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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if x -6 is one factor of x^2 - 10x +24, which is the other factor?
A vector a has a magnitude of 60m and directed as shown. find the x and y components of this vector
Final answer:
To find the x and y components of a vector, use the cosine and sine functions, respectively, with the given angle. For a vector of 60m at 38°, the components are approximately 47.28m (x) and 36.96m (y).
Explanation:
To find the x and y components of a vector given its magnitude and a direction, you can use trigonometric functions. Assuming the vector Δr is the one you're referring to, with a magnitude of 60m and an angle of 38° (from the x-axis, presumed direction), you can apply the cosine function for the x-component and the sine function for the y-component of the vector.
For the x-component: x = magnitude × cos(angle) = 60m × cos(38°) = 60m × 0.788 = 47.28m
For the y-component: y = magnitude × sin(angle) = 60m × sin(38°) = 60m × 0.616 = 36.96m
Therefore, the x and y components of the vector are approximately 47.28m and 36.96m, respectively.
Suppose that in a particular sample, the mean is 70.07 and the standard deviation is 10.27. what is the z score that corresponds to a raw score of 80?
Solve the equation.
-3(y - 5) = 24
y = ______?
The value of Equation is y = -3.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have Equation,
-3(y-5) = 24
Now, solving for y
Divide both side by (-3) we get
-3(y-5) / (-30= 24/ (-3)
y-5 = -8
Add 5 to both side
y- 5 +5 = -8 + 5
y = -3
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In a group of 48 children there are twice as many boys as girls how many girls are they
The tax rate is 8.5% what is the tax on $95? Rounded to the nearest hundredth.
The tax on $95 will be equal to $8.08 at the rate of 8.5%.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the tax rate is 8.5% the tax on $95 will be calculated as,
Sales tax = 8.5% of 95
Sales tax = 0.085 x 95
Sales tax = $8.08
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y=-3/8x-7 in standard form
To convert the slope-intercept form equation y = -3/8x - 7 into standard form, mulitply by 8 to remove the fraction, then rearrange to form 3x + 8y = -56, making sure the 'A' coefficient is positive.
The student's question asks about rewriting the slope-intercept form equation y = -3/8x - 7 into standard form. To do so, we need to rearrange the equation so that all variables and constants are on one side and the equation is set equal to zero. In standard form, the equation should be written as Ax + By = C, where A, B, and C are integers, and A should be non-negative.
Let's convert the given equation to standard form step by step:
Multiply both sides of the equation by 8 to clear the fraction: 8y = -3x - 56.
Move the 'x' term to the left side by adding 3x to both sides: 3x + 8y = -56.The equation now is in standard form; however, typically, we want A to be positive. Since our A is already positive, we are done.Find the equation, (f(x) = a(x-h)2+ k), for a parabola containing point (-1,0) and having (-3, 4) as a vertex. What is the standard form of the equation?
Answer:
D.The vertex form is f(x) = −(x +3)^2 + 4. The standard form is f(x) = −x2−6x−5.
Step-by-step explanation:
usatestprep
Twice the sum of a number and 3 is the same as 5 subtracted from the number. find the number.
Twice the sum of a number and 3 is the same as 5 subtracted from the number. Then the number will be -11.
Sum refers to the addition of terms, while subtraction means removal.
Let the number be x
Following the given information:
sum of a number and 3 = x+3
Expression 1
Twice the sum of a number and 3 =2(x+3)
Expression 2
5 subtracted from the number=x-5
On equating both the expressions as follows:
2(x+3)=x-5
Solving the equation to get the value of x:
2x+6=x-5
2x-x=-5-6
x=-11
Thus, the number is -11.
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Question 26(multiple choice worth 1 points) (02.02) simplify . −4 4
write an expression that represents the product the of q and 5 divided by 2
Convert 95 pints to gallons. Round to one decimal point. Please show your work
Dakota runs a half-marathon every 6 weeks, and Madison runs a half-marathon every 15 weeks. If they start now, in how many weeks will they again be running a half marathon at the same time?
Answer:
30 weeks
Step-by-step explanation:
Given : Dakota runs a half-marathon every 6 weeks,
Madison runs a half-marathon every 15 weeks
To Find : . If they start now, in how many weeks will they again be running a half marathon at the same time?
Solution :
Since Dakota runs a half-marathon every 6 weeks, Madison runs a half-marathon every 15 weeks
So, to calculate If they start now, in how many weeks will they again be running a half marathon at the same time
We will take the LCM (lowest common factor) of 6 and 15
3 | 6,15
2 | 2,5
5 | 1,5
| 1,1
LCM = 3*2*5 =30
The LCM of 6 and 15 is 30
So, If they start now, in 30 weeks they will again be running a half marathon at the same time
The point (2, -3) lies in quadrant I II III IV
Given quadrilateral XYWZ determine whether WX and YZ are parallel, perpendicular, or niether. W(0,-3), X(-1,5), Y(2,5), Z(-1,2)
Which equation correctly applies the distributive property?
A. 2.4⋅(−3.4)⋅(−1.25)=−3.4⋅2.4⋅(−1.25)
B. −3⋅(6.48)=(−3⋅6)+(−3⋅0.4)+(−3⋅0.08)
C. −2.5⋅(4⋅3.67)=(−2.5⋅4)⋅3.67
D. (42⋅3.5)+(42⋅1.3)+(42⋅5.2)=42+(3.5+1.3+5.2)
Answer:
B
Step-by-step explanation:
Find 3/7⋅9/10 . Write your answer as a fraction in simplest form.
The value of the multiplication of the fractions will be equal to 27 / 70.
What is multiplication?Multiplication is the process of determining the product of two or more numbers in mathematics. A product, or an expression that specifies factors to be multiplied, is what happens when you multiply two numbers in mathematics
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the fractions are 3/7 and 9/10. The multiplication of the number will be calculated as,
M = 3 / 7 x 9 / 10
M = 27 / 70
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A fair die will be rolled 11 times. what is the probability that 1, 2, or 3 is rolled exactly 4 times? round your answer to four decimal places.
The probability of a 1, 2, or 3 is 3/6 = 1/2. There are C(11,4) = 11!/(4!(11-4)!) = 330 ways the desired outcome can show up in the 11 rolls. The probability is
... 330×(1/2)⁴(1/2)⁷ = 330/2048 ≈ 0.1611
how many twelfths are in 3?
Answer:
36 twelfths.
Step-by-step explanation:
We are asked to find number of twelfths are in 3.
We can write 3 as a fraction as:
[tex]\frac{3}{1}[/tex]
To convert our given number to twelfths, we will multiply numerator and denominator of our fraction by 12 as:
[tex]\frac{3}{1}\times \frac{12}{12}[/tex]
[tex]\frac{3\times 12}{1\times12}[/tex]
[tex]\frac{36}{12}[/tex]
Therefore, there are 36 twelfths in 3.
The bottom floor of a parking garage has an elevation of -36 feet. The top floor is 124 feet higher. What is the elevation of the top floor
Find the slope of the line containing the points (3,8) (1,8)
A baseball used in major league games weighs at least 5 oz and not more than 5.25 oz.About what is that range measured in grams?Explain your reasoning.
There are 691 students at Palmer Elementary School and 1,293 students at Palmer Middle School. About how many students are there in all at both school?
There are 1,984 students in total at Palmer Elementary School and Palmer Middle School combined, showing an example of increasing school enrollments. This is calculated by simply adding the number of students from both schools.
Explanation:Calculating the Total Number of Students
To find out how many students are in all at both Palmer Elementary School and Palmer Middle School, we add the number of students at each school together. Palmer Elementary School has 691 students, and Palmer Middle School has 1,293 students.
To determine the total, we perform the following addition:
691 (Palmer Elementary School students)+ 1,293 (Palmer Middle School students)= 1,984 students in totalTherefore, there are approximately 1,984 students in total at both schools combined. This calculation helps us understand the scale of student populations within a small section of the education system, reflecting broader national trends where school enrollments are increasing.
630 meters in 18 seconds write this ratio as a unit rate
divide 630 by 18
630/18 = 35
so unit rate would be 35 meters per second
The set of possible values of m is {5,7,9}. What is the set of possible values of k if 2k=m+3?
Find the critical numbers of the function. (Enter your answers as a comma-separated list.)
f(θ) = 8sec θ + 4tan θ, 0 < θ < 2π
The critical numbers of the function f(θ) = 8sec(θ) + 4tan(θ) are where the derivative is undefined, specifically at θ = π/2 and θ = 3π/2.
Explanation:To find the critical numbers of the function f(θ) = 8sec(θ) + 4tan(θ), we need to take its derivative and set it equal to zero or find where the derivative does not exist. First, we compute the derivative of the function. Recall that the derivative of sec(θ) is sec(θ)tan(θ) and the derivative of tan(θ) is sec2(θ).
Thus, the derivative f'(θ) is 8sec(θ)tan(θ) + 4sec2(θ). We look for where this derivative is undefined or equal to zero. The derivative is undefined when sec(θ) is undefined, which occurs at θ = π/2 and θ = 3π/2. To find where the derivative is zero, we can factor out 4sec(θ):
4sec(θ)(2tan(θ) + sec(θ)) = 0
The second factor will never be zero because sec(θ) and tan(θ) will not be zero for the same θ in the interval given. Therefore, the critical numbers are where the derivative is undefined, which is θ = π/2 and θ = 3π/2.
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Using mental math, the approximate tip to leave for a bill of $81.79, if you tip 15% would be _____..
A direct variation function contains the points (2, 14) and (4, 28). Which equation represents the function?
Compare and Contrast: Below are two equations. Solve each equation and compare the two solutions. Choose the statement that is true about each solution. (3 points)
Equation #1
|2x - 3| = -17
Equation #2
|5x + 3| = 12
a-Equation #1 and Equation #2 have the same number of solutions.
b-Equation #1 has more solutions than equation #2.
c-Equation #1 has fewer solutions than equation #2.
d-None of the statements above describe the number of solutions to equations shown.
Listed below are four different cases in which a comparison of means was conducted. match the case to the appropriate set of equations needed to compare the means.
The cases can be categorized by comparing the means as follows: 'B. Two proportions' apply to situations like income bracket and voter likelihood comparison, 'C. Matched pairs, dependent groups' apply to dependent groups like a math test given to third graders, 'D. exclusive groups' represent separate unaffected and experimental groups, and 'A. Two independent means, normal distribution' refers to situations where two separate groups are compared.
Explanation:From the details given, we can classify the cases by comparing the means as follows:
B. Two proportions: This would apply to the question of politicians comparing the proportion of individuals from different income brackets who might vote for them. It implies two independent groups and hence a comparison of two population proportions. C. Matched pairs, dependent groups: This could describe a scenario like a math exam given to the third-grade children attending ABC school. Two random samples of scores were taken. This represents a dependent groups design in which two means are compared, for instance before and after a treatment. D. exclusive groups: These likely represent two independent means involving separate unaffected (control) groups and experimental groups. An example of this is studies that compare various diet and exercise programs. A. Two independent means, normal distribution: This refers to a situation where two separate groups are compared, such as studies involving independent samples where the sample values selected from one population are not related in any way to the sample values selected from the other population. Learn more about Comparison of Means here:
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