I assume you want the volume of the shape with the given cross sections. In the [tex]x,y[/tex]-plane, the base is set
[tex]\left\{(x,y) ~:~ 0\le x\le 2 \text{ and } 0 \le y \le 2-x\right\}[/tex]
Each cross section is a square plate with side length [tex]2-x[/tex] (the vertical distance between the [tex]x[/tex]-axis and the line [tex]y=2-x[/tex]) and thickness [tex]\Delta x[/tex], hence volume [tex](2-x)^2\,\Delta x[/tex].
As [tex]\Delta x\to0[/tex] and the number of cross sections grows to infinity, the total volume of the plates converges to volume of the solid [tex]S[/tex], given by the definite integral
[tex]\displaystyle \int_0^2 (2-x)^2 \, dx = \int_0^2 x^2 \, dx = \frac{2^3-0^3}3 = \boxed{\frac83}[/tex]
(where we make the substitution [tex]2-x\mapsto x[/tex])
what is the area of the parallelogram in square centimeters? show your work
The area of parallelogram is Base(B) × Height(H).
The quantity of square units that make up a polygon determines its area. Similar to a carpet or area rug, area is two dimensional.
A parallelogram is a four-sided structure made up of two parallel line pairs. The length of opposing sides and the magnitude of opposing angles are both equal. Multiply the base by the height to determine the area. The equation is:
A = B × H,
where B stands for base
H for height
A parallelogram must have a perpendicular base and height. A parallelogram's lateral sides aren't parallel to the base, though. As a result, the height is represented by a dotted line. Let's examine a few instances when the area of a parallelogram is involved.
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does anybody know this? i’ve been struggling for hours
12 lies between 9 and 16 so √12 lies between 3 and 4.
Perfect square-: Those whole numbers in which we can pair the factors are known as perfect square.
We can write the number 40 as 2 × 2 × 2 × 5. This is not a perfect square because we cannot pair the factors.
Factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly.
We write 40−−√ to be the square root of 40, and can investigate between which two whole numbers it lies.
Consider the table of perfect squares below:
Whole number 1 2 3 4 5 6 7 8 9 10 11 12
Whole number squared 1 4 9 16 25 36 49 64 81 100 121 144
The number 40 lies between 36 and 49 hence 40−−√ lies between 6 and 7.
Similarly, 12 lies between 9 and 16 so √12 lies between 3 and 4.
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The coordinate -2 has a weight of 1, the coordinate 0 has a weight of 1, and the coordinate 3 has a weight of 2. Find the
weighted average.
Weighted average:
The weight average of the coordinates is 1
How to determine the weight average?The given parameters are:
Coordinate -2 has a weight of 1Coordinate 0 has a weight of 1Coordinate 3 has a weight of 2The weight average is then calculated as:
Weight average = Sum of (Weight * Coordinate)/Sum of Weights
So, we have:
Weight average = (-2 * 1 + 0 * 1 + 3 * 2)/(1 + 1 + 2)
Evaluate the quotient
Weight average = 1
Hence, the weight average of the coordinates is 1
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hello fabulous1a please be in comments i need an answer for this question please when you answer tell me which one you're answering
Answer:
1. The answer is 8
20-3-1= $16
$16/2=8
meaning they've only been on 8 games or rides
2. The answer is 17 miles. Every mile = $1 so that means they travelled 17 miles
first u subtract 5 from 22 which will equal 17
3. $0.25
first u add up all the money from each item and then subtract it by 12 and u will get 0.25
Nvm I can only do 1-3
Step-by-step explanation:
14. Name three segments in this figure in order of length from shortest to longest.
A
B
C
15 Which property of multiplication is illustrated by this equation?
The three segments of Triangle is (1) 17 cm, 7 cm, 8 cm
Here, 17 > 7 + 8 or 17 > 15
In any triangle, the sum of the lengths of any two sides of a triangle is always greater than the third side.
Therefore, the triangle is not possible.
In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle. All triangles are enclosed in a single plane if all of the geometry is the Euclidean plane, however, this is no longer true in higher-dimensional Euclidean spaces.
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Which of the following could be the same graph as y=-2x+5
The equation shows that the slope of the line is -2 and the y-intercept is 4 that is the line will pass through the point (0, 5)
Graphing linear equationThe standard linear equation is expressed as y = mx + b where;
m is the slopeb is the y-interceptGiven the linear equation y=-2x+5
The equation shows that the slope of the line is -2 and the y-intercept is 5 that is the line will pass through the point (0, 5)
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while standing in front of the school, jace recorded the number of students who walked, rode their bikes, took the bus, and were driven there.
The method used to collect data for the given scenario is: observational study.
What is observational study?Observational study refers to a study design in which subjects are watched or specific outcomes are gauged. No effort is taken to influence the result (for example, no treatment is given).Now,
In the given scenario, Jace is taking records by observing all the students who are walking or riding the bike or taking the bus and are being driven, all by himself.He is taking notes and writing each and every student's respective mode of transportation.Hence, the method used to collect data is observation, i.e., observational study is being made here.
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(COMPLETE QUESTION:
Use the drop-down menus to identify the method used to collect data for each scenario.
While standing in front of the school, Jace recorded the number of students who walked, rode their bikes, took the bus, and were driven there.)
Which of the following is equal to 7 1/3
A. √7
B. √7.3
C. 73
D. 3√7
Robert manufactures dolls by hand. He sells them at $41.25,
but each one has a cost of $4.17 in materials. In addition, he
has to pay $935.84 monthly in other business expenses. This
year, Robert has sold 941 dolls. Which is the closest estimate
of Robert's net profits per month?
Can someone help plss
Answer:
Make y the subject of the formula which will give the answer below
y=1/3x-3
select C
Rewrite each sum in the form a(b+c) using the Distributive Property and the GCF.
12+ 20 =
36 +15=
24 +18=
20 +50=
6 +22=
60 + 25 =
Each sum using distributive property is given as follows:
1) 12+20= 3(4+5)
2) 36+15= 3(12+5)
3) 24+18= 6(4+3)
4) 20+50= 10(2+5)
5) 6+22= 2(3+11)
6) 60+25= 5(12+5)
Given, sum to be represented by distributive property.
1)
12+20= 3(4+5)
Factors of 12 = 2 × 2 × 3
Factors of 20 = 2 × 2 × 5
GCF of 12 and 20 = 4
Take 4 common from 12 and 20.
Representing in a(b+c) .
4(3+5)
2)
36+15= 3(12+5)
Factors of 36 = 2 × 2 × 3 × 3
Factors of 15 = 3 × 5
GCF of 36 and 15 = 3
Take 3 common from 36 and 15.
Representing in a(b+c) .
3(12+5)
3)
24+18= 6(4+3)
Factors of 24 = 2 × 2 × 2 × 3
Factors of 18 = 2 × 3 × 3
GCF of 24 and 18 = 4
Take 5 common from 24 and 18.
Representing in a(b+c) .
6(4+3)
4)
20+50= 10(2+5)
Factors of 50 = 2 × 5 × 5
Factors of 20 = 2 × 2 × 5
GCF of 50 and 20 = 10
Take 10 common from 50 and 20.
Representing in a(b+c) .
10(2+5)
5)
6+22= 2(3+11)
Factors of 22 = 2 × 11
Factors of 6 = 2 × 3
GCF of 22 and 6 = 2
Take 2 common from 22 and 6 .
Representing in a(b+c) .
2(3+11)
6)
60+25= 5(12+5)
Factors of 60 = 2 × 2 × 3 × 5
Factors of 25 = 5 × 5
GCF of 60 and 25 = 5
Take 5 common from 60 and 25.
Representing in a(b+c) .
5(12+5)
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The table shows the numbers y of students absent from school x days after a flu outbreak.
Write a function that models the data.
Use the model to approximate the number of students absent 10 days after the outbreak.
A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting points showing any association (correlation) between the data set.
What is a quadratic function?A quadratic function can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.
In Mathematics, the standard form of a quadratic equation is given by;
ax² + bx + c = 0
By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that the quadratic function is given by:
y = -0.4908x² + 5.8845x + 1.3572
For the number of students that are absent 10 days after the outbreak, we have:
y = -0.4908(10)² + 5.8845(10) + 1.3572
y = -0.4908(100) + 58.845 + 1.3572
y = -49.08 + 58.845 + 1.3572
Number of students, y = 11.12 ≈ 11 students.
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. What is a solution of x² + 6x = -5?
Ox=-6
Ox=-1
Ox=1
Ox=6
Answer:
x = -1
Step-by-step explanation:
x² + 6x = -5
x² + 6x -( -5) = 0
Use the quadratic formulaEvaluate the exponentMultiply the numberSubtract the numberEvaluate the square rootMultiply the numberx = (-x + 4)/2
Separate the equationsTo solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
x = (-6 + 4)/2
x = (-6 - 4)/2
Rearrange and isolate the variable to find each solutionx = -1
Solve: |-5| + |12| =
*
Answer:
17
Step-by-step explanation:
the absolute value function always gives a positive result , that is
| - a | = | a | = a
| - 5 | + | 12 |
= | 5 | + 12
= 5 + 12
= 17
given y left parenthesis z right parenthesis equals space fraction numerator z squared minus 1 over denominator z left parenthesis z minus 1 right parenthesis squared end fraction determine the final value
The simplification of the given algebraic expression is;
yz = (z + 1)/z(z - 1)
How to simplify algebraic expressions?We are given y left parenthesis z right parenthesis which is expressed as; yz
Now, we are given the algebraic expression that yz equals space fraction numerator z squared minus 1 over denominator z left parenthesis z minus 1 right parenthesis squared end fraction
z squared minus 1 over denominator z left parenthesis z minus 1 right parenthesis squared end fraction is expressed as; (z² - 1)/z(z - 1)²
Thus, our main expression is;
yz = (z² - 1)/z(z - 1)²
Factorizing the numerator and denominator gives;
yz = (z + 1)(z - 1)/z(z - 1)(z - 1)
(z - 1) is common to both numerator and denominator and as such, we now have;
yz = (z + 1)/z(z - 1)
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How do you know the difference between a odd, even, and neither graph?
Answer: Even functions
Symmetric about the yy-axis
When you plug -x−x into the function, it will simplify to be the same as the original function. This means that it doesn’t matter whether you plug in xx or -x−x, your output will be the same. So
f(-x)=f(x)f(−x)=f(x)
Below are graphs that are even and symmetric about the yy-axis.
even functions are symmetric about the y-axis
Odd functions
Symmetric about the origin
When you plug -x−x into the function, it will simplify to be negative of the original function, or the original function multiplied by -1−1. This means that when you plug -x−x into the function, you’ll get the same output as you do when you plug in xx, except it will be negative (or have the opposite sign as the original output). So
f(-x)=-f(x)f(−x)=−f(x)
Below are graphs that are odd and symmetric about the origin. Be sure to visually compare quadrants that are diagonal from each other (quadrants 1 and 3, and quadrants 2 and 4).
odd functions are symmetric about the origin
Neither even nor odd
Not symmetric about the yy-axis, and not symmetric about the origin
The function has no symmetry. It’s possible that a graph could be symmetric to the xx-axis, but then it wouldn’t pass the Vertical Line Test and therefore wouldn’t be a function.
functions that are neither even nor odd
hope this helps!!
Please help! radicals.
(Check picture)
Answer:
10√2
Step-by-step explanation:
You want the simplified form of the radical expression 2√200 -10√2.
SimplificationRadicals are simplified by removing perfect squares from under the radical. Radicals with the same radicand are "like terms" and can be combined.
[tex]2\sqrt{200}-10\sqrt{2}=2\sqrt{10^2\cdot2}-10\sqrt{2}\\\\=2\cdot10\sqrt{2}-10\sqrt{2}=(20-10)\sqrt{2}=\boxed{10\sqrt{2}}[/tex]
Answer:
[tex]10 \sqrt{2} [/tex]
Step-by-step explanation:
Simplify.
[tex]2 \sqrt{200} \\ = 2 \sqrt{100 \times 2 } \: \: \: \: \\ = 2 \sqrt{100} \times \sqrt{2} \\ = 2 \times 10 \times \sqrt{2} \\ = 20 \sqrt{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \:[/tex]
Now let us solve the given expression.
[tex]2 \sqrt{200} - 10 \sqrt{2} \\ 20 \sqrt{2} - 10 \sqrt{2} \\ 10 \sqrt{2} [/tex]
this is a pond in the shape of a prism it is completely full of water Collin uses a pump to empty the pond the level goes down by 20cm in the first 30 mins work out how many minutes Colin has to wait until the pond is completely empty
To empty the tank in the shape of prism completely, Colin has to wait 150 minutes for the water of the pond to at zero level.
What is the prism volume formula?
V=Bh, where B is the base area and h is the height, is the formula for a prism's volume. The prism has a rectangular base. The rectangle measures 9 cm in length and 7 cm in breadth. A rectangle's area A is equal to its length l and width w.Given :
A pond in the shape of a prism.
Colin uses a pump to empty the pond. The level goes down by 20 cm in the first 30 minutes.
Solution :
We know that the volume of the prism is given by,
Volume = ( Base area ) × height
Base area = 1/2 ( 1.4 + 0.6 ) × 2 ⇒2 m²
Volume = 2 × 1 = 2m³
Given that the level of pond goes down by 20 cm in the first 30 minutes. Therefore, the volume becomes,
Volume = 2 × 0.8 = 1.6m³
Now, the rate of emptying the tank is,
[tex]= \frac{2 - 16}{30} = \frac{1}{75}[/tex] m³/min
time = volume / rate
= [tex]\frac{2}{\frac{1}{75} }[/tex] = 150
Therefore, Colin has to wait 150 minutes for the pond to completely empty
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Samuel wanted to rent a bike. The rental fee cost $10 dollars plus $5 for each hour. Part A. Write an expression to represent this scenario where h represents the number of hours. Part B. Write and solve an equation to determine how many hours Samuel can rent the bike if he has a $30 budget. Show your work.?
An expression to represents the Samuel wanted to rent a bike if rental fee cost $10 plus $5 for each hour is x=10 + 5h, he can rent the bike for 4hours with $30 budget.
As given,
Let x represents total rental cost
h represents number of hours
Rental fee=$10
Per hour fee=$5
Expression:
x=10 +5h
Budget x= $30
30=10 +5h
⇒ 5h=20
⇒h=4hours
Therefore, an expression to represents the Samuel wanted to rent a bike if rental fee cost $10 plus $5 for each hour is x=10 + 5h, he can rent the bike for 4hours with $30 budget.
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kai is using clay to make bowls. each bowl uses 4/5 Ib of clay. Kai has 2 2/5 Ib of clay. How many bowls can Kai make? pls help!
The number of bowls of clay that is left will be 8/5 lb.
What is a fraction number?A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of a numerator and a denominator.
kai is using clay to make bowls. Each bowl uses 4/5 Ib of clay.
Kai has 2²/₅ Ib of clay.
Then the amount of clay that is left will be
⇒ 2²/₅ - 4/5
⇒ 12/5 - 4/5
⇒ (12 - 4) / 5
⇒ 8/5
The amount of clay that is left will be 8/5 lb.
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The temperature dropped from 27 degrees to -4 degrees in one day. Write and solve an expression to represent the
change in degrees. also with give branly to who answers first
Answer:
See explanation
Step-by-step explanation:
d=degree change
d=-4-27
d=-31 degrees
Given E(-2,4), F(-7,-4), G(-5,2),E(−2,4),F(−7,−4),G(−5,2), and H(x, -6). Find x such that EF∥GH.
Two lines are said to be parallel when slopes are same. If EF∥GH and E(−2,4),F(−7,−4),G(−5,2), and H(x, -6) then x is -3.
What are Parallel lines?Parallel lines are straight lines that never meet each other no matter how long we extend them.
Given;
G(-5,2),E(−2,4),F(−7,−4),G(−5,2), and H(x, -6).
Two lines are said to be parallel when slopes are same.
The equation of line passing through two points is y-y1=m(x-x1)
where m is the slope
The equation of line EF is
y-4=8/5(x+2)
Here slope is 8/5.
The equation of line GH is
y-2=-8/(x-2)(x+5)....*
As the two lines are parallel, the slopes must be equal.
In * the slope should be 8/5,so
x-2=-5
x=-3
Therefore the value of x is -3.
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The difference of 3 times a number and 12 is -24.
Write and solve an equation to find the number.
The equation formed for the expression "The difference of 3 times a number and 12 is -24", is 3x - 12 = - 24, which gives the number, x = -4.
In the question, we are asked to write and solve an equation to find the number, given that the difference between 3 times the number and 12 is -24.
We assume the number to be x.
The sentence given to us is the difference between 3 times the number and 12.
Three times the number is 3x.
The difference between 3 times the number and 12 can be shown as 3x - 12.
We are given that the difference between 3 times the number and 12 is -24.
This can be shown as 3x - 12 = - 24.
This is the required equation.
To solve this, we do the following steps:
3x - 12 = -24.
Adding 12 to both sides, we get:
3x - 12 + 12 = - 24 + 12,
or, 3x = -12.
Now, we divide both sides by 3, to get:
3x/3 = -12/3,
or, x = -4.
Thus, the equation formed for the expression "The difference of 3 times a number and 12 is -24", is 3x - 12 = - 24, which gives the number, x = -4.
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What the mean of 120, 60 , 0 , 30 , 15 , 0 , 0 , 10 , 20
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{28 1/3}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{We are given 9 numbers}[/tex]
Find: [tex]\textsf{Determine the mean of the numbers}[/tex]
Solution: In order to determine the mean of the numbers the first step that we need to do is to add up all of the numbers. After adding up all of the numbers we divide it by the amount of numbers that were provided to us.
Add up the numbers
[tex]\textsf{120 + 60 + 0 + 30 + 15 + 0 + 0 + 10 + 20}[/tex][tex]\textsf{255}[/tex]Divide it by the amount of numbers provided
[tex]\textsf{255 / 9}[/tex][tex]\textsf{((28 * 9) + 3) / 9}[/tex][tex]\textsf{28 (3/9)}[/tex][tex]\textsf{28 1/3}[/tex]Therefore, the mean of the numbers provided is [tex]\textsf{28 1/3}[/tex]
List all pairs of congruent angles, and write a proportion that relates the corresponding sides for each pair of similar polygons.
J K L M ≅ TSRQ
Pairs of congruent angles are: ∠J ≅ ∠T; ∠K ≅ ∠S; ∠L ≅ ∠R; ∠M ≅ ∠Q
A proportion of their corresponding sides is: JK/TS = KL/SR = LM/RQ = JM/TQ
What are Similar Polygons?When two polygons are similar to each other, they have the same shape but different sizes. Therefore, they will have pairs of angles that are congruent to each other and pairs of corresponding sides that have ratios that are the same, which means they have the same proportion.
Given polygons JKLM and TSRQ, the corresponding congruent angles are:
∠J ≅ ∠T
∠K ≅ ∠S
∠L ≅ ∠R
∠M ≅ ∠Q
A proportion of their corresponding sides would be:
JK/TS = KL/SR = LM/RQ = JM/TQ
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Tiffany has taken out a loan with a stated interest rate of 8.145%. how much greater will tiffany’s effective interest rate be if the interest is compounded weekly than if it is compounded semiannually? a. 0.3340 percentage points b. 0.1659 percentage points c. 0.1681 percentage points d. 0.1234 percentage points please select the best answer from the choices provided a b c d
Tiffany's effective interest is compounded weekly is 0.1604% greater than the compounded semiannually.
Compound interest is when you earn interest on both the money you've saved and the interest you earn.
Given,
The interest rate i= 8.145%
Number of weeks in an year n= 52
We know,
Effective interest rate =[tex](1+\frac{i}{n})^{n}-1[/tex]
Substitute the values
[tex]R_{1}=(1+\frac{0.08145}{52})^{52}-1\\ R_{1}= 0.084789[/tex]
Case 2
Compounded semiannually
[tex]R_{2}=(1+\frac{0.08145}{2})^{2}-1\\ R_{2}=0.083108[/tex]
The difference is
[tex]R_{1}-R_{2}= 0.084789-0.083185[/tex]
=0.001604
=0.1604%
Hence, the Tiffany's effective interest is compounded weekly is 0.1604% greater than the compounded semiannually
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Can someone PLEASE give me the solution to this question, my exams in 2 days.
Answer:
see explanation
Step-by-step explanation:
the shaded area is calculated as
outer circle area - inner circle area
since CAB is a tangent to the inner circle at A then OAB = 90° and
Δ OAB is right
using Pythagoras' identity in the right triangle to express R in terms of r and d , then
R² = d² + r²
------------------------------------------
A( outer Δ ) = πR² = π(d² + r² ) = πd² + πr²
A ( inner Δ ) = πr²
Then
shaded area = πd² + πr² - πr² = πd²
6. Write the following numbers in expanded exponential form:
a) 74009234 =
Answer:
74,009,234= 7^6+ 9^3+2^2+3^1+4^0
Step-by-step explanation:
Write the additive inverse of -7.
worth 20 points
Answer:
7
Step-by-step explanation:
a=additive inverse of -7
-7+a=0
-7+7+a=0+7 ==> add 7 on both sides to isolate 'a'
a=7
Write the following in factored form by factoring out the greatest common factor. 40p^6q+15p^5q^4 + 35p^3q^2
Answer:
5p^3q ( 8p^3 + 3p^2q^3 +7q)
Step-by-step explanation:
greatest common factor = GCF
40p^6q + 15p^5q^4 + 35p^3q^2
This expression has 3 terms: 40p^6q , 15p^5q^4 , and 35p^3q^2
Find the GCF for the 3 terms
The coefficient parts are 40, 15 and 35 their GCF is 5
The p part: p^6, p^5, and p^3 their GCF is p^3
The q part: q, q^4, and q^2 their GCF is q
The GCF for the 3 terms is 5p^3q
Factor the expression using the GCF
40p^6q + 15p^5q^4 + 35p^3q^2 =
5p^3q ( 8p^3 + 3p^2q^3 +7q)