The curve intersects the vertical lines when
[tex]x=2 \implies y = \dfrac1{2+2^3} = \dfrac1{10}[/tex]
and
[tex]x=3 \implies y = \dfrac1{2+3^3} = \dfrac1{29}[/tex]
Split up the region into washers of thickness [tex]\Delta y[/tex].
For [tex]-1\le y\le\frac1{29}[/tex], the inner and outer radii of each washer will be constant, with outer radius [tex]x=3[/tex] and inner radius [tex]x=2[/tex]. Each washer in this interval will contribute a total volume of
[tex]\pi (3^2 - 2^2) \Delta y = 5\pi\,\Delta y[/tex]
For [tex]\frac1{29} \le y \le \frac1{10}[/tex], the washers will have a varying outer radius of length
[tex]y=\dfrac1{2+x^3} \implies x = \sqrt[3]{\dfrac1y - 2}[/tex]
and inner radius [tex]x=2[/tex]. Their volumes are
[tex]\pi \left(\left(\sqrt[3]{\dfrac1y - 2}\right)^2 - 2^2\right) \, \Delta y = \pi \left(\left(\dfrac1y - 2\right)^{2/3} - 4\right) \, \Delta y[/tex]
Let [tex]\Delta y\to0[/tex]. Then as the number of washers goes to infinity, the total volume of the solid converges to the definite integral
[tex]\displaystyle 5\pi \int_{-1}^{1/29} dy + \pi \int_{1/29}^{1/10} \left(\left(\dfrac1y - 2\right)^{2/3} - 4\right) \, dy[/tex]
The first integral is trivial, but the second one requires hypergeometric functions to evaluate exactly. With a calculator, we find the approximate volume to be 0.117884.
Can you please tell me how to solve this????
Answer:
-2
Step-by-step explanation:
You have to simplify numerator and denominator through factoring. The you should get an expression involving only a + b which is given as -2
Take numerator
[tex]a^2-b^2-12b-36[/tex]
Factor
[tex]-b^2-12b-36[/tex]
[tex]= - (b^2 + 12b + 36)\\\\= -(b+6)^2[/tex]
So numerator becomes
[tex]a^2-\left(b+6\right)^2[/tex]
Apply difference of squares formula: [tex]\displaystyle x^2-y^2=\left(x+y\right)\left(x-y\right)[/tex]
[tex]\mathrm{with\;} x^2 == > a^2, and y^2 == > (b + 6)^2[/tex]
[tex]\implies a^2-\left(b+6\right)^2 \\== \left(a+\left(b+6\right)\right)\left(a-b-6\right)[/tex]
Denominator
[tex]a^2-6a-b^2-6b[/tex]
can be factored as follows
[tex]a^2-b^2 = (a + b) (a -b)[/tex]
[tex]-6a-6b = -6\left(a+b\right)[/tex]
So denominator becomes
[tex]\left(a+b\right)\left(a-b\right)+-6\left(a+b\right)[/tex]
Factor out common term (a+b) to get
[tex]\left(a+b\right)\left(a-b-6\right)[/tex]
So the original expression with Numerator and denominator
[tex]\displaystyle =\frac{\left(a+b+6\right)\left(a-b-6\right)}{\left(a+b\right)\left(a-b-6\right)}[/tex]
Cancel the common factor (a-b-6) to get
[tex]\displaystyle \frac{a+b+6}{a+b}[/tex]
Since a + b = -2, plug in this value of (a+b) in both numerator and denominator to get
[tex]\displaystyle \dfrac{-2 + 6}{-2}[/tex]
[tex]\displaystyle = - 2[/tex]
Answer: -2
4. The average mass of a grain of one type of sand is 7 x 10-4 gram. There are 1,000 grains of the sand in 1 cubic centimeter. What is the mass, in grams, of 1 cubic centimeter of the sand in scientific notation?
The mass, in grams, of 1 cubic centimeter of the sand in scientific notation is 7 x 10^(-1).
What is scientific notation?Scientific notation is a way of writing very large or very small numbers.
Now it is given that,
Average mass of grain = 7 x 10-4 gram
Number of grains in 1 cubic centimeter = 1,000 grains = 10^3 grains
Thus,
Mass of 1 cubic centimeter of the sand = Average mass of grain * Number of grains in 1 cubic centimeter
⇒ Mass of 1 cubic centimeter of the sand = 7 x 10-4 * 10^3 grams
⇒ Mass of 1 cubic centimeter of the sand = 7 x 10^(-4+ 3) grams
⇒ Mass of 1 cubic centimeter of the sand = 7 x 10^(-1) grams
Thus, the mass, in grams, of 1 cubic centimeter of the sand in scientific notation is 7 x 10^(-1).
To learn more about scientific notation :
brainly.com/question/22331466
#SPJ1
Elise and her mom are volunteering at an emergency relief center. To help prepare in case of a flood, they pack emergency kits with food and water. Elise puts 4 water bottles into each kit they pack. In all, she packs 120 water bottles. Which equation can you use to find the number of emergency kits K Elise packs?
4K = 120 can be used to find the number of emergency kits K Elise packs. The total number of emergency kits packed by Elsie and her mom are 30.
Here, we are given that Elise puts 4 water bottles into each emergency kit.
Let the number of kits packed = K
Then the total number of bottles packed = 4 × K
= 4K
Also, we are given that Elsie packs a total of 120 bottles.
Thus, we get the following linear equation-
4K = 120
We can use this equation to find the number of emergency kits K Elise packs.
dividing by 4 on both sides, we get
4K/4 = 120/4
K = 30
Hence, the total number of emergency kits packed by Elsie and her mom are 30.
Learn more about linear equations here-
https://brainly.com/question/13738061
#SPJ9
state whether each function is a linear function. write yes or no. explain.
xy = - 1
Answer: It's not linear.
Step-by-step explanation: A linear function must have a degree of 0 or 1. This function equals to y= -1/x. -1/x has a degree of negative 1 since x^-1 =1/x. So this is not linear.
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 5 large boxes and 2 small boxes has a total weight of 117 kilograms. A delivery of 3 large boxes and 8 small boxes has a total weight of 164 kilograms. How much does each type of box weigh?
THIS ANSWER WAS DELETED DUE TO NOT BEING TRUE.
Check all relationships
Complementary
Linear pair
Adjacent
Vertical
Supplementary
[tex]\implies[/tex]The answer is Adjacent and Complementary.
Step-by-step explanation:The two corners are complementary and adjacent to each other.So select Adjacent and Complementary.PLEASE HELP!!!!!
A. What is 4.186 rounded to the nearest tenth?
B. What is 2.758 rounded to the nearest tenth?
C. What is 72.05 rounded to the nearest tenth?
D. What is 45.64 rounded to the nearest tenth?
E. What is 82.156 rounded to the nearest tenth?
F. What is 41.31 rounded to the nearest tenth?
G. What is 29.16 rounded to the nearest tenth?
H. What is 17.054 rounded to the nearest tenth?
I. What is 11.65 rounded to the nearest tenth?
J. What is 0.83 rounded to the nearest tenth?
K. What is 29.16 rounded to the nearest tenth?
L. What is 12.48 rounded to the nearest tenth?
M. What is 0.91 rounded to the nearest tenth?
_______________________________________________________
N. What is 20.5 rounded to the nearest whole number?
O. What is 13.71 rounded to the nearest whole number?
P. What is 71.23 rounded to the nearest whole number?
Q. What is 36.57 rounded to the nearest whole number?
R. What is 17.89 rounded to the nearest whole number?
S. What is 50.147 rounded to the nearest whole number?
T. What is 19.05 rounded to the nearest whole number?
U. What is 7.61 rounded to the nearest whole number?
V. What is 92.38 rounded to the nearest whole number?
W. What is 57.25 rounded to the nearest whole number?
X. What is 16.3 rounded to the nearest whole number?
Y. What is 44.08 rounded to the nearest whole number?
Z. What is 17.9 rounded to the nearest whole number?
1. What is 9.06 rounded to the nearest whole number?
the sum of nine consecutive natural numbers, the first of which is n?
Answer:
What is the sum equal to?
Step-by-step explanation:
(3x-5) + (x+1) = 180
The value of 'x' for the given expression is calculated as (x = 48).
What is defined as the linear equation in one variable?A linear equation in one variable is an equation that has only one solution.
It is expressed in the form ax+b = 0, where a and b are two integers and x is a variable. The numbers a' and b' are real numbers.'a' and 'b' are both greater than zero.2x+3=8, for example, is a linear equation with a single variable.Now, for the given expression;
(3x-5) + (x+1) = 180
Open the brackets.
3x-5 + x+1 = 180
Add the similar parts;
4x - 4 = 180
Further simplifying;
4x = 180 + 4
4x = 184
x = 184/4
x = 48
Therefore, the value of 'x' is estimated as 48.
To know more about the linear equation in one variable, here
https://brainly.com/question/85774
#SPJ9
Check all relationships between 1 and 22.
Answer:
adjacent , linear pair ,
Step-by-step explanation:
and i don't think there is something else
The distance between City A and City B is 2700 miles. On a certain wall map, this distance is represented by 9 inches. The actual distance between City C and City D is 4100 miles. How far apart are they on the same map?
The distance between City C and City D is represented by 13.67 inches on a certain wall map.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
Let x inches would be far apart are they on the same map
We can write this as a ratio as
As per the given information,
9 inches : 2700 miles = x inches : 4100 miles
⇒ 9/2700 = x/4100
⇒ x = (4100×9)/2700
⇒ x = 13.67 inches
Therefore, on a certain wall map, the distance between City C and City D is represented by 13.67 inches.
Learn more about the Ratio here:
brainly.com/question/1504221
#SPJ1
Write an equation in slope- intercept form for the line described.
parallel to y = -3x + 4, x- intercept at 4
Answer:
y = -3x + 12
Step-by-step explanation:
If two lines are parallel, their slopes are equal, then m = -3
x intercept is 4 then y = 0
y = mx + b
0 = -3(4) + b
b = 12
y = -3x + 12
Sub: x=4 into
Y= x^2 +4x -3
Y= 5x + 3
given the function f(x)=-13+7x find the indicated function values
a. f(5)
b. f(-9)
c. f(0)
The answers of the following part are:
a) 22
b) -76
c) -13
For solving this particular sum we need to know the about functions Function is generaaly defined as a set of inputs having one output each. every function as a domain and a co-domain or range. A function is generally denoted by f(x) where x is the variable and it is also the input.The general representation of function is y = f(x).
In the given sum we will just put the values in place of x and will find the answer
The given equation is f(x)=-13+7x
a) Here it is given f(5) so we will put 5 in all places of x
Substituting the value x as 5 we will get :
f(5) = -13+7*5
= -13+35
=22
the value f(5) will be 22
b) In this part of the vaule of x is given as -9
Substituting the value of x as -9 we get
f(-9)=-13+7*(-9)
= -13-63
= -76
the valur of f(-9) is -76
c) here the value of x is given as 0
Substituting the value of x as 0
f(0)= -13+7*0
= -13+0
=-13
the value of f(0) is -13
Learn more about function here :
https://brainly.com/question/20337778
#SPJ9
Please help, been stuck on this for far too long and due in tmrw!
From rectangle F to G translation is -4 units to the x- direction and -3 units to the y- direction.
From rectangle G to H translation is 6 units to the x- direction and -1 units to the y- direction.
From rectangle F to H translation is 2 units to the x- direction and -4 units to the y- direction.
Given that,
In the picture we have a graph with 3 rectangles that is F, G, and H.
We have to find the translation of the rectangles.
We know that,
What is translation?The transformation, i.e., f: X X, is a function, f, that maps to itself. Following the transformation, the pre-image X changes into the image X. Any operation, including translation, rotation, reflection, and dilation, may be used to create this transformation. A function can be moved in one direction or another by translation, rotated around a point by rotation, reflected in its mirror image by reflection, and scaled by dilation.
So,
From rectangle F to G translation is -4 units to the x- direction and -3 units to the y- direction.
From rectangle G to H translation is 6 units to the x- direction and -1 units to the y- direction.
From rectangle F to H translation is 2 units to the x- direction and -4 units to the y- direction.
To learn more about translation visit: https://brainly.com/question/11805053
#SPJ1
Which is an illustration of the associative
property?
a. (b.c) = (b.c).a
α · b = α
a (b.c) = (a.b).c
a.b=b.a
PLS HELP ASAP
(50 POINTS)
3. Do the functions below show a direct linear variation or not? Explain why or why not.
You may want to use a graphing calculator, like Desmos, to look at the shapes these equations make.
Using proportional relationships, we have that:
A. The function does not show a direct linear relationship.
B. The function shows a direct linear relationship.
C. The function does not show a direct linear relationship.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality k, in the case of a direct relationship, as follows:
y = kx
In the case of an inverse relationship, we have that:
y = k/x.
From the format of these equations, we have that:
Item a shows an inverse relation, as x is in the denominator.Item b shows a direct relation, as x is in the numerator.A function is classified as linear if the exponent of x is of 1, hence item c does not show a linear function.
What is the missing information?The functions A, B, C are missing, and are given as follows.
A. 9/x.
B. x/11.
C. x²/8.
More can be learned about proportional relationships at https://brainly.com/question/10424180
#SPJ1
Write the slope-intercept equation of the function f whose graph satisfies the given conditions.
The graph of f passes through (-8,6) and is perpendicular to the line that has an x-intercept of 4 and a y-intercept of -8.
The equation of the function is
(Use integers or fractions for any numbers in the equation.)
Answer:
i don't know the answerStep-by-step explanation:
33575357853222467
ufee
PLEASE HELP FAST I ONLY HAVE ONE HOUR!!!!!!!
The probability that if 3 donations are made, all 3 of them can be safely used on blood transfusion with someone that has type A will be D. (0.27 + 0.49)³ = 0.4390
How to calculate the probability?It should be noted that probability simply means the chance that a particular event will occur.
In this case, the probability that if 3 donations are made, all 3 of them can be safely used on blood transfusion with someone that has type A will be:
= (27% + 49%)³
= (0.27 + 0.49)³
= 0.4390
The probability is 0.4390.
Learn more about probability on:
brainly.com/question/24756209
#SPJ1
The function is not differentiable at x
The correct value of m = 6 and b = -9.
The function f(x) is differentiable at x = 3 and we know that if a function is differentiable at some point means that it is continuous at that point also.
Here function is continuous at x = 3 piecewise
m(3) + b = (3)²
3m + b = 9 .....(1)
and function is differentiable at ( x = 3 ) piecewise
d/dx ( m * x + b ) = d/dx (x)² at ( x= 3 )
( m + 0 ) = 2x at ( x = 3 )
m = 2 * 3
m = 6
By placing the value of m in equation (1)
3m + b = 9
3 * 6 + b = 9
18 + b = 9
b = 9 - 18
b = -9
Therefore, the value of m = 6 and b = -9.
Learn more about differentiable here:
https://brainly.com/question/24898810
#SPJ9
Find all integer solutions of each system of inequalities.
a) 6-4b>0
3b-1>0
b) 3-18x<0
0.2-0.1x>0
Answer:
A: [tex]b < \frac{3}{2}[/tex] and the second equation is: [tex]b > \frac{1}{3}[/tex]
B: [tex]x > \frac{1}{6}[/tex] and the second equation is: [tex]x < 2[/tex]
---------------------------------------------------
Hope this helps!
Have a great day and God bless! :)
Please show me how you got the answer. Will give brainliest.
Answer: 410 possible points
To solve for the possible points in the course, use a proportion and cross multiply.
What is a proportion?
A proportion is two fractions that are equal to each other. For the fractions to be equal, they are proportionate. In our math problem, percentage is proportionate the the number of points.
The fractions represent information you have, and one variable will represent what you are solving for.
GivenYour points = 361
Points to get an 'A' = your points + 8
'A' = 90% of possible points
Find the points needed for an 'A' at 90%Points to get an 'A' = your points + 8
= 361 + 8
= 369
State variableslet x be the amount of possible points
Write a proportionWe know the number of points for 90% is 369 points. Remember that 90% is the same as 90/100.
Keep the information with the same units inside the same fraction. Here, percentage is represented by the first fraction. Points is represented by the second fraction.
[tex]\displaystyle{\frac{90}{100}=\frac{369}{x}}[/tex]
SolveWe can solve using cross multiplication. This is when we multiply each numerator by the denominator from the other fraction.
[tex]90x = 369*100[/tex] Simplify by multiplying.
[tex]90x = 36,900[/tex] Isolate the variable x.
[tex]\displaystyle{\frac{90x}{90} = \frac{36,900}{90}}[/tex] Divide both sides by 90 to cancel out 90 on the left.
[tex]\displaystyle{x = \frac{36,900}{90}}[/tex] Divide.
[tex]x = 410[/tex] Solved for x, representing the possible points.
∴ The possible points in the art course is 410.
Learn more about finding a missing number given percentage here: https://brainly.com/question/26535441
Answer:
410 possible points
Step-by-step explanation:
PLEASE GEKO ME EHFND
Answer: 164 degrees
Step-by-step explanation:
IHG=JHG+IHJ
19x-7=84+7x+17
19x-7=101+7x
12x-7=101
12x=108
x=9
IHG=19x-7
IHG=19(9)-7
IHG=171-7
IHG=164 degrees
The table shows some values of x and y that satisfy the equation y = acosx + b
180
120
150
4 -3V3
-2
0
30
60
10
4 + 3V3
7
Find the value of y when x = 45
X
90
4
147 divided by 7
(Explanation needed please)
Answer: 21
Step-by-step explanation:
Use a calculator
Please help with this question I will give you brainliest
Answer:
89.50 = 7.75 + 27.25p
subtract 7.75 from both sides
89.50 - 7.75 = 27.25p
81.75 = 27.25p
divide both sides by 27.25
p = 81.75 / 27.25
p = 3
Step-by-step explanation:
The number of people who can go to the amusement park is 3 people
Answer: p=3
Hence, the Linear Equation in two variables is used to determine the total number of people who go to the park is - y=7.75+27.25p
Step-by-step explanation:
89.50=7.75+27.25p
89.50-7.75+27.25p
81.75=27.25
81.75/27.25
p=3
The area of a rectangular garden is 7584 ft squared If the width of the garden is 79 feet, what is its length?
Answer: 96
Step-by-step explanation:
Length = Area/Width
7584/79 = 96 feet
96 x 79 = 7584 ft²
II. What are the coordinates
of A' using the rule
(x, y) (x-3, y+7)?
A(2, 5)
Need help
Answer:
so xtime sy ,fe fwvnvf nfdv bregbrrsikrwnknrhvnk vnf vknvns;;abjwrjkgwnkgwjknnnxnfnfsvmsr
Express the formula V = r². H in terms of the height, H. Use that formula to find the height when the volume is
45 and the radius is 3.
H =
-²; H = 30
H =
₁H=5
C H =
₁; H = 7.5
2.zr
C H = 1; H = 15
The formula in terms of H is H = V ÷ πr². Value of height is 5.
We are given the formula -
V = πr²H, where V represents volume and H represents height. To rewrite the formula in terms of H, we will shift it to Left Hand Side -
H = V ÷ πr²
Keep the value of Volume and radius in formula to find the height.
H = 45π ÷ π(3)²
Taking square of 3 and cancelling π
H = 45 ÷ 9
Performing division to find the value of height
H = 5
Therefore, the formula is V ÷ πr² and value of height is 5.
Learn more about volume -
https://brainly.com/question/463363
#SPJ9
The complete question is attached in figure.
Kathi and Robert Hawn had a pottery stand at the annual Skippack Craft Fair. They sold some of their pottery at the original price of $13.50 each, but later decreased the price of each by $4.00. If they sold all 91 pieces and took in $972.50, find how many they sold at the original price and how many they sold at the reduced price.
The number sold at the original price is 27 and they sold 64 at the reduced price.
How to calculate the value?Let x = number of pieces sold at 13.50
Let y = number of pieces sold at 9.50
The equation will be:
x + y = 91. ..... i
13.50x + 9.50y = 972.50 ..... ii
From equation i x = 91 - y
13.50x + 9.50y = 972.50
13.50(91 - y) + 9.50y = 972.50
1228.50 - 13.50y + 9.50y = 972.50
1228.50 - 4y = 972.50
4y = 1228.50 - 972.50
4y = 256
y = 256/4
y = 64
Since x + y = 91
x = 91 - 64 = 27
Therefore, the number sold at the original price is 27 and they sold 64 at the reduced price.
Learn more about expressions on:
brainly.com/question/2972832
#SPJ1