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]
A panel of 10 interviewers was to interview two candidates A and B to decide who was suitable for a job. 7 said A was suitable, 5 said B was suitable while 2 said neither A nor B was suitable. (i) How many said both A and B were suitable. (ii) How many said A alone was suitable.
Answer:
(i) 4 interviewers
(ii) 3 interviewers
in the box of Stones ,the ratio of red marbles is 2:5. the ratio of green stones to the total stones is 3:10 .if the stones that are neither red nor green are blue ,how many blue are in the box.if there are 40 marbles in the box?.
given that the following two are geometric series are convergent: 1+x+x^2+x^3+...and 1-x+x^2-x^3+... determine the value(s) of x for which the sum of the two series is equal to 8
Let S and T denote the two finite sums,
S = 1 + x + x ² + x ³ + … + x ᴺ
T = 1 - x + x ² - x ³ + … + (-x) ᴺ
• If both S = 8 and T = 8 as N goes to infinity:
Then
xS = x + x ² + x ³ + x ⁴ + … + x ᴺ⁺¹
-xT = -x + x ² - x ³ + x ⁴ + … + (-x) ᴺ⁺¹
so that
S - xS = 1 - x ᴺ⁺¹ ==> S = (1 - x ᴺ⁺¹)/(1 - x)
and similarly,
T = (1 - (-x) ᴺ⁺¹)/(1 + x)
For both sums, so long as |x| < 1, we have
lim [N → ∞] S = 1/(1 - x)
lim [N → ∞] T = 1/(1 + x)
Then if both sums converge to 8, this happens for
S : 1/(1 - x) = 8 ==> x = 7/8
T : 1/(1 + x) = 8 ==> x = -7/8
• If the sum S + T = 8 as N goes to infinity:
From the previous results, we have
1/(1 - x) + 1/(1 + x) = 8 ==> x = ±√3/2
Hi.
• Easy question.
• No Copy paste
1) 40 + 5 × 5 =
Note : actually i come from another country •-•
Answer:
65
Step-by-step explanation:
40 + 5 × 5
40 + 25
65
Good Luck!Note: I also come from another country •-•
[tex]{ \boxed {\huge{ \sf{ \color{blue}{answer : }}}}}[/tex]
65
Step-by-step explanation:
= 40 + 5 × 5
= 40 + 25
= 65
-
#Good_LuckIf a^2+b^2= 4 and ab = 5, what is the value of
(a+b)^2?
A. 10
B. 12
C. 14
D. 16
Answer:
14
Step-by-step explanation:
(a+b)^2
(a+b)(a+b)
FOIL
a^2 + ab+ab + b^2
Combine like terms
a^2 +2ab + b^2
Rearranging
a^2+b^2 +2ab
We know a^2+b^2 = 4 and ab= 5
4 + 2(5)
4+10
14
Answer:
C. 14.
Step-by-step explanation:
We use the identity:-
a^2 + b^2 = (a + b)^2 - 2ab
So 4 = (a + b)^2 - 2(5)
(a + b)^2 = 4 + 2(5)
= 14.
Please Help! I will give you the brainiest and a lot of points!
Solve using the addition principle. 3y - 11 ≤ 2y - 2
Answer:
y ≤ 9
Step-by-step explanation:
3y - 11 ≤ 2y - 2
Subtract 2y from each side
3y-2y - 11 ≤ 2y-2y - 2
y - 11 ≤ - 2
Add 11 to each side
y - 11+11 ≤ - 2+11
y ≤ 9
Answer:
[tex]y \leqslant 9[/tex]
Step-by-step explanation:
[tex]3y - 11 \leqslant 2y - 2 \\ 3y - 2y \leqslant 11 - 2 \\ y \leqslant 9[/tex]
Martina got a prepaid debit card with $20 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 19 cents per yard. If after that purchase there was $15.63 left on the card, how many yards of ribbon did Martina buy?
Phone card = $20
You need to minus 17.92 from 20 = $2.08
$2.08 / 0.13 = how many minutes
= 16
Abdul's gas tank is 1/3 full. After he buys 12 gallons of gas, it is 7/9 full. How many gallons can abdul's tank hold
Answer:
Abdul's tank can hold 27 gallons of gas.
Step-by-step explanation:
Given that Abdul's gas tank is 1/3 full, and after he buys 12 gallons of gas, it is 7/9 full, to determine how many gallons can Abdul's tank hold the following calculation must be performed:
1/3 = 0.3333
7/9 = 0.7777
0.777 - 0.333 = 0.444
0.444 = 12
1 = X
12 / 0.444 = X
27 = X
Therefore, Abdul's tank can hold 27 gallons of gas.
Evaluate 5x – 2y + (7x – y) for x = 7 and y = –2
Answer:
90
Step-by-step explanation:
5x – 2y + (7x – y)
Combine like terms
12x -3y
Let x = 7 and y = -2
12(7) -3(-2)
84 +6
90
Answer:
90
Step-by-step explanation:
Hi there!
We are given this expression:
5x-2y+(7x-y) and we want to evaluate it if x=7 and y=-2
First, let's combine like terms, as that will make it easier for when we substitute the values into the expression
Open up the parentheses
5x-2y+7x-y
Combine like terms
12x-3y
Now substitute 7 as x and -2 as y into the expression
12(7)-3(-2)
Multiply
84+6
Add
90
Hope this helps!
Need it done ASAP please help
Answer:
[tex]M_{st} = (\frac{-2+4}{2}, \frac{-4+6}{2})[/tex]
[tex]M_{st}=(\frac{2}{2}, \frac{2}{2} )[/tex]
[tex]M_{st}=(1, 1)[/tex]
[tex]M_{cd}=(\frac{-6+4}{2} , \frac{10-8}{2} )[/tex]
[tex]M_{cd}=(\frac{-2}{2} , \frac{2}{2} )[/tex]
[tex]M_{cd}=(-1, 1)[/tex]
Solve each equation for the specified variable
Answer: Solve for the specified variables
Step-by-step explanation:
1. w= A/l
2. d=C/pi
3. s=v-gt
4. y= 5/2x-11/2
5. P^2= P^1V^1 / P^2 Put ^ as lowercase as shown, can't find symbol on my keboard T.T
6. W= Ke2g / V^2
7. h= V / 2/3 pi r^2
8. n=2S/a+k
9. S=A/pi r - r (not 100% sure on that one)
10. r= E/I-R
11. h= E-1/2mv^2/mg
12. a=K+5b/b+3
13. c=ab/b+a
Wooh, finally finished all that. Hope I didn't make any mistakes. Have a great day!
plot the following points on a xy-plane.
(5,2) , (-2, 1) , (-1,-3)
Answer: See below
Step-by-step explanation:
Answer:
Answer below
Step-by-step explanation:
The ratio of total interior angles to total exterior angles of a quadrilateral is
Select one:
a. 3:1
b. 1:2
c. 1:1
d. 2:1
9514 1404 393
Answer:
c. 1 : 1
Step-by-step explanation:
The total of exterior angles of any convex polygon is 360°. The total of interior angles of a quadrilateral is 360°. So, the ratio of interest is ...
interior : exterior = 360° : 360° = 1 : 1
What is the measure of b, in degrees
Answer:
B) 32
Step-by-step explanation:
(sin 74) / 10 = (sin c) / 10
c = 74
180 - 74 -74
= 32
a. 1.5
b. 2.3
c. 2.4
d. 1.9
Answer:
2.3
Step-by-step explanation:
.5 - .3 = .2
.8 - .5 = .3
1.2 - .8 = .4
1.7 - 1.2 = .5
We should add .6 next
1.7+.6 = 2.3
plz help I will give Brianly
A pair of linear equations is shown below: y = −x + 1 y = 2x + 4 Which of the following statements best explains the steps to solve the pair of equations graphically? (4 points) Select one: a. On a graph, plot the line y = −x + 1, which has y-intercept = −1 and slope = 1, and y = 2x + 4, which has y-intercept = 2 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution. b. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = 1, and y = 2x + 4, which has y-intercept = 1 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution. c. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = −2 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution. d. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.
Answer:
the answer is 89
Step-by-step explanation:
this is a hard one to salve but basically if you know and lern hout to do it it is not that hard
Karen is having a party. She'll have 4 tables for every 12 guests. Complete the table below showing the number of tables and the number of guests.
Teresita wanted to buy a dress for $50, but she decided to wait because she didn't have
enough money. A week later, the price had gone up 20%. Now she definitely had to wait to
buy it. A week later, she went back to the store, and the price had gone down 20% from the
last price. Teresita finally bought the dress. What did she pay for it?
Answer:
$48
Explanation:
> 50 x .20 = $10
$50 + $10= $60
-----------------------------
> 60 x .20 = $12
$60 - $12= $48
Please help I’m really stuck!!
Step 1: Solve for one variable
---I will be using the first equation and solving for a.
a + c = 405
a = 405 - c
Step 2: Substitute into the other equation
---Now that we have a value for a, we can substitute that value into the second equation. Then, we can solve for c.
12a + 5c = 3950
12(405 - c) + 5c = 3950
4860 - 12c + 5c = 3950
-12c + 5c = -910
-7c = -910
c = 130
Step 3: Plug back into the first equation
---We now know one variable, which means we can plug back into our first equation and solve for the other.
a = 405 - c
a = 405 - 130
a = 275
Answer: 275 adults, 130 children
Hope this helps!
URGENT 100 POINTS AND BRAINIEST!!!!!!
Question 4 (Essay Worth 10 points)
(02.05 HC)
The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x):
A graph with two linear functions; f of x passes through 5, 0 and 10, 10, and g of x passes through negative 3, 0 and 2, 10.
Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points)
Part B: Solve for k in each type of transformation. (4 points)
Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)
Using the points stated in the original problem, I have determined the lines for the graph.
f(x)=3x-1
g(x)= 3x+17
Using the basic descriptions of transformations, we can determine the movement of the lines as being either horizontal or vertical shifts. (to put a visual to this problem, I the diagram in Desmos and then marked the stated points on the graph.)
Horizontal shifts move the line either to the left or to the right. Vertical shifts move the line either up or down.
If you look at the graphs as being the same x-value for the functions, the change in the y- value is +18, which is a vertical shift.
If you look at the graphs as being the same y-values, the change in x is -6 which is a horizontal shift.
So, the value of k is the amount of change each equation has to have to match the points given. (from f(x) to g(x))
The vertical shift is g(x)=f(x) +18
The horizontal shift is g(x)=f(x-6)
Answer:
The vertical shift is g(x)=f(x) +18
The horizontal shift is g(x)=f(x-6)
Step-by-step explanation:
What is the length of the line?
WILL GIVE BRAINLIEST!!
Answer:
18
Step-by-step explanation:
6^2 plus 3^2 = 324, square root 324 =18
Answer:
[tex]\sqrt{45}[/tex]
Step-by-step explanation:
The line represents the hypotenuse of a right triangle with legs 6 and 3. For any right triangle, the Pythagorean Theorem states that [tex]a^2+b^2=c^2[/tex], where [tex]a[/tex] and [tex]b[/tex] are two legs of the triangle and [tex]c[/tex] is the hypotenuse.
Therefore, we have:
[tex]6^2+3^2=c^2,\\c^2=36+9,\\c=\boxed{\sqrt{45}}[/tex]
A soda can measures 10 centimeters high and has a radius of 2 centimeters. How many milliliters of liquid will it hold?
*note: 1 cubic centimeter = 1 milliliter. Use 3.14 for pi.
Answer: 125.6 ml
Step-by-step explanation:
V = (3.14) (2^2) (10)
V = (3.14) (4)(10)
V= 125.6 cm^3
1 cubic centimeter = 1 milliliter
The mother was fed 21 fish, how many fish was the cub fed?
Find the measure of the missing angles.
Answer:
Step-by-step explanation:
e = 61°, f = 119°, and d = 90°
We know that vertically opposite angles are equal.
So, e = 61° [Vertically opposite angles]
We know that linear pair of angles are supplementary (180°).
So, f + 61° = 180° [Linear pair of angles]
=> f = 180° - 61°
=> f = 119°
and d + 90° = 180° [Linear pair of angles]
=> d = 180° - 90°
=> d = 90°
Becky Anderson must pay a lump sum of $6000 in 5 yr. If only $5000 is available to deposit right now, what annual interest rate is necessary for the money to increase to $6000 in 5 yr?
Hello!
Out equation is: [tex]A=P(1+\frac{r}{n} )^t^n[/tex]
A= 6000
P=5000
N=1
T=5
R= What we are trying to find
This means we will have [tex]6000=5000(1+r)^5[/tex]
Divide both sides by 5000:
[tex]\frac{6000}{5000} = (1+r)^5[/tex]
Move the power to the other side by rooting both sides:
[tex]\frac{6000}{5000} ^1^/^5 = 1+r[/tex]
Subtract 1 from both sides:
[tex]\frac{6000}{5000} ^1^/^5 -1 = r[/tex]
Now we just need to calculate: R = 0.03713728...
I don't know how many decimal places you can have, but I will round to 2. This will give you an Interest Rate of 3.71%.
I hope this helps! :)
Find h(-5) when: h(x) = x2 + 2x + 2
Answer:
17
Step-by-step explanation:
h(x) = x^2 + 2x + 2
Let x = -5
h(-5) = (-5)^2 + 2(-5) + 2
= 25 -10 +2
= 17
A textbook store sold a combined total of 473 chemistry and sociology textbooks in a week. The number of sociology textbooks sold was 59 less than the number of chemistry textbooks sold. How many textbooks of each type were sold?
Answer:
I. C = 266 textbooks.
II. S = 207 textbooks.
Step-by-step explanation:
Let the chemistry textbook be C.
Let the sociology textbook be S.
Translating the word problem into an algebraic expression, we have;
C + S = 473 ..... equation 1
S = C - 59 ..... equation 2
Substituting eqn 2 into eqn 1, we have;
C + C - 59 = 473
2C - 59 = 473
2C = 473 + 59
2C = 532
C = 532/2
C = 266 textbooks.
Next, we would determine the value of S;
S = C - 59
S = 266 - 59
S = 207 textbooks.
Check:
C + S = 473
266 + 207 = 473
473 = 473
Please help explanation if possible
Answer:
10% gain
Step-by-step explanation:
[P2-P1]/P1
(33-30)/30=3/30=.1 or 10% gain.
Answer:
10%
Step-by-step explanation:
→ Minus the new share from the old one
33 - 30 = 3
→ Divide the answer by the original price
3 ÷ 30 = 0.1
→ Multiply the answer by 100
0.1 × 100 = 10%
I NEED HELP ASAP, I DON'T UNDERSTAND THIS PROBLEM!!!!!
Answer:
1
Step-by-step explanation:
Cosine is a trigonometric function that is represented by adjacent divided by the hypotenuse. The side adjacent to angle A is AC and the hypotenuse is AB, so we can say cos(A) = [tex]\frac{AC}{AB}[/tex]. We can do the same for angle B. The side adjacent to it is BC, and the hypotenuse is again AB. So, we can say
cos(B) = [tex]\frac{BC}{AB}[/tex]. We are solving for [tex]\frac{cosA}{cosB}[/tex], so we can substitute the value of those two and solve:
[tex]\frac{\frac{AC}{AB}}{\frac{BC}{AB} }[/tex]
[tex]\frac{AC}{AB} * \frac{AB}{BC} = \frac{AC}{BC}[/tex]
AC is given to be 3 and BC is also 3, so [tex]\frac{AC}{BC}[/tex] is [tex]\frac{3}{3}[/tex] which is just 1.
