.5)

2) (17,-1.5)

Step-by-step explanation:

1)

In order to solve this problem, we have to divide the segment into 8 equal parts, and find the point that sits at 3/8 of the whole segment.

The end points of the segment in this problem are:

A(3,-5)

and

B(19,-1)

First of all, we find the distance between the x-coordinates and between the y-coordinates:

d_x = |19-3|=16\\d_y=|-1-(-5)|=4

Then we divide the distances by 8 parts:

\frac{d_x}{8}=\frac{16}{8}=2\\\frac{d_y}{8}=\frac{4}{8}=0.5

Now we find the coordinates of point C, which sits 3/8 of the way along the segment, by using the equations:

x_c = x_a + 3 \frac{d_x}{8}=3+3\cdot 2 =9\\y_x = y_a + 3 \frac{d_y}{8}=-5+3\cdot 0.5 =-3.5

2)

Here instead we want to find the coordinates of point C such that

\frac{CB}{AC}=\frac{1}{7} (1)

The coordinates of the endpoints of the segment AB are:

A(3,-5)

and

B(19,-1)

We call the coordinates of point C as:

C(x_c,y_c)

To satisfy eq.(1) for the x-coordinate, we have:

\frac{x_b-x_c}{x_c-x_a}=\frac{1}{7}

Substittuing the values of the x-coordinates of A and B we find:

\frac{19-x_c}{x_c-3}=\frac{1}{7}\\7(19-x_c)=x_c-3\\133-7x_c=x_c-3\\8x_c=136 \rightarrow x_c = 17

And similarly for the y-coordinate we have:

\frac{-1-y_c}{y_c-(-5)}=\frac{1}{7}\\7(-1-y_c)=y_c+5\\-7-7y_c=y_c+5\\8y_c=-12 \rightarrow y_c = -1.5

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Answer:

8 hours

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6 0
3 years ago
-3x + 7 = 1<br> what dose x represent
olchik [2.2K]

Answer:

the answer is x=3

Step-by-step explanation:

-3x=1-7

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x=3

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3 years ago
f(x) = 2<img src="https://tex.z-dn.net/?f=x%5E%7B2%7D" id="TexFormula1" title="x^{2}" alt="x^{2}" align="absmiddle" class="latex
loris [4]

Answer:

No answer is possible

Step-by-step explanation:

First, we can identify what the parabola looks like.

A parabola of form ax²+bx+c opens upward if a > 0 and downward if a < 0. The a is what the x² is multiplied by, and in this case, it is positive 2. Therefore, this parabola opens upward.

Next, the vertex of a parabola is equal to -b/(2a). Here, b (what x is multiplied by) is 1 and a =2, so -b/(2a) = -1/4 = -0.25.

This means that the parabola opens upward, and is going down until it reaches the vertex of x=-0.25 and up after that point. Graphing the function confirms this.

Given these, we can then solve for when the endpoints of the interval are reached and go from there.

The first endpoint in -2 ≤ f(x) ≤ 16 is f(x) = 2. Therefore, we can solve for f(x)=-2 by saying

2x²+x-4 = -2

add 2 to both sides to put everything on one side into a quadratic formula

2x²+x-2 = 0

To factor this, we first can identify, in ax²+bx+c, that a=2, b=1, and c=-2. We must find two values that add up to b=1 and multiply to c*a = -2  * 2 = -4. As (2,-2), (4,-1), and (-1,4) are the only integer values that multiply to -4, this will not work. We must apply the quadratic formula, so

x= (-b ± √(b²-4ac))/(2a)

x = (-1 ± √(1-(-4*2*2)))/(2*2)

= (-1 ± √(1+16))/4

= (-1 ± √17) / 4

when f(x) = -2

Next, we can solve for when f(x) = 16

2x²+x-4 = 16

subtract 16 from both sides to make this a quadratic equation

2x²+x-20 = 0

To factor, we must find two values that multiply to -40 and add up to 1. Nothing seems to work here in terms of whole numbers, so we can apply the quadratic formula, so

x = (-1 ± √(1-(-20*2*4)))/(2*2)

= (-1 ± √(1+160))/4

= (-1 ± √161)/4

Our two values of f(x) = -2 are (-1 ± √17) / 4 and our two values of f(x) = 16 are (-1 ± √161)/4 . Our vertex is at x=-0.25, so all values less than that are going down and all values greater than that are going up. We can notice that

(-1 - √17)/4 ≈ -1.3 and (-1-√161)/4 ≈ -3.4 are less than that value, while (-1+√17)/4 ≈ 0.8 and (-1+√161)/4 ≈ 2.9 are greater than that value. This means that when −2 ≤ f(x) ≤ 16 , we have two ranges -- from -3.4 to -1.3 and from 0.8 to 2.9 . Between -1.3 and 0.8, the function goes down then up, with all values less than f(x)=-2. Below -3.4 and above 2.9, all values are greater than f(x) = 16. One thing we can notice is that both ranges have a difference of approximately 2.1 between its high and low x values. The question asks for a value of a where a ≤ x ≤ a+3. As the difference between the high and low values are only 2.1, it would be impossible to have a range of greater than that.

7 0
2 years ago
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aliina [53]
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Then 
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ln(e^(7k))=ln(153/147)
7k=0.0400 => k=0.005715

Year 2017=>t=2017-1991=26
P(26)=147e^(26*.005715)=170.55
Answer: in 2017, the projected population is 170.55 millions.
6 0
3 years ago
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saul85 [17]

Answer:

It has no value.

Step-by-step explanation:

8 0
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