Answer:
the required parametric equation is:
x = 1
y = t + 3
z = -12t - 17
Step-by-step explanation:
From the given information:
We are to express x,y, and z in terms of t.
The purpose of this question is to find the parametric equations in terms of t.
Given that the tangent line related to the parabola is the point (1,3, -17)
Provided that the paraboloid z = 3 - x - x² - 2y² intersect the plane x = 1 in a paraboloid; then:
z = 3 - 1 - (1)² - 2y²
z = 1 - 2y²
Suppose y = t, then the parametrization is given by:
(x (t), y(t), z(t) ) = (1, t, 1 - 2t²)
(x' (t), y'(t), z'(t) ) = (0,1, -4t)
At the point (x,y,z) = (1,3, -17)
For t (=y) = 3
Hence, (x'(3),y'(3),z'(3)) = (0,1, -12)
Therefore, the equation of the tangent line can be expressed as:
[tex]\dfrac{x-1}{0}=\dfrac{y-3}{1}=\dfrac{z-(-17)}{-12}=(t)[/tex]
x - 1 = 0, y -3 = t, z + 17 = -12t
x = 1, y = t + 3 , z = -12t - 17
Thus, the required parametric equation is:
x = 1
y = t + 3
z = -12t - 17
Find the equation of line b described below, in slope-intercept form
Line a is perpendicular to line b
Line a passes through the points (1,-8) and (9,-12)
Line b passes through the point (-8, -16)
The equation of line b is y= ______
Given:
Line a is perpendicular to line b .
Line a passes through the points (1,-8) and (9,-12) .
Line b passes through the point (-8, -16).
To find:
The equation of b.
Solution:
Line a passes through the points (1,-8) and (9,-12) . So, slope of line a is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m_a=\dfrac{-12-(-8)}{9-1}[/tex]
[tex]m_a=\dfrac{-12+8}{8}[/tex]
[tex]m_a=\dfrac{-4}{8}[/tex]
[tex]m_a=-\dfrac{1}{2}[/tex]
Product of slopes of two perpendicular lines is -1.
[tex]m_a\times a_b=-1[/tex]
[tex]-\dfrac{1}{2}\times a_b=-1[/tex]
[tex]b=2[/tex]
Slope of line b is 2.
If a line passing through a point [tex](x_1,y_1)[/tex] with slope m, then equation of line is
[tex]y-y_1=m(x-x_1)[/tex]
Line b passing through (-8,-16) with slope 2. So, equation of line b is
[tex]y-(-16)=2(x-(-8))[/tex]
[tex]y+16=2(x+8)[/tex]
[tex]y+16=2x+16[/tex]
Subtract 16 from both sides.
[tex]y=2x[/tex]
Therefore, the equation of line b is [tex]y=2x[/tex].
Help quick The engineers designing the All Aboard Railroad between Boca Raton and Jupiter decide to create parallel tracks through this portion of the railway. To illustrate their plans to the county commission, they use a coordinate plane. The southbound track will have an equation of 2x + 5y = 15. What is the equation of the parallel northbound track that runs through the point (4, – 2)?
A. 2x + 5y = −2
B. 2x − 5y = 18
C. 5x + 2y = 16
D. 5x − 2y = 24
Answer:
Step-by-step explanation:
The answers is A
The required equation of the parallel track that runs through the point (4 , -2) is 2x + 5y = −2.
The engineers designing the All Aboard Railroad between Boca Raton and Jupiter decided to create parallel tracks through this portion of the railway.The southbound track will have an equation of 2x + 5y = 15. What is the equation of the parallel northbound track that runs through the point (4, – 2) TO determine.
The equation is the relationship between variables and represented as y=ax + b is an example of a polynomial equation.
Equation of the southbound track,
2x + 5y = 15
slope of the above equation is m = -2/5
Since the slope of the parallel lines are equal.
The equation of the parallel northbound track that runs through the point (4, – 2),
(y + 2) = -2/5 (x - 4)
5(y + 2) = -2 (x-4)
5y + 10 = - 2x +8
2x + 5y = 8-10
2x + 5y = -2
Thus, the required equation of the parallel track that runs through the point (4 , -2) is 2x + 5y = −2.
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what is 4 to the power of 4
Answer:
256
Step-by-step explanation:
Answer:
256
Step-by-step explanation:
4 to 4th power=
4^4 or 4x4x4x4=
4x4= 16
4x4x4= 64
4x4x4x4= 256 <===== Answer
Find the vertex and y-intercept of the quadratic function.
y = - x2 + 4x + 7
Answer:
Vertex: (2, 11)
Y-Intercept: (0, 7)
Step-by-step explanation:
A line passes through the points (3, 5) and (2, 0). What is the slope?
Answer:
y= -4x - 5
Step-by-step explanation:
5 is your y-intercept
The slope of the line which passes through the points (3,5) and (2,0) is 5
From the question,
We are to determine the slope of the line
The slope of a line with two given points can be determined from the formula
[tex]m = \frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
Where m represents the slope
From the given information
x₁ = 3
y₁ = 5
x₂ = 2
y₂ = 0
Putting these into the formula,
We get
[tex]m = \frac{0-5}{2-3}[/tex]
Then,
[tex]m = \frac{-5}{-1}[/tex]
∴ m = 5
Hence, the slope of the line which passes through the points (3,5) and (2,0) is 5
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Can someone help please?
Answer:
just substitute the numbers for the variable y, and see whichs are greater than or less than 6
Answer:
1
Step-by-step explanation:
13 - 7(-1) = 20 so no
13 - 7(0) = 13 so no
13 - 7(1) = 6 so yes
[is there a 2 there?] 13 - 7(2) = -1 so no
13 - 7(3) = -8 so no
what is the greatest common factor shared by 51 and 21
what is the product of -3 1/4 and -1 1/2
Answer:
-4 and 3/4, also written as -4.75
Step-by-step explanation:
If you can fit 50 people into one bus, how many buses would you need to transport 940 people? Show your work.
Answer: 19
Step 1: Divide.
940 ÷ 50 = 18.8
Step 2: Round 18.8 to the nearest one.
18.8 - 19
Answer to the question is 19.
Answer:
About 19 buses
Step-by-step explanation:
940/50 = 18.8 ≈ 19
A line contains the points (82, −96) and (87, −86).
What is the slope of the line in simplified form?
Enter your answer in the box.
Answer:
The answer is 2Step-by-step explanation:
The slope of a line given two points can be found by using the formula
[tex]m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\[/tex]
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(82, −96) and (87, −86)
We have
[tex]m = \frac{ - 86 - - 96}{87 - 82} = \frac{ - 86 + 96}{5} = \frac{10}{5} = 2 \\ [/tex]
We have the final answer as
2Hope this helps you
Does a parallelogram have to have equal sides
Answer:
Yes
Step-by-step explanation:
A Parallelogram is a flat shape with opposite sides parallel and equal in length. NOTE: Squares, Rectangles and Rhombuses are all Parallelograms
Hope this helps (:
4(2x - 2) + 2 = 4(x - 2)
Answer:
X=-1/2
Step-by-step explanation:
Hope this helps. Plz give brainliest.
Answer:
x = -1/2 or -0.5
Step-by-step explanation:
4(2x - 2) + 2 = 4(x - 2)
open the parenthesis
8x - 8 + 2 = 4x - 8
add 8 to both sides of the equation
8x - 8 + 2 + 8 = 4x - 8 + 8
combine like terms
8x + 2 = 4x
subtract 4x from both sides of the equation
8x - 4x + 2 = 0
4x + 2 = 0
subtract 2 from both sides of the equation
4x + 2 - 2 = 0 -2
4x = -2
divide both sides by 4
4x/4 = -2/4
x = -1/2
Evaluate each of the following expressions if x=5, y=6, z=-6
X+3y+z=____
(x-12)+3(y+z)=____
100x+yz=___
True of False?
2) A fraction can multiply with another fraction
Answer:
True.
Step-by-step explanation:
Hope this helps!
Answer:
TRUE!!
Step-by-step explanation:
Good luck
Solve 14m = 98
A. M=7
B. M=112
C. M= 84
D. M=8
Answer:
A) m=7
Step-by-step explanation:
Just divide 98 by 14
Answer:
A is the answer
Step-by-step explanation:
7×14 = 98
Line JK passes through points J(–4, –5) and K(–6, 3). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b?
–21
–4
11
27
Find the slope that passes between the points.
(y₂ - y₁) / (x₂ - x₁)
J(-4, -5)
K(-6, 3)
(3 - (-5)) / (-6 - (-4))
(3 + 5) / (-6 + 4)
8 / -2
-4
Now slap that slope into the formula and substitute on of the coordinates to the formula to solve for b (I'll take point K's coordinate):
y = mx + b
y = -4x + b
3 = -4(-6) + b
3 = 24 + b
3 - 24 = b
- 21 = b
b = -21
If the equation of the line is written in slope-intercept form, y = mx + b, then the value of b is -21 and is denoted as option A.
What is Slope?This is also referred to as the gradient of a line and measures its steepness and direction.
Slope = (y₂ - y₁) / (x₂ - x₁)
ParametersJ(-4, -5) and K(-6, 3)
= (3 - (-5)) / (-6 - (-4))
= (3 + 5) / (-6 + 4)
= 8 / -2
= -4
Substitute one of the coordinates into the formula to solve for b
y = mx + b
y = -4x + b
3 = -4(-6) + b
3 = 24 + b
3 - 24 = b
b = - 21
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find the domain and range of the function represented by the graph.
If a point within the density curve is chosen at random,
what is the probability that the value lies between 2.25 and 4.75?
0.025
0.375
0.417
0.639
0.75
Determine the x-intercept of the
equation below. Write your answer as
an ordered pair.
-3x + 5y = 15
Answer: -5
Step-by-step explanation:
substitute 0 for y
can you name some of the respectful disagreement skills
Answer: Listen to what the other person has to say, try to see from other perspectives, don't show anger or other person won't listen to what you have to say.
Step-by-step explanation:
Answer:
no sorry
Step-by-step explanation:
Find the slope of the line passing through each of the following pairs of points.
(0, −8), (0, 4)
Answer:
Undefined.
Step-by-step explanation:
[tex]m=\frac{rise}{run}=\frac{4+8}{0-0}=\frac{12}{0}= undefined[/tex]
The slope is undefined.
Hope this helps.
Answer:
Undefined( If this is wrong then it is zero)
Step-by-step explanation:
The formula for this problem is y2 - y1/x2-x1. You can name any of those points 1 or 2 as long as they have the right coordinate.
4 - (-8)/0 - 0= 12/0 = Undefined
During the 2010 Great Backyard Bird Count, an average of
42 bald eagles were counted in each of 20 locations throughout
Alaska. In 2009, an average of 32 bald eagles were counted in
each of 26 locations throughout Alaska. Based on this data, how
many more bald eagles were counted in 2010 than in 2009?
Use the graphic organizer to help you solve the problem.
Answer:
good luck
Step-by-step explanation:
Help help help help help help help help help help
I am not really sure, but I can say that I would go with; either B or C. Sorry...
30 = [(10 - 8) + (17-14)]
Answer:yes
Step-by-step explanation:kubjubjugjugjugjugjugjugju
Renting video games from Store S cost $2.50 per game plus a monthly fee of $5. Renting video games from Store T cost $5 per game with no monthly fee. The monthly cost to rent video games depends on the number of video games, v, rented. What inequality represents the situation when the monthly cost of Store S is less than the monthly cost at Store T?
Answer:2.5v+5>5v
Step-by-step explanation:this definitely right
What is the slope of the line?
Answer:
1/2
Step-by-step explanation:
Slope equals rise over run. To find this use two points that land evenly on the graph then count how ever many spaces up and then to the side. In this case, it goes up 1 and right 2, so put that into fraction form, 1/2, and that is your answer.
Answer:
1/2
Step-by-step explanation:
what is an explicit representation for the nth term of the sequence (-1/2, -2 , - 8, -32)
Answer:
sdvsvsdv
Step-by-step explanation:
Answer:
Step-by-step explanation:
It’s B
Simplify each of the expressions.
Answer:
5y2 + -3y + 2
Step-by-step explanation:
Sorry only have the first one.
brainliest for correct answers
Answer:
impossible
unlikely
neither unlikely nor likely
likely
certain
Step-by-step explanation:
Anyone know how to do??
Answer:
x = 15°
Step-by-step explanation:
∠2 and ∠4 are same-side interior angles, meaning they add up to 180
2x + 10 + 4x + 80 = 180
Rearrange (collect like terms)
6x = 180 - 80 - 10
6x = 90
x = 15°
Answer:
x = 15Step-by-step explanation:
∠2 = 2x + 10
∠4 = 4x + 80
∠2 and ∠4 are supplementary angles, this mean ∠2 + ∠4 = 180
2x + 10 + 4x + 80 = 180
combine similar terms: 6x = 180 - 80 - 10
simplify: 6x = 90
solve for x = 90 / 6
x = 15