Find the total mass of the triangular region shown below. All lengths are in cm, and the density of the region is sigma(x) = 1 + x grams/cm^2
Answers
Answer:
3 grams
Step-by-step explanation:
We are going to take the mass of a bunch of little strips below the triangle "roof." To do this, we must figure out what formula for the mass we'll use, in this case, we'll use:
Mass of strip = denisty * area = (1+x)*y*deltax grams
now, because the "roof" of the triangle contains two different integrals (it completely changes direction), we will use TWO integrals!
**pretend ∈ is the sum symbol
Mass of left part = lim x->0 ∈ (1+x)*y*deltax = inegral -1 to 0 of (1+x)*3*(x+1) = 3 * integral -1 to 0 of (x^2 + 2x + 1) = 3 * 1/3 = 1
Mass of left part = lim x->0 ∈ (1+x)*y*deltax = inegral 0 to 1 of (1+x)*3*(-x+1) = 3 * integral 0 to 1 of (-x^2 + 1) = 3 * 2/3 = 2
Total mass = mass left + mass right = 1 + 2 = 3 grams
Related Questions
Write an equation in point-slope form for the line. Slope is -2 and (1, 1) in on the line.
Answers
Answer:
The point-slope form is y - 1 = -2 (x-1)
Step-by-step explanation:
What is the domain of the following relation: Is this relation a function? Why or
why not?
R: {(1, 2), (-3,5), (1, -2), (2, -3)}?
Answers
And it is not a function cuz two 1 x value has two picture in y value
What P:X equals 4 let q:y equals -2 which represents if x = 4 then y = -2
Answers are as followed
A. p V q
B. p V q
C. p -> q
D. p q
Answers
Answer:
p - > q is a = 4 then y = 3 equals
the table represents a linear function
X
-2
-1
0
1
2
Y
8
2
-4
-10
-16
What is the slope of the function
-6
-4
4
6
Answers
Brainliest please???
The solution is Option A.
The slope of the equation is given by slope m = -6
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
The values of x = { -2 , -1 , 0 , 1 , 2 }
The value of y = { 8 , 2 , -4 , -10 , -16 }
Now , let the first point be represented as P
The coordinates of P = P ( -2 , 8 )
Let the second point be represented as Q
The coordinates of Q = Q ( -1 , 2 )
Now , the slope of the line between the two points is
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 2 - 8 ) / ( -1 - ( - 2 )
On simplifying the equation , we get
Slope m = ( -6 ) / ( -1 + 2 )
Slope m = -6/1
Slope m = -6
Therefore , the value of m is m = -6
Hence , the slope of the line is m = -6
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You start at(-5, -4) you move down 1 unit and up 1 unit where do you end?
Answers
Answer:
-5,-4
Step-by-step explanation:
-5,-4
down 1 unit: -5,-3
up 1 unit: -5,-4
What is the value of x in the equation below? Round to the nearest hundredths place.
0.45 (x + 1.6) + 5 x = 18
3.01
3.17
36.44
38.4
Answers
Answer:
the answer is "B"
Step-by-step explanation:
took da quiz
Answer:
B
Step-by-step explanation:
Five girls and two boys are standing in a line randomly. What is the probability that two boys are next to each other?
Answers
========================================================
Explanation:
Let's say the teacher pulls the two boys out of the line, and stands in their place. So we have 5 girls and 1 teacher making 6 people total.
There are 6! = 6*5*4*3*2*1 = 720 different permutations here. Order matters. This involves the teacher, so let's have him/her step out of the line and have the two boys replace the teacher's position. This guarantees the boys stick together. For any permutation, we have 2 different ways to arrange the boys. So we have 2*720 = 1440 different ways to arrange the students so that the two boys are next to each other.
This is out of 7! = 7*6*5*4*3*2*1 = 5040 different permutations overall (we're arranging 5 girls+2 boys = 7 people).
The probability we're after is going to be 1440/5040 = 2/7
--------
Or you could see it like this
1440 = 2*6!
5040 = 7! = 7*6!
So,
1440/5040 = (2*6!)/(7*6!)
1440/5040 = 2/7
An expression is shown below if this expression is equivalent to 60, what must be the value of a? A.) 3 B.) 4 C.) 9 D.)16
Answers
Answer:
Option (A)
Step-by-step explanation:
Given expression is,
[tex]5\sqrt{48a}=60[/tex]
Squaring on both the sides of the equation,
[tex](5\sqrt{48a})^2=(60)^2[/tex]
25(48a) = 3600
1200a = 3600
By dividing the equation by 1200,
a = [tex]\frac{3600}{1200}[/tex]
a = 3
Therefore, Option (A) will be the answer.
Find the common ratio of the geometric sequence 20,80,320,...
Answers
Answer:
1:4
Step-by-step explanation:
all of the numbers are being multiplied by 4
What is the length of the hypotenuse of the triangle?
Answers
Answer:
In geometry, a hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle. The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides. For example, if one of the other sides has a length of 3 (when squared, 9) and the other has a length of 4 (when squared, 16), then their squares add up to 25. The length of the hypotenuse is the square root of 25, that is, 5.
Step-by-step explanation:
Hope this helps! <3
What is the volumn of a shoe box that is 15 x 10 x 8 =
Answers
Answer:
12 inches
Step-by-step explanation:
[tex]1200^{3}[/tex] units
15 * 10 * 8 = 1200
What is the center of the circle represented by the equation x2 + y2 - 4x + 2y + 1 = 0?
Answers
Answer:(2,-1)
Step-by-step explanation:
The required center of the given circle is given as (2, -1).
What is a circle?The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by
(x - h)² + (y - k)² = r²
where h, k is the coordinate of the center of the circle on coordinate plane and r is the radius of the circle.
Here,
The standard form of the equation of the circle s is given as,
x² + y² -2hx -2ky + c = 0
Given the equation of the circle is
x² + y² - 4x + 2y + 1 = 0
Comparing the equations,
-2h = -4
h = 2
-2k = 2
k = -1
Thus, the required center of the given circle is given as (2, -1).
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if a man pay #357 for a book,how much will he pay for 78 books?
Answers
Answer: 27,846
Step-by-step explanation: 357 x 78 = 27,846
Answer:
$27846
Step-by-step explanation:
One book cost = $357
So, for 78 books, it will be $357 * 78
=> $27846
If my answer helped, kindly mark me as the brainliest!!
Thanks!!
match each retirement planes to it's description
Answers
Answer:
1. 401(k)
2. IRA
3. 403(b)
Step-by-step explanation:
1. 401(k) is a employer-sponsored defined-contribution pension account
2. IRA stands for individual retirement account (hence individual)
3. 403(b) is a tax-advantaged retirement savings plan
hope this helps!!
Answer:
1.401k
2.425k
3.740k
Step-by-step explanation:
hehe naisip ko lang haha
How would I do this
Answers
Answer:
15
Step-by-step explanation:
Since the two triangles are similar you can use the ratio 6/9 = 10/x. Then you would cross multiply. 6x=90. 90/6=15. So the answer is 15
The authors of a certain paper describe a study to evaluate the effect of mobile phone use by taxi drivers in Greece. Fifty taxi drivers drove in a driving simulator where they were following a lead car. The drivers were asked to carry on a conversation on a mobile phone while driving, and the following distance (the distance between the taxi and the lead car) was recorded. The sample mean following distance was 3.80 meters and the sample standard deviation was 1.19 meters.
Construct a 95% confidence interval (in meters) for μ, the population mean following distance while talking on a mobile phone for the population of taxi drivers. (Round your answers to three decimal places.)
Answers
Answer:
CI = (3.462, 4.138)
Step-by-step explanation:
We are given;
Sample mean; x¯ = 3.8
Sample standard deviation; s = 1.19
Sample size; n = 50
DF = n - 1 = 50 - 1 = 49
Confidence level; CL = 95%
Significance level = (1 - 0.95)/2 = 0.025
Now,from the table attached using DF = 49, significance level = 0.025, one tail and by interpolation, we have; t = 2.01
Now, formula for confidence interval is;
CI = x¯ ± t(s/√n)
CI = 3.8 ± 2.01(1.19/√50)
CI = 3.8 ± 0.338
CI = (3.8 - 0.338, 3.8 + 0.338)
CI = (3.462, 4.138)
Can anyone help me please?? Thank you.
Answers
Answer:
okay well the total distance is 3 and 1/3 km and the speed that it was for him to go downstream was 2/3 km per hour
Find two numbers if their ratio is 9:11 and their difference is 6
Answers
Answer:
27 , 33
Step-by-step explanation:
Let the numbers be 9x & 11x
so
11x-9x=6
2x=6
x=3
First number is =9x=9*3=27
Second number is =11x=11*3=33
plz mark as brainliest if it helps
Answer:
27 and 33
Step-by-step explanation:
Here I would set up a system of equations:
1. I make the proportion 9/11=x/y and this cross-multiplies into 9y=11x
2. I use the other part of the problem to make my second equation, and since y is greater than x (assumed by looking at first step) this second equation is y-x=6
3. now, I will use substitution, if y-x=6, then y=x+6, so 9(x+6)=11x
4. simplify, 9x+54=11x
5. solve, 2x=54, x=27, y=x+6=33
Imran and Sarah share 24 sweets between them in the ratio 2:1
How many sweets does Imran get?
Answers
The correct answer is 12.
I hope this helps you!!
At 8 a.m. the temperature was -14ºF. By noon, the temperature was 12ºF. Find the difference in temperature. Did it rise or drop?
Answers
Answer:
Difference=26 degrees
It rose
Step-by-step explanation:
Answer: The difference is 28 degrees and the temp. increased or was raised.
Step-by-step explanation:
Given f(x) = x − 7 and g(x) = x2 . Find f(g(−1)).
Answers
Answer:
-9
Step-by-step explanation:
ya want me to explain or not?
Choose the more precise measurement A 5.7 yd B) 5.89 yd
Answers
When the unit digits are the same , we have to look at the decimal places . Since the unit digits in 5.7 and 5.89 are same , which is 5 , let us look at the decimals . As 5.89 has more decimal digits when compared with 5.7 , we say that the measurement 5.89 has more precision .
Therefore , 5.89 us has more precision .
Please Help!!!!
∠A and ∠B are vertical angles with m∠A=x and m∠B=4x−30.
What is m∠A?
Answers
Answer:
m<A=10
Step-by-step explanation:
I left the image below to show my work of how i got to that answer. I hope this helps!
We know vertical angles have same measure!
Thus!
A = B
=> X = 4X -30
=> 3X = 30
=> X = 10
Thus measure of angle A is 10°Tara bought 2 bottles of juice each day for 18 days. On the 19th day, Tara bought 7 bottles of juice.
Choose the expression that matches the description.
A (2 × 18) − 7
B (2 × 19) + 7
C (2 × 18) + 7
Answers
Estimate by rounding the first number to the nearest ten and the second number to the nearest hundred. 19 Х 307 II ? Х ? = ?
Answers
Answer:
6,200
Step-by-step explanation:
19-20
307-310
310 x 20= 6,200 or 20 x 310= 6,200
Estandieu's cell phone plan includes 4 GB of data. On the 2nd day of his 31 day billing
cycle he received a text message from his service provider that he has already used
16% of his data. At this rate, will he use more than 4 GB this month?
Answers
Answer:78
Step-by-step explanation:
Solve -12t ≥-6
.......
Answers
Answer:
t=2
Step-by-step explanation:
Someone please help. If you don’t want to answer all that’s fine
Answers
Answer:
1. ) Plane ABC
2.) Segment AD
3.) Segment DE
4.) Segment AC
I'm sorry I don't know how to complete the 2nd half, but I hope these help. :)
f (x) = (x + 5)^3(x - 9)(x + 1)
Answers
Answer:
F (x) = (x + 5)^3(x - 9)(x + 1) = 5
Step-by-step explanation:
Hope this helps! :)
Answer:
3
Step-by-step explanation:
edge
Does a linear relation exist between age and HDL cholesterol? A. There appears to be a positive linear association because r is positive and greater than the critical value. B. There is little or no evidence of a linear association because r is positive and greater than the critical value. C. There appears to be a negative linear association because r is negative and less than the negative critical value. D. There is little or no evidence of a linear association because the absolute value of r is less than the critical value. More
Answers
Answer:
The correct answer is - option D. There is little or no evidence of a linear association because the absolute value of r is less than the critical value.
Step-by-step explanation:
Given:
Age Cholesterol
49 55
27 45
52 40
38 57
44 28
The linear correlation coefficient between age and HDL cholesterol can be computed by the=
r = Cov (X, Y)/ δx.δy
=v∑XY /√∑X2. ∑Y2
rv= negative 0.192
The absolute value of r is less than the critical value so there is no or very little evidence of linear association.
