Find the tangent vector T to the given line (t) = 〈 x(t), y(t), z(t) 〉, with parametric equations,
x(t) = -1 + 3t
y(t) = 6 - 3t
z(t) = 3 + 7t
by differentiating (t) component-wise:
T = '(t) = 〈 dx(t)/dt, dy(t)/dt, dz(t)/dt 〉
T = 〈3, -3, 7〉
Scale T by any real number t to get the line through the origin (when t = 0) and the point (3, -3, 7) (when t = 1), which of course runs parallel to '(t). This gives the vector tT. Translate this by any vector v = 〈a, b, c〉 to force this line to pass through the point (a, b, c) instead of the origin, while still remaining parallel. You want the new line to pass through (0, 11, -9), so take v = 〈0, 11, -9〉.
Then the vector equation of the new line is
tT + v = t 〈3, -3, 7〉 + 〈0, 11, -9〉 = 〈3t, 11 - 3t, -9 + 7t〉
with parametric equations
x(t) = 3t
y(t) = 11 - 3t
z(t) = -9 + 7t
The lines represented by the equations 5y – 6x = –15 and y = x + 5
are
the same line?
perpendicular?
parallel?
neither parallel nor perpendicular?
Answer:
The lines are neither parallel nor perpendicular.
Therefore, we conclude that the statement ''neither parallel nor perpendicular'' is the correct answer.
Step-by-step explanation:
The slope-intercept form of the line equation
[tex]y = mx+b[/tex]
where
m is the slopeb is the y-interceptGiven the line equations
5y – 6x = –15
y = x + 5
Analyzing the equation 5y – 6x = –15
Given the equation
5y – 6x = –15
writing in the slope-intercept form of the line equation
5y = 6x - 15
divide both sides by 5
[tex]y=\frac{6}{5}x-3[/tex]
comparing with the slope-intercept form y = mx+b of the line equation
Thus, the slope of the line 5y – 6x = –15 is:
m₁ = 6/5
Analyzing the equation y = x + 5
Given the equation
y = x + 5
comparing with the slope-intercept form y = mx+b of the line equation
Thus, the slope of the line y = x + 5 is:
m₂ = 1
Conclusion:
The slope of the line 5y – 6x = –15 is:
m₁ = 6/5The slope of the line y = x + 5 is:
m₂ = 1We know that when two lines are parallel, they have equal slopes
But
m₁ ≠ m₂
6/5 ≠ 1
As the m₁ and m₂ are not equal.
Hence, the lines are NOT parallel.
We know that when two lines are parallel, the product of their slopes is -1.
Let us check the product of two slopes m₁ and m₂
m₁ × m₂ = 6/5 × 1
= 6/5
As
m₁ × m₂ ≠ -1
Thus, the lines are not perpendicular.
In a nutshell,
The lines are neither parallel nor perpendicular.
Therefore, we conclude that the statement ''neither parallel nor perpendicular'' is the correct answer.
Zoom
Based on Passage 2, which of the following is most likely to
affect whether a river has a tidal bore?
A the depth of the water in the river
B the size of islands near the river
© the direction of the river's flow
the speed of the river's currents
It takes you 0.8 of a minute to read each page of your health book. It takes you 5.5 minutes to take the test at the end. How long will it take you to read 6.25 pages and also take the test?
3. There are 2 girls and 3 boys on a camping trip. What is the ratio of girls to boys on the trip? Choose all that apply. 2:3 2 to 5 2:5 2 to 3
Answer:
2:3
Step-by-step explanation:
5 in total as you subtract the dudes
Help! if Joey scored a 70% on a test and got 35 questions correct, how many question in total are there?
Answer:
15
Step-by-step explanation:
If you got 35 on a test right, then you 15 wrong making you 70% which is a C-.
Brainliest?? Please? There are 50 total.
16. In a group of 6 boys and 4 girls, four
children are to be selected. In how many
different ways can they be selected such
that at least one boy should be there?
10
D
201
D 212
Answer:
209 different ways.
A
D
O
T
M
H
B
G
R
I
V
W
P
E
Q
F
C
U
J
S
X
K
Which letter am I missing ( not including Y or Z)
Answer:
You are missing J, K, L, N, S, U, X
Step-by-step explanation:
Help!
(Brainliest If You ANswer)
Answer:
c
Step-by-step explanation:
i need help ASAP!: Solve the equation: 13x - 9x + 20 = 30 + 2
2p
X = 3
X = 4
X = 5
X = -3
Nelson did 44 push-ups in 4 minutes.
What is the unit rate?
Answer:
5
Step-by-step explanation:
good luck
I NEED HELP ASAP Which of the following possibilities will form a triangle
Answer:
The answer is D!
Step-by-step explanation:
I GIVEEEEE BRAINLILSTE
Answer:
39 in³
Step-by-step explanation:
Pyramid volume: v = 1/3Bh b=13 h=9
volume; 1/3 * 13 * 9 = 39
a
Question
Simplify
the
[tex] \sqrt{ \frac{9 - {x}^{2} }{ {x }^{2} } } [/tex]
Answer:
[tex]\frac{\sqrt{9-x^2} }{x}[/tex]
Step-by-step explanation:
The simplification of the following equation is:
Given that
[tex]= \sqrt{\frac{9-x^2}{x^2} } \\\\=\frac{\sqrt{9-x^2} }{\sqrt{x^2} } \\\\=\frac{\sqrt{9-x^2} }{x}[/tex]
Here we assume [tex]\sqrt{x^2}[/tex] be x
Hence, in this way it should be simplified
Solve for x in degrees
Answer:
B. 24.3°
Step-by-step explanation:
Apply the sine rule to solve for x
Thus:
[tex] \frac{sin(x)}{8} = \frac{sin(112)}{18} [/tex]
[tex] \frac{sin(x)}{8} = \frac{sin(112)}{18} [/tex]
Multiply both sides by 8
[tex] sin(x)= \frac{sin(112)}{18}*8 [/tex]
[tex] sin(x) = 0.4121 [/tex]
[tex] x = sin^{-1}(0.4121} [/tex]
x = 24.3° (nearest tenth)
Please help me answer this with the correct answer :)
Explain your answer
I will give braisnlt :) c
The proportional relationship between the number of hours a buisness operates and its total cost of electricity is shown in the following graph which statements about the graph are true
Answer:
The yy-coordinate of point A represents the total cost of electricity when the business operates for 4 hours. Or just A on khan :)
As an estimation we are told 5 miles is 8 km.
Convert 17.8 miles to km.
Answer:
the answer would be about 28.60 km
Answer:
28 KM
Step-by-step explanation:
As an estimation we are told 5 miles is 8 km
mathematically , 5 miles = 8 KM
So , therefore 1 miles = 8/5 KM
now just , multiply 17.8 with 8/5
K. Tony is thinking of a number. If you
add 7 to the number, and then
subtract 11, you get 6. What is the
number?
Answer: The answer is 10
Answer:
10
Step-by-step explanation:
x + 7 - 11=6
x - 11 = -1
x = 10
What is the equation of the line?
Answer:
[tex]y = \frac{2}{3} + 7[/tex]
Find the measure of an exterior angle of a regular 50-gon.
Answer:
7.2º
Step-by-step explanation:
all polygon's exterior angles measure 360º, so we just need to divide by 50 to get and individual exterior angle measure. 360/50=7.2º
The measure of an exterior angle of a regular 50-gon should be considered as the 7.2º.
Calculation of an exterior angle:Since we know that
All polygon's exterior angles should have the total of 360º,
So basically we divide 360 by 50 so that the measure of an exterior angle should be determined
i.e.
[tex]= 360\div 50[/tex]
= 7.2 degrees
Hence, The measure of an exterior angle of a regular 50-gon should be considered as the 7.2º.
Learn more about an angle here: https://brainly.com/question/24855153
find each missing number 67 subtract B = 16
Answer:
51
Step-by-step explanation:
67 minus 16 equals 51
Answer:
The missing number is 51.
6th grade math help me pleaseee
Answer:
-2y +-y will go together since they ar elike terms
5 and 7 will go because they also like terms
3. 1/3*4/5 Please I need help please
Answer:
1/3 x 3/4 is equal to 1/4
Step-by-step explanation:
First multiply 1x3 and 3x4 which equals to 3/12
Next you do 3 divided by 3 and 12 divided by 3 which gets you the answer:
1/4
Two more than 5 times a number,n, is greater than 3.
Answer:
5n + 2 > 3 (If you're writing the equation)
n > 1/5 (If you're solving for n.
Step-by-step explanation:
Answer: n > 1/5
Step-by-step explanation:
2 + 5n > 3
5n > 1
n > 1/5
Tai designed a staircase with a height-to- base ratio of 3 : 5. The height of the staircase is 9 feet. What should the base of Tai's staircase measure?
Answer:
15
Step-by-step explanation:
9/3 = 3
5x3 = 15
Answer:
Base is 15 feet
Step-by-step explanation:
3:5 = 9:x
9/3 = 3
3*5 =15
A book Probably cost $21.50 today it was on sale for $15.05 percent discount was offered during the sale
A group of 12 adults and 26 children go to a theme park. The total cost of tickets was £1804.80.
An adult's ticket cost £51.60.
Find the cost of a ticket for a child.
45.60 ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
Which property is illustrated? 6(12 − x) = 6(12) − 6(x)
Answer:
Distributive property
Step-by-step explanation:
Distributive property is the stuff you do in the parentheses
Will mark brainliest thanks
Answer:
the answer is 252 degrees
Identify a set of parallel and a set of perpendicular lines in this image.
