All categories

2 years ago

Write the point-slope form of the equation of the line through the given point woth the given slope

Mathematics

1 answer:

Andrej [43]2 years ago

3 0

Answer:

3.) $\displaystyle y - 4 = 4[x - 1]$

2.) $\displaystyle y + 5 = 2[x + 2]$

1.) $\displaystyle y + 3 = 1\frac{1}{5}[x + 5]$

Step-by-step explanation:

In the Point-Slope Formula, $\displaystyle y - y_1 = m[x - x_1],$ all the negative symbols give the OPPOSITE terms of what they really are, so be EXTREMELY CAREFUL inserting the coordinates into the formula with their CORRECT SIGNS.

* $\displaystyle 1\frac{1}{5} = \frac{6}{5}$

I am joyous to assist you anytime.

You might be interested in

Two particles travel along the space curves r1(t) = t, t2, t3 r2(t) = 1 + 2t, 1 + 6t, 1 + 14t . Find the points at which their p

GuDViN [60]

Answer:

A) points at which paths intersect : (1,1,1) ; (2,4,8)

B) DNE

Step-by-step explanation:

A) To find the points in which the particle paths intersect, it is necessary to find the values of t for which the three components of both vectors are equal:

$t_1=1+2t_2\\\\t_1^2=1+6t_2\\\\t_1^3=1+14t_2$

you replace t1 from the first equation in the second equation:

$(1+2t_2)^2=1+6t_2\\\\1+4t_2+4t_2^2=1+6t_2\\\\4t_2^2-2t_2=0\\\\t_2(2t_2-1)=0\\\\t_2=0\\\\t_2=\frac{1}{2}$

Then, for t2 = 0 and t2=1/2 you obtain for t1:

$t_1=1+2(0)=1\\\\t_1=1+2(\frac{1}{2})=2$

Hence, for t1=1 and t2=0 the paths intersect. Furthermore, for t1=2 and t2=1/2 the paths also intersect.

The points at which the paths intersect are:

$r_1(1)=(1,1,1)=r_2(0)=(1,1,1)\\\\r_1(2)=(2,4,8)=r_2(\frac{1}{2})=(2,4,8)$

B) You have the following two trajectories of two independent particles:

$r_1(t)=(t,t^2,t^3)\\\\r_2(t)=(1+2t,1+6t,1+14t)$

To find the time in which the particles collide, it is necessary that both particles are in the same position on the same time. That is, each component of the vectors must coincide:

$t=1+2t\\\\t^2=1+6t\\\\t^3=1+14t$

From the first equation you have:

$t=1+2t\\\\t=-1$

This values does not have a physical meaning, then, the particle do not collide

answer: DNE

5 0

3 years ago

Write the rational number as a decimal -8/5 -9 3/8 -9/11 6 7/27

marissa [1.9K]

$-\frac{8}{5}$ = -1.6

$-9\frac{3}{8}$ = -11.625

$-\frac{9}{11}$ = -0.81818...

$6\frac{7}{27}$ = 2.4814

7 0

2 years ago

1. Two dice are thrown at the same time . What is the probability that the sum will be 7 or 11 ?

netineya [11]

Answer:

1. 0.2222222

2. .6667

Step-by-step explanation:

for question 1

there can only be 36 outcomes so you find out how many time you could get 7and2 which is 8 from so u write 8.36=.2222

for question 2

divide the outcome by the total out comes example(there are 6 red balls and 4 white out of 15 so you do 10/15=.6667)

8 0

3 years ago

Read 2 more answers

Write an expression which solves for the radius of an object having the circumference of 30 feet

Likurg_2 [28]

$circumference=30ft.\\\\circumference=2\pi r\ (r-radius)\\\\2\pi r=30\ \ \ \ /:2\pi\\\\r=\frac{30}{2\pi}\\\\r=\frac{15}{\pi}\ (ft)\\\\\frac{15}{\pi}\approx\frac{15}{3.14}\approx4.78\ (ft)$

8 0

3 years ago

Read 2 more answers

Help!<br><br> If a sphere has a radius of 8mm, what is its volume? (Show work)

babymother [125]

The formula for the volume of a sphere is V = (4/3) * π * r³. Knowing this, we can plug in the radius:

$V = \frac{4}{3} \pi *8^{3} \\ V = \frac{4}{3} \pi*512 \\ V = 2144.66$

The sphere's volume is approximately 2144.66 mm^3.

7 0

3 years ago