Find the mass of lamina bounded by circles x2 + y2 = 1 and x2 + y2 = 4in the first quadrant if the density is (x2 + y2). Could please anyone solve this...
Since density is equal to mass per unit volume, mass is equal to density times volume. So we split up the lamina into tiny regions with "volume" (area) equal to dA, multiplied by the density, and integrated over the entirety of the lamina.
This is best done in polar coordinates:
[tex]\begin{cases}x=u\cos v\\y=u\sin v\end{cases}\implies\mathrm dA=\mathrm dx\,\mathrm dy=u\,\mathrm du\,\mathrm dv[/tex]
so that [tex]x^2+y^2=u^2\cos^2v+u^2\sin^2v=u^2[/tex].
The lamina is then the set of points
[tex]L=\left\{(u,v)\mid1\le u\le2\land0\le v\le\dfrac\pi2\right\}[/tex]
Now compute the integral: the mass of the lamina is
[tex]\displaystyle\iint_L(x^2+y^2)\,\mathrm dA=\int_0^{\pi/2}\int_1^2u^3\,\mathrm du\,\mathrm dv=\frac\pi2\int_1^2u^3\,\mathrm du=\frac{15\pi}8[/tex]
A cup of coffee is cooling down such that its temperature is decreasing at a constant rate of 8% per minute. Let’s say the coffee starts at a temperature of 200 degrees Fahrenheit.
What’s its temperature after one minute by finding 8% of 200 and then subtracting?
Answer:
Temperature after 1 minute = 184 ° F
Step-by-step explanation:
starting temperature = 200 °F
rate of decrease = 8% per minute
Temperature lost = 8% of 200 = 8/100 × 200 = 0.08 × 200 = 16 °F
It therefore means that after 1 minute, the cup of coffee loses 16 °F,
∴ Temperature after 1 minute = (starting temperature) - (lost temperature)
= 200 - 16 = 184 °F
Find the point based on the parametric
equations. t = 3
X = 1 - 2t
y = 4t + 1
Answer:
(-5,13)
Step-by-step explanation:
because t=3
[tex]x = 1 - 2 \times 3 = - 5 \\ y = 4 \times 3 + 1 = 13[/tex]
1. Michel buys a leash for his dog. The leash is 6 ft 3 inches. How long, in inches, is the leash?(1 ft = 12 inches)
A) 48 inches
B) 51 inches
C) 72 inches
D) 75 inches
2. What is the area of a triangular garden with base of 6 ft and a height of 9 ft? (A = 1/2BH)
A) 27 square feet
B) 48 square feet
C) 54 square feet
D) 24 square feet
Answer:
1 = D 75 inches
2 = A 27
Step-by-step explanation:
1 - 6.3 times 12 = 75.6
2 - 6 times 9 = 54
54/2 = 27
:)
Carole ordered 4 dresses for $80 each, a $25 sweater, and a coat. The cost of the items without sales tax was $430. What was the cost of the coat?
Explanation:
The equation for the total cost of the clothes is 4×80+25+c=430, where c is the cost of the coat.
320 + 25 + c = 430
345 + c = 430
345 - 345 + c = 430 - 345
c = 85
The cost of the coat was $85.
Answer:
$85 for the coat
Step-by-step explanation:
1 dress = $80
4 dress =$80×4
=$320
sweater=$25
coat=?
4 dresses plus the sweater cost :
$320+$25=$345
The cost of all the item $430
cost of the coat :
$430-$345=$85
Parker invested $7,800 in an account
paying an interest rate of 1.7%
compounded continuously. Assuming no
deposits or withdrawals are made, how
much money, to the nearest dollar, would
be in the account after 11 years?
Answer:
A=9404
Step-by-step explanation:
Answer:
9404
Step-by-step explanation:
The ACT is an achievement test given nationally with normally distributed scores. Tim
scored a 24 on the mathematics portion of his ACT. The mean for the mathematics portion of
the ACT was 22.0 and the standard deviation was 5.1. What percent of the population scored
higher than Tim on the mathematics portion of the ACT?
Answer:
34.83% of the population scored higher than Tim on the mathematics portion of the ACT
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 22, \sigma = 5.1[/tex]
Tim scored 24. What percent of the population scored higher than Tim on the mathematics portion of the ACT?
The proportion is 1 subtracted by the pvalue of Z when X = 24. The percentage is the proportion multiplied by 100.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{24 - 22}{5.1}[/tex]
[tex]Z = 0.39[/tex]
[tex]Z = 0.39[/tex] has a pvalue of 0.6517
1 - 0.6517 = 0.3483
34.83% of the population scored higher than Tim on the mathematics portion of the ACT
Daniel is packing his bags for his vacation. He has
5
55 unique socks, but only
4
44 fit in his bag
Answer:
yes
Step-by-step explanation:
what is the solution to 2.8(2+0.5n)=2.4(n+1.2)
Answer:
Step-by-step explanation:
If Triangle M N O is congruent to triangle N M O, what statement best describes triangle MON?
The triangle is scalene.
The triangle is equilateral.
The triangle is isosceles and possibly equilateral.
The triangle is isosceles but definitely not equilateral.
Answer:
The answer is c
Step-by-step explanation:
The statement that best describes triangle MON is (c) The triangle is isosceles and possibly equilateral.
The congruent triangles are:
Triangle MNO and Triangle NMO
The above means that:
Sides MN and NO or MN and MO are equal
So, the triangles are isosceles triangles
However, it is possible that sides NO and MO are congruent
Hence, the statement that best describes triangle MON is (c) The triangle is isosceles and possibly equilateral.
Read more about congruent triangles at:
https://brainly.com/question/1675117
una persona cobra 7/4 de una cantidad, gasta 1/4 y presta 1/8 ¿Que fraccion de la cantidad cobrada le quedo?
Answer: (11/8)
Step-by-step explanation:
I will answer this in English.
a person collects 7/4 of an amount, spends 1/4 and lends 1/8. What fraction of the amount collected is left?
If the amount is A, then he collects:
C = (7/4)*A
Now, he spends 1/4 and lends 1/8 of the amount A, so the fraction left is:
Left = (7/4)*A - (1/4)*A - (1/8)*A
now i will write 7/4 as 14/8 and 1/4 as 2/8.
left = (14/8)*A - (2/8)*A - (1/8)*A = ((14 - 2 - 1)/8)*A = (11/8)*A
Given: 1; -5; -13 ; -23 ; ...
Derive a formula for the nth term in the pattern.
Answer:
f(n) = -n^2 -3n +5
Step-by-step explanation:
Suppose the formula is ...
f(n) = an^2 +bn +c
Then we have ...
f(1) = 1 = a(1^2) +b(1) +c
f(2) = -5 = a(2^2) +b(2) +c
f(3) = -13 = a(3^2) +b(3) +c
__
Here's a way to solve these equations.
Subtract the first equation from the second:
-6 = 3a +b . . . . . 4th equation
Subtract the second equation from the third:
-8 = 5a +b . . . . . 5th equation
Subtract the fourth equation from the fifth:
-2 = 2a
a = -1
Then substituting into the 4th equation to find b, we have ...
-6 = 3(-1) +b
-3 = b
and ...
1 = -1 +(-3) +c . . . . . substituting "a" and "b" into the first equation
5 = c
The formula is ...
f(n) = -n^2 -3n +5
3. Candace drew quadrilateral ABCD with vertices A(3, 3), B(5, 3), C(7, 1), and D(1, 1). Miguel wants to dilate Candace's quadrilateral by a scale factor of 5/5. Which statement is true? *
A-Quadrilateral ABCD is smaller than quadrilateral A'B'C'D'.
B-The algebraic expression of the dilation is (x, y) -> (5x, 5y).
C-The coordinates of quadrilateral A'B'C'D' will be A'(15, 15), B'(9, 15), C'(5, 35), D'(5, 5).
D-Quadrilateral A'B'C'D' will be congruent to quadrilateral ABCD.
Answer:
D-Quadrilateral A'B'C'D' will be congruent to quadrilateral ABCD.
Step-by-step explanation:
The scale factor is equal to 1. Hence, the quadrilateral A'B'C'D' will be identical to quadrilateral ABCD, whose vertices are the same.
The algebraic expression of the dilation is:
[tex](x',y') = (x,y)[/tex]
Besides, the coordinates of the new quadrilateral are A'(3, 3), B'(5, 3), C'(7, 1), and D'(1, 1)
And quadrilateral A'B'C'D' will be congruent to quadrilateral ABCD.
Therefore, the right answer is D.
Answer: D-Quadrilateral A'B'C'D' will be congruent to quadrilateral ABCD.
Step-by-step explanation: just did a test with this question and got it right. Hope this helped! thx for the points :D
Which of these generalizations is true?
A. All rectangles are squares.
В. All parallelogram s are rectangles.
C. All squares are parallelograms.
D. All trapezoids are parallelograms.
PLEASE HELP QUICKLY !THANK YOU :)
The students in Mr. Sanchez's class are converting distances measured in miles to kilometers. To estimate the number of kilometers, Abby takes the number of miles, doubles it, then subtracts 20% of the result. Renato first divides the number of miles by 5, then multiplies the result by 8. Write an algebraic expression that shows the process that both students used. Abby's expression: Renato's expression:
Step-by-step explanation:
Abby’s Expression:
Double m, giving 2m. She then takes 20% of the result, which we can write 0.2(2m). Finally she subtracts this from 2m, giving 2m−(0.2)2m
2m − (0.2)2m
Renato’s Expression:
Divide m by 5, giving m ÷ 5 = m/5, and then multiplies the result by 8, giving:
8(m/5)
How would you simplify a negative square root?
Provide a detailed explanation, with an example, to receive full credit.
Answer:
To simplify
√(-x) = √((x)(-1)) = √((x)(i^2))
√(-x) = √(i^2) × √x = i√x
For example;
Simplify √-9
√-9 = √(-1×9) = √-1 × √9
√-9 = √(i^2) × √9 = i × 3
√-9 = 3i
Step-by-step explanation:
Given a negative square root √(-x);
From our knowledge of complex numbers, we know that
i^2 = -1 and vise versa
To simplify
√(-x) = √((x)(-1)) = √((x)(i^2))
√(-x) = √(i^2) × √x = i√x
For example;
Simplify √-9
√-9 = √(-1×9) = √-1 × √9
√-9 = √(i^2) × √9 = i × 3
√-9 = 3i
Step-by-step explanation:
The square root of a number A, is a number B such that, when it is multiplied by itself, the result is A.
If A × A = B
Then √B = A.
Now the multiplication of two numbers gives a positive number if both numbers are positive, or both numbers are negative.
2 × 2 = -2 × -2 = 4
3 × 3 = -3 × - 3 = 9
And so on.
So, the square root of 4 = 2 or -2
The square root of 9 = 3 or -3
But if one of the numbers is positive while the other is negative, then the result is negative.
2 × -2 = -4
3 × -3 = -9
Clearly, √(-4) ≠ 2 ≠ -2
√(-9) ≠ 3 ≠ -3
It is impossible to find the square root of negative numbers on the real line. This gives rise to the introduction of Complex Number.
Let i² = -1, then we have that
√(-1) = i.
This is the idea of Complex number, and it helps solve the problem of the negative square roots, and every negative number can be written as the multiplication of -1 and the inverse of the number.
-A = -1 × A
So, √(-A) = √(-1 × A)
= √(-1) × √A
= i × √A
= i√A
Example, to simplify √(-16)
√(-16) = √(-1 × 16)
= √(-1) × √16
= i × ±4
= ±4i
PLEASE HELP ME PLEASE LOOK AT THE PICTURE I NEED AN ANSWER ASAP
Answer:
1st one is 2. 2nd one is 5. 3rd one is less than. 4th one is, is smaller
Step-by-step explanation:
triangle ABC a = 4 and m angle C=30 If the area of the triangle is 6 what is the length of side b
Answer:
6m = b
Step-by-step explanation:
The area of triangle when angle and sides are given = 1/2* sin angle*ab
Area = 1/2 * sin 30 * 4*b
Area = 6m²
6 = 1/2 * sin 30 * 4*b
(6*2)/(sin 30 * 4)= b
12/(0.5*4) = b
12/2 = b
6m = b
Sam and Joe are painters. Sam makes $2 an hour less than Joe. On a job that took them both 40 hours to complete they made $440. How much does Sam make an hour?
Answer:
$4.50Step-by-step explanation:
If they earned $440 in 40 hours
This means they earned 440÷40=11 in one hour
Sam makes x-2 amount of money per hour so the difference between Sam's and Joe's salary is $2
Find two numbers that add up to Ten and can subtract to make a difference of 2 (I am starting with ten as it is easier) 6+4=10 6-4=2
So to make 6 and. 4 add to make a 11 we need to add a 0.5 to each of them so 6.5+4.5=11 and 6.5-4.5= $2.
Therefore Joe makes $6.50 an hour and Sam makes £4.50
I need to know if the graph makes sense based on how Naoya shoots, everything is in the photo.
Answer:
Not correct
Step-by-step explanation:
Sample 8 has one free throw, sample 9 has 3 free throw success,
sample 10 has 3 free throw success
sample 11 has 5 free throw success
sample 12 has 5 free throw success
sample 13 has 2 free throw success
sample 14 has 1 free throw success;
See one sample should contain 15 free throw and the probability of success should be 0.7
Let's look at sample 8
Total no of success is 1
Total no of free throws 15
Probability is 1/15 = 1/15 * 100 =6.67%
Similarly you can do so for the others.
Which is the completely factored form of 4X cubed +10 X squared minus 6X
Answer:
2x(2x - 1)(x + 3)
Step-by-step explanation:
4x^3 + 10x^2 - 6x =
Factor out the common factor 2x.
= 2x(2x^2 + 5x - 3)
Factor the trinominal.
= 2x(2x - 1)(x + 3)
Answer:
[tex]=2x\left(2x-1\right)\left(x+3\right)[/tex]
Step-by-step explanation:
[tex]4x^3+10x^2-6x\\\mathrm{Factor\:out\:common\:term\:}2x:\quad 2x\left(2x^2+5x-3\right)\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c\\x^2=xx\\x^3=x^2x\\=4x^2x+10xx-6x\\\mathrm{Rewrite\:}6\mathrm{\:as\:}2\cdot \:3\\\mathrm{Rewrite\:}10\mathrm{\:as\:}2\cdot \:5\\\mathrm{Rewrite\:}4\mathrm{\:as\:}2\cdot \:2\\=2\cdot \:2x^2x+2\cdot \:5xx-2\cdot \:3x\\\mathrm{Factor\:out\:common\:term\:}2x\\=2x\left(2x^2+5x-3\right)\\\mathrm{Factor}\:2x^2+5x-3:\quad \left(2x-1\right)\left(x+3\right)[/tex]
[tex]2x^2+5x-3\\\mathrm{Break\:the\:expression\:into\:groups}\\=\left(2x^2-x\right)+\left(6x-3\right)\\\mathrm{Factor\:out\:}x\mathrm{\:from\:}2x^2-x\mathrm{:\quad }x\left(2x-1\right)\\2x^2-x\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c\\x^2=xx\\=2xx-x\\\mathrm{Factor\:out\:common\:term\:}x\\=x\left(2x-1\right)\\\mathrm{Factor\:out\:}3\mathrm{\:from\:}6x-3\mathrm{:\quad }3\left(2x-1\right)\\6x-3\\\mathrm{Rewrite\:}6\mathrm{\:as\:}3\cdot \:2\\=3\cdot \:2x-3[/tex]
[tex]\mathrm{Factor\:out\:common\:term\:}3\\=3\left(2x-1\right)\\=x\left(2x-1\right)+3\left(2x-1\right)\\\mathrm{Factor\:out\:common\:term\:}2x-1\\=\left(2x-1\right)\left(x+3\right)\\=2x\left(2x-1\right)\left(x+3\right)[/tex]
lee and maya are collecting leaves for an art project. lee collects 24-100 of the total leaves needed. maya collects 4-10 of the total leaves needed. What fraction of the total number leaves did they collect altogether
Answer:
1/8 but idk im not good with math
Step-by-step explanation:
Answer:
16-25
Step-by-step explanation:
Step 1 :
2
Simplify —
5
Equation at the end of step 1 :
24 2
——— + —
100 5
Step 2 :
6
Simplify ——
25
Equation at the end of step 2 :
6 2
—— + —
25 5
[tex]\left[\begin{array}{ccc}1&0&-2\\&&\\&&\end{array}\right] +\left[\begin{array}{ccc}1&2&3\\&&\\&&\end{array}\right][/tex]
The answer is [ 2 2 1]
look at the attached picture
Hope it helps
Good luck on your assignment
As part of his dissertation, Joe wanted to know if math anxiety differs between males and females. He developed a new measure to assess math anxiety with a scale of 0 – 100, a higher number indicating more anxiety. He went to a large university and asked several sections of an introductory math class to participate.What is the dependent variable?
Answer:
Maths anxiety
Step-by-step explanation:
In a typical research study, there are basically 2 types of variables involved, which are the dependent and the independent variable.
The dependent variable is affected by other factors or the independent variable involved in the study. The dependent variable would change is the independent variable is manipulated, changed or varied.
The dependent variable in Joe's dissertation is MATHS ANXIETY, which is dependent on the gender of students. Gender is the independent variable as he wants to find out if there's any difference in maths anxiety between males and females.
The dependent variable is Math Anxiety which is dependent on gender of the students.
Meal can be considered symmetric and mound-shaped with mean 1075 calories and standard deviation 302 calories. Use the 68-95-99.7 rule to answer the following questions. NOTE. This web site 68-95-99.7 rule graphically depicts the 68-95-99.7 rule and may help with the following questions. a. What is the approximate percentage of the Chipotle meals that have more than 471 calories
Answer:
The approximate percentage of the Chipotle meals that have more than 471 calories is 95%.
Step-by-step explanation:
We are given that meal can be considered symmetric and mound-shaped with mean 1075 calories and standard deviation 302 calories.
Let X = Chipotle meals having calories
So, X ~ Normal([tex]\mu=1075, \sigma^{2} =302^{2}[/tex])
Now, the 68-95-99.7 rule states that;
68% of the data values lies within one standard deviation points.95% of the data values lies within two standard deviation points.99.7% of the data values lies within three standard deviation points.So, the approximate percentage of the Chipotle meals that have more than 471 calories is given by;
[tex]\frac{X-\mu}{\sigma} = \frac{471-1075}{302}[/tex]
= -2
Since, it is stated above that 95% of the data values lies within two standard deviation points which means 95% values lies between -2 and 2 z score values.
SO, the approximate percentage of the Chipotle meals that have more than 471 calories is 95%.
Use the fundamental theorem of calculus to find the area of the region between the graph of the function x^5 + 8x^4 + 2x^2 + 5x + 15 and the x-axis on the interval [-6,6]. Round off your answer to the nearest integer.
A) 25,351 units^2
B) 149,473 units^2
C) 3,758 units^2
D) 2,362 units^2
Answer:
The area of the region is 25,351 [tex]units^2[/tex].
Step-by-step explanation:
The Fundamental Theorem of Calculus: if [tex]f[/tex] is a continuous function on [tex][a,b][/tex], then
[tex]\int_{a}^{b} f(x)dx = F(b) - F(a) = F(x) | {_a^b}[/tex]
where [tex]F[/tex] is an antiderivative of [tex]f[/tex].
A function [tex]F[/tex] is an antiderivative of the function [tex]f[/tex] if
[tex]F^{'}(x)=f(x)[/tex]
The theorem relates differential and integral calculus, and tells us how we can find the area under a curve using antidifferentiation.
To find the area of the region between the graph of the function [tex]x^5 + 8x^4 + 2x^2 + 5x + 15[/tex] and the x-axis on the interval [-6, 6] you must:
Apply the Fundamental Theorem of Calculus
[tex]\int _{-6}^6(x^5+8x^4+2x^2+5x+15)dx[/tex]
[tex]\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx\\\\\int _{-6}^6x^5dx+\int _{-6}^68x^4dx+\int _{-6}^62x^2dx+\int _{-6}^65xdx+\int _{-6}^615dx[/tex]
[tex]\int _{-6}^6x^5dx=0\\\\\int _{-6}^68x^4dx=\frac{124416}{5}\\\\\int _{-6}^62x^2dx=288\\\\\int _{-6}^65xdx=0\\\\\int _{-6}^615dx=180\\\\0+\frac{124416}{5}+288+0+18\\\\\frac{126756}{5}\approx 25351.2[/tex]
A carpenter bought some tools to build chairs. The cost of the materials for each chair was the same. The total cost y (tools and materials) to make x chairs is shown in the graph below. The cost of the tools was $_____ and the cost of materials for one chair was $________
Answer:
Cost of tools: $100
Cost for each chair: $25
Step-by-step explanation:
You can see that before 1 chair, the cost is at 100. This means that the cost of the tools is $100. Another way to determine this is to see that at 1 chair, the cost is $125. At 2, it's $150, and at 3 it's $175, etc. This tells you that the cost to produce each chair is $25, but it also tells you that the tools cost 100 dollars, since the total cost at 1 chair is $125, and each chair only costs $25.
Hope this helps!
Answer:
100,25
Step-by-step explanation:
What is x to the nearest tenth?
Answer:
x= 13.7 (nearest tenth)
Step-by-step explanation:
Please see attached picture for full solution.
Find the product. (3x 2 - 5x + 3)(3x - 2)
Answer:
9x^3-21x^2+19x-6
Step-by-step explanation:
First you have to distribute the first equation into the second since the two are being multiplied:
(3x^2-5x+3)(3x-2)
9x^3-6x^2-15^2+10x+9x-6
(simplify)
9x^3-21x^2+19x-6
9x^3-21x^2+19x-6
First you have to distribute the first equation into the second since the two are being multiplied:
(3x^2-5x+3)(3x-2)
9x^3-6x^2-15^2+10x+9x-6
(simplify)
9x^3-21x^2+19x-6 is the answer to the question
Please help me understand this!!
Step-by-step explanation:
3 + 15 + 75 + 375 + 1,875
This is a geometric series. The first term is 3, the common ratio is 5, and the number of terms is 5.
∑₁⁵ 3 (5)ⁿ⁻¹
∑₀⁴ 3 (5)ⁿ
3 + 12 + 48 + 192 + 768
This is a geometric series. The first term is 3, the common ratio is 4, and the number of terms is 5.
∑₁⁵ 3 (4)ⁿ⁻¹
∑₀⁴ 3 (4)ⁿ
4 + 32 + 256 + 2048 + 16,384
This is a geometric series. The first term is 4, the common ratio is 8, and the number of terms is 5.
∑₁⁵ 4 (8)ⁿ⁻¹
∑₀⁴ 4 (8)ⁿ
2 + 6 + 18 + 54 + 162
This is a geometric series. The first term is 2, the common ratio is 3, and the number of terms is 5.
∑₁⁵ 2 (3)ⁿ⁻¹
∑₀⁴ 2 (3)ⁿ
