The paraboloid z = 3 − x − x2 − 2y2 intersects the plane x = 1 in a parabola. Find parametric equations in terms of t for the tangent line to this parabola at the point (1, 3, −17). (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of t.
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
What is the sum of angles A + B + C?
George earns $9.50 per hour and $35.00 commission per sale, but he pays $12.00 in license fees each week. Mary earns $13.50 per hour and $11.25 for every defect she corrects, but she must pay $37.00 for tool rentals each week. The expressions below represent their individual earnings for every two-week pay period. George: 9.5h+35s−2(12) Mary: 13.5h+11.25d−2(37) where: h = the number of hours worked s = the number of sales George makes d = the number of defects Mary corrects
Answer:
23h+35s+11.25d-98Step-by-step explanation:
the question is incomplete here is the complete question
"George earns $9.50 per hour and $35.00 commission per sale, but he pays $12.00 in license fees each week. Mary earns $13.50 per hour and $11.25 for every defect she corrects, but she must pay $37.00 for tool rentals each week. The expressions below represent their individual earnings for every two-week pay period. George: 9.5h+35s−2(12) Mary: 13.5h+11.25d−2(37) where: h = the number of hours worked s = the number of sales George makes d = the number of defects Mary corrects if George and mary work the same hour each period, which expression represents their combined earning for one day earning period"
given
week pay period.
George: 9.5h+35s−2(12)
Mary: 13.5h+11.25d−2(37)
their combined earning is the sum of the individual earning
9.5h+35s−24
+13.5h+11.25d-74
23h+35s+11.25d-98
The expression is 23h+35s+11.25d-98
5 + x - 14 = -15. Solve for X
Answer:
x=-6
Step-by-step explanation:
x+-9=-15
x+9=15
x=15-9
x=6
Answer:
x= -6
Step-by-step explanation:
5+x-14=-15
x-14=-20
x=-6
Anyone who is kind to answer please
why are there two values of theta if tan theta = 0.4226
Answer:
[tex]22.91^\circ, 202.91^\circ[/tex]
Step-by-step explanation:
Given that:
[tex]tan\theta=0.4226[/tex]
To find:
The two values of [tex]\theta = ?[/tex]
Solution:
By given equation:
[tex]\theta = tan^{-1}(0.4226)[/tex]
[tex]\theta[/tex] can be equal to [tex]\approx 20.91^\circ[/tex]
Also, we know the property that, [tex]tan\theta[/tex] is positive in the 3rd quadrant.
and following is also true:
[tex]tan\theta = tan(180^\circ+\theta)[/tex]
Therefore, another value possible for [tex]\theta[/tex] can be:
[tex]\theta =180^\circ+22.91\\\Rightarrow \theta \approx 202.91^\circ[/tex]
Therefore, the answer is:
[tex]22.91^\circ, 202.91^\circ[/tex]
A bakery has 72 half gallons of milk. It takes 1 2/3 cups of milk to make a cake. Note that 1 cup = 1/8 half gallon = 0.125 half gallon. How many cakes can the bakery make?
A. 43 cakes
B. 288 cakes
C. 345 cakes
D. 576 cakes
Answer:
cStep-by-step explanation:
72 half gallons /( 1 2/3 cup/cake *.125 half gal/cup ) = 345.6 = 345 cakes.
.
.
mark as brainnliest pls
Samuel needs to mail a package to his friend in New York. He places an address label with the length represented by
the function l(x) = 3x
3 + 2x
2 − 4x + 5 and the width represented by the function w(x) = x + 2.
Part A: Find the area of the label.
Part B: Which of the following statements are true about the area of the label? Select ALL that apply.
A(x) = l(x) + w(x)
The resulting polynomial for A(x) will be a 4th degree polynomial
l(x) =
A(x)
w(x)
The resulting polynomial for A(x) will have a leading coefficient of 6
A(x) = l(x) ∙ w(x)
The resulting polynomial for A(x) will have a constant term of 10
Answer:
The answers are
°the resulting polynomial for A(x) will be a 4th degree polynomial
°l(x)= a(x)/w(x)
°A(x)= l(x)·w(x)
I did the algebra CFU so trust me it's correct ;)
For a rotation r ( x ∘ , P ), which of the following is not true?
For a pre-image point P, m∠PAP′=x degrees.
For the a preimage point A, PA=PA′
The expression A=B r ( x ∘ , P ) A = Br ( x ∘ , P ) A = Br ( x ∘ , P ) A = Br ( x ∘ , P ) A = B means that when point A is rotated x° around point P its image is located at point B
The transformation rotates every point in the preimage x° about a point P
Answer:
For a pre-image point P, m∠PAP′=x degrees.
Step-by-step explanation:
i just took the test, this was the correct answer. :)
4(2q - 3) = 8q - 12 | one solution, no solution, or many soulutons
Answer:
0
Step-by-step explanation:
8q-12=8q-12
0=0
Amy is 1 year older than Ben. The sum of their ages is greater than 33 and less than 45 Find all possible ages of Ben
Answer:
17, 18, 19, 20, 21
Step-by-step explanation:
Solve for x
5x/6-2=8
Please help me quick!!
Jenny earns $30 a day working part time at a supermarket. She also earns $12 per hour for
babysitting. How much money does she earn from herTWO DIFFERENT JOBS? (Hint: Use two different
variables)
Answer: how many hours is she working
Step-by-step explanation:
pls help before 11:59
Answer:
78 Degrees
Step-by-step explanation:
Two supplementary angles:
4x + 2 + 3x + 3 = 180
Combine like terms:
7x + 5 = 180
Simplify
7x = 175
x = 25
(25)3 + 3 = 75 + 3 = 78
Angle DCB is 78 degrees
Answer:
78 Degrees
Step-by-step explanation:
Two supplementary angles: (GIven)
4x + 2 + 3x + 3 = 180
Combine like terms:
7x + 5 = 180
Simplify
7x = 175
x = 25
(25)3 + 3 = 75 + 3 = 78
So,
Angle DCB is 78 degrees.
I hope it will help you :)
Graph: y – 3=1/2(x+2)
If I have a Siberian Husky, then I have a dog." Identify the hypothesis
Answer:
the hypothesis is correct
Step-by-step explanation:
If multiple people answer i will mark the the first brainliest
Answer:
nice
Step-by-step explanation:
Which one is correct
Answer:
I believe it is systematic system
Step-by-step explanation:
Choose one of the formulas, i do not know which one to choose from.Explanation as well please.
At the end of week one, a stock had increased in value from $5.75 a share to $7.50 a share.Find the percent of increase at the end of week one to the nearest tenth of a percent.At the end of week two, the same stock had decreased in value from $7.50 to $5.75.Is the percent of decrease at the end of week two the same as the percent of increase at the end of week one?Justify your answer.
First, we will find the increase. I don't think it's any of the 3 formulas listed.
The formula I'll be using is Increase = Increased value - Original value
Let x be increase.
x = $7.50 - $5.75
x = $1.75
We then divide the increase by the original value.
Percent of increase = Increase/Original value
Let x be percent of increase.
x = $1.75/$5.75
x is approximately 0.30437
To turn a decimal into a percent, multiply it by 100.
0.30437 x 100 = 30.437
30.437 can be rounded to 30.4
The percent of increase at the end of week one is 30.4%
At the end of week two, the same stock had decreased in value from $7.50 to $5.75.We will first need to find the percent of decrease.
The formula will be Decrease = Original value - Decreased value
Let x be decrease
x = $7.50 - $5.75
x = $1.75
We then divide the decrease with the original value.
Percent of decrease = Decrease/Original Value
Let x be percent of decrease
x = $1.75/$5.75
x is approximately 0.30437
To turn a decimal into a percent, multiply it by 100.
0.30437 x 100 = 30.437
30.437 can be rounded to 30.4
The percent of decrease at the end of week one is 30.4%
Is the percent of decrease at the end of week two the same as the percent of increase at the end of week one? Justify your answer.No because the full percent of increase at the end of week one is 100% + 30.4% so that would be like a 130.4% increase while at the end of week two, it would be 130.4% - 30.4% and that would lead us back to 100%.
I need help with this
Answer: obviously 3 and 1
Step-by-step explanation: There are 4 answers in the number line :/
there are 2 answers in the answer choices
this is a multi answer question so it is
3 and 1
Help please before its taken:)
Answer:
A variable whose variation does not depend on that of another.
the registration fee for a used car is 0.8% of the sale price of 5,700. How much is the fee
Answer:
1,140
Step-by-step explanation:
subtract the percentage from the total
select all expressions equivalent
this is confusing and my stomach really hurts rn and im not in the mood to do geometry so can someone please help me
Answer:
second, third, and fourth
Help! I'm really confused! (I used Math because I got wrong answers in other subjects)
P.S The Answer isn't A or B :/
Answer: I would say the first one
Step-by-step explanation:
Answer:
Best Bet probably the last one
NEED HELP LOTS OF POINTS
Read the passage. Which statement best describes how Belle changes over the course of the story?
Riding a Bicycle
It was a bright Sunday morning when Belle woke up with the biggest smile on her face. She had been looking forward to this day for a long time. Her father was going to teach her to ride a bicycle. She dressed quickly and gulped down her breakfast.
After breakfast, Belle’s father showed her the different parts of a bike. Then he said he would hold onto the back of the bike while she peddled. But Belle’s excitement got the better of her. She said she wanted to try riding by herself. Her father let go. Belle quickly lost her balance and crashed to the ground. The fall dazed her. She grumpily agreed to let her father keep holding the bike while she rode.
Every once in a while, he would let go. The moment he did, Belle would lose her balance and topple over. Her father explained that this was perfectly normal. He said that all first-time riders fall. Even so, Belle’s mood darkened with each fall. After a while, she wanted to give up and return home.
Belle’s father tried to talk her out of quitting. He pointed toward some other children biking nearby. He showed her how happy they looked as they rode their bicycles. He told her she needed to keep trying. With a little more effort, she would soon enjoy riding just like the other children. His words gave Belle the determination to keep going.
After several more failed tries, Belle finally got the hang of it. She began gently peddling by herself, beaming with pride. She had finally done it! That night, she went to bed with a couple of bruises and cuts. But she had an even bigger smile on her face than she’d had in the morning. She would forever remember this day and the lesson she learned about never quitting.
A.
Belle starts showing more trust in her father as he teaches her how to ride a bike.
B.
Belle becomes less excited as the story goes on, until her excitement for bike riding disappears.
C.
Belle learns both how to ride a bike and how important it is not to give up.
D.
Belle gets hurt from falling off her bike, which scares her away from bike riding for good.
Which equation shows the ASSOCIATIVE property?
Question 3 options:
6 - 9 + 5 = 6 - (-9) + 5
(6 + (-9) + 5) = (6 + 5) + (-9)
-9 + (6 + 5) = -9 - 6 - 5
(6 + (-9)) + 5 = 6 + (-9 + 5)
Answer:
69............ I see 69
Step-by-step explanation:
NEED HELP ASAP
Functions can be defined using graphs, tables, and ordered pairs. What is the range of a function?
A.The range is all numbers.
B.The range is the output.
C.The range is the input.
D.The range is any x-value.
Answer:
B. the range is the output
Step-by-step explanation:
Find the missing side. Round to the nearest tenth.
Step-by-step explanation:
1. have info for adjacent side and hypotenuse
so use; cosine
cos32=x/19
x=cos32×19
=15.9
2. have info for opposite side and hypotenuse
so use; sine
sin63=16/x
x=16/sin63
=95.6
3. have info for opposite side and adjacent side
so use; tangent
tan26=17/x
x=17/tan26
=14.4
4. have info for opposite side and adjacent side
so use tangent
tan42= x/13
x=tan42×13
x=29.8
A packaging company makes package peanuts in two containers, rectangular prisms and cylinders. The rectangular prism has a length of 6 feet, a width of 3 feet, and a height of 5 feet. The cylinder of peanuts has a diameter of 7 feet and a height of 10 feet. How many rectangular prisms contain the same amount of peanuts as one cylinder container? Round your answer to the nearest tenth.
Answer:
4.3
Step-by-step explanation:
length = 6 feet
width = 3 feet
height = 5 feet
Volume of rectangular prism = length × width × height
= (6 × 3 × 5) feet
= 90 cubic feet
cylinder of peanuts has a diameter of 7 feet and a height of 10 feet
Volume of a cyclinder = πr^2h
π = 3.14
r = diameter / 2
= 7/2 = 3.5 feet
h =10 feet
Volume of a cyclinder = πr^2h
= 3.14 × (3.5)^3 × 10
= 3.14 × 12.25 × 10
= 384.65 cubic feet
How many rectangular prisms contain the same amount of peanuts as one cylinder container = volume of cylinder container / volume of rectangular prism container
= 384.65 / 90
= 4.274
To the nearest tenth = 4.3