Parameterize S by the vector function
[tex]\vec s(u,v) = \left\langle 4 \cos(u) \sin(v), 4 \sin(u) \sin(v), 4 \cos(v) \right\rangle[/tex]
with 0 ≤ u ≤ π/2 and 0 ≤ v ≤ π/2.
Compute the outward-pointing normal vector to S :
[tex]\vec n = \dfrac{\partial\vec s}{\partial v} \times \dfrac{\partial \vec s}{\partial u} = \left\langle 16 \cos(u) \sin^2(v), 16 \sin(u) \sin^2(v), 16 \cos(v) \sin(v) \right\rangle[/tex]
The integral of the field over S is then
[tex]\displaystyle \iint_S \vec f \cdot d\vec s = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \vec f(\vec s) \cdot \vec n \, du \, dv[/tex]
[tex]\displaystyle = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \left\langle 8 \cos(u) \sin(v), -12 \cos(v), 12 \sin(u) \sin(v) \right\rangle \cdot \vec n \, du \, dv[/tex]
[tex]\displaystyle = 128 \int_0^{\frac\pi2} \int_0^{\frac\pi2} \cos^2(u) \sin^3(v) \, du \, dv = \boxed{\frac{64\pi}3}[/tex]
Whoever answers correctly gets BRAINLIEST and 100 points
A regular-size box of crackers measures 214 inches by 912 inches by 14 inches. The manufacturer also sells a snack-size box that has a volume that is 15 of the volume of the regular-size box.
What is the volume of the snack-size box of crackers?
Enter your answer as a mixed number in simplest form by filling in the boxes.
$$
in³
Answer:
[tex]\sf 59 \frac{17}{20} \: in^3[/tex]
Step-by-step explanation:
Regular-size box of crackers
Dimensions: [tex]\sf 2 \frac{1}{4} \: in \times 9 \frac{1}{2}\:in \times 14\: in[/tex]
Snack-size box of crackers
Volume = [tex]\sf \frac{1}{5}[/tex] of the volume of a regular-size box
To calculate the volume of the snack-size box of crackers, calculate the volume of the regular-size box then multiply it by [tex]\sf \frac{1}{5}[/tex].
[tex]\begin{aligned}\textsf{Volume of a rectangular prism} & = \textsf{width x length x height}\\\\\implies \textsf{Volume of regular-size box} & = \sf 9 \frac{1}{2} \times 14 \times 2 \frac{1}{4}\\\\& = \sf \dfrac{19}{2} \times 14 \times \dfrac{9}{4}\\\\& = \sf \dfrac{19 \times 14 \times 9}{2 \times 4}\\\\& = \sf \dfrac{1197}{4}\: in^3\end{aligned}[/tex]
[tex]\begin{aligned}\implies \textsf{Volume of snack-size box} & = \sf \dfrac{1}{5} \times \textsf{volume of regular-size box}\\\\& = \sf \dfrac{1}{5} \times \dfrac{1197}{4}\\\\& = \sf \dfrac{1 \times 1197}{5 \times 4}\\\\& = \sf \dfrac{1197}{20}\\\\& = \sf 59 \dfrac{17}{20}\: in^3\end{aligned}[/tex]
Therefore, the volume of the snack-size box is [tex]\sf 59 \frac{17}{20} \: in^3[/tex]
Marcia needs a packing box with a volume of at least 180 cubic inches.
Part A
Is the box the correct size? Explain.
Question 2
Part B
Shipping costs $0.15 per cubic inch. How much will Marcia pay to ship the box?
Answer:
Part A: Yes
Part B: $30
Step-by-step explanation:
Some information is missing, but I did see a similar problem that shows a box shaped like a rectangular prism with length 5 in., width 4 in., and height 10 in.
Part A.
volume = length × width × height
volume = 5 in. × 4 in. × 10 in.
volume = 200 in.³
Since the volume has to be at least 180 in.³, then a volume of 200 in.³ will be ok since 200 is greater than 180.
Answer: Yes
Part B.
$0.15/in.³ × 200 in.³ = $30
Answer: $30
Solvex - 5+ 7 = 15.
A. x = 13 and x = -3
-13 and x = 3
C. x = -13 and x = -3
OD. x = 13 and x = -13
OB. x =
Answer:
A. X= 13 and X= -3
Step-by-step explanation:
subtract 7 from both sides, simplify, break down the problems into 2 equations, solve equations, and boom once solve both equations you get 2 solutions.
The solutions to the equation are x = 13 and x = -3.
Therefore, the correct option is A.
Given is an expression |x-5| + 7 = 15, we need to solve for x,
To solve the equation |x - 5| + 7 = 15 for x, we'll need to isolate the absolute value expression and then solve for x.
Here's the step-by-step process:
Step 1: Subtract 7 from both sides of the equation:
|x - 5| = 15 - 7
|x - 5| = 8
Step 2: Break the equation into two cases, one with the positive value inside the absolute value and one with the negative value inside the absolute value.
Case 1: x - 5 is positive:
For this case, the equation |x - 5| = 8 becomes:
x - 5 = 8
Now, solve for x:
x = 8 + 5
x = 13
Case 2: x - 5 is negative:
For this case, the equation |x - 5| = 8 becomes:
-(x - 5) = 8
Simplify and solve for x:
-x + 5 = 8
-x = 8 - 5
-x = 3
Multiply both sides by -1 to isolate x:
x = -3
So, the solutions to the equation are x = 13 and x = -3.
Learn more about absolute value click;
https://brainly.com/question/17360689
#SPJ7
The first steps in determining the perimeter of triangle ABC are shown.
To the nearest whole unit, what is the perimeter of triangle ABC?
6 units
8 units
14 units
16 units
Answer:
C) 14 Units
Step-by-step explanation:
E2020
given that x = 7.4 m and θ = 32°, work out bc rounded to 3 sf.
(not drawn to scale)
Answer:
BC ≈ 11.8 m
Step-by-step explanation:
using the tangent ratio in the right triangle
tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{x}{BC}[/tex] , that is
tan32° = [tex]\frac{7.4}{BC}[/tex] ( multiply both sides by BC )
BC × tan32° = 7.4 ( divide both sides by tan32° )
BC = [tex]\frac{7.4}{tan32}[/tex] ≈ 11.8 m ( to 3 sf )
7. The sum of 42 and a certain number is
divided by 4. The result is twice the
number. Find the number.
Answer:
Let the number be X
42 + 2x/4 =2X
cross multiply
42+2X=8x
42=8X-2x
42=6X
6X=42
X=7
Step-by-step explanation:
I'm just a smart guy
Given the circle below secant kjI and tangent hi find the length of hi round to the nearest tenth if necessary.
The length of the segment HI in the figure is 32.9
How to determine the length HI?To do this, we make use of the following secant-tangent equation:
HI² = KI * JI
From the figure, we have:
KI = 21 + 24 = 45
JI = 24
So, we have:
HI² = 45 * 24
Evaluate the product
HI² = 1080
Take the square root of both sides
HI = 32.9
Hence, the length of the segment HI is 32.9
Read more about secant and tangent lines at:
https://brainly.com/question/14962681
#SPJ1
The population of a town is growing exponentially and can be modeled by the
equation f(t) = 42. e(0.015). The population is measured in thousands, and time is
measured in years 1950.
C. According to this model approximately what is the population in 1960?
The population of the town in 1960 is 48.80 thousands
How to determine the population in 1950?The equation of the model is given as:
f(t) = 42e^(0.015t)
1960 is 10 years after 1950.
This means that:
t = 10
Substitute t = 10 in f(t) = 42e^(0.015t)
f(10) = 42e^(0.015 * 10)
Evaluate
f(10) = 48.80
Hence, the population of the town in 1960 is 48.80 thousands
Read more about exponential functions at:
https://brainly.com/question/11464095
#SPJ1
In the statement 10 +(-10) =0, how would you describe the -10?
Answer:
-10 is the opposite of 10
Step-by-step explanation:
-10 is the opposite of 10 ,because The sum of a number and its opposite equals to zero.
what is the full answer to pie
Answer:
[tex]\pi[/tex]= 3.1415926...= c/d
Step-by-step explanation
Pie is infinite so there is no simple answer.
circumference divided by the diameter = pie
In the following diagram, BC is parallel to DE.
What is the measure of Zx?
Angles are not necessarily drawn to scale.
W
103°
B
D
4x =
F
42°
H
E
Answer: 35
Step-by-step explanation:
Angles in a triangle add to 180 degrees, so in triangle ABC, [tex]m\angle C=180-103-42=35^{\circ}[/tex].
Sp, by the corresponding angles theorem, x=35
What is the degree measure of ∠COA?
The degree measure of angle COA = 128 degree.
What is Angle Sum Property?It is defined by the property that the sum of the interior angles of a triangle is equal to 180 degrees.
To determine the value of angle COA ,
we have to draw a line connecting CA ,
as OC and OA are the radius of the circle and therefore the sides of the triangle formed will be equal and also the angle made by them ,
angle OAC = angle OCA
Therefore angle DCA = angle DAC
By angle sum property
2x + 52 = 180
2x = 128
x = 64 degree
angle DCO = 90 degree
Therefore angle ACO = 90-64 = 26 degree
Similarly, angle CAO = 26 degree
By angle sum property
26+26+x = 180
52+x = 180
x = 128 degree
The degree measure of angle COA = 128 degree.
To know more about Angle Sum Property
https://brainly.com/question/4316040
#SPJ1
Ronald compared the rate at which water is used from two different water storage tanks by measuring the volume of the water remaining. The results are shown in the table
The statement that best describes the results is in tank 1, the rate at which water is used is higher.
What is the rate for each tank?Tank 1:
Total of water used/ time177.12/4 = 44.28 gallons per hourTank 2:
160/ 4 = 40 gallons per hourWhat are the results?The rate in tank 1 is higher than the rate in tank 2.
Learn more about rate in: https://brainly.com/question/14731228
#SPJ1
how many 4 digit numbers n have the property that the 3 digit number obtained by removing the leftmost digit is one ninth of n
Answer:
7
Step-by-step explanation:
We want to find the number 4-digit of positive integers n such that removing the thousands digit divides the number by 9.
__
Let the thousands digit be 'd'. Then we want to find the integer solutions to ...
n -1000d = n/9
n -n/9 = 1000d . . . . . . add 1000d -n/9
8n = 9000d . . . . . . . . multiply by 9
n = 1125d . . . . . . . . . divide by 8
The values of d that will give a suitable 4-digit value of n are 1 through 7.
When d=8, n is 9000. Removing the 9 gives 0, not 1000.
When d=9, n is 10125, not a 4-digit number.
There are 7 4-digit numbers such that removing the thousands digit gives 1/9 of the number.
i need help pleaseee
Answer: $7448
Step-by-step explanation:
Year 1: 1.218x
Year 2: 1.218(1.218x)
Year 3: 1.218(1.218(1.218x))
Year 4: 1.218(1.218(1.218(1.218x)))
Year 5: 1.218(1.218(1.218(1.218(1.218x))))
Year 6: 1.218(1.218(1.218(1.218(1.218(1.218x)))))
Year 7: 1.218(1.218(1.218(1.218(1.218(1.218(1.218x))))))
Year 8: 1.218(1.218(1.218(1.218(1.218(1.218(1.218(1.218x)))))))
Year 9: 1.218(1.218(1.218(1.218(1.218(1.218(1.218(1.218(1.218x))))))))
Year 10: 1.218(1.218(1.218(1.218(1.218(1.218(1.218(1.218(1.218(1.218x)))))))))
Year 11: x(1.218¹¹)
Year 12: x(1.218¹²) = 79,400
x(10.6602517) = 79,400
x = 79,400/10.6602517
x=7448.22939
x = $7448
Hope this helps!
What percent of 72 is 9? 1/8% 1 1/4% 12 1/2% 125%
Answer:
[tex]12\dfrac 12\%[/tex]
Step by step explanation:
[tex]\text{Let it be}~ x\%,\\\\~~~~~72 \cdot x \% = 9\\\\\\\implies 72\cdot \dfrac{x}{100} = 9\\\\\\\implies x = \dfrac{9 \times 100}{72}\\\\\\\implies x = \dfrac{100}{8}\\\\\\\implies x = \dfrac{25}2\\\\\\\implies x = 12 \dfrac 12\\\\\\\text{Hence 9 is}~ 12\dfrac 12\% ~ \text{of}~ 72[/tex]
An angel measures 122 degree more than the measures of supplementary angle. what is the measure of each angle.
Answer:
302 degrees
Step-by-step explanation:
Write a equation of a line through (4, 6) and (-10, 2)
Answer:
y=2/7x+34/7
Step-by-step explanation:
the slope of this line is 2/7.
y=2/7x+?
? is the y-intercept.
Looking at the line that we have graphed, we can see that it intersects at 34/7 y.
the equation for the line that goes through 4,6 and -10, 2 is
y=2/7x + 34/7
Are any of the sides perpendicular? Is the triangle a right triangle? Yes, AB and Bc are perpendicular
Use a net to find the surface area of the cylinder. Use 3.14 for .
Answer:
Formula = 2nr
= 2(3,14 + 3 + 4)
= 2(10,14)
= 20,28
There are 9 red and 6 green marbles in a bag. A child reaches in the bag and randomly takes one marble. What is the probability
of that child getting a green marble?
A .66
B.40
с .33
D .10
Answer:
THE OPTIONS ARE WRONGStep-by-step explanation:
N(S)=9 + 6 = 15N(R) = 9N(G) = 6P(G) = N(G)/N(S) = 6/ 15 = 0.4___________________________DONE successfulWhat is the ratio of the wavelengths of these two notes? a. 5 to 4 b. 3 to 2 c. 6 to 5 d. 2 to 1
The ratio of the wavelengths of the two notes is 2:1 option fourth 2 to 1 is correct.
What is wavelength?The wavelength is the distance between two successive troughs or crests. The highest point on the wave is the crest, while the lowest point is the trough.
We have two notes
Number of cycle for blue = 8
Number of cycle for red = 4
Ratio = 8:4 = 2:1
Or
2 to 1
Thus, the ratio of the wavelengths of the two notes is 2:1 option fourth 2 to 1 is correct.
Learn more about the wavelength here:
brainly.com/question/7143261
#SPJ1
Yan is somewhere between his home and the stadium. To get to the stadium he can walk directly to the stadium, or else he can walk home and then ride his bicycle to the stadium. He rides 7 times as fast as he walks, and both choices require the same amount of time. What is the ratio of Yan's distance from his home to his distance from the stadium
Answer:
3/4
Step-by-step explanation:
The relationship between time, speed, and distance can be used together with the travel time relations to find the desired ratio.
__
setupLet H represent the distance from Yan's location to home. Let S represent the distance to the stadium, and let w represent Yan's walking speed.
The time required for Yan to walk home is ...
time = distance/speed = H/w
The time required for Yan to walk to the stadium is ...
time = S/w
The time required for Yan to ride his bike from home to the stadium is ...
time = (H +S)/(7w) . . . . . his riding speed is 7 times his walking speed.
In order for the travel times to be equal, we must have ...
time to walk home + time to bike to stadium = time to walk to stadium
H/w + (H +S)/(7w) = S/w
__
solutionMultiplying by 7w gives ...
7H +(H +S) = 7S
8H = 6S . . . . . . . . . subtract S
H/S = 6/8 = 3/4 . . . . divide by 8S
The ratio of Yan's distance from home to his distance from the stadium is 3/4.
_____
Additional comment
Another way to think about this is ...
The stadium is farther away than home by a distance that Yan can walk in the same time he can bike the entire distance from home to the stadium. That is, the difference in distances must be 1/7 of the total distance. Now, we have a "sum and difference" problem: S +H = 7, S -H = 1. The solution is S = (7+1)/2 = 4, H = (7-1)/2 = 3. H/S = 3/4.
What is the measure of angle c in the parallelogram shown
Answer:
35°
Step-by-step explanation:
Same-Side interior angles (consecutive angles) are supplementary.
Supplementary meaning that those two angles add up to make 180°.
So Angles C is 35°
Using the curve of best fit, what would be the output (y) when the input (x) is 7?
Answer:
y = 260
Step-by-step explanation:
locate x = 7 on the x- axis, go vertically up to meet the graph at (7, 260 )
when input is 7 then output y = 260
A triathlon requires participant to complete the following tasks:
Task 1: Swim 750 m
Task 2: Cycle 20 km
Task 3: Run 5 km
Mr Lee swam at 10 km/h, cycled at 85 km/h and ran at 14 km/h during the triathlon. Find the total time taken by him to complete the triathlon, leaving your answer in minutes and the nearest second.
Answer:
Step-by-step explanation:
Time taken for task 1:
Distance= 750m= 0.75 km
Speed= 10 km/hr
Time taken1= S (distance)/ V (speed)= 0.75/10= 0.075 hr= 4 mins and 30 sec
Time taken for task 2:
t2=S/V= 20/85= 0.24 hr= 14 mins and 24 sec
Time taken for task 3:
t3= S/V = 5/14= 0.36 hr= 21 mins and 36 sec
Total time took:
T1 +T2+T3= 40 mins and 30 second (approximately)
Given the diagram below, what is cos(45")?
45° 6
A. √2
B. 6/√2
C. 1/√2
D. 3√2
ANSWER ASAP PLEASE! 14 POINTS
Answer:
the first one
Step-by-step explanation:
the formul is y=mx+b
m is slope which is -3/2
b is y intercept and it is -3
and the addition sign will change based on if the y intercept is negative or not
Hope this helps
Whoever answers first will get brainliest answer!
mrs. mank is decorating a 4-foot by 9-foot bulletin board in her classroom. if she decides to put a purple border around the entire board, what is the length of border that she needs?
Answer:
36 feet
Step-by-step explanation:
To find the area of a square or rectangle you multiply the width by the length.
) The gym teacher divided a class into four teams with 7 students per team. How many students are in the class?
Answer:
28 students
Step-by-step explanation:
7 times 4 = 28
there are are seven students in 4 teams, so that means there are 4 groups of seven, and you multiply them together to get how many students in the class
Answer:
28
Keyword(s):
divided, four, 7, per team, how many
Step-by-step explanation:
7 × 4 = 28