Mathematics College

At what points does the curve r(t) = ti + (4t â t2)k intersect the paraboloid z = x2 + y2? (if an answer does not exist, enter dne.)

Answers

Answer 1

Final answer:

To find the intersection points of the curve r(t) with the paraboloid z = x^2 + y^2, we substituted the parametric forms into the equation and solved for t, yielding the points (0, 0, 0) and (2, 0, 4).

Explanation:

The student is asking about the intersection points of a curve r(t) with a paraboloid defined by z = x2 + y2. To find these points, we must substitute the parametric forms of x, y, and z from the curve into the equation of the paraboloid and solve for t.

Given the curve r(t) = ti + (4t - t2)k, we can identify the components of the curve as x(t) = t and z(t) = 4t - t2. The y-component is missing, which implies that y = 0. Now, substituting x(t) into the paraboloid equation, we get:

z = x2 + y2

4t - t2 = t2 + 02

By solving for t, we can determine the intersection points. Simplifying the equation, we get:

0 = 2t2 - 4t

Which gives us the solutions t = 0 and t = 2. Substituting these back into r(t) gives the intersection points (0, 0, 0) and (2, 0, 4).

Related Questions

What are the maximum data rates of 802.11 legacy, 802.11a, 802.11b, and 802.11g?

Answers

802.11 legacy = 2 Mbps
802.11a = 54 Mbps
802.11b = 11 Mbps
802.11g = 54 Mbps
Final answer:

The 802.11 standards designate maximum data rates: 802.11 legacy offers 2 Mbps, 802.11a and 802.11g both offer 54 Mbps, and 802.11b offers 11 Mbps. These maximum rates depend on ideal conditions and can be lower in real-world usage.

Explanation:

The 802.11 wireless standards determine the maximum achievable data rates between a wireless device and a wireless access point. Here are the maximum data rates for the 802.11 legacy, 802.11a, 802.11b, and 802.11g:

802.11 legacy: The theoretical maximum speed is 2 Mbps.802.11a: It has a maximum data rate of 54 Mbps.802.11b: This standard allows for a maximum data rate of 11 Mbps.802.11g: This offers a maximum data rate of 54 Mbps, the same as 802.11a, but it is more widely compatible with other devices as it operates on the 2.4 GHz band.

It's important to note that these are the maximum possible data rates, under ideal conditions. In real-world usage, the actual data rate can be lower due to factors such as distance from the access point, interference, and the number of devices connected to the network.


Learn more about 802.11 wireless standards here:

https://brainly.com/question/32217816

#SPJ12

The length of a rectangle is five times its width. If the area of the rectangle is 125 m2 , find its perimeter.

Answers

It is 125 divided by 5

L = length 
W = width

L = 5W     ---- Length is 5 times the width
A = LW= 125

first lets find L and W 

A = LW = 125-----LW is the formula for area of a rectangle
 we know L = 5W 
we'll plug in 5W for L
A = (5W)W = 125
A = 5W^2 = 125
W^2 = 125/5
W^2 = 25
Take the squareroot 
W = 5

L = 5W
L = 5 * 5
L = 25

P = Perimeter = 2(L + w)  ----- formula for perimeter of a rectangle
P = 2(25 + 5)
P = 60 

write an addition problem that has sum of 8/5

Answers

3/5 + 5/5 = 8/5

4/5 + 4/5 = 8/5

7/5 + 1/5 = 8/5

8/10 + 8/10 = 8/5

These are just a few examples

hope this helps

rewrite 19/30 and 13/20 so that they have a common denominator then Then, use
<
,
=
, or
>

Answers

Must determine the LCD.  Think:  what is the smallest (least) number divisible by both 30 and 20?  You could, of course, just multiply 30 and 20, obtaining 600, but that would not be the LCD.

Note that 30 and 20 share the common factor 10.  Multiplying 3 and 2 together produces 6.  The LCD is 10*6 = 60.  Note that both 30 and 20 divide into 60 with no remainder.

Then  19/30  = 2(19) / 2[30]  = 38/60, and 

13/20 = 3(13) / 3[20]  = 39/60.

Which is larger, 38/60 or 39/60?

Write the relationship between these 2 numbers using the appropriate inequality operator.

Answer: [tex]\dfrac{38}{60}<\dfrac{39}{60}[/tex]

Step-by-step explanation:

The given fractions : [tex]\dfrac{19}{30}\text{ and }\dfrac{13}{20}[/tex]

The denominators of the above fraction : [tex]30, 20[/tex]

Least common multiple (LCM) of (30,20)=[tex]3\times2\times5\times2=60[/tex]

Multiply 2 to the numerator and denominator of  [tex]\dfrac{19}{30}[/tex] and 3 to the numerator and denominator of [tex]\dfrac{13}{20}[/tex], we get

[tex]\dfrac{19\times2}{30\times2}=\dfrac{38}{60}[/tex]

[tex]\dfrac{13\times3}{20\times}=\dfrac{39}{60}[/tex]

Clearly , [tex]\dfrac{38}{60}<\dfrac{39}{60}[/tex]

What best describes the greatest height a ball will bounce off the ground after being dropped from a height of 50 centimeters? Less than 50 centimeters, as the ball transforms some of its thermal energy into sound energy Less than 50 centimeters, as the ball transforms some of its potential energy into sound energy Greater than 50 centimeters, as the ball transforms some of its thermal energy into potential energy Greater than 50 centimeters, as the ball transforms some of its potential energy into thermal energy

Answers

Answer:
Less than 50 centimeters , as the ball transforms some of its potential energy into ound energy

Explanation:
When a ball is dropped from a height of 50 cm, several factors reduce the initial potential energy (PE) of the ball.
a. Between the time the ball is dropped and when it strikes the ground, aerodynamic frictional forces consume some of the PE.
b.  When the ball hits the ground, the remaining PE is converted into kinetic energy (KE) as it strikes the surface.
c. The KE is dissipated by energy required to deform the ball, some of the KE is transformed into sound energy, and some of the KE is lost by frictional forces that generate heat (thermal energy).
d. The remaining energy is stored in the ball, and it causes the ball to rebound as if it was a wound spring with stored energy. The coefficient of restitution defines how much of the PE is stored for the rebound.

Answer:

B) Less than 50 centimeters , as the ball transforms some of its potential energy into sound energy

Explain why the hypotenuses of the triangles below have the same slope.

Answers

They have the same slope because they are similar. The smaller one is 1/2 the size of the bigger one and they have a ratio of 1:2 which makes them similar. 
The hypotenuses are the same because they fall on the same line.

I mean obviously u.s prices are cheaper but is it really better? I need help

Answers

no because quality over quantity as you wouldn't want a hat for $14 that could easily break when if you paid a dollar more it would be more long lasting

An elevator descends 1500 feet in 60 seconds. Find the change in height per second.

Answers

1500ft/60s = 25seconds

The answers is height=25

How can you use transformations to graph this function?

y=3x[tex] 7^{-x} [/tex]+2

Answers

[tex]\bf \qquad \qquad \qquad \qquad \textit{function transformations} \\ \quad \\\\ % left side templates \begin{array}{llll} f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}} \\ \quad \\ y=&{{ A}}({{ B}}x+{{ C}})+{{ D}} \\ \quad \\ f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}} \\ \quad \\ f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}} \\ \quad \\ f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}} \end{array}\\\\ --------------------[/tex]

[tex]\bf \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]

[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{{{ B}}}[/tex]

with that template in mind, let's check

[tex]\bf y=\stackrel{A}{3}(7^{\stackrel{B}{-1}x})\stackrel{D}{+2}[/tex]    <---- so the parent function will then be y = 7⁻ˣ

A = 3    it shrinks, in relation the y-axis, by a factor of 3 times, so is narrower.

B=-1     well, it flips it sideways, reflection over the y-axis.

D= +2  well, that's just a vertical shift of 2 units.

Sketch the graph of Y=7^X.

Reflect the graph across the y-axis to show the function y=7^-x.

Stretch the graph vertically by a factor of 3 to show the function y=3 x 7^-x.

Shift the graph up 2 units to show the function y= 3 x 7^-x +2

John drives to work each morning and the trip takes an average of µ = 38 minutes. the distribution of driving times is approximately normal with a standard deviation of σ = 5 minutes. for a randomly selected morning, what is the probability that john's drive to work will take between 36 and 40 minutes?​

Answers

The Answer to this is 0.2743

whole numbers includes zero but natural numbers do not

Answers

That is most certainly true!

I'm currently learning about this too. 

I hope this helps you! :)

This is a true statement!

The set of counting numbers {1, 2, 3, 4, 5, ...} is called the set of natural numbers. The natural numbers begin at 1 and go on indefinitely.

When we include 0 in the natural numbers, we then have a new set of numbers called the whole numbers. All the natural numbers are contained within the set of whole numbers.

Which property is demonstrated below?

17/3 * 3/17=1

associative property of multiplication
inverse property of multiplication
identity property of multiplication
commutative property of multiplication

Answers

we know that

The Inverse Property of Multiplication states that the product of any number and its multiplicative inverse is one

so

[tex]\frac{a}{b}* \frac{b}{a}=1[/tex]

in this problem we have

[tex]\frac{a}{b}=\frac{17}{3}[/tex]

[tex]\frac{b}{a}=\frac{3}{17}[/tex] -----> multiplicative inverse of [tex]\frac{a}{b}[/tex]

substitute

[tex]\frac{17}{3}*\frac{3}{17}=1[/tex]

therefore

the answer is

inverse property of multiplication


Answer:

inverse property of multiplication or b on edg 2021

Step-by-step explanation:

How many grains of sand in a 10kg bag if one grain weighs 10 to the negative third gram

Answers

If one grain of sand weighs 10^-3 gram, it is one thousandths of a gram. A kilogram (kg), is 1000 times the mass of a gram. So, you take the 10 kg and multiply by a conversion factor of 1 kg equaling 1000g. This results in you having 10000 grams. Multiply that by another thousand, seeing as each grain of sand weighs one thousandth of a gram. This should result in you getting 10000000, or 1.0 x 10^7 grains of sand.

Final answer:

To determine the number of grains of sand in a 10kg bag with each grain weighing 10 to the negative third gram, convert the weight to grams and then divide by the weight of one grain. The answer is 10 million grains.

Explanation:

Grains of sand in a 10kg bag can be calculated by converting the weight to grams first: 10kg = 10,000g. Then, since each grain weighs 10-3g, we divide the total weight by the weight of one grain: 10,000g / 10-3g = 10,000,000 grains. So, there are 10 million grains of sand in a 10kg bag.

A quotient of 8.4×10^9 and a number n results in 5.6×10^27 what is the value of n

Answers

Translated to notation, this question is asking you to solve for n when:

[tex] \frac{8.4\times10^9}{n}=5.6\times10^{27} [/tex]

A good first step would be to multiply both sides by n, cancelling out the n in the denominator on the left side and leaving you with:

[tex]8.4\times10^9=(5.6\times10^{27})n[/tex]

And of course, to get n by itself from here, you simply divide both sides by [tex]5.6\times10^{27}[/tex]:

[tex]n= \frac{8.4\times10^9}{5.6\times10^{27}} [/tex]

What are the amplitude, period, and midline of f(x) = −4 cos(2x − π) + 3?

Answers

[tex]\bf \qquad \qquad \qquad \qquad \textit{function transformations} \\ \quad \\ % function transformations for trigonometric functions \begin{array}{rllll} % left side templates f(x)=&{{ A}}sin({{ B}}x+{{ C}})+{{ D}} \\\\ f(x)=&{{ A}}cos({{ B}}x+{{ C}})+{{ D}}\\\\ f(x)=&{{ A}}tan({{ B}}x+{{ C}})+{{ D}} \end{array} \\\\ -------------------\\\\[/tex]

[tex]\bf \bullet \textit{ stretches or shrinks}\\ \left. \qquad \right. \textit{horizontally by amplitude } |{{ A}}|\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]

[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}[/tex]

[tex]\bf \bullet \textit{function period or frequency}\\ \left. \qquad \right. \frac{2\pi }{{{ B}}}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\ \left. \qquad \right. \frac{\pi }{{{ B}}}\ for\ tan(\theta),\ cot(\theta)[/tex]

with that template in mind, let's check

[tex]\bf f(x)=-\stackrel{A}{4}(\stackrel{B}{2}x\stackrel{C}{-\pi } )\stackrel{D}{+3}\\\\ -------------------------------\\\\ Amplitude\implies 4\\\\ Period\implies \cfrac{2\pi }{B}\implies \cfrac{2\pi }{2}\implies \pi [/tex]

now, the function is just the parent cos(x), shrunk some, -4, and shifted about, now D = +3, that means it has a vertical shift of 3 units up.

the parent function cos(x), has a midline of y = 0, now, if we shift it upwards by 3 units, the new midline will then be y = 3.

write the equation for a line that intersects points (1,3) and (2,5)

Answers

y=2x+1 is your answer
y=2x+1 is the correct answer

6 people share 3/5 pounds of peanuts equally what fraction of a pound of peanuts does each person receive

Answers

Hello! To solve this problem, we have to do 3/5 / 6, because you are dividing 3/5 of a bag among six people. In other words, it would be 3/5 * 1/6. You keep the first fraction, change the division sign into a multiplication one, and flip 6 into 1/6. 3/5 * 1/6 = 3/30 or 1/10 in simplest form. Each person receives 1/10 of a pound of peanuts.

which is greater - 0.2 ml. or 0.15 ml.

Answers

0.15 ml is greater than -0.2 ml by 0.17 ml

hope this helps
.15 because it is positive 

A pyramid-shaped building is 340 ft tall and has a square base with sides of 567 ft. The sides of the building are made from reflective glass. What is the surface area of the reflective glass?

Answers

check the picture below.

now, notice, the reflective glass part of the building, is just the triangular faces, it has four of those.

now, notice that each triangular face has a base of 567 and a height or altitude of 442.69.

so the surface area with the reflective glass will be, the area of those four triangles, get the area of each and add them up.

Valerie earns $24 per hour. Which expression can be used to show how much money she earns in 7 hours?

A. ( 7 + 20 ) + ( 7 + 4 )

B. ( 7 x 20 ) + ( 7 x 4 )

C. ( 7 + 20 ) x ( 7 + 4 )

D. ( 7 x 20 ) x ( 7 x 4 )

Who ever answers the best gets brainliest!

Answers

The answer is B) (7x20) + (7x4)
The answer is B (7•20)•(7+4)

Find the LCM of 8 and 12.

Answers

✨24✨

the least common multiple is 24, the greatest common diviser is 4
You need to write out the 8 and the 12 times table and you then find the lowest number that is the same:

8:
8,16,24,32

12:
12,24,36,48

As you can see the lowest number that is the same for both of them is 24, thus the lowest common multiple is 24.

Hope this helps! :)

At a rate of 4%, you paid $144.00 in interest over a two-year period. What was the original amount of your loan?

A. $2,000.00
B. $2,550.00
C. $2,250.00
D. $1,800.00

Answers

Simple interest - not compounded you got $ 1,800 
Formula

I= P x r x t
where:
I= Interest 
P is the principal amount, $1800.00.
r is the interest rate, 4% per year, or in decimal form, 4/100=0.04.
t is the time involved, 2 year(s) time periods.

So, t is 2 year time periods.
To find the simple interest, we multiply 1800 × 0.04 × 2 to get that: $144.00
The formula that will be used here is: I = PRT,
Where I = interest = $144.00
P = principal = ?
R = rate = 4% = 0.04
T = time = 2 years
I = PRT
P = I / RT
P = 144 / [0.04 * 2] = 144 / 0.08
P = 1800.
Therefore, the principal is $1,800.00.
The correct answer is D.

A car dealer recently sold five cars for the following profits 10, 126, 9,999, 12,398, 12,007, and 4,567. What was the mean for the profits of the sales

Answers

The answer is 9,819.4 Hope this helped :)
If you want to calculate the mean of several products, there is an easy way to do it - just add all of those numbers and divide the product by the number of items.
So, here is how to do it:
10,126 + 9,999 + 12,398 + 12,007 + 4,567 = 49,097
Now divide that number by 5 (the number of numbers):
49,097 / 5 = 9,819.4

The correct answer is 9,819.4

Six hikers shared 4 1/2 lbs of trail mix. How much trail mix did each hiker receive?

Answers

6 hikers = 4.5 lbs of trail mix

4.5 divided by 6= .75 lbs each hiker.
Divide 4 1/2 lb by 6 to determine the share given to each of the 6 hikers:
                                  
4 1/2 divided by 6 is the same as 9/2 divided by 6, or   

  9      1      9
--- * ---- = -------  = 3/4 lb.     (answer)
 2      6        12

Check by mult. 3/4   lb by 6:     18/4 = 9/2 = 4 1/2 lb.  This is correct.

Which number sentence correctly solves this problem?

Mount Everest is 8,848 meters high. K2 Mountain is 8,611 meters high. How much higher is Mt. Everest than K2 Mountain?



A.
8,848 + 8,611 = 17,459


B.


8,848 – 8,611 = 1,237


C.


8,848 – 8,611 = 237


D.
8,848 + 8,611 = 16,459

Answers

its c because when you subtract the two mountains you will get 237

you have 5 quarts of paint. It takes 5/8 quarts to paint each chair you are asked to paint. How many chairs can you paint?

Answers

You can pain 8 chairs; (5/8*8=5)

Services provided by public-service companies, such as water, electricity, and gas, are all known as

Answers

Public Utility or Public Services

Answer:


Step-by-step explanation:

A. UTILITIES

Rewrite the expression 2(1+2)-9 using the distributive property.

Answers

2(1+2) - 9 =

2 + 4 - 9 =

6 - 9 =

-3

this is using the distributive property and not using the 'correct' way

hope this helps

A package of 10 cans of soup costs $14. An individual can costs $2. You need at least 25 cans. Find the price of each combination of items.You decide to buy 3 packages of 10 cans. How much do you pay for each can?

Answers

$14×3=$42 price per package of 10
25×$2=$50 individual can cost
30×$2=$60, cost of cans individually bought
so the third problem would be the correct answer because it asks how much for each can

Answer:

$1.4

Step-by-step explanation:

Given, Price of a package of 10 cans = $14

and, Price of an individual can = $2

Now, if I have to purchase at least 25 cans their are two possible ways:

Purchasing 2 packages of the can and then purchase rest individual cans. Thus, if I have to purchase 25 cans it costs: 14 × 2 + 5 × 2 = $38.Purchasing 3 packages of cans. It will cost me: 3 × 14 = $42. But it will give me an extra 5 cans.

Further, if I decided to buy 3 packages of 10 cans it will cost me $42 and I will pay $1.4 for each can.

At each turn, a gambler bets a certain amount, wins it with probability p and loses it with probability q = 1−p. when he begins playing, he has $k for some integer k > 0 and his goal is to reach $n for some integer n > k, after which he stops playing. he also stops playing if he loses all his money. the gambler has the option of betting $1 at each turn and the option of betting $0.5 at each turn. show that betting $0.5 is a better option if p > 1/2 and that betting $1 is a better option if p < 1/2.

Answers

Here two cases of the probability,
p > 1/2 or p <1/2

Here, q = 1 - p
So, When p > 1/2 the q < 1/2 &
When p < 1/2 the q > 1/2

So, in first case (p > 1/2 the q < 1/2) Winning chances is more compare to Loosing, So put the Bet maximum and is of $1

Another case (p < 1/2 the q > 1/2) Winning chances is less compare to Loosing, So put the Bet minimum and is of $0.5
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