All categories

3 years ago

Write a vector equation of the line that passes through p(–1 6) and is parallel to a = (3, -1).

Mathematics

2 answers:

Phoenix [80]3 years ago

7 0

Answer:

Step-by-step explanation:

(x,y) = p + t(a)

(x,y) = (-1,6) + t(3,-1)

(x,y) - (-1,6) = t(3,-1)

(x + 1, y - 6) = t(3, -1)

Serjik [45]3 years ago

3 0

Answer:

Step-by-step explanation:

You might be interested in

Suppose that p is the probability that a randomly selected person is left handed. The value (1-p) is the probability that the pe

solmaris [256]

Answer:

a) 1/2

b) 250

Step-by-step explanation:

The start of the question doesn't matter entirely, although is interesting to read. What we are trying to do is find the value for $p$ such that $1000p(1-p)$ is maximized. Once we have that $p$ , we can easily find the answer to part b.

Finding the value that maximizes $1000p(1-p)$ is the same as finding the value that maximizes $p(1-p)$ , just on a smaller scale. So, we really want to maximize $p(1-p)$ . To do this, we will do a trick called completing the square.

$p(1-p)=p-p^2=-p^2+p=-(p^2-p)=-(p^2-p+1/4)-(-1/4)=-(p-1/2)^2+1/4$ .

Because there is a negative sign in front of the big squared term, combined with the fact that a square is always positive, means we need to find the value of $p$ such that the inner part of the square term is equal to $0$ .

$p-1/2=0\\p=1/2$ .

So, the answer to part a is $\boxed{1/2}$ .

We can then plug $1/2$ into the equation for p to find the answer to part b.

$1000(1/2)(1-1/2)=1000(1/2)(1/2)=1000*1/4=250$ .

So, the answer to part b is $\boxed{250}$ .

And we're done!

3 0

2 years ago

What is an equation of the line that passing through the points (-2, -5) and (4, 7) ?

monitta

Answer:

$y=2x-1$

Step-by-step explanation:

Use the slope-intercept formula: $y=mx+b$ where m is slope and b the y-intercept.

$(-2,-5)(4,7)$

Use the slope formula for when you have two points:

$\frac{y(2)-y(1)}{x(2)-x(1)}=\frac{rise}{run}$

Rise over run is the change in the y-axis over the change in the x-axis. Insert values:

$\frac{7-(-5)}{4-(-2)}$

Simplify parentheses (negative+negative=positive)

$\frac{7+5}{4+2}$

Simplify

$\frac{12}{6}=2$

2 is the slope:

$y=2x+b$

Now use one of the points to find the y-intercept by substituting the x and y values into the equation. Solve for b:

(4,7)

$y=2x+b\\7=2(4)+b$

$7=8+b\\7-8=8-8+b\\7-8=b\\-1=b\\b=-1$

The y-intercept is -1. Insert into the equation. Change the + symbol to -:

$y=2x-1$

Done.

6 0

3 years ago

Please help! Sketch the graph of each line.

madam [21]

Answer:

1) (-3,0) (0,-3)

2) (-2,0)

3) (5,0) (0,-1)

4) (12,0) (0,3)

5) (-16,0) (0,4)

6) (-0.8333,0) (0,5)

4 0

2 years ago

Suppose y varies inversely with x. Write an equation if y=-3 when x=17

vodka [1.7K]

Answer:

y = -51 ÷ x

Step-by-step explanation:

The standard format of a inversely proportional equation goes by the format of y = k ÷ x. The question asks us to write an equation if y = -3 when x = 17 and y varies inversely with x.

So we substitute the values y = -3 and x = 17 in the equation y = k ÷ x

K = constant, we have to work this out

-3 = k ÷ 17

-3 × 17 = k

k = -3 × 17

k = -51

k = -51 So then we put this back into the original y = k ÷ x to find our final equation which is y = -51 ÷ x

6 0

3 years ago

What is the length of side s of the square shown below?

Dmitry_Shevchenko [17]

Answer:

Have you ever had a dream that, that, um, that you had, uh, that you had to, you could, you do, you wit, you wa, you could do so, you do you could, you want, you wanted him to do you so much you could do anything?

Step-by-step explanation:

8 0

2 years ago