Step-by-step explanation:
To find the volume of this solid, we will use the method of cylindrical shells. We will integrate the cross-sectional area of a cylinder, given by πr^2, over the height of the solid. The height of the solid is given by the difference between the upper and lower bounds of the region, which are y = x^2 and y = 0, respectively. The radius of each cylindrical shell is given by the distance of the cross-sectional circle from the y-axis, which is x.
So, the volume of the solid is given by the integral:
V = ∫[0, 1] π * x^2 dx
Using the antiderivative of π * x^2, which is π * x^3 / 3, we can find the definite integral:
V = (π * x^3)/3 from 0 to 1
Evaluating the definite integral and simplifying, we get:
V = π/3 units^3
So, the volume of the solid is π/3 units^3.
Answer:
Step-by-step explanation:
Find the volume of the solid generated by rotating the region bounded by y = x^2, y = 0, and x = 1, about the y-axis.
(x+y+z)(x^2+y^2+z^2-xy-yz-zx)=
The product of (x+y+z)(x^2+y^2+z^2-xy-yz-zx) is x³ + y³ + z³ -2x²y - 2xyz- xy² - y²z - xz²
How to determine the productIt is important to note that algebraic expressions are expressions that are composed of terms, coefficients, variables, factors and constants.
These expressions are also made up of arithmetic or mathematical operations. These operations are;
AdditionMultiplicationBracketDivisionSubtractionParenthesesFrom the information given, we have that;
(x+y+z)(x^2+y^2+z^2-xy-yz-zx)
expand the bracket by multiplying the variables
x³ + xy² + xz² - x²y - xyz - x²z -xy²+ y³ + yz² - x²y - y²z - x² + x²z +y²z + z³ - xyz -yz² - xz²
collect like terms
x³ + y³ + z³ -2x²y - 2xyz- xy² - y²z - xz²
Hence, the expression is x³ + y³ + z³ -2x²y - 2xyz- xy² - y²z - xz²
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Marta’s jump rope is 10 inches shorter than three times the length of David’s rope.
If both of their ropes lay together end to end, they measure 120 inches long. How long is each person’s jump rope?
Marta's rope is 10 inches shorter than three times the length of David's rope and they measure 120 inches long together , then Marta's rope is 77.5 inches long and David's rope is 32.5 inches long.
Let's call the length of David's rope x.
According to the problem, Marta's rope is 10 inches shorter than three times the length of David's rope, so we can write an equation for Marta's rope:
length of Marta's rope = 3 * x - 10
And the combined length of both of their ropes is 120 inches, so we can write another equation:
x + (3 * x - 10) = 120
Expanding the second equation and solving for x, we get:
4x - 10 = 120
Adding 10 to both sides:
4x = 130
Dividing both sides by 4:
x = 32.5
So, David's rope is 32.5 inches long.
We can use the first equation to find the length of Marta's rope:
length of Marta's rope = 3 * x - 10 = 3 * 32.5 - 10 = 87.5 - 10 = 77.5 inches
So, Marta's rope is 77.5 inches long.
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What would be the answer for the Area of a Triangle if the b=6 and the h=10?
Answer: A = 30
Step-by-step explanation:
Hello, to find the area of a triangle, you first have to follow,
Step 1. The area of a triangle is A = 1/2 * b * h, so plug in the other numbers
Step 2. A = 1/2 * 6 * 10
Step 3. Get rid of the fraction by doing 10 * 1/2. A = 6 (10 * 1/2)
Step 4. A = 6 * 5
Step 5. A = 30
An angle measures 67.4° more than the measure of its supplementary angle. What is the measure of each angle?
Supplementary angles are angles that have a sum of 180 degrees.
Solving the QuestionLet the angle be x.
We're given:
x measures 67.4° more than the measure of 180-x⇒ Change this into a mathematical sentence:[tex]x=67.4+(180-x)[/tex]Solve for x:
[tex]x=67.4+(180-x)\\x=67.4+180-x\\2x=247.4\\x=123.7[/tex]
Solve the the supplementary angle:
[tex]180-x\\= 180-123.7\\= 56.3[/tex]
AnswerThe angle measures 123.7 degrees and its supplementary angle measures 56.3 degrees.
Evaluate the variable expression for x=5, and enter your answer in the box below.
6*(x-9)-5
The variable expression for x = 5 given 6×(x - 9) - 5 is evaluated to give a result of -24 using PEDMAS.
What is PEDMASP – Parentheses First: B – Brackets First
E – Exponents
D – Division
M – Multiplication
A – Addition
S – Subtraction
We shall evaluate the value of the expression 6×(x - 9) - 5 for x = 5 as follows:
we deal with bracket first;
6×(x - 9) - 5 = 6 × (5 - 9) - 5
we multiply next;
6×(x - 9) - 5 = 6 × -4 - 5
6×(x - 9) - 5 = -24 - 5
lastly we subtract
6×(x - 9) - 5 = -29.
Therefore, the variable expression for x = 5 given 6×(x - 9) - 5 is evaluated to give a result of -24 using PEDMAS.
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What is the distance between the points (-2, 3) and (5, -1)?
A.) Square root of 121
B.) Square root of 65
C.) Square root of 3
D.) Square root of 63
Answer:
B
Step-by-step explanation:
Use the distance formula.
volume of a sphere = 4/3pir^3 where r is the radius volume of a cone = 1/3pir^2h where r is the radius and h is the height the shape below is made from a cone and a hemisphere work out the volume of the shape give your answer to the nearest integer 8cm 12cm
Answer: To find the volume of the combined shape, we need to find the volume of the cone and the volume of the hemisphere and add them together.
For the cone:
Volume = 1/3 * pi * r^2 * h
Where r is the radius and h is the height. In this case, r = 8 cm and h = 12 cm. So,
Volume = 1/3 * pi * 8^2 * 12 = (1/3) * pi * 64 * 12 = 256 * pi cm^3
For the hemisphere:
Volume = (2/3) * pi * r^3
Where r is the radius. In this case, r = 8 cm. So,
Volume = (2/3) * pi * 8^3 = (2/3) * pi * 512 cm^3
Adding the volumes of the cone and the hemisphere, we have:
Volume = 256 * pi + (2/3) * pi * 512 cm^3 = 256 * pi + 341.3333 * pi cm^3
To the nearest integer, the volume of the combined shape is:
Volume = round(256 * pi + 341.3333 * pi) = round(597.3333 * pi) = 1876 cm^3
Step-by-step explanation:
how do i solve this problem
Answer:
No, it is not.
Step-by-step explanation:
remember PEMDAS (parenthesis, exponents, mult., etc)
use distributive property, but solve parenthesis first
3x(x+4)²
(x+4)(x+4) = x² + 8x + 16
3x(x² + 8x + 16) >>> 3x³ + 24x² + 48x
so the equation is not equal
27 children sit at table of 6, fillling where possible. Express how are filled using mixed number.
The number of table in the form of mixed number will be 4 ¹/₂ tables.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
27 children sit at table of 6, fillling where possible. Then the number of table is given as,
⇒ 27 / 6
⇒ 4 ³/₆
⇒ 4 ¹/₂ tables
The number of table in the form of mixed number will be 4 ¹/₂ tables.
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A caterer charges $110 to cater a party for 10 people and $220 for 20 people. Assume the cost, y, is a linear function of the number of x people. Write an equation in slope-intercept form for this function. What does the slope represent? How much would a party for 60 people cost?
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the cost per people.b is the intercept, representing the fixed cost.Two points on the function are given as follows:
(10, 110) and (20, 220).
The slope is given by the change in the output divided by the change in the input, hence:
m = (220 - 110)/10
m = 11.
Hence:
y = 11x + b.
When x = 10, y = 110, hence the intercept b is given as follows:
110 = 11(10) + b
b = 0.
Hence the function giving the cost for x people is of;
y = 11x.
The cost for 60 people would be of:
y = 11(60)
y = $660.
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Anna compra helado y naranjas en la tienda.
• Ella paga un total de $59.53.
• Ella paga un total de $6.49 por el helado.
• Ella compra 8 bolsas de naranjas que cuestan la misma cantidad ca
Escribe y resuelve una ecuación que se pueda usar para determinar X, cuánto cuesta
cada bolsa de naranjas.
Ecuación:
Respuesta: X=
Answer:
La respuesta de su problemamatemático es X= 6.63
3c + b² + (27a) - d
a = 1/3
b = 9
c = 5
d = -10
Answer:
Step-by-step explanation:
Rephrase it.
3(5) + 9² + (27 x 1/3) - (-10)
15 + 9x9 + 9 - (-10)
15 + 81 + 9 - (-10)
96 + 9 - (-10)
115
9+10=
????????????????????????????????????
Answer: 21
Step-by-step explanation:
Answer:
19
Step-by-step explanation:
9 + 10 = (1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1) + (1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1)
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 19
Calculate
-73 - 110
Answer:
Step-by-step explanation:
-183
Answer:
Any negative minus a positive is a negative:
-183
Step-by-step explanation:
Hope it helps! =D
If C.P. of 100 pencils is Rs.250 and S.P. of 1 dozen pencils is Rs.33, find the gain or loss per cent.
CP of 100 pencils = Rs.250
CP of 1 pencil = 250/100 = 2.5
SP of 1 dozen pencils = Rs.33
SP of 12 pencils = Rs.33
SP of 1 pencil = \frac{33}{12}=2.75
SP>CP
So, Profit% = SP - CP/ CP × 100 = 2.75 - 2.5/2.5 × 100 = 10 %
Hence The profit % is 10%
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Solve.
320e=18
e= what?
Answer: e = 1/18
Step-by-step explanation:
e = 18/320
e = 1/18
Answer: 0.05625
Step-by-step explanation: So, you divide 18 by 320, and that gives you 0.05625, and you can double check by multiplying 0.05625 by 320, which gives you 18.
Compare Jurgis’s response after his injury to his earlier attitudes. How did his attitude change? Describe your opinion in at least four sentences
Answer:
Step-by-step explanation:
In "The Jungle" by Upton Sinclair, Jurgis is a character who starts out with a positive and optimistic outlook on life. He is full of hope and ambition when he arrives in America with his family, eager to make a better life for himself. However, after he is injured on the job and becomes unable to work, his attitude changes dramatically. He becomes disillusioned and bitter, losing his hope and faith in the American Dream.
In my opinion, Jurgis's response to his injury reflects the harsh realities of life for immigrants and the working class in America during that time. The injury not only physically incapacitates him, but it also robs him of his ability to provide for his family and live out his dreams. The experience shows the extent to which the system is stacked against those in Jurgis's position and serves as a powerful commentary on the injustices and inequalities of the time.
find the inverse function of f(x) = 2x +3
Answer:
So the inverse function of f(x) = 2x + 3 is f⁻¹(x) = (x - 3) / 2.
Step-by-step explanation:
To find the inverse of a function, we switch the x and y variables and solve for y. So, we start with:
y = 2x + 3
Switching x and y, we get:
x = 2y + 3
Now, we solve for y:
x - 3 = 2y
y = (x - 3) / 2
So the inverse function of f(x) = 2x + 3 is f⁻¹(x) = (x - 3) / 2.
Answer & Step-by-step explanation:
To determine f's inverse function (x)= 2x + 3, we can follow these steps:
Step 1: Replace f(x) with y: y = 2x + 3
Step 2: Solve for x in terms of y:
y = 2x + 3
y - 3 = 2x
x = (y - 3) / 2
Step 3: Replace x with f^(-1)(x):
f^(-1)(x) = (x - 3) / 2
Therefore, the inverse function of f(x) = 2x + 3 is f^(-1)(x) = (x - 3) / 2.
Hope it helps!for my homework i need to factorise 14x^2-x-3
Answer:
the factorisation of 14x^2 - x - 3 is (7x + 3)(2x - 1).
Step-by-step explanation:
To factorise the quadratic expression 14x^2 - x - 3, we can use the following steps:
Look for two numbers that multiply to 14 and add to -1. The numbers we need are -7 and 2.Write the expression as a product of two binomials: (14x^2 - 7x) + (-x - 3).Now, we use the difference of squares factorization to separate the middle term: (7x + 3)(2x - 1).Check our answer by multiplying the two binomials together and comparing the result to the original expression.So, the factorisation of 14x^2 - x - 3 is (7x + 3)(2x - 1).
Answer:
Step-by-step explanation:
14×14-×-3
196-×-3=196-3
=193
the rocket coaster has 15 cars, some that hold 3 people and some that hold 5 people. there is room for 63 people altogether. how many 3-passenger cars are there? how many 5-passenger cars are there?
There are 6 cars that hold 3 people and 9 cars that hold 5 people.
How to determine the number of passengersLet's call the number of 3-passenger cars "x" and the number of 5-passenger cars "y".
We know the total number of cars is 15, so:
x + y = 15
We also know that the total number of passengers is 63, so:
3x + 5y = 63
Now we can use the first equation to solve for one of the variables in terms of the other:
y = 15 - x
Substitute this expression for y into the second equation:
3x + 5(15 - x) = 63
Expand
3x + 75 - 5x = 63
Evaluate like terms:
2x = 12
Divide both sides by 2:
x = 6
Recall that
y = 15 - x
So, we have
y = 15 - 9
y = 6
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or A line passes through the points (1,1) and (2,7). Write its equation in slope-intercept form.
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{7}-\stackrel{y1}{1}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{1}}} \implies \cfrac{ 6 }{ 1 } \implies 6[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ 6}(x-\stackrel{x_1}{1}) \\\\\\ y-1=6x-6\implies {\Large \begin{array}{llll} y=6x-5 \end{array}}[/tex]
Can anybody help me on this question?
Answer: x = 46°
Step-by-step explanation:
A triangle has a 60 degree angle, and the two adjacent sides are 12 and 12 square root 3. Find the radius of a circle with the same vertex as a center, if the arc inside the triangle divides it into two regions of equal area.
The radius of a circle with the same vertex as a center, if the arc inside the triangle divides it into two regions of equal area is (18 × ✓π) / π
How to calculate the radiusFrom the information, the triangle has a 60 degree angle, and the two adjacent sides are 12 and 12 square root 3.
The area of a triangle will be;
A = 1/2 × a × b × sin C
= 1/2 × 12 × 12✓3 × sin 60
= 108
Area of sector = πr² / 360 × 60.
r² = (108/2) × 6 ) π
r² = 324 / π
r = 18✓π / π
The radius is 18✓π / π.
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Mariah is planting a rectangular rose garden. In the center of the garden, she puts a smaller rectangular patch of grass. The grass is 2 feet by 3 feet. What is the area of the rose garden?
The area of the rose garden =129 square feet.
Consider the following diagram.
From the figure we can observe that the dimensions of the rectangular garden are: length = 15 ft and width = 9 ft
Let us assume that A₁ be the area of the rectangular garden.
Using the formula for the area of rectangle,
The area of the rectanguler garden would be,
A₁ = 15 × 9
A₁ = 135 ft²
Also, the dimensions of the rectangular patch of grass is 2 feet × 3 feet.
Let us assume that A₂ represents the area of the rectangular patch of grass.
Using the formula for area of rectangle, the area of rectangular patch of grass is:
A₂ = 2 × 3
A₂ = 6 ft²
Let a be the area of the rose garden.
So, the required area would be,
A = A₁ - A₂
A = 135 - 6
A = 129 ft²
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Find the complete question below.
Steve is driving at 35 mi/h when he makes an emergency stop. His brakes lock and his tires leave four skid marks of equal length. The drag factor for the road surface was 0.97 and his brakes were operating at 90% efficiency. How long might the skid marks be to the nearest foot?
The skid marks be to the nearest foot is 913 ft.
The length of the skid marks can be calculated using the formula d = μV2/2gdf, where μ is the coefficient of static friction, V is the velocity, g is the acceleration due to gravity, and df is the drag factor. In this case, the coefficient of static friction can be assumed to be 0.9, the velocity is 35 mi/h, the acceleration due to gravity is 32.2 ft/s2, and the drag factor is 0.97. Plugging these values into the formula, we get [tex]d = 0.9(35 mi/h x 5280 ft/mi/h)2/2(32.2 ft/s2)(0.97) = 912.5 ft[/tex]. To the nearest foot, this is 913 ft.
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6300000 in standard form
Answer:
6.3×10^6
Step-by-step explanation:
6.3×10^6
in standard form
is the sample mean for these data more or less descriptive as a center of location than the trimmed mean?
(a) The sample size for the above sample is 15.
(b) The sample mean for these data is 3.8.
(c) The sample median is 3.6.
(d) To compute the 20% trimmed mean for the above data set is 3.7.
(e) The sample mean is less descriptive as the location's center (median) than the trimmed mean.
The following measurements were recorded for the drying time, in hours
3.4 2.5 4.8 2.9 3.6 is:
2.8 3.3 5.6 3.7 2.8
4.4 4.0 5.2 3.0 4.8
(a) We have to determine the sample size for the above sample.
The number of participants or observations included in a study is referred to as the sample size. This number is commonly represented by the symbol n.
Sample Size (n) = 15
(b) We have to calculate the sample mean for these data.
Sample Mean = Total Sum of data/Total Number
Sample Mean = (3.4 + 2.5 + 4.8 + 2.9 + 3.6 + 2.8 + 3.3 + 5.6 + 3.7 + 2.8 + 4.4 + 4.0 + 5.2 + 3.0 + 4.8)/15
Sample Mean = 56.8/15
Sample Mean = 3.8
(c) We have to calculate the sample median.
To define the sample median we first represent the data in ascending order.
2.5, 2.8, 2.8, 2.9, 3.0, 3.3, 3.4, 3.6, 3.7, 4.0, 4.4, 4.8, 4.8, 5.2, 5.6
Sample Size(n) = 15
So Median = (n+1)/2th term
Median = (15 + 1)/2th term
Median = 16/2th term
Median = 8th term
So the 8th term in the given data is 3.6. So,
Median = 3.6
(d) We have to compute the 20% trimmed mean for the above data set.
To compute the 20% termed mean, remove 20% of the largest and 20% of the smallest elements from the sample and compute the mean of the new sample.
New sample: 2.9 3.0 3.3 3.4 3.6 3.7 4.0 4.4 4.8
New Mean = 33.3/9
New Mean = 3.7
(e) We have to check is the sample mean for these data more or less descriptive as a center of location than the trimmed mean.
The mean value is 3.8, the median value is 3.6, and the trimmed mean value is 3.7. As a result, the sample mean is less descriptive as the location's center (median) than the trimmed mean.
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The complete question is:
The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint.
3.4 2.5 4.8 2.9 3.6
2.8 3.3 5.6 3.7 2.8
4.4 4.0 5.2 3.0 4.8
Assume that the measurements are a simple random
sample.
(a) What is the sample size for the above sample?
(b) Calculate the sample mean for these data.
(c) Calculate the sample median.
(d) Compute the 20% trimmed mean for the above data set.
(e) Is the sample mean for these data more or less descriptive as a center of location than the trimmed mean?
After midnight, the cost of any taxi journey increases by 45%. One journey costs $84.10 after midnight.
Calculate the cost of the same journey before midnight.
Answer:
$121.95
Step-by-step explanation:
Taxi ride cost before midnight = $84.10There is an increase of 45% in cost after midnightThis increase in $ terms is 45% x $84.1045% = 45/100 = 0.45 in decimalSo $ increase in cost = 0.45 x 84.10The cost of the same journey before midnight is,
⇒ $58
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
We have to given that;
After midnight, the cost of any taxi journey increases by 45%.
And, One journey costs $84.10 after midnight.
Now, Let the cost of the same journey before midnight is x
Hence, WE can formulae;
x + 45% of x = 84.10
x + 0.45x = 84.10
1.45x = 84.10
x = $58
Thus, The cost of the same journey before midnight is,
⇒ $58
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Une enquête faite auprès des collégiens d'une ville a permis de recueillir les informations suivantes : 7
30 des élèves interrogés n'ont pas de téléphone portable;
400 élèves possèdent un téléphone portable et un ordinateur;
1 6 des élèves interrogés n'ont pas d'ordinateur;
1 15 des élèves interrogés n'ont ni téléphone portable
ni ordinateur.
Combien de collégiens ont été interrogés pour réaliser
cette enquête ?
600 élèves :
On sait que 7/30+1/6 ne font pas partie des 400 élèves qui possèdent téléphone portable et ordinateur . 7/30+1/6=12/30=2/5 mais parmi ces élèves figurent ceux qui n'ont ni l'un, ni l'autre. Ils font donc partie des 2/5 qui viennent d'être dénombrés
Il faut donc les retrancher, sinon ils seraient comptés deux fois
donc le nombre n'ayant ni l'un ni l'autre est : 2/5-1/15=5/15=1/3
Par conséquent 2/3 ont unt téléphone et un ordinateur
Comme ces 2/3 correspondent à 400 élèves, le nombre total d'élèves interrogés sera donc de 400*3/2=600 élèves.
A scale drawing of Julie's living room is shown below: A rectangle is shown. The length of the rectangle is labeled as length equal to 8 cm, and the width is labeled as width equal to 6 cm. If each 2 cm on the scale drawing equals 4 feet, what are the actual dimensions of the room? (5 points) a Length = 16 feet, width = 12 feet b Length = 10 feet, width = 8 feet c Length = 32 feet, width = 24 feet d Length = 14 feet, width = 12 feet