Answers
The best method would certainly be integration :)
The area is given by the integral,
[tex]\displaystyle\int_0^2\frac{\mathrm dx}{9-x^2}[/tex]
We can split up the integrand into partial fractions:
[tex]\dfrac1{9-x^2}=\dfrac16\left(\dfrac1{3-x}+\dfrac1{3+x}\right)[/tex]
Then the area is
[tex]\displaystyle\frac16\int_0^2\left(\frac1{3-x}+\frac1{3+x}\right)\,\mathrm dx[/tex]
[tex]=\dfrac16(-\ln|3-x|+\ln|3+x|)\bigg|_0^2[/tex]
[tex]=\dfrac16\left((\ln5-\ln1)-(\ln3-\ln3)\right)=\boxed{\dfrac{\ln5}6}[/tex]
Related Questions
Mrs.Hogan made 24 cupcakes for Keira's birthday. She put pink frosting on 1/4 of the cupcakes. She put purple frosting on 1/2 of the remaining cupcakes. The rest had blue frosting. How many cupcakes get blue frosting?
Answers
Answer:
9 Blue Cupcakes
Step-by-step explanation:
First, draw a diagram.
(suppose the blank stars are the pink cupcakes, black stars are the purple cupcakes and the half blank-half black stars are the blue cupcakes)
oooo
oooo
oooo
oooo
oooo
oooo
Then, figure out how much is 1/4 of 24, which is 6.
✩✩✩✩
✩✩oo
oooo
oooo
oooo
There are 18 cupcakes left. Then, figure out what 1/2 of 18 is, which is 9.
✩✩✩✩
✩✩★★
★★★★
★★★o
oooo
oooo
Finally, see how many are remaining, which are 9 cupcakes left.
✩✩✩✩
✩✩★★
★★★★
★★★✯
✯✯✯✯
✯✯✯✯
Hopefully this helped!
-✩sandwichchan✩
Evaluate the expression when x = 10 and y = -2.
-x+y
6
Answers
Answer: [tex]-12[/tex]
Step-by-step explanation:
[tex]-x+y=-(10)+(-2)=-10-2=\boxed{-12}[/tex]
What must be true of the units in two rates if one rate can be converted to the units of the other rate? In other words, the units of the
first rate are both/all distinct from that of the converted rate, but it still represents the same measurement?
Answers
Answer:
Yes, unit of the first rate can be be different from and second and still represent the same measurement/value.
Step-by-step explanation:
Yes, if we have two units rate and one rate is converted to another, both measurement will still remain the same even after the conversion but the rate will be different.
For example if we want to convert $2 to naira, note that the unit rates for are distinct but after conversion the amount of both money will be the same.
If $1 = #386
2$ = 2×#386
$2 = #772
Hence the measurement of $2 is equivalent to 386 naira even though the rates are distinct (naira and $)
simplify 4(12* 6-4^2) +9
PLEASE HELP!!!!
Answers
Answer:
233
Step-by-step explanation:
Rice weighing 33/4 pounds was divided equally and placed in 4 containers. How many ounces of rice were in each?
Answers
Answer:
15 ounces
Step-by-step explanation:
33/4 ÷ 4 pounds.
= (4 × 3 + 3)/4 ÷ 4 pounds.
= 15/4 ÷ 4 pounds.
= 15/4 × 1/4 pounds.
= 15/16 pounds.
Now we know that, 1 pound = 16 ounces.
Therefore, 15/16 pounds = 15/16 × 16 ounces.
= 15 ounces
Answer:
2.0625 or 2 1/16
Step-by-step explanation:
What is the value of "b" in the following equaiton? 4b = 6b - 10
Answers
Answer:
5
Step-by-step explanation:
4b=6b-10
subtract 6b from both sides which is -2
new equation is -2b=-10
divide -2 from both sides and the answer is b=5
Please help ASAP!!!!
Answers
Answer:
Step-by-step explanation:
figure it out kid
What is m < M? enter your answer in the box
Answers
Answer:
Sorry this is late, but for future reference the answer is 98°.
Step-by-step explanation:
I took the quiz.
Use £1 = $1.92 dollars to work out how much 45p is in dollars
Answers
Answer:
around 58 dollars
Step-by-step explanation:
EASY POINTS. PLEASE CLICK HERE
Answers
Answer:
Free points you say?!
Brainiest too please ;)
Step-by-step explanation:
what is 3+3-2 divided by 2
Answers
6-2=4
4/2=2
Answer=2
The ratio number of people who like
Chocolate ice cream to Vanilla is 4:3
If 500 more people like Chocolate,
how many people like each?
Help!!
Answers
Suppose a train travels 30 miles in 1/3 of an hour. What is the trains average speed?
Answers
Answer:
90 mph
Step-by-step explanation:
30 / (1/3) = 90
f(x)= squad root of x plus 3. find the inverse
Answers
Answer:
inverse of [tex]\sqrt{x}[/tex]-3 : x^2 +3
Step-by-step explanation:
y=[tex]\sqrt{x-3}[/tex]
x=[tex]\sqrt{y-3}[/tex]
y=[tex]x^{2}[/tex]+3
[tex]x^{2}[/tex]+3
please solve 4x - 3(x - 2) = 21
Answers
Answer:
x = 15
Explanation:
4x-3(x-2)=21
4x-3x+6=21
x+6=21
x=15
Finish the sequence 1, 1/4, 1/9, 1/16, 1/25, __, __
Answers
Answer:
1/36, 1/49
Step-by-step explanation:
we notice that the sequences are the inverses of the square numbers, so the next one is
[tex](6^{2} )^{-1},(7^2)^{-1}\\\\36^{-1},49^{-1}\\\\\frac{1}{36}, \frac{1}{49}[/tex]
A partial sum of an arithmetic sequence is given. Find the sum.
14 (3 + 0.26k) k = 0
Answers
Answer:
72.3
Step-by-step explanation:
Given that:
The arithmetic sequence:
[tex]\sum \limits ^{14}_{k=0} (3 + 0.26k)[/tex]
The first term of the sequence [tex]a_0[/tex] = 3 since k = 0
i.e (3 + 0.26(0)) = 3
The last term of the sequence [tex]a_{14}[/tex] = 6.64
i.e (3+ 0.26(14)
= (3 + 3.64)
= 6.64
Total no of terms = 15 i.e from 0 to 14
∴
The partial sum of the arithmetic sequence = [tex]\dfrac{Total \ no \ of \ terms }{2} \times (a_o+a_{15})}[/tex]
[tex]=\dfrac{15 }{2} \times (3+6.64)}[/tex]
= 72.3
Question 1 (1 point) 3 If the dimensions of the box are L= 5cm W=2.5cm H= 2.5 cm, and the a kernel is 0.6cm; How many kernels could fit inside of the box?
Answers
Answer:
145 kernels
Step-by-step explanation:
The dimensions of the box are L= 5cm W=2.5cm H= 2.5.
Size of a kernal is 0.6 cm
We need to find number of kernels that could fit inside of the box. Let n be such kernals. So,
[tex]n=\dfrac{\text{volume of box}}{\text{volume of one kernel}}[/tex]
Kernal is in the shape of cube
So,
[tex]n=\dfrac{\text{volume of cuboid}}{\text{volume of one cube}}\\\\n=\dfrac{LWH}{a^3}\\\\n=\dfrac{5\times 2.5\times 2.5}{(0.6)^3}\\\\n=144.67\\\\\text{or}\\\\n=145\ \text{kernels}[/tex]
Hence, 145 kernels could fit inside of the box.
What is the measurement of
Answers
Answer:
of?????????????????????????
Answer:
it matters so of what?
Step-by-step explanation:
Why is a capacity of 25 fluid Ounces more than a capacity of 3 cups? O Because when you divide 25 by 8, the result is less than 3. Because when you multiply 25 by 8, the result is less than 3. O Because when you divide Ty by 8, the result is greater than 3. O Because when you multiply 25 by 8, the result is greater than 3.
Answers
Answer: Because when you divide 25 by 8, the result is greater than 3.
The solution is, Because when you multiply 25 by 8, the result is less than 3.
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
given that,
a capacity of 25 fluid Ounces more than a capacity of 3 cups
we have to find why it is correct.
now, we get,
if we divide 25 by 8
i.e. 25/8
now, we know,
24/8 = 3
so, 25/8 = 3.125
i.e. 25/8 > 3
as, we have, the result is greater than 3.
Hence, a capacity of 25 fluid Ounces more than a capacity of 3 cups is,
Because when you divide 25 by 8, the result is greater than 3.
To learn more on division click:
brainly.com/question/21416852
#SPJ7
I'm giving 50 POINTS and I mark BRAILIEST the question is provided. in the picture Please include ALL WORK and simplify. TYYY ❤️
Answers
[tex]\sf\longmapsto3 \times \frac{1}{3} \div \frac{2}{3} [/tex]
[tex]\sf\longmapsto \dfrac{3 \times \frac{1}{3} }{ \dfrac{2}{3} } [/tex]
[tex]\sf\longmapsto \dfrac{ \dfrac{10}{3} }{ \dfrac{2}{3} } [/tex]
[tex]\sf\longmapsto \: \dfrac{10}{3} \times \dfrac{3}{2} [/tex]
[tex]\sf\longmapsto \: \dfrac{10 \times 3}{3 \times 2} [/tex]
[tex]\sf\longmapsto \dfrac{30}{6} [/tex]
[tex]\sf\longmapsto \: 5[/tex]
a rectangular retaining wall has an area of 15 square feet. the height of the wall is two feet lesss than its length. find the height and the length of the wall.
Answers
x^2 - 2x = 15
x^2 - 2x - 15 = 0
(x-5)(x+3)=0
x-5=0 x+3=0
x=5 x=-3
The length is 5 because -3 cannot be the answer as it is negative. The height of the wall is 3 because 5-2 is 3.
Solve for x: |2x + 12| = 18 (5 points) x = 3, x = −3 x = 3, x = −15 x = 15, x = −15 x = −3, x = 15
Answers
Answer:
[tex]x=3\text{ or } x=-15[/tex]
Step-by-step explanation:
So we have the equation:
[tex]|2x+12|=18[/tex]
Definition of Absolute Value:
[tex]2x+12=18\text{ or } 2x+12=-18[/tex]
Subtract 12 from both sides for both equations:
[tex]2x=6\text{ or } 2x=-30[/tex]
Divide both sides by 2 for both equations:
[tex]x=3\text{ or } x=-15[/tex]
And we're done!
A population of voters contains 46% Republicans, 45% Democrats and the rest are Independents. Assume 50% of Republicans, 40% of Democrats, and 60% of Independents favor an election issue. A person chosen at random from this population is found to favor the issue in question. Find the conditional probability this person is a democrat. (Round off up to two decimal points.) Group of answer choices 0.18 0.51 0.71 0.39
Answers
Answer:
The probability is 0.18
Step-by-step explanation:
Here, we are interested in calculating a conditional probability;
Let the event that a voter is a Republican be R , the event that a voter is a Democrat be D and that a voter is an independent is I
Let the event that the election issue is favored be F
We have the following probabilities;
P(R) = 46% = 0.46
P(D) = 45% = 0.45
P(I) = 1-0.45-0.46 = 0.09
The conditional probability we want to calculate is;
P(D | F) which can be read as probability of event D given event F
From the question, we can identify the following conditional probabilities;
P(F|R) = 0.46 * 0.5 = 0.23 (0.5 is gotten from 50% = 50/100)
P(F | D) = 0.45 * 0.4 = 0.18
P( F | I) = 0.09 * 0.6 = 0.054
P(F) = 0.054 + 0.18 + 0.23 = 0.464
Mathematically; From Baye’s theorem
P( D | F) ={ P ( F | D) * P(D) }/ P(F)
P( D | F) = (0.18 * 0.45)/0.464 = 0.1745
Which of the following could be classified as a census?
a survey of a percentage of each state’s population about voting choices
a survey of each student in a school about school lunch options
a survey of all the children in a supermarket to determine the favorite cereal brands of the general population
a survey of all the women on Main Street to determine the current movie preferences of all people over age 20
Answers
Answer:
a survey of each student in a school about school lunch options
Step-by-step explanation:
The answer above is correct.
Answer: B. a survey of each student in a school about school lunch options
Step-by-step explanation:
2. What is the value of
|3|?
A. -3
B. 0
C. 3
D. 6
Answers
A cyclist rode the 1st 28 mile portion of his workout, at a constant speed. For the 18 mile cool down portion of his workout, he reduced his speed by 5 miles per hour. Each portion of the workout took the same time. Find the cyclist speed during the first portion, and find his speed during the cool down portion
Answers
Answer:
a uno
Step-by-step explanation:
espero que te cirba
A point has the coordinates (0, k).
Which reflection of the point will produce an image at the same coordinates, (0, k)?
a reflection of the point across the x-axis
a reflection of the point across the y-axigting
a reflection of the point across the line yex
a reflection of the point across the line y = -x
Answers
Answer:
The answer is (B). Tust me. I took the quiz.
Answer:
B) a reflection of the point across the y-axis
Step-by-step explanation:
Find the unknown angle measure
Answers
Answer:50
Step-by-step explanation:
Since the total of angles is 180, you just substract two numbers given by 180. Then, you will get 50. 180-(58+72) = 50
L is the midpoint of KM. If KL = 2x and LM = x + 6, what is KL?
Answers
Answer:
KL = 12
Step-by-step explanation:
Given that L is the midpoint of KM , then
KL = KM , substitute values
2x = x + 6 ( subtract x from both sides )
x = 6
Thus
KL = 2x = 2 × 6 = 12
The measure of the segment KL is 12 units if the L is the midpoint of KM. If KL = 2x and LM = x + 6
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
L is the midpoint of KM. If KL = 2x and LM = x + 6.
Given that L is the midpoint of KM, then
From the question:
KL = KM
2x = x + 6
After simplification:
x = 6
KL = 2x
Plug x = 6 in the above equation:
KL =2(6)
KL = 12
The measure of the segment KL is 12 units.
Thus, the measure of the segment KL is 12 units if the L is the midpoint of KM. If KL = 2x and LM = x + 6.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ2
