It looks like the integral in polar coordinates is given to be
[tex]\displaystyle\int_{\pi/2}^\pi \int_0^2 r^3\sin(\theta)\cos(\theta)\,\mathrm dr\,\mathrm d\theta[/tex]
Converting back to Cartesian, we take
x = r cos(θ)
y = r sin(θ)
dx dy = r dr dθ
so we can easily recover the integrand in Cartesian:
[tex]r^3\sin(\theta)\cos(\theta)\,\mathrm dr\,\mathrm d\theta = (r\sin(\theta))(r\cos(\theta))(r\,\mathrm dr\,\mathrm d\theta) = xy\,\mathrm dx\,\mathrm dy[/tex]
This leaves us with the limits:
• π/2 ≤ θ ≤ π corresponds to the second quadrant of the (x, y)-plane (that is, where x < 0 and y > 0)
• 0 ≤ r ≤ 2 correspond to the disk of radius 2 centered at the origin
Taken together, we see the region of integration is a quarter-disk of radius 2 in the second quadrant, which we can capture by the set
{(x, y) : -√2 ≤ x ≤ 0 and 0 ≤ y ≤ √(2 - x ²)}
So, in Cartesian coordinates, the integral would be
[tex]\displaystyle \boxed{\int_{-\sqrt2}^0 \int_0^{\sqrt{2-x^2}} xy\,\mathrm dy\,\mathrm dx}[/tex]
what is 3-4 pls pls pls
Answer: for 3) 427 hikers
Step-by-step explanation: b + 178 + b = 676
2b + 178 = 676
2b = 498
b = 249 bikers
h = 249 + 178 = 427 hikers
What is the percent of decrease from 80 to 68?
Answer:
-15%.
Step-by-step explanation:
Subtract 68 by 80 to get -12.
Divide -12 by the absolute value of 80 to get -0.15.
Multiply 100 to -0.15 to get -15.
Evaluate: 3cos 80° cosec 10° + 2 sin 59° sec 31°
correct answer will be marked as Brainliest.
Given that
3 cos 80° cosec 10° + 2 sin 59° sec 31°
⇛3 cos(90°-10°) cosec 10°+2 sin (90°-31°) sec 31°
We know that
sin (90° - A) = cos A
cos (90°-A) = sin A
⇛3 sin 10° cosec 10° + 2 cos 31° sec 31°
⇛3 sin 10° (1/sin 10°) + 2 cos 31° (1/cos 31°)
⇛3 (sin 10°/sin 10°) + 2 (cos 31°/cos 31°)
⇛3 (1) + 2(1)
⇛3+2
⇛5
Answer: Therefore, 3cos 80°cosec 10°+2cos 59°sec 31° = 5.
also read similar questions: (sin teta + sec teta)^ + (cos teta+ cosec teta )^ = (1 + sec x cosec)^
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Answer:
5
Step-by-step explanation:
you can rewrite this as
3cos(90*-10*) x 1/sin(10*) + 2sin(90*-31*) x 1/cos(31*)
=3sin(10*) x 1/sin(10*) + 2cos31* x 1/cos(31*)
reduce with sin(10*) to get
3+2cos(31*) x 1/cos(31*)
cross out the cos 31* on both sides to leave you with
3+2
5
4x>=112
A.25
B.27
C.28
D.33
E.1
F.21
Answer:
C
Step-by-step explanation:
112 divided by 4 equals 28
On a basketball court the free throw line is marked off geometrically this area of the court is called a key and is topped
by a semi circle that has a diameter of 12 feet find the arc length of the semi circle to the nearest foot find the area of a semi circle to the nearest square foot
Step-by-step explanation:
Arc length formula is
[tex]s = rx[/tex]
where x is radinas.
A semi circle has a radian measure of
[tex]\pi[/tex]
The radius is half of the diameter, 12 so the radius is
[tex]12 \times \frac{1}{2} = 6[/tex]
So the arc length is
[tex]6 \times \pi = 6\pi[/tex]
Area of semi circle is
[tex] \frac{1}{2} \pi {r}^{2} [/tex]
where r is the radius.
[tex] \frac{1}{2} \pi6 {}^{2} [/tex]
[tex] \frac{1}{2} 36\pi[/tex]
[tex]18\pi[/tex]
Frank rented a truck for one day. There was a base fee of $18.99, and there was an additional charge of 76 cents for cach mile driven. Frank had
S152.75 when he returned the truck. For how many miles did he drive the truck?
Answer:
Frank drove 176 miles.
Step-by-step explanation:
Subtract the base fee from the total payment
152.75 - 18.99 = 133.76
divide the remaining amount(price for miles driven) by the cost for each mile
133.76 / .76 = 176
176 miles.
On solving the linear equation in one variable, given that there was a base fee of $18.99, and there was an additional charge of 76 cents for each mile driven, Frank had $152.75 when he returned the truck, the number of miles driven were 176 miles.
The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable.
Let the number of miles driven be x.
Given in the question,
base fees = $18.99
charge per mile = 76 cents = $0.76
The equation of the total cost becomes :
= base fees + charge per mile * number of miles
= 18.99 + 0.76x
Given the total cost = $152.75
Equating the two values,
= 18.99 + 0.76x = 152.75
= 0.76x = 133.76
= x = 176
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how can you find 72-25? circle all the correct answers
Answer:
eeeeeeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
Choose the equation of the horizontal line that passes through the point (2,4).
Oy = 2
O x= 2
O y = 4
O x=4
Answer:
y = 4
Step-by-step explanation:
Refer to the two images below
For the graph:
y = 2 - red
x = 2 - blue
y = 4 - green
x = 4 - purple
Horizontal lines are parallel to the x axis. The only two equations parallel to the x axis are y = 2 and y = 4 so x = 2 and x = 4 cannot be the answer.
The point (2,4) is graphed as well as the equations and the only equation that's horizontal and passes through the point (2,4) is y = 4
Find the measure of the following: m arcTR = m arcTL = m ∠L = m ∠R = m ∠RTV =
Applying the inscribed angle theorem, the missing measures are:
measure of arc TR = 106°
measure of arc TL = 74°
m∠L = 50°
m∠R = 37°
m∠RTV = 37°
The Inscribed Angle TheoremMeasure of an inscribed angle = half the measure of the arc it intercepts
Central angle = measure of intercepted arc
We are given the following:
LR and TV are diameters of the circle O.
m∠TOR = 106° (central angle)
Find measure of arc TR:
measure of arc TR = m∠TOR
measure of arc TR = 106°
Find measure of arc TL:
measure of arc TL = 180° - m∠TOR
measure of arc TL = 180° - 106°
measure of arc TL = 74°
Find m∠L:
m∠L = ½(measure of arc TR)
m∠L = ½(106°)
m∠L = 50°
Find m∠R:
m∠R = ½(measure of arc TL)
m∠R = ½(74°)
m∠R = 37°
Find m∠RTV:
m∠RTV = ½(measure of arc RV)
m∠RTV = ½(180 - 106)
m∠RTV = ½(74)
m∠RTV = 37°
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Drag each statement on the left to the correct word on the right to tell whether each is true or false. The words "True" and "False" may be
used more than once.
1/ When rounding, you usually round to the closest number.
2/ When a number is halfway between the two possible numbers, round down to the
smaller number.
3/ When a number is halfway between the two possible numbers, round up to the
greater number.
4/ If you are rounding 897 to the nearest hundred, 890 and 900 are the two possible
numbers you choose between based on whether you are rounding up or down.
1. True
2. False
3. True
4. False
What is rounding?Rounding represents replacing a numeral with an approximate value that includes a shorter, easier, or more explicit representation.
Rounding suggests making a number simpler but keeping its value close to what it existed.
Hence,
1. True
2. False
3. True
4. False
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PLEASE HELP ILL GIVE5 STARS HELP ASAP
Answer:
H+2
Step-by-step explanation:
Please mark brainliest
What is the area of the rhombus? 10 km 7 km
Answer:
A=pq
2
Step-by-step explanation:
A=35
Answer:
70KM
Step-by-step explanation:
AREA MEANS MULTIPLY SO 10X7=70
Tara wants to put a white fence aroung the yard including the garden. Write an
expression for the perimeter of her yard (including the garden).
Then simply the expression.
The perimeter of a rectangle is 2L + 2W, where L and W are the length and width, respectively. The dimensions of the garden are given, 6 x 12 ft.
The amount of fencing needed is 2(6) + 2(12) = 12 + 24 = 36 ft of fencing
Type the correct answer in the box. Use numerals instead of words. Find the missing side length, x. 18° 18° 20 B D The value of the missing side length labeled as x is _____
Answer:
7.2
Step-by-step explanation:
20/12 = 12/x
20x = 144
x = 144/20
x = 7.2
Check to make sure your answer is right:
20/12 = 1.66666666667
12/7.2 = 1.66666666667
PLS HELP ASAP PICTURE ATTACHED
Answer:
100000+)9(87)238388292838
If you will subtract 5.789 from 56.1, what is the difference?
Answer:
50.311
Step-by-step explanation:
n applicant receives a job offer from two different companies. Offer A is a starting salary of $58,000 and a 3% increase for 5 years. Offer B is a starting salary of $56,000 and an increase of $3,000 per year.
Part A: Determine whether offer A can be represented by an arithmetic or geometric series and write the equation for An that represents the total salary received after n years. Justify your reasoning mathematically. (3 points)
Part B: Determine whether offer B can be represented by an arithmetic or geometric series and write the equation for Bn that represents the total salary received after n years. Justify your reasoning mathematically. (3 points)
Part C: Which offer will provide a greater total income after 5 years? Show all necessary math work. (4 points)
The amount provided by each offer after each year depends on the first
salary and the added amount or percentage series.
Part A: Offer A can be represented by a geometric seriesThe salary received after n years is Aₙ = 58,000·1.03⁽ⁿ ⁻¹⁾Part B: Offer B can be represented by an arithmetic seriesThe equation for the salary after n years is Bₙ = 58,000 + (n - 1)×3,000Part C: The offer that will provide a greater income after 5 years is offer B, with an income of $70,000Reasons:
The given parameters of the job offers are;
Starting salary of offer A = $58,000
Amount by which the salary increases for 5 years = 3%
The starting salary offer B = $56,000
Amount by which the salary increases per year = $3,000
Part A: The salary amount received in the first month = $58,000
The salary in the second month, aₙ = 58,000 × (1 + 0.03)
a₂ = 58,000 × (1 + 0.03) = 58,000 × (1.03)
The salary in the third month is given as follows;
a₃ = a₂ × (1.03) = 58,000 × (1.03) × (1.03) = 58,000 × (1.03)²
The salary on the nth month is therefore;
aₙ = 58,000 × (1.03)⁽ⁿ⁻¹⁾
The above formula is in the form of the geometric series formula, which is presented as follows;
aₙ = a·r⁽ⁿ⁻¹⁾
Where;
a = The first term = 58,000
r = The common ratio = 1.03
n = The number of years
Therefore;
Offer A can be represented by an arithmetic series
Part B: The first year salary for offer B = $58,000
The salary on the second year, B₂ = 58,000 + 3,000 = 61,000
Salary on the third year, B₃ = 58,000 + 3000 + 3000 = 58,000 + 2 × 3,000
Therefore;
Salary on the nth year, Bₙ = 58,000 + (n - 1)×3,000
The above equation is in the form of aₙ = a + (n - 1)·d
Where;
a = The first term = 58,000
n = The number of years
d = The common difference = 3,000
Therefore;
Offer B can be represented by an arithmetic series
Part C: The income gained on offer A after 5 years, a₅, is given as follows;
a₅ = 58,000 × (1.03)⁽⁵ ⁻ ¹⁾ = 58,000 × 1.03⁴ ≈ 65,279.51098
The income gained on offer A after 5 years ≈ $65,279.51098
On offer B, we have;
a₅ = 58,000 + (5 - 1) × 3,000 = 70,000
The income gained on offer B after 5 years = $70,000
Therefore;
After 5 years, the income offered by offer B is greater than the income offered by offer A.Learn more about arithmetic and geometric series here:
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11. Scott made 21 treat bags for his sister's birthday party. Each treat bag has the same
number of items inside. He used another 14 items after that. Write an expression to represent
the total number of items Scott used for the treat bags.
Answer:
21 x n + 14
Step-by-step explanation:
The number of items in each bag times the number of bags plus the 14 items.
a. How much higher is 500 than 400 m?
b. How much higher is 500 than -400 m?
C. What is the change in elevation from 8,500 m to 3,400 m?
d. What is the change in elevation between 8,500 m and -300 m?
Marcus sleeps 60 hours a week this is 5 times as many hours as he plays chess. How many hours a week does Marcus play chess?
Answer: 12 hours a week
Step-by-step explanation:
60/5 = 12
Since he plays chess 5 times the amount of time he sleeps, simply divide the amount of time he sleeps by 5.
Correct me if I am incorrect.
At M & P’s Deli, two pastrami sandwiches and five sodas cost $12.65, while three pastrami sandwiches and two sodas also cost $12.65. How many dollars would seven pastrami sandwiches and twelve sodas cost?
Answer:
37.95
Step-by-step explanation:
MATH
The cost of seven pastrami sandwiches and twelve sodas is $40.08.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that at M & P’s Deli, two pastrami sandwiches and five sodas cost $12.65, while three pastrami sandwiches and two sodas also cost $12.65.
2P + 5S = 12.65
3P + 2S = 12.65
2P + 5S = 3P + 2S
P = 3S
3 x 3S + 2S = 12.65
6S + 2S = 12.65
8S = 12.65
S = $1.58
P = $3.16
The cost of seven pastrami sandwiches and twelve sodas will be:-
Cost = 7P = 12S
Cost = ( 7 x 3.16 ) + ( 1.58 x 12 )
Cost = $41.08
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The image shows the linear graph for a family that hired a babysitter for a day. The family gave the
babysitter some money up front to buy herself some lunch, and then paid her a constant hourly rate
for the hours she worked. Click the thumbnail image to see the full size image.
Which 2 of the following statements are TRUE about the EQUATION of this line? Select the TWO
statements that are accurate.
35 devide 28 with decimals pls help I need help
Answer:
1.25
Step-by-step explanation:
28 * 1 = 28. 35 - 28 = 7.
Add a decimal after the 1 in your answer and after the 35 in your problem. Add a zero to make your 7 into 70.
28 * 2 = 56. 70 - 56 = 14
Add a zero to make your 14 into 140.
28 * 5 = 140
Two handymen can do a home repair in 2 hours if they work together. One of the men takes 3 hours more than the other man to finish the job by himself. How long does it take for each handyman to do the home repair individually?
Using the together rate, it is found that:
It takes 3 hours for the first handyman to do the home repair individually.It takes 6 hours for the second handyman.The together rate is the sum of each separate rate.
In this problem, we have that:
The together rate is of [tex]\frac{1}{2}[/tex].The first man takes x hours, hence his rate is of [tex]\frac{1}{x}[/tex]The second man takes x + 3 hours, hence his rate is of [tex]\frac{1}{x + 3}[/tex]Applying the together rate:
[tex]\frac{1}{x} + \frac{1}{x + 3} = \frac{1}{2}[/tex]
[tex]\frac{x + 3 + x}{x(x + 3)} = \frac{1}{2}[/tex]
[tex]4x + 6 = x^2 + 3x[/tex]
[tex]x^2 - x - 6 = 0[/tex]
Which is a quadratic equation with coefficients [tex]a = 1, b = -1, c = -6[/tex], hence:
[tex]\Delta = b^2 - 4ac = (-1)^2 - 4(1)(-6) = 25[/tex]
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{1 + \sqrt{25}}{2} = 3[/tex]
[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{1 - \sqrt{25}}{2} = -2[/tex]
We are interested into the positive root, then [tex]x = 3[/tex], [tex]x + 3 = 6[/tex], which means that:
It takes 3 hours for the first handyman to do the home repair individually.It takes 6 hours for the second handyman.You can learn more about the together rate at https://brainly.com/question/25159431
change 93 to base 4
How many solutions does the nonlinear system of equations graphed below
have?
O A. Two
O B. Zero
C. One
O D. Four
Answer:
d four
Step-by-step explanation:
How many solutions does the nonlinear system of equations graphed below have?
Look at the number of points where the graphs intersect each other...the points where the graphs of the functions cross each other are the solutions to the system.
Upon looking, you should see 4 points where the graphs intersect, so there are 4 solutions to the non-linear system of equations.
Find the slope of the line that passes through the pair of points (4,3) (-1,6)
Answer:
-3/5
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(6-3)/(-1-4)
m=3/(-5)
m=-3/5
HELP
HOW AM I MEANT TO ANSWER THIS QUESTION I WOULD ASO LIKE ANSWER.
THX
Please find the attached photograph for their positions.
Hope you could get an idea from here
Doubt clarification - use comment section.
Y<-3 which is the solution:
A) 5
B) 0
C)-2
D)-5
Y needs to be less than -3 the larger the negative number the further from 0 it is so -5 would be less than -3
Answer: -5
Please help me with this. thank you. :)
Answer:
11,550
Step-by-step explanation:
1200- 675( because its descending) + 250 ( its ascending) - 525 = 11,550
