A possible vector function that represents the curve of intersection of the two surfaces is r(t) = (5 cos(t), 5 sin(t), 5 cos(t) sin(t))
The cylinder x^2 + y^2 = 25 represents the set of points in 3D space where the distance from the origin to the point (x, y, z) is equal to 5. The surface z = xy represents the set of points in 3D space where the height of the point (x, y, z) is equal to its x-y coordinate.
The curve of intersection of the two surfaces is given by the set of points in 3D space that are simultaneously on the cylinder and on the surface z = xy. This means that for any point on the curve of intersection, the distance from the origin to the point must be equal to 5, and the height of the point must be equal to its x-y coordinate.
We can find a vector function that represents the curve of intersection by parameterising the points on the curve in terms of a scalar parameter t. For example, a possible parameterization of the curve of intersection is:
r(t) = (5 cos(t), 5 sin(t), 5 cos(t) sin(t))
where t is a scalar parameter that ranges over all values between 0 and 2π. The values of x, y, and z are given by 5 cos(t), 5 sin(t), and 5 cos(t) sin(t), respectively, and represent a point on the curve of intersection for each value of t.
To learn more about the curve of intersection click here:
brainly.com/question/29987415
#SPJ4
Find the distance between the following numbers on the real number line a=12, b=3
Answer: 9
Step-by-step explanation:
12-3=9 or count up from 3 until you get too 12
The length of a rectangle is 5 cm, and the width is 4 cm. If both the length and the width are increased by equal amounts, the are of the rectangle is increased by 70 cm2. Find the length and width of the longer rectangle.
Answer:
Length = 10cm, Width = 9 cm
Step-by-step explanation:
Let's call the amount that both the length and width are increased by "x". So, the new length is 5 + x and the new width is 4 + x.
The original area of the rectangle was 5 * 4 = 20 cm2.
The new area of the rectangle after the increase is (5 + x) * (4 + x) = 20 + 70 + 2x^2.
Expanding the right-hand side, we have 20 + 70 + 2x^2 = 90 + 2x^2.
Equating the two areas, we get:
20 + 70 + 2x^2 = 90 + 2x^2
Subtracting 2x^2 from both sides:
20 + 70 = 90
Subtracting 20 from both sides:
70 = 70
So x^2 = 50 / 2 = 25.
Taking the square root of both sides, we get:
x = 5
So the length of the longer rectangle is 5 + x = 5 + 5 = 10 cm, and the width is 4 + x = 4 + 5 = 9 cm.
Graph all vertical and horizontal asymptotes of the Rational function.
f(x)= -7/x^2+4
The function has no vertical asymptotes and horizontal asymptotes are at y = 0.
What are Asymptotes?A straight line that continuously approaches a certain curve without ever meeting it is an asymptote. In other words, an asymptote is a line that a curve travels toward as it approaches infinity.
A straight line that serves as the asymptote of the curve y = f(x) or, in its implicit form, f(x,y) = 0, where the distance between the two lends to zero as the points on the curve approach infinity.
Given function,
f(x) = -7/(x² + 4)
in the given function the degree of the denominator is more than the numerator so The horizontal asymptote lies at y = 0 because, as we can see, the degree of the numerator is less than the denominator.
and there will be no vertical asymptote.
The graph of the equation is attached.
Hence horizontal asymptote lies at y = 0 and ni vertical asymptote.
Learn more about asymptote;
https://brainly.com/question/4084552
#SPJ1
Add −13 1/4 + 4 3/4 . Write your answer as a mixed number in simplest form.
Answer:
- 8.5
Step-by-step explanation:
Machine Trades A machine tech must bolt together two steel plates that are 7/8in. thick and 1 1/4in.thick. If the bolt must be at least 1/2in. longer than the combined thickness of the plates, how long a bolt is needed?
The total length of the bolt should be 21/8 inches.
What are arithmetic operations?The study and application of numbers in all other fields of mathematics are covered in the area of mathematics known as arithmetic operations. Addition, subtraction, multiplication, and division are included in the basic operations.
Given the thickness of plate 1 = 7/8 inches
the thickness of plate 2 = [tex]1\frac{1}{4}[/tex] inches = 5/8 inches
total thickness of both plates = 7/8 + 5/4
5/4 is equaivalent to (5*2)/(4*2) = 10/8
the total thickness of both plates = 7/8 + 10/8
the total thickness of both plates = 17/8 inches
and the bolt must be at least 1/2 inch longer
total length of bolt = 17/8 + 1/2
convert 1/2 to the same denominator as 17/8
1/2 = (1*4)/(2*4) = 4/8
total length of bolt = 17/8 + 4/8
the total length of the bolt = 21/8 inches
Hence the bolt should be 21/8 inches longer.
Learn more about arithmetic operations;
https://brainly.com/question/25834626
#SPJ1
Linear equation that passes through the points of (1,4) and (6,-1)
Answer:
y = -x+5
Step-by-step explanation:
Use point slope formula to find the equation of the line
First find the slope: (-1-4)/(6-1) = -5/5, slope = -1
Then, use the formula: y - y1 = m(x - x1)
y - 4 = -1(x - 1)
y - 4 = -x+1
y = -x + 5
The average groundhog weighs about 8 pounds and eats 1/3 of their weigh each day in apples, beans, clover, bark, and flowers. If a den has five groundhogs living in it, how many pounds of vegetation will the group eat in the month of February if it isn't a leap year?
Answer: Vegetable consumption per month is 17.33 pounds and fruits consumption per month is 10.47 pounds.
Step-by-step explanation:
Frank's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Frank $4.20 per pound, and type B coffee costs $5.60 per pound. This month's blend used four times as many pounds of type B coffee as type A, for a total cost of $984.20. How many pounds of type A coffee were used?
The quantity of type A coffee will be 37 pounds.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Frank's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Frank $4.20 per pound, and type B coffee costs $5.60 per pound.
The quantity of Type A coffee will be calculated as:-
B = 4A
4.20A + 5.6B = 984.20
4.20A + 4 x 5.6 x A = 984.20
4.20A + 22.4A = 984.22
26.6A = 984.22
A = 37
Therefore, the amount of each type of 37 pounds will equal one coffee.
To know more about an expression follow
https://brainly.com/question/29395040
#SPJ1
Similar polygons
State if polygons are similar
Answer:
The polygons are similar.
Step-by-step explanation:
The polygons are similar due to the SAS Similarity Theorem.
Hope this helped! :)
helpppp
A map of a farm is shown in a coordinate plane in which the coordinates are measured in yards. The map shows the barn at (-1, 2). A well is dug at (-1, y). What are two values of y such that the barn is 50 yards from the well?
The two values of y such that the barn is 50 yards from the well
51 OR -49How to find length of lineThe length of line in an ordered pair is calculated using the formula
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
where
d = distance between the points
x₂ and x₁ = points in x coordinates
y₂ and y₁ = points in y coordinates
distance between points (-1, 1) and (-1,, y) is calculated to be 50 yards and hence we solve for y
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
50 =√{(-1 - -1)² + (1 - y)²}
50 =√{ (1 - y)²}
2500 = (1 - y) (1 - y)
2500 = 1 - 2y + y²
y² - 2y - 2499 = 0
solving the quadratic equation gives
y = 51 OR -49
Learn more about length of line segment here:
https://brainly.com/question/29706244
#SPJ1
Which of the following is NOT an impact of American consumerism?
A. Exorbitant personal debts
B. Lack of unemployment and homelessness
C. Cash generators for several nations
D. Stress
The terms which is not an impact of American consumerism is -
Option C: Cash generators for several nations.
What is consumerism?
The tendency to continuously consume is known as consumerism. It is the need to acquire more possessions and establish one's identity via them. Consumer spending and GDP growth are seen as benefits of consumerism by economists.
The American consumerism includes -
Debts : Due to introduction of credit cards the consumers have ore and more debt on their credit cards whilst they spend on materialistic goods.
Lack of Unemployment : Economists point out that a decline in product demand causes an economic downturn or even depression, which is accompanied by high unemployment.
Stress: Due to debt, recession and unemployment people are constantly under stress for surviving.
Since, consumerism helps in GDP growth of a country it does not help generate cash for other nations.
Therefore, " Cash generators for several nations" is not an impact.
To learn more about consumerism the given link
https://brainly.com/question/9933702
#SPJ1
yin starts to use the standard algorithm to solve 5,819 x 8. her work is shown below PLEASE HELP ME
5
,
8
y
1
7
9
× 8
52
The expression when evaluated is 46552
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
5,819 x 8.
Using the standard algorithm, we have:
5,819 x 8 = (5800 + 19) * 8
Open the brackets
So, we have the following representation
5,819 x 8 = 5800* 8 + 19 * 8
Evaluate
5,819 x 8 = 46400 + 152
So, we have
5,819 x 8 = 46552
Read more abut expression at
https://brainly.com/question/15775046
#SPJ1
A horse with no name
Father and son make a 64km journey through the desert starting at 4 pm.
They reach their location at 9:24 the next morning.
What is the relative speed between two moving objects?The relative speed is the net speed of two different objects with respect to each other.
If two objects move in the same direction we take the difference between their speeds.
If two objects move in the opposite direction we take the sum of their speeds.
We can utilize the following parameters in our calculation based on the question,
Time = 4 pm
Distance = 64 km
Calculate how long it took the father to ride his horse and the son to walk the first 32 miles.
Time = Distance / (Difference between rates of father and son)
Time = 32 km / (8 km/h - 3 km/h)
Time = 32 km / 5 km/h
Time = 6.4 hours
Determine how long it will take the father to walk the final 32 miles and the son to ride the horse.
Time = Distance / (Difference in Speed)
Time = 32 km / (8 km/h - 4 km/h)
Time = 32 km / 4 km/h
Time = 8 hours
Therefore,
Total time = 6.4 hours + 8 hours + 3 hours break + 4 pm is 9:24 am the next day.
Learn more about relative speeds here :
https://brainly.com/question/11476119
#SPJ1
what is the value of x!!!!
Answer:100 or it just means 10 times
Step-by-step explanation: you need to learn the angles when the number are put on each side and then your answer will come!
help
The perimeter of a rectangle is 430 meters. Express the area A as a function of the length L, and state the domain of this function
A(L) = ? m²
Answer:
A(L) = - L² + 215L
Domain
0 < L < 215
or
(0, 215) in interval notation
Step-by-step explanation:
Let L represent the length and W the width
Perimeter of a rectangle = 2(L+W) and is given as 430 meters
Therefore 2(L + W) = 430
L + W = 430/2
L + W = 215
W = 215-L
The area A is given by L x W
Substituting for W in terms of L this becomes
A = L x(215 - L)
A = 215L - L²
which can be expressed as a function of in the form
A(L) = 215L - L² or in standard form(highest degree first)
A(L) = - L² + 215L
The domain of this function are the values of L which result in a defined , real value for A
Without restrictions, the domain for L is -∞ < L < ∞. However real world facts coming into play
1. Area cannot be zero
So A(L) > 0 (upper bound on area)
-L² + 215L > 0
-L² > - 215L Move 215L to right side
L² < 215L (dividing by -1 changes signs of variables and also inequality)
L < 215 (divide by L both sides)
2. Length cannot be negative
So lower bound on L is L > 0
Together the domain is
0 < L < 215
or
(0, 215) in interval notation
Classify whether it's Discreet or Continuous 4.1.1 I am fifty years old 4.1.2 I can drink 400,5ml of juice in a minute 4.1.3 I have 2 brothers and 1 sister
4.1.1 and 4.1.3 are discrete variables and 4.1.2 is a continuous variable.
What are discrete and continuous variables?
Discrete variables are those that have distinct, countable values. A continuous variable can be assigned to any value that falls inside a range, which has an infinite number of possible values.
4.1.1 "I am fifty years old"
It is a discrete variable because age is represented in whole numbers.
4.1.2 "I can drink 400.5 ml of juice in a minute"
It is a continuous variable because the amount of juice is consumed every minute so, we can obtain values even in fraction.
4.1.3 "I have 2 brothers and 1 sister"
It is a discrete variable because the given value is countable.
Hence, 4.1.1 and 4.1.3 are discrete variables and 4.1.2 is a continuous variable.
Learn more about discrete and continuous variable from the given link
https://brainly.com/question/18763328
#SPJ1
A clothing store has each customer roll a 12-sided die with faces numbered 1−12 to win a free T-shirt. Customers who roll a 9 win. As a percent to the nearest tenth, what is the probability that a customer wins a prize?
it’s 100 points if you answer so please do it correctly so i’ll mark you brainliest
Answer: The probability that a customer wins a prize 8.3%
Step-by-step explanation:
First off, the dice has twelve sides and only of the sides, 9, will allow a customer to win.
this means that there is a 1/12 chance that the customer will win a prize.
We can rewrite this into a decimal: 0.0833
and then to a percentage rounded to the nearest tenth: 8.3%
The probability that a customer wins a prize is 8.3% to the nearest tenth.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Given that,
A clothing store has each customer roll a 12-sided die with faces numbered 1−12 to win a free T-shirt.
Customers who roll a 9 win.
Total possible outcomes = 12
Number of outcomes which results in a win = 1
Probability that a customer wins = 1/12
= 0.08333
= 8.3%
Hence the required probability is 8.3%.
Learn more about Probability here :
https://brainly.com/question/8311361
#SPJ2
Find the value of X.
Answer: E
Step-by-step explanation: Since this is a special right triangle(45,45,90), you know that the ratios of the leg to the hypotenuse is 1:1:sqrt2. 15 sort root two hold true to that rule and is the right answer.
uploaded
33D47FCE-DF4B-485B-8648-FC618
B9E5C44.jpeg
The m∠1 and m∠2 which are linear pairs of angles are 72° and 108°.
What is a transversal?We know when a transversal intersects two parallel lines at two distinct points,
Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.
We know that the sum of linear pair of angles is equal to 180°.
therefore, From the given information, (x + 36)° + 3x° = 180°.
4x + 36° = 180°.
4x = 144°.
x = 36°.
So, m∠1 = 72° and m∠2 = 108°.
learn more about linear pairs of angles here :
https://brainly.com/question/16591354
#SPJ1
A worker is tiling the floor of a rectangular room that is 12 x 15’. The tiles are squares with side length of one and 1 1/3 feet. How many tiles are needed to cover the entire floor?
Answer:
102
Step-by-step explanation:
A = L + BHelp with these questions
Answer: 1. 27/72 = 3/8, 2. 24/40 = 3/5, 3. 6/42 = 1/7
Step-by-step explanation:
1. 27/72 divided by 9/9 equals 3/8.
2. 24/40 divided by 8/8 equals 3/5.
3. 6/42 divided by 6/6 equals 1/7.
Please help due tonight!!!!
Answer:
[tex]x=42; \ y=14\sqrt{5}.[/tex]
Step-by-step explanation:
1. if the angles of the given triangle are 30-60-90°, then
2. y=0.5*28√5=14√5;
[tex]3. \ x=28\sqrt{5}*sin(60)=28\sqrt{3}*\frac{\sqrt{3} }{2}=42.[/tex]
4. finally, x=42; y=14√5.
I DONT NEED THE ANSWER ANYMORE
What is the range of possible sizes for side x? x 8.0 2.5 (for a triangle)
NEVERMIND, I GOT IT WRONG BUT I DONT NEED THE ANSWER ANYMORE
Answer:
okay have a nice day haha
new flat screen tv are measured diagonally. if the dimensions of a new tv are 28 inches by 15.7 inches, what is the exact length of the diagonal?
How many times does 1/2 go into 3/4
Answer:
1/2 goes into 3/4 1 1/2 or 1.5 times
Step-by-step explanation:
If 7x-43=5x+43 what is x equal to?
Answer:
7x-43=5x+43
7x-5x=43+43
2x=86
x=86/2
x=43
Answer this Fraction based Question I will provide you 50point + make you as brainliest.
It is given that 2/5 of all patients admitted to ward 17.
Remining fraction is:
1 - 2/5 = 5/5 - 2/5 = 3/5So 3/5 of patients admitted to ward 18.
Since 1/6 of all patients moved to another ward, and the reminder assigned as before, the initial fraction becomes:
1 - 1/6 = 6/6 - 1/6 =5/6Now, 3/5 of the new fraction, 5/6 is admitted to ward 18.
That is:
3/5*5/6 = 3/6 = 1/2This is half of the patients.
The difference of the number of the patients admitted to ward 17 is the same fraction of the number of infected:
10*2/5 = 4So the difference of patients is 4.
I need help on this. I will give 10 points of it
Answer:
150 units (Option C)
Step-by-step explanation:
Perimeter of rectangle = Perimeter of triangle
= {2 × (Length + Width)} = Sum of all three sides
= {2 × [(2x) + (x + 12)]} = [(4x) + (2x) + (x + 3)]
The parenthesis are expanded using the Distributive Law:
= {2 × [2x + x + 12]} = [4x + 2x + x + 3]
= {2 × [3x + 12]} = [7x + 3]
= 6x + 24 = 7x + 3
Bring all the like terms together and isolate x:
= 24 - 3 = 7x - 6x
= 21 = x
∴x = 21
Substitute this calculated value of x to determine the perimeter of rectangle:
6x + 24
= 6(21) + 24
= 126 + 24
= 150 units
∴Option C
Write the equation of the line that passes through the points (0,9) and (0,7). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
A line's point slope form equation is y - y1 = m. (x – x1). Consequently, y - 0 = m(x = 0), or y = mx, is the equation of a line passing through the origin with a slope of m.
How do I represent a line that travels through the points in an equation?Finding the slope between two points on a line and then solving for the y-intercept in the slope-intercept equation y=mx+b allow us to build an equation for that line.
The slope of the line passing through these points,
[tex]m=\frac{y2-y1}{x2-x1} \\\\m=\frac{7-9}{0} =infinity[/tex]
infinity slope means y axis.
The equation of line will be x=0.
To know more about equation visit:-
brainly.com/question/10413253
#SPJ1
How can the complete transformation be described to a person who cannot see the transformations to the right?
Select the correct choice below and fill in the answer box(es) to complete your choice.
OA. The complete transformation is T
B. The complete transformation is R, where k is the line with equation
Video Textbook Get more help.
Review Progress
Question 2 of 14
24
AM
B
d"
Clear all
2
Back
C
Q
OO
Next
Q
Check answer
Answer:
T〈-7,0〉
Step-by-step explanation:
You want a description of the transformation of triangle ABC to triangle A"B"C".
Transformation∆A"B"C" has the same orientation as ∆ABC, so no reflection is involved (eliminates choice B).
Point A" is 7 units to the left of point A, so the translation is 7 units left (and no units up or down).
The transformation is ...
[tex]\boxed{T_{\langle-7,0\rangle}}[/tex]