Complete Question
find a vector function that represents the curve of intersection of the two surfaces. The cylinder [tex]x^2+y^2= 36[/tex] an the surface [tex]z=xy[/tex]
Answer:
The function is [tex]r(t) = 6cos(t) \ i + 6sin (t) \ j + 36costsint \ k[/tex]
Step-by-step explanation:
From the question we are told that
The equation of the cylinder is [tex]x^2+y^2= 36[/tex]
The equation of the surface is z = xy
Generally the general form of this function is
[tex]r(t) = x(t)i + y(t)j + z(t) k[/tex]
Generally to confirm the RHS and the LHS of the equation for the cylinder
Let take x (t) = 6cos(t)
and y(t) = 6sin (t)
So
[tex]x^2 + y^2 = [ 6cos(t)]^2 + [6 sin (t)]^2[/tex]
=> [tex]x^2 + y^2 = 6^2 cos^2t + 6^2 sin ^2t[/tex]
=> [tex]x^2 + y^2 = 6^2 [cos^2t + sin ^2t] [/tex]
Generally [tex]cos^2t + sin ^2t = 1[/tex]
So
[tex]x^2 + y^2 = 36[/tex]
So at x (t) = 6cos(t) and y(t) = 6sin (t) the RHS is equal to LHS
So
[tex]z(t) = x(t) * y(t)[/tex]
[tex]z(t) = (6 cos(t)) * (6 sin(t))[/tex]
=> [tex]z(t) =36costsint[/tex]
So the function is
[tex]r(t) = 6cos(t) i + 6sin (t) j + 36costsint k[/tex]
Evaluate 64 to the power of 1/2 x 10 to the power of -2
Sherry is paid an annual salary of $26,000 biweekly. Her friend Donna makes the same salary but is paid quarterly. How much more money does one of Donna's checks have than Sherry's.
Answer:
5000
Step-by-step explanation:
Assuming they both work 365days
roughly 52 weeks
number of time sherry is paid per year = [tex]\frac{52}{2} = 26[/tex]
because she is paid every two weeks
number of time donna is paid per year = [tex]4[/tex]
because she is paid 4 times a year (quarterly)
let s = amount sherry is paid biweekly
let d = amount donna is paid quarterly
[tex]s = \frac{26000}{26} = 1000\\\\d = \frac{26000}{4} = 6500\\\\difference = 65000 - 1000 = 5000\\[/tex]
Answer:
5500
Step-by-step explanation:
Area =
44 ft?
(x - 12) ft
(x - 5) ft
length:
width:
ft
Answer:
x= 16 ft
length = 4 ft
width = 11 ft
Step-by-step explanation:
The area is length* width
so the length is ( x - 12 )
and the width is ( x - 5 )
the area is 44ft
so now set up an equation and solve for x
( x - 12 ) ( x - 5 ) = 44
distribute
x^(2) - 17x + 60 = 44
inverse operations
x^(2) - 17x + 60 = 44
- 60 - 60
x^(2) - 17x = -16
factor
x^(2) - 17x = -16
x ( x - 17 ) = -16
now it is pretty clear that the answer is:
x = 16
just substitute it into the equation and check
( x - 12 ) ( x - 5 ) = 44
( 16 - 12 ) ( 16 - 5 ) = 44
( 4 ) ( 11 ) = 44
44 = 44
this also shows that
the length is 4
because:
( x - 12 )
= ( 16 - 12 )
= 4
and the width is 11
because:
( x - 5 )
= ( 16 - 5 )
= 11
Convert 6 feet to meters.
Conversion table:
1 meter = 3.281 feet
Answer:
6 feet = 1.8288 meters
Step-by-step explanation:
Hope this helps and have a phenominal day!
Draw the triangle ABC on a coordinate plane given the following points A (0,0) B (4,-10) C (10,-4)
draw a picture of ur triangle
Answer:
plot those points on a graph and then label the points with the correct letter and then connect the dots and you should have a triangle on your graph.
Step-by-step explanation:
Step-by-step explanation:
First plot the points on a graph and then connect those points forming a triangle
How would you graph y = -4/9x + 6
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Answer:
graph the y-interceptfind another point (down 4, right 9)draw the line through the 2 pointsStep-by-step explanation:
When the equation of a line is given in slope-intercept form, as this one is, it is usually convenient to make use of those values (intercept and slope).
Here, the y-intercept is 6. The slope is -4/9, which means the line goes down 4 units for each 9 units to the right.
The y-intercept is graphed at (0, 6). An additional point can be graphed at (9, 2). Then the line can be drawn through these points.
help please will mark brainliest
Answer:
step 2
Step-by-step explanation:
sorry if im wrong. Please mark me brainleast
what is the value of the Expression below
Your answer is -2 (aka option b that would be)
The slope of AB is 6/5 if point A is (3,y) and point B is (-2,-1) find the value of y
Use the product rule to answer each of the questions below. Throughout, be sure to carefully label any derivative you find by name. It is not necessary to algebraically simplify any of the derivatives you compute.
a. Let m (w) = 3 w^17 4^w. Find m ′(w) .
b. Let h (t) = ( sin (t) + cos (t)) t 4. Find h ′(t).
c. Determine the slope of the tangent line to the curve y = f (x) at the point where a = 1 if f is given by the rule f(x) = e^x sin (x).
d. Find the tangent line approximation L(x) to the function y = g (x) at the point where a = − 1 if g is given by the rule g (x) = ( x^2 + x ) 2^x .
Answer:
A) M'(w) = w^16 * 4^w [ 51 + 3w In4 ]
B) h'(t) = [ cos (t) - sin (t) ] t^4 + [ sin(t) + cos (t) ] 4t^3
C) f'(1) = e' [sin(1) + cos(1) ]
D) g'(a) = 0 - 1/2
L(x) = - 1/2 ( x + 1 )
Step-by-step explanation:
Attached below is the detailed solution of the problem
A) m(w) = 3w^17 * 4^w
M'(w) = w^16 * 4^w [ 51 + 3w In4 ]
B) h(t) = [sin(t) + cos(t) ] t^4
h'(t) = [ cos (t) - sin (t) ] t^4 + [ sin(t) + cos (t) ] 4t^3
C) f(x) = e^x sin (x). at a = -1
f'(1) = e' [sin(1) + cos(1) ]
D) g (x) = ( x^2 + x ) 2^x .
g'(a) = 0 - 1/2
L(x) = - 1/2 ( x + 1 )
can you guys help me??
Answer:
37 used beeds
Step-by-step explanation:
May i get brainiest
HELP PLEASE WILL MARK BRAINLIEST
Answer:
15
Step-by-step explanation:
Help Please! :(
108 students went on a field trip. Three buses were filled and 27 students traveled in cars. How many students were in each bus?
Please include algebraic equation and answer.
Answer:
81
Step-by-step explanation:
-6K – 3 = 39. Please solve this equation for K. Type your work in.
Answer:
k = -7
Step-by-step explanation:
-6k-3 = 39
Add 3 to each side
-6k-3+3 = 39+3
-6k = 42
Divide each side by -6
-6k/-6 = 42/-6
k = -7
6 apples cost exactly the same as 9 oranges. 10 apples and 10 oranges cost $7.50. Find the cost of 1 apple and the cost of 1 orange.
Answer:6 apples cost exactly the same as 9 oranges. 10 apples and 10 oranges cost $7.50. Find the cost of 1 apple and the cost of 1 orange.
Step-by-step explanation:
Identify the coefficients: -3h - 2h + 6h +9
Answer:
-23h
Step-by-step explanation:
What is the slope of the line?
*************
Answer:1.5
Step-by-step explanation:
Answer: 4/5
Step-by-step explanation:
Slope=rise/run
In this case we start at (-2,0)
We rise up 4 and run to the right 5 until we are at (3,4)
About Each statement below involves odd and even integers. An odd integer is an integer that can be expressed as 2k+1 , where k is an integer. An even integer is an integer that can be expressed as 2k , where k is an integer. Prove each of the following statements using a direct proof.
a. The sum of an odd and an even integer is odd.
b. The sum of two odd integers is an even integer.
c. The square of an odd integer is an odd integer.
d. The product of two odd integers is an odd integer.
Answer:
a. The sum of an odd and an even integer is odd: 3 + 2 = 5
b. The sum of two odd integers is an even integer: 3 + 5 = 8
c. The square of an odd integer is an odd integer: 3² = 9
d. . The product of two odd integers is an odd integer.: 3 x 5 = 15
Step-by-step explanation:
Proving the following statements using a direct proof;
a. The sum of an odd and an even integer is odd:
let the odd integer = 3
let the even integer = 2
3 + 2 = 5
5 is an odd integer, proved
b. The sum of two odd integers is an even integer.
let the first odd integer = 3
let the second odd integer = 5
3 + 5 = 8
8 is an even integer, proved
c. The square of an odd integer is an odd integer. .
let the odd integer = 3
3² = 9
9 is an odd integer, proved
d. The product of two odd integers is an odd integer.
let the first odd integer = 3
let the second odd integer = 5
3 x 5 = 15
15 is an odd integer, proved
Answer:
a. The sum of an odd and an even integer is odd: 3 + 2 = 5
b. The sum of two odd integers is an even integer: 3 + 5 = 8
c. The square of an odd integer is an odd integer: 3² = 9
d. . The product of two odd integers is an odd integer.: 3 x 5 = 15
Step-by-step explanation:
Proving the following statements using a direct proof;
a. The sum of an odd and an even integer is odd:
let the odd integer = 3
let the even integer = 2
3 + 2 = 5
5 is an odd integer, proved
b. The sum of two odd integers is an even integer.
let the first odd integer = 3
let the second odd integer = 5
3 + 5 = 8
8 is an even integer, proved
c. The square of an odd integer is an odd integer. .
let the odd integer = 3
3² = 9
9 is an odd integer, proved
d. The product of two odd integers is an odd integer.
let the first odd integer = 3
let the second odd integer = 5
3 x 5 = 15
15 is an odd integer, proved
Bill and Jerry are both taking their hot-air balloons to the balloon show.
They are good friends and like to share experiences. The especially like that when
they get to fly their balloons next to each other. Unfortunately they did not get
cleared to depart at the same time. Bill got to go up first and had already started
to descend by the time that Jerry was cleared. Five seconds before Jerry takes
off Bill’s balloon basket was 1032 feet above the ground falling at a constant rate.
Five seconds after Jerry takes off Bill’s basket was 985 feet above the ground
and Jerry’s balloon basket was 57 feet off the ground and rising at the same
constant rate the whole time. To the nearest tenth of a second, how long after
Jerry’s balloon took off will the height of the two balloon baskets be the same
height?
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Answer:
62.6 seconds
Step-by-step explanation:
We can use the 2-point form of the equation for a line to write equations for the heights of the balloons.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
__
For Bill's balloon, the two given points are ...
(t, h) = (-5, 1032) and (5, 985)
Then the equation is ...
h = (985 -1032)/(5 -(-5))(t -(-5)) +1032
h = -47/10(t +5) +1032
__
For Jerry's balloon, the two given points are ...
(t, h) = (0, 0) and (5, 57)
Then the equation is ...
h = (57-0)/(5-0)(t -0) +0
h = (57/5)t
__
The heights are equal when ...
-47/10(t +5) +1032 = (57/5)t
1008.5 = t(57/5 +47/10) = 16.1t
Then the time until heights are the same is ...
t = 1008.5/16.1 ≈ 62.6 . . . seconds
Help ASAP
Find the difference
(2x + 6) - (7x + 3).
(2x + 6) - (7x+3)
= 2x + 6 - 7x - 3
=2x - 7x + 6 - 3
= -5x + 3
Answer:
The answer is (-5x + 3).
Step-by-step explanation:
Write an equation of the line passing through the point (8, -5) that is parallel to the line 2x -6y = -3
Answer:
y=1/3x+10.5
Step-by-step explanation:
y=mx+b, the equation of the parallel line is y=1/3x+1/2. So we know the slope is 1/3 and all we need is the Y intercept (b). We can find that manually with arithmetic because we know the slope. It turns out to be 10.5
3
Assignment
♡ Find the product of 419 and 321
Find the product of 326 and 124
③ If a mais pay #354 for a book how mac
alle le gay for 7s boots?
④ The price of a big fan is 8494. How
much will 198 big fans cost?
③ Find the product of 3102 and 480
Dictionary Meaning
② Anounced
Step-by-step explanation:
1. 419*321=134499
2. 326*124 = 40424
3. 354* 7 = 2478
here mac paid 2478
4. 8494*198= 1681812
here it will cost 1681812
5. 3102*480=1488960
6. announced = to reveal something
There are four blue marbles and 6 red marbles. What is the ratio of blue marbles to red marbles. Write the ratio in simplest form
Answer:
2:3
Step-by-step explanation:
2 is the greatest common factor, so divide both 4 and 6 by 2, which should result as 2:3.
hope this helps :)
In order to test for the significance of a regression model involving 5 independent variables and 123 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are
Answer: The numerator and denominator degrees of freedom (respectively) for the critical value of F are 4 and 118 .
Step-by-step explanation:
We know that , for critical value of F, degrees of freedom for numerator = k-1
and for denominator = n-k, where n= Total observations and k = number of independent variables.
Here, Numbers of independent variables(k) = 5
Total observations (n)= 123
So, Degrees of freedom for numerator = 5-1=4
Degrees of freedom for denominator =123-5= 118
Hence, the numerator and denominator degrees of freedom (respectively) for the critical value of F are 4 and 118 .
Which inequality is true?
Answer:
8 pi > 24 true
Step-by-step explanation:
12/pi >4
12 > 4pi
pi is slight greater than 3
12 > 4* a number greater than 3
12 > a number greater than 12 false
pi + 3 < 6
a number slightly greater than 3 + 3 < 6
a number lightly greater than 6 < 6 false
8 pi > 24
8 * a number slightly greater than 3 > 24
a number greater than 24 > 24 true
6 - pi > 3
6 - a number slightly greater than 3 > 3
a number less than 3 > 3 false
Line t has a slope of 3/5 line u is perpendicular to t what is the slope of line u
Answer:
[tex]\frac{5}{3}[/tex] is the slope of the line
Step-by-step explanation:
When two lines are perpendicular, their slopes are inverse.
[tex]\frac{3}{5}[/tex] becomes [tex]\frac{5}{3}[/tex] because they are inverse. Just flip the numerator (top number) and denominator(bottom number).
Hope this helps!
Write an equation in point-slope form for the line that is parallel to y = 3/4x -
3 and passes through point (4,3).
Answer:
The point-slope form of the equation of the parallel line is y - 3 = [tex]\frac{3}{4}[/tex] (x - 4)
Step-by-step explanation:
Parallel lines have the same slopes and different y-intercepts
The slope-intercept form of the linear equation is y = m x + b, where
m is the slopeb is the y-interceptThe point-slope form is of the linear equation is y - y1 = m(x - x1), where
m is the slope(x1, y1) are the coordinates of a point lies on the line∵ The equation of the given line is y = [tex]\frac{3}{4}[/tex] x - 3
→ Compare it with the first form of the equation above
∴ m = [tex]\frac{3}{4}[/tex]
∴ The slope of it is [tex]\frac{3}{4}[/tex]
∵ Parallel lines have the same slopes
∴ The slope of the parallel line is [tex]\frac{3}{4}[/tex]
∵ The point-slope form is y - y1 = m(x - x1)
→ Substitute the value of the slope in the form of the equation above
∴ y - y1 = [tex]\frac{3}{4}[/tex] (x - x1)
∵ The line passes through the point (4, 3)
∴ x1 = 4 and y1 = 3
→ Substitute them in the equation above
∴ y - 3 = [tex]\frac{3}{4}[/tex] (x - 4)
∴ The point-slope form of the equation of the parallel line is
y - 3 = [tex]\frac{3}{4}[/tex] (x - 4)
**100** The given data represent the total compensation for 10 randomly selected CEOs and their company's stock performance in 2009. Analysis of this data reveals a correlation coefficient of r = 0.1887. What would be the predicted stock return for a company whose CEO made $15 million? What would be the predicted stock return for a company whose CEO made $25 million?
Answer:
Your answer is: Look Below
Step-by-step explanation:
Hope this helped : )
pls help i have 2 minutes find length
Answer:
2.4 cm
Step-by-step explanation:
i hope that I helped you.
1. Michael deposited $500 in his bank account that pays 4% semi-annual compounded interest. If he does not touch the money for 5 years, how much money will be in the account?
Answer:
$609.50
Step-by-step explanation:
A = P(1 + r/n)^nt
= 500(1 + [tex]\frac{.04}{2}[/tex])^2(5)
= 500(1.02)¹⁰
= 500(1.218994)
= 609.497
Round answer up to $609.50