Answers
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It's important to understand and apply various mathematical concepts taught in high school, including basic algebra, arithmetic, and vector representation. Success also often comes from group work and discussions, which can provide new perspectives.
Explanation:In mathematics, figuring for yourself and collaborative group activities are essential aspects of learning. When we talk about basic algebra and arithmetic, it means we are dealing with mathematical operations such as addition, subtraction, multiplication, division, and solving equations. The principles given in a chapter can be applied to various questions. For instance, if you understand the concept of 'solving for x', you can apply it in different scenarios and questions.
Similarly, when vectors are represented with an arrow above them, this is one of the common notations in mathematics, specifically in vector algebra. It is also important to note that working in groups and participating in discussions can bring another perspective and help understand the subject better.
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Related Questions
Use spherical coordinates. evaluate (x2 + y2) dv e , where e lies between the spheres x2 + y2 + z2 = 1 and x2 + y2 + z2 = 25.
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[tex]x^2+y^2=\rho^2\cos^2\theta\sin^2\varphi+\rho^2\sin^2\theta\sin^2\varphi=\rho^2\sin^2\varphi[/tex]
[tex]\displaystyle\iiint_E(x^2+y^2)\,\mathrm dV=\int_{\varphi=0}^{\varphi=\pi}\int_{\theta=0}^{\theta=2\pi}\int_{\rho=1}^{\rho=5}\rho^4\sin^3\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi[/tex]
[tex]=\displaystyle2\pi\left(\int_{\varphi=0}^{\varphi=\pi}\sin^3\varphi\,\mathrm d\varphi\right)\left(\int_{\rho=1}^{\rho=5}\rho^4\,\mathrm d\rho\right)[/tex]
[tex]=\dfrac{24992\pi}{15}[/tex]
To solve this problem, it is necessary determine the integrations limits first.
The solution is:
V = 1666,13×π vol units
In order to express the information in spherical coordinates, we have:
x = ρ×cosθ×sinφ
y = ρ×sinθ×sinφ
z = ρ×cosφ
and dV = ρ²×sinφ×dρ×dθ×dφ
0 ≤ φ ≤ π
0 ≤ θ ≤ 2×π
x² + y² + z² = 25 and x² + y² + z² = 1 are two concentric spheres with center at the origin and radius 5 and 1 respectevely .
According to that:
1 ≤ ρ ≤ 5
V = ∫∫∫ ( x² + y² )× dV
V = ∫∫∫ ( x² + y² )×ρ²×sinφ×dρ×dθ×dφ
V = ∫∫∫ ( ρ²×cos²θ×sin²φ + ρ²×sin²θ×sin²φ ) ×ρ²×sinφ×dρ×dθ×dφ
V = ∫∫∫ [ ρ²×sin²φ ( cos²θ + sin²θ ) ×ρ²×sinφ×dρ×dθ×dφ
V = ∫∫∫ [ ρ²×sin²φ×ρ²×sinφ×dρ×dθ×dφ
V = ∫∫∫ [ ρ⁴×sin³φ×dρ×dθ×dφ
V = ∫₁⁵ρ⁴×dρ ×∫dθ ×∫sin³φ×dφ
V = ρ⁵/5 |₁⁵×∫dθ ×∫sin³φ×dφ
ρ⁵/5 |₁⁵ = 5⁵/5 - 1⁵/5 = 3125 / 5 - 1/5 = 3124/5
V = 3124/5× θ |₀²π×∫sin³φ×dφ
θ |₀²π = 2×π - 0
V = 3124/5× (2×π) ×∫sin³φ×dφ
∫sin³φ×dφ [ 0 y π ] = 4/3 (from Simbolab)
V = 3124/5× (2×π) ×4/3
V = 1666,13×π vol units
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How do you solve 792 divided by 22
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You can represent this as a subtraction problem as well.
792-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22-22=36
Addition: 792=22+22+22+22+22+22+22+22+22+22+22+22+22+22+22+22+22+22+22+22+22+22+22+22+22+22+22+22+22+22+22+22+22+22+22+22
Multiplication:
792=22*36
The sum of eight and a number is one hundred. What is the number?
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x = 100 - 8
x = 92 <== ur number
Let the number be [tex]x[/tex]
Your equation would be [tex]x+8=100[/tex]
Now that we have our equation, lets solve this!
Solve this by keeping the variables aside, and the numbers aside
[tex]x=100 -8[/tex]
The sign would change because your are isolating the number
[tex]x=100-8[/tex]
[tex]x= 92[/tex]
Hope I helped (:
Have a great day!
Translate this sentence into an equation. The difference of Rhonda's height and 16 is 52. Use the variable to represent Rhonda's height.
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The sentence 'The difference of Rhonda's height and 16 is 52' translates into the equation 'h - 16 = 52'. Here, 'h' represents Rhonda's height.
Explanation:The subject matter of this question falls under Mathematics. Specifically, it deals with basic algebra where you have to translate word problems to an algebraic equation. Remember that the phrase 'the difference of' in math refers to the operation of subtraction. So, when you read 'the difference of Rhonda's height and 16 is 52,' that means Rhonda's height (which we’ll denote as 'h') minus 16 equals 52 (52 comes from the phrase 'is 52' because 'is' usually represents equal '='). Therefore, when this sentence is written in the form of an equation, it will look like: h - 16 = 52.
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At 3 p.m. an oil tanker traveling west in the ocean at 14 kilometers per hour passes the same spot as a luxury liner that arrived at the same spot at 2 p.m. while traveling north at 16 kilometers per hour. if the "spot" is represented by the origin, find the location of the oil tanker and the location of the luxury liner t hours after 2 p.m. then find the distance d between the oil tanker and the luxury liner at that time.
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Follow below steps:
The location of the oil tanker and the luxury liner at time t hours after 2 p.m.:
The oil tanker's location: (-14t, 0)
The luxury liner's location: (0, 16t)
The distance d between the oil tanker and the luxury liner at time t:
The distance formula = √((-14t - 0)^2 + (0 - 16t)^2) = √(196t^2 + 256t^2) = √(452t^2) = 2√(113)t
The distance d between the oil tanker and the luxury liner at that time is [tex]\( \sqrt{452} \cdot t \)[/tex] kilometers.
To solve this problem, we'll use the concepts of distance, speed, and coordinate geometry.
Let ( t ) be the number of hours after 2 p.m.
Location of the Oil Tanker:
At ( t ) hours after 2 p.m., the oil tanker has traveled ( 14t ) kilometers west from the origin.
So, its location is (-14t, 0) .
Location of the Luxury Liner:*
At ( t ) hours after 2 p.m., the luxury liner has traveled ( 16t ) kilometers north from the origin.
So, its location is (0, 16t).
Distance between the Oil Tanker and the Luxury Liner:
We'll use the distance formula: [tex]\( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).[/tex]
[tex]\[ d = \sqrt{(-14t - 0)^2 + (0 - 16t)^2} \][/tex]
[tex]\[ d = \sqrt{(-14t)^2 + (-16t)^2} \][/tex]
[tex]\[ d = \sqrt{196t^2 + 256t^2} \][/tex]
[tex]\[ d = \sqrt{452t^2} \][/tex]
[tex]\[ d = \sqrt{452} \cdot t \][/tex]
So, the location of the oil tanker is [tex]\( (-14t, 0) \)[/tex], the location of the luxury liner is [tex]\( (0, 16t) \)[/tex], and the distance between them at ( t ) hours after 2 p.m. is [tex]\( \sqrt{452} \cdot t \)[/tex] kilometers.
Given the triangle below which of the follwing is a correct statement?
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Consider an angle M with measure m degrees. The trigonometric ratios sec, and csc are defined as follows:
sec(m)=Hyp/Adj, and csc(m)=Hyp/Opp
Thus we can check that
[tex]\displaystyle{csc(\angle C)= \frac{6}{4}= \frac{3}{2} [/tex]
[tex]\displaystyle{sec(\angle C)= \frac{6}{5} [/tex]
[tex]\displaystyle{csc(\angle B)= \frac{6}{5}= \frac{3}{2} [/tex]
[tex]\displaystyle{sec(\angle C)= \frac{6}{4}=\frac{3}{2} [/tex]
Answer: A
Carlie works at a bakery making bagels and donuts. the oven timer for the donuts buzzes every 30 minutes, and the timer for the bagels buzzes every 40 minutes. if she started both timers at 8:00
a.m., when will the timers buzz at the same time?
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which is 120 minutes so the time when they will buzz together is 8:00 + 120/60 = 10.00 am
The donut and bagel timers at Carlie's bakery will buzz together every 2 hours, so they will buzz at the same time for the first time at 10:00 a.m.
Explanation:This question is about finding the Least Common Multiple (LCM) of the two numbers - 30 minutes (the time the donut timer buzzes) and 40 minutes (the time the bagel timer buzzes). The LCM of 30 and 40 is 120 minutes. This means that the timers for the bagels and the donuts will buzz at the same time every 120 minutes, or 2 hours. Since Carlie starts both timers at 8:00 a.m., the timers will buzz together for the first time at 10:00 a.m.
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If c – 8 is an odd integer, which of the following could be the value of c?
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If c – 8 is an odd integer, then c could be any even number greater than 8 such as 10, 12, 14, 16, because when you subtract 8 from these even numbers, the result is an odd integer.
Explanation:The question requires us to find the value of c if c : 8 is an odd integer. So, if c : 8 is an odd integer, that means whatever number c is, when you subtract 8 from it, you should get an odd number. Odd numbers are integers that are not divisible by 2 and they usually end in 1, 3, 5, 7, or 9. Therefore, the possible values for c can be any even number greater than 8, such as 10, 12, 14, 16, and so on. That's because when you subtract 8 from these even numbers, the result will be an odd integer.
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A scatter plot is used to visualize the association between two quantitative variables tru false
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29,141 write in expanded form
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387,422 rounded to the nearest hundred thousand
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hope this helps
y and x have a proportional relationship, and y = 15 when x = 3. What is the value of x when y = 4?
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Hope it helps!
Answer: 0.12
Step-by-step explanation:
I want to test for symmetry when theta=pi-theta...........r=4cos 2theta
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[tex]\bf cos(2\pi -2\theta )\implies \stackrel{1}{cos(2\pi )}cos(2\theta )+\stackrel{0}{sin(2\pi )}\stackrel{}{sin(2\theta ) } \\\\\\ 1\cdot cos(2\theta )+0\cdot sin(2\theta )\implies cos(2\theta )+0\implies cos(2\theta )\\\\ -------------------------------\\\\ r=4cos(2\theta )\impliedby \textit{is symmetric with respect to }\theta =\frac{\pi }{2}~line[/tex]
A laboratory technician needs to make a 108-liter batch of a 20% acid solution. How can the laboratory technician combine a batch of an acid solution that is pure acid with another that is 10% to get the desired concentration?
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what is the distance between points A and B?
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A ski club charges a $48 membership fee, plus $18 to rent ski equipment per day. Which of the following equations can be used to find the total cost of membership at the club, when renting equipment for x days?
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So if someone wants to rent ski equipment for x days, the charges will be 18x dollars. In addition to that, he needs to pay 48 dollars as membership fee. So in total, he needs to pay 48 + 18x.
So the equation y = 48 + 18x represents the total cost of membership at the club when renting equipment for x days.
Hope this helps! :)
The equation for the given situation is y=48+18x.
Given that, a ski club charges a $48 membership fee, plus $18 to rent ski equipment per day.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, equipment is renting for x days.
Let the total cost of membership at the club be y.
Now, y=48+18x
Therefore, the equation for the given situation is y=48+18x.
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Let w be the set of all points in r3 that lie in the xz-plane. is w a subspace of r3?
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What is fifteen out of eighteen in simplest form
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15/3 = 5
18/3 = 6
5/6 is your answer
hope this helps
A certain breed of mouse was introduced onto a small island with an initial population of 320 mice, and scientists estimate that the mouse population is doubling every year. (a) find a function that models the number of mice m after t years.
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x being the number of years and 320 being the initial population of mice
gwen borrows $300 from her parents to buy a bike she agrees to pay them back plus 3% intrest over year write an equation to represent the total amount she owes her parents? what is the total amount she will owe her parents?
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Gwen will owe her parents a total of $309.
To represent the total amount Gwen owes her parents after borrowing $300 with 3% interest over a year, we can use the formula for simple interest:
[tex]\[ \text{Total amount} = \text{Principal} + \text{Interest} \][/tex]
Given:
Principal (P) = $300
Interest rate (r) = 3% or 0.03 (as a decimal)
Time (t) = 1 year
Now, plug the values into the formula:
[tex]\[ \text{Interest} = P \times r \times t \][/tex]
[tex]\[ \text{Interest} = 300 \times 0.03 \times 1 \][/tex]
[tex]\[ \text{Interest} = 9 \][/tex]
Now, add the interest to the principal to get the total amount:
[tex]\[ \text{Total amount} = 300 + 9 \][/tex]
[tex]\[ \text{Total amount} = \$309 \][/tex]
So, the equation to represent the total amount Gwen owes her parents is:
[tex]\[ \text{Total amount} = 300 + 300 \times 0.03 \times 1 \][/tex]
[tex]\[ \text{Total amount} = 300 + 9 \][/tex]
[tex]\[ \text{Total amount} = \$309 \][/tex]
Therefore, Gwen will owe her parents a total of $309.
Write 2.1111111 as a mixed number
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2.0 = 2
2 1/9 is your answer
1. How much heat is absorbed by a 50g iron skillet when its temperature rises from 10oC to 124oC? Joules
2. If a refrigerator is a heat pump that follows the first law of thermodynamics, how much heat was removed from food inside of the refrigerator if it released 492J of energy to the room? Joules
3. How much heat is needed to raise the temperature of 45g of water by 63oC? Joules
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Formula: Heat = mass * specific heat * ΔT
Data:
mass = 50 g = 0.050 kg
specific heat of iron = 450 J/ kg °C
ΔT = 124°C - 10°C ¿ 114 °C
=> heat = 0.050kg * 450 J / kg°C * 114°C ≈ 2.6 J
2. If a refrigerator is a heat pump that follows the first law of thermodynamics, how much heat was removed from food inside of the refrigerator if it released 492J of energy to the room? Joules
The firs law of thermodynamics is conservation of energy => energy removed from inside of the refrigerator = energy released to the room
=> Answer = 492 J
3. How much heat is needed to raise the temperature of 45g of water by 63oC? Joules
Formula: heat = mass * specific heat * ΔT
specific heat of water = 4186 J / Kg °C
heat = 0.045 kg * 4186 J/kg °C * 63°C = 11,867.31 J
Write the slope intercept form of the equation of each line algebra 1
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a. The function that is represented by the equation y=-10x+6 has a steeper slope and a greater y-intercept.
b. The function that is represented by the equation y=-10x+6 has a steeper slope, and the function that is represented by the equation y-36=8(x-4) has a greater y-intercept.
c. The function that is represented by the equation y-36=8(x-4) has a steeper slope, and the function that is represented by the equation y=-10x+6 has a greater y-intercept.
d. The function that is represented by the equation y-36=8(x-4) has a steeper slope and a greater y-intercept.
Evaluate a/b for a = 1/2 and b = -3/7
Answers:
3/14
-32/21
-3/14
-7/6
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The greatest common factor of 18 and a and 20 AB
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Answer:
1
Step-by-step explanation:
GCF(18, a, 20ab) = 1
18 and a do not necessarily have any factor in common, so their GCF is 1. Adding more terms to the list will not increase the GCF beyond that value.
A town has two high schools. The town has only one baseball field. There are 1,000 seats available for students to watch baseball games. All of the 10th grade students at both high schools want to attend a game. The greatest percentage of 10th grade students who will have a seat is
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The model was shaded two different ways to show a product. Which product is shown by the model?
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Answer:
3/4.
Step-by-step explanation:
4/8 simplified=1/2 6/8 simplified=3/4.
(-5)(2)-2(-3)+3
Expression
Perform Multiplication
Simplify
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-4 + 3
-1
i have a 5 in my ones place the digit in my tens place is 3 plus the digit in my ones place the digit in hundreds place is 2 less than the digit in my ones place what number am i
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A rectangle has a base of 2 yd and a height of 5 ft. Find the area of the rectangle. 30 yd2 30 ft2 10 yd2 10 ft2
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Answer: [tex]30\ ft^2[/tex]
Step-by-step explanation:
We are given that
The base of the rectangle = 2 yards
The height of the rectangle = 5 feet
We know that
1 yard = 3 feet
Then , the base of the rectangle = [tex]2 \times3=6\text{ feet}[/tex]
Now, the are of the rectangle will be :-
[tex]\text{Area}=\text{Height x Base}\\\\\Rightarrow\ \text{Area}=5\times6\text{ square feet}\\\\\text{Area}= 30\text{ square feet}[/tex]
Hence, the area of the rectangle = [tex]30\ ft^2[/tex]
Answer:
i think is 30ft2
Step-by-step explanation: