The iterated integral by converting to polar coordinates is [tex]\frac{2a^{2} }{5}[/tex]
Evaluating an iterated integral by converting it to polar coordinates involves the following steps:
Identify the region of integration in the xy-plane.Convert the region of integration to polar coordinates. This typically involves finding the bounds for r and theta in terms of x and y.Write the iterated integral in terms of polar coordinates, with the outer integral being with respect to r and the inner integral being with respect to theta.Evaluate the integral by using the bounds found in step 2 and the appropriate substitution.Here, [tex]\int\limits^a_0 \int\limits^0_{-\sqrt{a^{2} - y^{2} } } {6x^{2} y} \, dx dy[/tex]
Now, converting it into the polar form:
[tex]\int\limits^\pi _\frac{\pi }{2} \int\limits^a_0} {6\cos^{2}\theta}\ {sin\theta\ r^{4} dr\ d \theta[/tex]
[tex]= \int\limits^\pi _{\frac{\pi}{2} } [\frac{6cos^2\theta}{5}\ r^5 sin\theta]^{a}_{0} \, d\theta[/tex]
[tex]= \int\limits^\pi _{\frac{\pi}{2} } [\frac{6\ a^2 \cos^2\theta sin\theta}{5}] \, d\theta[/tex]
[tex]= [-\frac{2a^{2} }{5}\ cos^{3}\theta ]^{{\pi} }_\frac{\pi}{2}[/tex]
[tex]= \frac{2a^{2} }{5}[/tex]
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The complete question is:
Evaluate the iterated integral by converting it to polar coordinates:
[tex]\int\limits^a_0 \int\limits^0_{-\sqrt{a^{2} - y^{2} } } {6x^{2} y} \, dx dy[/tex]
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23:
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Determine the x- and y- intercepts for the graph defined by the given equation.
y = 7x + 3
a. X-intercept is (3,0)
CH
x-intercept is 0.-
y-intercept is 0,-
y-intercept is (3,0)
b.
d. x-intercept is (3, 0)
x-intercept is
0
y-intercept is
10
y-intercept is (0,3)
Please select the best answer from the choices provided
А
ОВ
Answer:
[tex](-\frac{3}{7}, 0)[/tex] -- x intercept
[tex](0,3)[/tex] -- y intercept
Step-by-step explanation:
Given
[tex]y = 7x + 3[/tex]
Required
Determine the x and y intercept
For x intercept.
Set [tex]y = 0[/tex]
So, we have:
[tex]y = 7x + 3[/tex]
[tex]0 = 7x + 3[/tex]
Collect Like Terms
[tex]7x = -3[/tex]
Make x the subject
[tex]x = -\frac{3}{7}[/tex]
Hence, the x intercept is: [tex](-\frac{3}{7}, 0)[/tex]
For the y intercept;
Set [tex]x = 0[/tex]
So, we have:
[tex]y = 7x + 3[/tex]
[tex]y = 7*0 + 3[/tex]
[tex]y = 0 + 3[/tex]
[tex]y = 3[/tex]
Hence, the y intercept is: [tex](0,3)[/tex]
AnswerB
Step-by-step explanation:
find the image of (-4,2) obtained by translating 3 units up, followed by a reflexion over the x axis
Answer:
(-4,-5)
Step-by-step explanation:
1. Image is the points after the transformation
2. Pre-Image is the original points
3. our x value is left to right and our y value is up and down (x,y)
4. Our points are (-4,2)
5. They first want us to translate three units up, so we add to our y value (y is up and down)
6. 2+3 = 5
7. Our new points are (-4,5)
6. Now we are asked to reflect over the x axis. Remember their are a lot of rules concerning reflections. For a reflection across x-axis our equation is this : (x,y) → (x,-y)
7. (-4,5) → (-4,-5)
8. (-4,-5) is our answer
find the area of given figure
Answer:
hope it helped have a good day mate
According to the National Beer Wholesalers Association, U.S. consumers years and older consumed gallons of beer and cider per person during . A distributor in Milwaukee believes that beer and cider consumption are higher in that city. A sample of consumers years and older in Milwaukee will be taken, and the sample mean beer and cider consumption will be used to test the following null and alternative hypotheses:_______.
H0 : µ ≤ 26.9
Ha : µ > 26.9
a. Assume the sample data led to rejection of the null hypothesis. What would be your conclusion about consumption of beer and cider in Milwaukee?b. What is the Type I error in this situation? What are the consequences of making this error?c. What is the Type II error in this situation? What are the consequences of making this error?
Step-by-step explanation:
H0 : µ ≤ 26.9
Ha : µ > 26.9
a. since the null hypothesis is rejected, we would accept the alternative hypothesis and come to the conclusion that there is enough evidence that beer and cider consumption are higher than 26.9 in the city.
b. type 1 error happens when we reject a true null hypothesis.
this error error in this question would be that our conclusion that beer and cider consumption is greater than 26.9 is not true. what is true is that it is equal to or less than 26.9.
the consequence is that is h0 is false it would be harder to reject it at a lower level of significance.
c. type ii error happens when the null hypothesis is accepted even though it is false. here, error would be that cider we accepted that cider and beer consumption is less than or equal to 26.9 when it is actually greater than 26.9
the consequence is that it would be harder to accept a true h0 at a high level of significance
what is 893 :9 in long division
2x +5y = -7
7x + y = -8
Solve by substitution SHOW WORK!
Answer:
x = 1, y = -15
Step-by-step explanation:
7x + y = -8 ⇒ y = -7x-8
2x + 5y = -7
substitute -7x-8 for y:
2x + 5(-7x-8) = -7
2x - 35x - 40 = -7
-33x - 40 = -7
-33x = -33
x = 1
y = -7x-8 = -15
Evaluate the following: a. 4|−8| b. 2|−3| + 4(7) c. 8|−2| − 6 d. 5|−4| + 2|−6|
Step-by-step explanation:
a. 4×|-8| = 4×8 =32
b. 2×3+4×7= 6+28 = 34
c. 8×2-6 = 10
d. 5×4+2×6 = 32
help asap, i will mark brainliest!
Answer:
150m
Step-by-step explanation:
[tex]Length=120-(-30)=120+30=150m[/tex]
Si un ladrillo de adobe pesa 20kg. mas de la mitad de su peso. ¿Cuanto pesara un ladrillo y medio?
Answer:
pesaria 2.25 kilos
explicacion
I need help so please be nice and help me hurry cause I have to turn this in!!
Answer:
16 easy
Step-by-step explanation:
How do I solve x, y, z?
Answer:
z=[tex]\sqrt{14^{2} -5^{2} }[/tex]
z=13.08
(5)[tex]\sqrt{171}[/tex]=14x
x=4.67
y=[tex]\sqrt{5^{2} -4.67^{2} }[/tex]
y=1.79
if it helps, please give me brainliest
An underground aquifer near Seiling, Oklahoma, sits on an impermeable layer of limestone. West of Seiling the limestone layer is thought to slope downward in a straight line. In order to map the limestone layer, hydrologists started at Seiling heading west and drilled sample wells. Two miles west of Seiling the limestone layer was found at a depth of 220 feet. Three miles west of Seiling the limestone layer was found at a depth of 270 feet
(a) What would you expect to be the depth of the limestone layer 5 miles west of Seiling
(b) You want to drill a well down to the limestone layer as far west from Seiling as you can. Your budget will allow you to drill a well that is 275 feet deep. How far west of Seiling can you go to drill the well? (Round your answer to one decimal place.)
Answer:
(A) 490ft.
(B) 2.8 miles
Step-by-step explanation:
Important points to note:
- The limestone layer is thought or assumed to slope downward in a straight line.
- 2 miles west of Seiling, the limestone layer was found at a depth of 220ft.
- 3 miles west of Seiling, the limestone layer was found at a depth of 270ft.
(A) What would you expect to be the depth of the limestone layer, 5 miles west of Seiling?
The expected depth of the limestone layer is:
2 miles + 3 miles = 5 miles
220ft + 270ft = 490ft
(B) Your budget will allow you drill a well that is 275ft deep. How far west of Seiling (in miles) can you go, to drill the well?
If 490ft ~ 5 miles
then 275ft ~ K miles
K = [275 x 5] / 490 = 2.80612245 miles
Rounding to 1 decimal place, the distance is 2.8 miles.
PLEASE HELP ASAP I WILL GIVE YOU BRAINIEST!! Marcus is 14 years younger than twice Kimi's age. Marcus is 8 years old. How old is Kimi?
Answer: kimi is 22
Step-by-step explanation:
Answer:
Kimi is 11 years old
Step-by-step explanation:
We can read 'twice Kimi's age' as Kimi's age times 2 and
'14 years younger' as minus 14.
Our equation is
2(Kimi's age)-14= Marcus' age
Since Marcus is 8:
2(Kimi's age)-14= 8
Now we manipulate the equation so that it equals Kimi's age. Remember that whatever we do to the right side, we also do to the left.
First we add 14 to both sides
2(Kimi's age)-14(+14)= 8(+14)
2(Kimi's age)= 22
Then we divide by 2
2(Kimi's age)/2= 22/2
Kimi's age=11
Usually we would us X to represent our unknown, Kimi's age, but I left it as Kimi's age so that it is easier to follow.
Subtract: (x^2+ 5x – 4) - (6x2 – 7)
Will give brainliest
Answer:
x^2+5x-9
Step-by-step explanation:
First multiply 6x2 because that's a number that isn't solved in the parenthesis.
(x^2+5x-4) - (12-7)
Then you subtract 12-7 which equals 5.
(x^2+5x-4)-(5)
You now take the parenthesis off
x^2+5x-4-5
-4-5 equals -9
Now you get the answer: x^2+5x-9
Answer:
-5x² + 5x + 3
Step-by-step explanation:
Five higschool friends all happen to be female born in 2003 assuming that the survival of each ine is independent what is the proablity that at least one lives to be 100 year old
Answer:
15%
Step-by-step explanation:
The volume Vof a cylindrical can is represented by the formula V=πr2h, where h is the height and r is the radius. A cylindrical can has a volume of 1014π cubic centimeters and a height of 6 centimeters. What is the radius of the can?
Answer:
Step-by-step explanation:
V = πr²h
1014π = πr²·6
r² = 1014/6 = 169
r = 13 cm
The flower shop has 40 times as many flowers in the cooler as Kendall has in her bouquet. Kendall has 15 flowers. How many flowers are in the cooler?
Can anyone help me thank you
Answer:
tu debes de saber las respuestas por qué tú estás como en onceavo
you want branliest.more branliest giving out
Answer:
that is a cute dog
Step-by-step explanation:
1. very fluffy
2. small
3. sleeping
4. teddy bear dog :D
*) Simplify the second expression
2(2m + 2) + m.
2(2m + 2) + m =
m +
?
Answer:
5m + 4
Step-by-step explanation:
First, use the distributive property to open the parentheses.
2(2m + 2) + m = _m + 4
4m + 4 + m = _m + 4
Simplifiy:
5m + 4
Hope this helps!
Answer:
5m+4
Step-by-step explanation:
open up the bracket
that will be 4m+4+m (since 4m and m are alike we can add them together)
5m+4
if this helped please give me brainlest
el resultado de 20+(-60)-40-20es
Answer:
140 by the number like I know this
Step-by-step explanation:
I did the test
Guys I suck at this stuff so can someone Just PLEASE HELP ME
Answer:
I only
Step-by-step explanation:
The others have irrational & unsolvable numbers!
Hope that helps!
- 3x + 5y = -2
2x - 2y = 1
Solve by elem inaction
Answer:
x=1/4 , y=-1/4. You can confirm this by substituting the numbers in.
Step-by-step explanation:
1.) Some banks charge a fee on savings accounts that are left inactive for an extended period of time. The equation y = 5000 * (0.98) ^ x represents the value, y of one account that was left inactive for a period of x years .
a. What was the initial amount of money that was left in this savings account?
b. What is the percent of change each year in this savings account?
Answer:
a. The initial amount of money that was left in this savings account was of 5000.
b. Decrease of 2% each year.
Step-by-step explanation:
Exponential function:
An exponential function, with an initial value of A(0), and a decay rate of r, as a decimal, is given by:
[tex]A(t) = A(0)(1-r)^t[/tex]
In this question, we have:
[tex]y = 5000*(0.98)^x[/tex]
a. What was the initial amount of money that was left in this savings account?
This is y(0) = 5000
The initial amount of money that was left in this savings account was of 5000.
b. What is the percent of change each year in this savings account?
First as a decimal.
1 - r = 0.98
r = 1 - 0.98
r = 0.02
So a decrease of 2% each year.
Troy and Lisa were shopping for school supplies. Troy bought 3 notebooks and 5 thumb drives for $20.25. Lisa bought 8 notebooks and 8 thumb drives for $38. Find the cost of each notebook and the cost of each thumb drive.
Answer:
Step-by-step explanation:
3n + 5d = 20.25
24n + 40d = 162
8n + 8d = 38
-24n - 24d = -114
24n + 40d = 162
-24n - 24d = -114
—————————
16d = 48
d = 3
A drive costs $3
3n + 5(3) = 20.25
n = 1.76
A notebook costs $1.75
Divide. Then, check your work with multiplication. 12.21 / 11
Answer:
1.11
Step-by-step explanation:
Answer:
1.11
Step-by-step explanation:
12.21/11 is equal to 1.11
to check with multiplication, 1.11*11 = 12.21
A researcher is conducting a study of charitable donations by surveying a simple random sample of households in a certain city. The researcher wants to determine whether there is convincing statistical evidence that more than 50 percent of households in the city gave a charitable donation in the past year. Let p represent the proportion of all households in the city that gave a charitable donation in the past year. Which of the following are appropriate hypotheses for the researcher?
a. H_o : p=0.5 and H_a:p>0.5
b. H_o:p=0.5 and H_a:p≠0.5
c. H_o:p=0.5 and H_a:p<0.5
d. H_o:p>0.5 and H_a:p≠0.5
e. H_o:p>0.5 and H_a:p=0.5
Answer: a. [tex]H_o : p=0.5[/tex] and [tex]H_a:p>0.5[/tex].
Step-by-step explanation:
Let p represent the proportion of all households in the city that gave a charitable donation in the past year.
Reseracher wants to check whether p > 50% or p > 0.5
Since Alternative hypothesis contains ">, <, ≠" and null hypothesis is the opposite of alternative hypothesis.
So Null hypothesis: [tex]H_o: p=0.5[/tex]
Alternative hypothesis: [tex]H_a:p>0.5[/tex]
The correct option is a. [tex]H_o : p=0.5[/tex] and [tex]H_a:p>0.5[/tex].
Hi!
The measure of an angle is 12°. What is the measure of its supplement?
Thank you!!
Step-by-step explanation:
12° + x° = 90°
x. = 90 - 12
x =78°
a shopper pays $45 for 3 packs of t shirts. if each pack costs the same amount and contains 5 tshirts what is the cost per t shirt
A: $3
B: $6
C: $8
D: $9
Answer:
$3
Step-by-step explanation:
45/3=15
15/5=3
A train travels at a speed of 65 miles per hour. How long did it take the train to travel 227.5 miles?
Answer:
3.5 hours
Step-by-step explanation:
227.5÷65=3.5
A new animal hospital is planning to purchase a total of 36 cages for dogs, cats, and
rabbits. They want to purchase the same number of cages for dogs as for cats, but only
one-fourth as many cages for rabbits. How many of each cage should they buy?
Number of dogs cages = 16
Number of cats cages = 16
Number of rabbits cages = 4
What is an expression?
Expression in math is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
For simplicity’s assume;
D = number of dogs cages, C = number of cats cages,
R = number of rabbits cages.
Since, The dogs and the cats cages are the same number,
We can say, C = D.
Only one fourth as many cages for rabbits,
So, we can formulate,
R = 1/4D
Since, A new animal hospital is planning to purchase a total of 36 cages for dogs, cats, and rabbits.
2D + 1/4D = 36
Combine like terms and get the same denominator;
9/4D = 36
9D = 144
D = 16
So,
Number of dogs cages = 16
Number of cats cages = 16
And, Number of rabbits cages = 36 - (16 + 16)
= 36 - 32
= 4
Thus,
Number of dogs cages = 16
Number of cats cages = 16
Number of rabbits cages = 4
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