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.)
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).
-4(n - 6) = 12
Solve the Equation.
solve the equation .......x/9 = 2/45 +x/10
What does e equal in e/2 < 3? Please help. I need a quick answer.
Which graph represents the solution set of the system of inequalities? {3y≥x−93x+y>−3
That is the correct graph that represents
{3y≥x−9 3x+y>−3
hope i helped =D
we have
[tex]3y\geq x-9[/tex] ----> inequality A
The solution of the inequality A is the shaded area above the solid red line
See the attached figure N [tex]1[/tex]
[tex]3x+y> -3[/tex] ----> inequality B
The solution of the inequality B is the shaded area above the dotted blue line
See the attached figure N [tex]2[/tex]
The solution of the system of inequalities is the shaded area between the solid red line and the dotted blue line
See the attached figure N [tex]3[/tex]
therefore
the answer in the attached figure
Write the slope intercept form of the equation of the line through the given points.
Explanation, please! Thank you!
Based on a sample survey, a company claims that 75% of their customers are satisfied with their products. Out of 1,176 customers, how many would you predi be satisfied?
how do you know that the decimal for 2/11 repeats without end
Glenn invested $22,000 at 7% interest compounded annually. How much interest will Glenn earn in 3 years?
$19,826.24
$20,837.25
$2340.23
$4950.95
An equivalent equation has been written by multiplying the second equation by 2. 4x – 9y = 7 4x – 9y = 7 2(–2x + 3y = 4) → –4x + 6y = 8
Answer: answer is (-19/2,-5)
Step-by-step explanation:
7,746.90 times x = 7,901.84 what's x
7,746.90 times x = 7,901.84
divide both sides by x
x = 7,901.84 / 7,746.90
x = 1.020000258
round to 1.02
what is 645 round to the nearest ten
Help me answer this? Thanks :)
Use the definition of the derivative to find the derivative of: f(t)=14−5tf(t)=14−5t.
f′(t)=
f′(t)=
Miss Martin has 7000 in her savings account. Alonso has 1/10 as much money in his account as Miss Martin. How much money does Alonso have in his account.
A pile of coins, consisting of quarters and half dollars, it worth $11.75. If there are 2 more quarters than half dollars, how many of each are there?
Let the number of half dollars be x,
number of quarters = x + 2
amount of half dollars = 0.5x
amount of quarters = 0.25(x + 2)
= 0.25x + 0.5
total amount = 0.5x + 0.25x + 0.5
= 0.75x + 0.5
0.75x + 0.5 = 11.75
0.75x = 11.25
x = 15
number of quarters = x + 2
= 15 + 2
= 17
There are 17 quarters and 15 half dollars.
The normal body temperature of a camel is 37°C. This temperature varies by up to 3°C throughout the day. Write and solve an absolute value inequality that represents the range of normal body temperatures (in degrees Celsius) of a camel throughout the day.
The range of normal body temperatures for a camel throughout the day is from 34°C to 40°C, inclusive.
To represent the range of normal body temperatures for a camel throughout the day, we'll use an absolute value inequality. Given that the normal body temperature is 37°C and it varies by up to 3°C, we can express this as:
|T - 37| ≤ 3
Where T represents the temperature of the camel throughout the day. This inequality ensures that the temperature remains within 3 degrees above or below the normal body temperature of 37°C.
To solve this inequality, we'll consider two cases:
1. When T - 37 is positive:
T - 37 ≤ 3
T ≤ 40
2. When T - 37 is negative:
-(T - 37) ≤ 3
-T + 37 ≤ 3
-T ≤ -34
T ≥ 34
Combining the two cases, the range of normal body temperatures for a camel throughout the day is 34°C to 40°C.
Daily output of marathon's garyville, lousiana, refinery is normally distributed with a mean of 232,000 barrels of crude oil per day with a standard deviation of 7,000 barrels. (a) what is the probability of producing at least 232,000 barrels?
jake rounded 18,752 to the nearest ten thousand which is his number
1 1/4mi = ft, can someone explain this to me
Expressions that simplify to the same expression are called ____
Answer:
They are called equivalent expressions since they are two expression that equal the same thing.
If this helped then please mark as brainliest.
You have diving lessons every fifth day and swimming lessons every third day. Today you have both lessons. In how many days will you have both lessons on the same day again?
20 points!!!
Solve this system of lineal equations.separate the x- and y- values with a comma
12x=54-6y
-17x=-62-6y
General house cleaning (sweeping the floor vacuuming laundry) can burn 470 calories every two hour determine the unit rate
Answer:
The unit rate is 235 calories per hour.
Step-by-step explanation:
General house cleaning (sweeping the floor vacuuming laundry) can burn 470 calories every two hour determine the unit rate.
Unit rate means we have to find the calories burned in 1 hour.
Hence, calories burned in 1 hour = [tex]\frac{470}{2}= 235[/tex]
Answer :
The unit rate is 235 calories per hour.
Find the rate of change of q with respect to p when p = 20 q 2 + 5 .
The rate of change of q with respect to p is the derivative of q with respect to p. However, the function seems to be incorrect as p is expressed as a function of q, not the other way around. The derivative of a typical function q = 20p^2 + 5 would be 40p.
Explanation:
The rate of change of q with respect to p is found by taking the derivative of the given function with respect to p. The function given is p = 20q^2 + 5. Unfortunately, we cannot find the derivative of p with respect to q. Instead, it seems more likely that we need to find the derivative of q with respect to p, which is typically what is intended when asked for the rate of change of one variable with respect to another. If the function was q = 20p^2 + 5, then, the derivative (rate of change) would be dq/dp = 40p. Although in your question, there may be an error as typically we would expect q to be expressed as a function of p.
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Between white pair of numbers is a product of 200 and 89 and 7
the sinclair family live 5.4 miles from southside middle school. how many feet away do they live?
The Sinclair family lives 28,512 feet away from Southside Middle School, calculated by multiplying 5.4 miles by the number of feet in one mile, which is 5,280 feet.
Explanation:The Sinclair family lives 5.4 miles from Southside Middle School. To convert this distance from miles to feet, we use the conversion factor that 1 mile is equal to 5,280 feet. To find the distance in feet, we multiply the number of miles by the number of feet in one mile:
5.4 miles imes 5,280 feet/mile = 28,512 feet.
Therefore, the Sinclair family lives 28,512 feet away from Southside Middle School.
On an average, the number of students that choose to study arts subjects at greyin tide university is 17 each year.what is the probability that exactly 13 students will take up arts in the coming year?
The probability that exactly 13 students will take up arts in the coming year is; 76.47%
What is the probability?We are given;
Number of students that study art each year = 17
Now, we want to find the probability that 13 students will take up arts in the following year. This is;
P(13 will take art the next year) = 13/17 * 100%
P(13 will take art the next year) = 76.47%
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Find and sketch the domain of the function. f(x, y, z) = 4 − x2 − y2 − z2
The domain of the function [tex]\(f(x, y, z) = 4 - x^2 - y^2 - z^2\)[/tex] is the set of all real numbers for [tex]\(x\)[/tex], [tex]\(y\),[/tex] and [tex]\(z\)[/tex].
To find and sketch the domain of the function [tex]\(f(x, y, z) = 4 - x^2 - y^2 - z^2\)[/tex], we need to determine the set of values for [tex]\(x\)[/tex], [tex]\(y\)[/tex], and [tex]\(z\)[/tex] for which the function is defined, i.e., the values that do not lead to any mathematical inconsistencies.
In this case, the function involves three variables, and it is defined for all real values of [tex]\(x\)[/tex], [tex]\(y\)[/tex], and [tex]\(z\)[/tex]. There are no restrictions on the domain because the square of a real number is always non-negative. Thus, [tex]\(x^2\)[/tex], [tex]\(y^2\)[/tex], and [tex]\(z^2\)[/tex] are non-negative for any real \(x\), \(y\), and \(z\).
In interval notation, we can express this as:
[tex]\[\text{Domain} = (-\infty, \infty) \times (-\infty, \infty) \times (-\infty, \infty)\][/tex]
This domain represents the entire three-dimensional space, and the function is defined for all points within this space. As such, sketching the domain involves visualizing the entire 3D space, which is an unbounded region without any specific shape or boundary.
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Alex was hired to unpack 576 items of glass wear, at five cents per piece unpacked. For every item broken in the process, however, Alex had to pay $1.98. At the end of the job, Alex received $22.71. How many items did Alex break.
Alex broke 3 glasses during the unpacking of the glasses.
As mentioned in the question, Alex was hired to unpack 576 items of glass wear, at five cents per piece unpacked. For every item broken in the process, however, Alex had to pay $1.98. At the end of the job, Alex received $22.71.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
The total amount earned for 576 glasses is given as,
= 576 × 0.05
= $28.80.
Amount earned = $22.71
Amount paid by Alex for the broken glass = $28.80 - $22.71 = 6.09
Total glass broked = 6.09 / 1.98 ≈ 3
Thus, Alex broke 3 glasses during the unpacking of the glasses.
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