Evaluate the integral by interpreting it in terms of areas. integral -3 to 0(1+(9-x^2)^1/2)dx
Answers
Answer:
[tex]\int\limits^0_{-3}(1+\sqrt{9-x^{2}})\, dx=3+\frac{9\pi}{4}=10.068[/tex]
Step-by-step explanation:
We need to evaluate the following integral by interpreting it in terms of areas :
[tex]\int\limits^0_{-3}(1+\sqrt{9-x^{2}})\, dx[/tex]
The first step is to separate the integral into two easier integrals
[tex]\int\limits^0_{-3}(1+\sqrt{9-x^{2}})\, dx=\int\limits^0_{-3} 1 \, dx+\int\limits^0_{-3}\sqrt{9-x^{2}}\, dx[/tex] (Integral of the sum)
Now we can calculate each integral by studying the area below each function.
For the first integral the function is [tex]f(x)=1[/tex]
(I will attach a file with the functions)
The area below this function is the area of a rectangle with sides 1 and 3 ⇒
[tex]\int\limits^0_{-3}1 \, dx=3[/tex]
For the second integral the function is
[tex]f(x)=y=\sqrt{9-x^{2}}[/tex]
If we study this function :
[tex]y=\sqrt{9-x^{2}}[/tex]
[tex]y^{2}=9-x^{2}[/tex] (I)
[tex]x^{2}+y^{2}=9[/tex]
Which is the equation of a circle centered at (0,0) with radius equal to 3
From the equation (I)
[tex]y^{2}=9-x^{2}[/tex]
[tex]|y|=\sqrt{9-x^{2} }[/tex]
The two possible solutions are :
[tex]y=\sqrt{9-x^{2}}[/tex] (II) and [tex]y=-\sqrt{9-x^{2}}[/tex]
We will use (II) to solve the integral (which is the upper part of the circle)
The area of a circle with radius equal to 3 is
[tex]\pi.3^{2}[/tex]
In the integral we only need a quarter of circle ⇒ We divide the total area by 4 ⇒ [tex]\frac{\pi.3^{2}}{4}[/tex] ⇒ [tex]\frac{9\pi }{4}[/tex]
Finally the integral is equal to
[tex]\int\limits^0_{-3}(1+\sqrt{9-x^{2}})\, dx=3+\frac{9\pi}{4}=10.068[/tex]
Related Questions
What are the coordinates of G, H, and I after a rotation about (0,0) by 90 degrees clockwise? Thank you.
Answers
Answer:
Ok, when we have a point (x, y) and we do a rotation of 90° the new points will actually depend on the quadrant where we are, but it will always change the order to (y, x) but this does not end here, because depending on the quadrant where the point ends, the signs will change as follows.
1st quad (+y, +x)
2nd quad (-y, +x)
3rd quad (-y, -x)
4th quad (+y, -x)
So if we are in the second quadrant, the transformed point will be in the first quadrant
Now, we have that the points G and H are:
G = (-1, 3)
This point is in the second quadrant, so it moves to the first quadrant (where bot values must be positive).
The new point will be:
G´ = (3, 1)
And the other point is:
H = (-4, 0)
It also rotates to the first quadrant, so the new point will be:
H' = (0, 4)
Answer:
Because the person above already explained I’ll just give the answers.
Step-by-step explanation:
G = (-1,3) H = (-4,0) I = (3,-2)
Evaluate the expression when c=-6.
c2 +6c+5
Answers
Answer:
the evaluation gives 5 as the result
Step-by-step explanation:
We just replace -6 instead of "c" in the expression and perform the appropriate operations:
[tex]c^2+6\,c+5\\(-6)^{2} +6\,(-6)+5\\36-36+5\\5[/tex]
Answer: NEGATIVE 1
Step-by-step explanation:
I got the answer wrong and it told me the right answer was -1 so lol
Determine whether the equation is always, sometimes, or never true.
2/3 x + 4 = 2x
Answers
Answer:
Always true
Step-by-step explanation:
Given
[tex]\frac{2}{3}x + 4 = 2x[/tex]
Required
Determine its type of solution
[tex]\frac{2}{3}x + 4 = 2x[/tex]
Collect Like Terms
[tex]2x - \frac{2}{3}x = 4[/tex]
Take LCM
[tex]\frac{6x - 2x}{3} = 4[/tex]
[tex]\frac{4x}{3} = 4[/tex]
Multiply both sides by [tex]\frac{3}{4}[/tex]
[tex]\frac{4x}{3} * \frac{3}{4}= 4 * \frac{3}{4}[/tex]
[tex]x = 4 * \frac{3}{4}[/tex]
[tex]x = 3[/tex]
Hence, the equation is always true for x = 3
What is $12.78 rounded to the nearest dollar?
Answers
Answer:
$13
Step-by-step explanation:
[tex]\$12.78 = \$13[/tex]
Answer:$13
Step-by-step explanation:
.7 rounds to 1 if it is 5 or above it rounds up
Employee Time Card
DATE
IN
OUT
IN
OUT
HOURS
Sun.
Mon.
7:00 AM
11:00 AM
12:00 P.M.
a.
4:04 PM
3:59 P.M.
Tue.
7:05 AM
11:55 PM
b.
Wed.
7:01 AM
11:10 AM
10:59 AM
10:55 AM
12:05 PM
C.
Thur.
6:59 AM
3:58 P.M.
4:03 P.M.
3:49 PM
12:01 PM
12:02 PM
d.
Fri.
6:55 AM
11:01 AM
e.
Sat
TOTAL HOURS
Answers
In most jobs, the employees round up so that would make it 32 hours.
32x7.50= 240
If they wanted to be technical you could do 31.57x7.5 and that would make it 236.78
It’s up to you which one you go with
Answer:
31 hours 57 minutes.
In most jobs, the employees round up so that would make it 32 hours.
32x7.50= 240
If they wanted to be technical you could do 31.57x7.5 and that would make it 236.78
It’s up to you which one you go with
Step-by-step explanation:
A carpenter sands of a dresser in hour. At this rate, how long does it take the
carpenter to sand 1 dresser?
o hour
o hour
O 1 hours
O 23 hours
Answers
Question:
A carpenter sands 1/2 of a dresser in 3/4 hour. At this rate, how long does it take the carpenter to sand 1 dresser?
Answer:
[tex]1\ dresser = \frac{3}{2} hour[/tex]
Step-by-step explanation:
Given
[tex]\frac{1}{2} dresser = \frac{3}{4} hour[/tex]
Required
How long will it take to sand 1 dresser
[tex]\frac{1}{2} dresser = \frac{3}{4} hour[/tex]
Multiply both sides by 2
[tex]2 * \frac{1}{2} dresser = \frac{3}{4} hour * 2[/tex]
[tex]1\ dresser = \frac{3}{4} hour * 2[/tex]
[tex]1\ dresser = \frac{3}{2} hour[/tex]
Hence;
It'll take 3/2 hour to sand 1 dresser
Answer:
Step-by-step explanation:
hey babe
What is the product of (5/5)(614) ? Simplify your answer.
Answers
Answer:
614
Step-by-step explanation:
5/5 is just 1 because 5÷5=1
1 multiplied by 614 = 614
Hope this helped!
In the Atlanta metropolitan area, 723 new cases of invasive cancer of the cervix occurred among white women between 1975 and 1984, inclusive. An estimated 620,000 white women lived in this area on average during this time period. What is the average annual incidence rate of invasive cervical cancer in this population?
Answers
Answer:
1.166 per 1000 of population
Step-by-step explanation:
Given the following :
Newly recorded cases of invasive cervical cancer = 723
Period of time = 1975 - 1984 ( inclusive)
Estimated average Population of white women in the area at the time = 620,000
Average annual. Incidence rate invasive of cervical cancer in the population.
Incidence rate = (new cases / total population) × 10^n
Incidence rate = (723/620000) × 10^n
= 0.0011661
= 1.166 per 1000 of population
Which of the following is a true statement?
a. To square a number, multiply the number
by 2.
b. The inverse of squaring a number is to
divide the number by 2.
c. To square a number, multiply the number
by itself.
d. A perfect square is a number who’s
square root is an even number.
Answers
Answer: The answer is c. To square a number is to divide the number by 2.
Step-by-step explanation:
y< 4 3 x+3 y≤−2x−1 Which graph represents the system of inequalities?
Answers
Answer:
Don't see any graphs
Step-by-step explanation:
Answer:
its A
Step-by-step explanation:
I am a pair of numbers and my product is 1, what am I?
Answers
Answer:
Step-by-step explanation:
How I Al's have doubts
order the number from greatest to least
3 1/3,3.34,300%
Answers
Answer:
3.34, 3 1/3 300%
Sorry if I’m wrong
Solve −5x = 30 a.) 6 b.) -6 c.) 25 d.) 35
Answers
Where is the point of intersection? x − 2y + 2 = 3 and x − y = 3
Answers
Answer:
Step-by-step explanation:
x -2y = 1
x - y = 3
x - 2y = 1
-x + y = -3
-y = -2
y = 2
x - 2 = 3
x = 5
(5, 2)
Someone help
Plssssssssssssssssssssssssss
Answers
The federal tax code allows some items used for business purposes to be depreciated. That is, their taxable value decreases over time. A new van used in your delivery business has a taxable value of $22,000. The tax code allows you to depreciate this van by $1900 per year. Find a formula that gives the taxable value T, in dollars, of the van after n years of depreciation.
Answers
Answer: T = 22,000 - 1,900n
Step-by-step explanation:
Taxable value is $22,000
The tax code allows for the depreciation of this van by $1,900 per year.
After n years therefore the total depreciation is;
= 1,900 * n
This depreciation will need to be removed from the taxable value of $22,000 to find out the taxable value left.
Formula is therefore;
T = 22,000 - 1,900n
1. Explain how measurements taken by standard rulers and scales are limited,
2. Include two to three examples to demonstrate these limitations. Include at least one limitation of using
a ruler and at least one limitation of using a scale,
3. Make sure to write your answer using five to ten complete sentences,
Answers
Answer:
Please find the answer in the explanation
Step-by-step explanation:
RULER
measurements taken by ruler can be limited due to absolute errors, zero error and uncertainties.
1.) If the end of the ruler is worn out giving rise to a zero error
2.) The calibration of the ruler may give rise to another systematic error if the makings are incorrect.
3.) If the object to be measured is not on the same level as graduated surface of the ruler, the angle at which the scale is viewed will affect the result. This is known as parallax error.
SCALE
Systematic error can occur in a scale when the scale is wrongly calibrated.
Also, reading a scale from different angles introduces a variable parallax error.
random uncertainty could be a parallax error caused by taking readings from different angles. This can be reduced by the use of a mirror behind the scale and viewing normally.
Seven times the sum of 4 and some number is 42
Answers
Answer:
[tex]x=2[/tex]
Step-by-step explanation:
[tex]7\times{(4+x)}=42[/tex]
Divide both sides by 7:
[tex]4+x=42\div{7}\\4+x=6[/tex]
Subtract 4 from both sides:
[tex]x=6-4\\x=2[/tex]
Solve : 3x – 4 = 2(x-1)
Answers
Answer:
Step-by-step explanation:
Answer:
x=2
Step-by-step explanation:
3x-4=2(x-1)
=>3x-4=2x-2
=>3x-2x=-2+4
=>x=2
A rope 5 meters long was cut into 7 equal parts. What is the length of each part?
Answers
Answer:
5/7 meters
Step-by-step explanation:
Take the 5 meters and divide into 7 parts
5/7 = 5/7 meters
To find the length of each part, we can divide.
5 / 7 = 0.714...
We can just keep it as a fraction.
The answer is 5/7m
Best of Luck!
Solve for y.
4y2 = 7y+2
If there is more than one solution, separate them with commas.
If there is no solution, click on "No solution."
Answers
Answer:
y=-1/4, 2.
Step-by-step explanation:
4y^2=7y+2
4y^2-7y-2=0
factor,
(4y+1)(y-2)=0
zero property,
4y+1=0, y-2=0,
4y=0-1=-1,
y=-1/4,
y=0+2=2.
Evaluate the expression when c=-6.
c? +6c+5
Answers
Answer: -31
Step-by-step explanation: 1.) Plug in -6 for c
2.) equation will then be: 6(-6)+5
3.) use PEMDAS: multiply first then addition
4.) 6(-6) equals -36
5.) add -36+5 which equal -31
Therefore your answer should be -31
Explanation:
The inventory of a restaurant needs replenishing of its supply of apples. The food supplier charges $7/bag of apples. The restaurant needs a 30 day-supply. If the restaurant uses 2 bags of apples per day, how much will it cost for a 30-day supply?
(You do not need to include the units. You only need to enter your answer as a number.)
Answers
and if the charge for a bag is $7, then multiply 7 times your total number of bags (7x60) for the cost.
the answer should be $420
Rewrite with positive exponents a^-3 b^-5
Answers
Answer:
1/a^3 and 1/b^5
Solve for x: 3/2 + 1/2x=2x
Answers
What is the solution to the equation?
{+55 - 466
{+55 = 466
O [+55-55-466+55
f=521
+55 = 466
O +55+55-466+55
{ = 521
(+55 = 466
O +55-55-466-55
f=411
f+55 = 466
Of+ 55+55-466-55
f = 411
Answers
Answer:
f=55=466
f+55-55=466-55
Step-by-step explanation:
Find the solution of the term.
Ellie drives 22.5 miles in 45 minutes. If she drove three hours in total at the same rate, how far did she go?
Answers
Answer:
90
Step-by-step explanation:
3 hours = 180 mins
180 ÷ 45 = 4. so Ellie will drive 4x more miles in 3 hours.
22.5 × 4 = 90
7k-k+19 Combine like terms
Answers
Step-by-step explanation:
7k-k+19
6k+19 should be fine
Steps to solve:
7k - k + 19
~Combine like terms
6k + 19
Best of Luck!
-2.5 + d = -3.6 What is the sum?
Answers
Answer:
-1.1
Step-by-step explanation:
we take -3.6 minus -2.5
which we get -1.1 hav a nice day :]
Answer:
d = -1.1
Step-by-step explanation:
-3.6 - ( -2.5) = -1.1
Simplify the expression. Write the answer with positive exponents only. Assume the variable represents a nonzero real number.
Answers
Answer:
[tex]\frac{1}{w^{29}}[/tex]
Step-by-step explanation:
The given expression is [tex]\frac{w^{-7}(w^{-9})^2}{w^4}[/tex].
Since, [tex]w^{-7}=\frac{1}{w^7}[/tex]
And [tex]w^{9}=\frac{1}{w^9}[/tex]
Expression will become,
[tex]\frac{w^{-7}(w^{-9})^2}{w^4}=\frac{\frac{1}{w^7}(\frac{1}{w^9})^2}{w^4}[/tex]
[tex]=\frac{\frac{1}{w^7\times w^{18}}}{w^4}[/tex]
[tex]=\frac{\frac{1}{w^{(7+18)}}}{w^4}[/tex]
[tex]=\frac{1}{w^{25}}\times \frac{1}{w^4}[/tex]
[tex]=\frac{1}{w^{25}\times w^4}[/tex]
[tex]=\frac{1}{w^{29}}[/tex]
Therefore, Simplified form of the given expression will be [tex]\frac{1}{w^{29}}[/tex].