Change from rectangular to spherical coordinates. (Let rho ≥ 0, 0 ≤ θ ≤ 2π, and 0 ≤ ϕ ≤ π.)
(a)
(0, −5, 0)
(rho, θ, ϕ) =
In spherical coordinates (ρ, θ, ϕ), the point (0, -5, 0) can be represented as (5, π/2, π/2).
To convert from rectangular coordinates to spherical coordinates, we use the following formulas:
ρ = √(x² + y² + z²)
θ = arctan(y / x)
ϕ = arccos(z / √(x² + y² + z²))
In this case, since the point lies on the negative y-axis, the x-coordinate is 0, and the y-coordinate is -5. Therefore, we have:
ρ = √(0² + (-5)² + 0²) = √25 = 5
Since the point lies in the negative y-axis, the angle θ is π/2.
Since the point lies on the xz-plane, the z-coordinate is 0. Therefore, we have:
ϕ = arccos(0 / √(0² + (-5)² + 0²)) = arccos(0 / 5) = arccos(0) = π/2
Combining these values, the point (0, -5, 0) in rectangular coordinates is equivalent to (5, π/2, π/2) in spherical coordinates.
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Which is NOT true?
A 9 + 4 = 17 - 4
B 8 + 7 = 14 + 3
C 11 = 19 - 8
D 5 + 8 = 20 - 7
Answer:
B is not true
Step-by-step explanation:
8+7= 15 and 14+3= 17
15 is not equal to 17
Answer:
B is the one equation that is NOT true.
Step-by-step explanation:
A: 9+4 is 13, and 17-4 is 13 as well. This equation is true, 13=13.
B: 8+7 is 15, and 14+3 is 17. This equation is false, because 15 is not equal to 17. Although we have our answer, we need to still check the other equations.
C: 11 is, well, 11, because nothing changed on that side of the equation. 19-8 is 11, so this is true because 11=11.
D: 5+8 is 13, and 20-7 is 13. This equation is also true, because 13=13.
The only equation that is not true, is B. (8+7 = 14+3)
Question 1 (1 point)
A decorator is wallpapering a wall with a circular window of diameter 1.00 m.What is the
area of the wall in square feet? (1 m - 3.2808 feet)
3
Answer:
95.875 [tex]ft^{2}[/tex]
Step-by-step explanation:
1.) Calculate the area of the trapezoid
A(trapezoid) = (1/2)*(base1 + base2)*h = (1/2)*(2.6+3.6)*3 = (1/2)*6.2*3 = 9.3
2.) Calculate the area of the circle
radius = (1/2)*(diameter) = (1/2)*1 = 0.5
A(circle) = (1/2)*[tex]\pi[/tex]*[tex]r^{2}[/tex] = (1/2)*[tex]\pi[/tex]*([tex]0.5^{2}[/tex]) = (1/2)*[tex]\pi[/tex]*0.25 = 0.125*[tex]\pi[/tex] = 0.392699
3.) Because the area of the circle is not included in the wall, subtract the area of the circle from the area of the trapezoid:
A(trapezoid)-A(circle) = 9.3-0.392699 = 8.9073 [tex]m^{2}[/tex]
4.) Convert to [tex]ft^{2}[/tex]:
Because 3.2808 feet are in a meter and the unit of the answer is in [tex]m^{2}[/tex], we need to multiply the answer by ([tex]3.2808^{2}[/tex]) to get to [tex]ft^{2}[/tex].
8.9073*([tex]3.2808^{2}[/tex]) = 8.9073*10.7636 = 95.875 [tex]ft^{2}[/tex]
Which expression is equivalent to 21x + 9 - 3x? A. 9(2x - 1) B. 9(x + 1) C. 9(2x + 1) D. 18(x + 1)
Answer: C
Step-by-step explanation:
21x+9-3x = 18x + 9
If you factor out the 9, you would be left with
9 (2x+1)
Answer: A. 9(2x - 1)
Step-by-step explanation:
combine like terms
21x+9-3x
21x-3x
18x+9
Factor the expression
factor out 9 from the expression
you get 9(2x - 1)
2/5 of 16 simplify if you can thank you
Answer:
6 and 2/5
Step-by-step explanation:
Answer:
Decimal form: 6.4
Fraction form: 32/5
Step-by-step explanation:
of = times
2/5 x 16 = 6.4
Three lines intersect at a common point. In the figure below, m∠1=x°, m∠2=2x°, and m∠3=75°.
Which equations can be used to determine the value of x? Select all that apply.
A:3x°=75°
B:3x°=105°
C:3x°=255°
D:3x°+75°=180°
E:x°+2x°+75°=180°
F:x°+2x°+3x°=360
Answer:
3x=105,x°+2x°+75°=180°,and 3x°+75°=180°
Step-by-step explanation:
no explanation sorry,your welcome
38. The vertices of a trapezoid are points (0, a), (0,0), (6,0), and (c, a). Find the area in terms
of a, b, and c.
Answer:
(0,6), (6,0)
Step-by-step explanation:
Answer:
Whatttttttttttttttttt
PLEASE HELP!!!!! (screenshot)
Answer:
The answer is A. y <= -3x + 3
Write the polnt-slope form of the equation of the line passing through the points (-5, 6) and (0, 1).
y- 6 = 1(x + 5)
y+6= -1(x - 5)
y- 6 = -1(x + 5)
y+ 6 = 1(x - 5)
Answer:
y - 6 = -1 (x+5)
Step-by-step explanation:
1) First, find the slope of the line. Use the slope formula [tex]m = \frac{y_2-y_1}{x_2-x_1} \\[/tex]. Substitute the x and y values of (-5,6) and (0,1) into the formula and simplify like so:
[tex]m = \frac{(1)-(6)}{(0)-(-5)} \\m = \frac{1-6}{0+5} \\m = \frac{-5}{5} \\m = -1[/tex]
So, the slope of the line is -1.
2) Now we have enough information to write the equation of the line in point-slope form. Use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] and substitute real values for the [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex].
Since [tex]m[/tex] represents the slope of the line, substitute -1 in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line intersects, substitute the x and y values of (-5, 6) in those places as well. This gives the following equation and answer:
[tex]y-6 = -1(x+5)[/tex]
Find the missing side lengths.
Need help please.
This is the 6th time I post.
Answer:
x = 9.238 y = 4.619
Step-by-step explanation:
I kind of forgot how to do sohcahtoa but we do cosine for one of them. I used a calculator but the lengths seems reasonable so I'm sure they should be right.
NO LINKS PLZ, BUT I RLLY NEED HELP!
Answer:
Step-by-step explanation:
b
Arrange the given polynomial in descending order.
9x? + 9x +3+2x
Does there exist an 8 x 8 matrix A = (a) satisfying the following three conditions? (i) If i j then a = 0 (ii) a18 #0 (a18 denotes the entry in the first row and eighth column of A) (iii) A is diagonalizable If such a matrix exists, provide an example of one and prove that it satisfies the given three conditions. If no such matrix exists, prove that no such matrix exists
We need to determine whether an 8x8 matrix A exists that satisfies three conditions:
(i) having zeros below the main diagonal,
(ii) having a non-zero entry in the first row and eighth column, denoted as a18
(iii) being diagonalizable. In the second paragraph.
we will either provide an example of such a matrix and prove that it satisfies the conditions, or prove that no such matrix exists.
To provide an example of an 8x8 matrix A that satisfies the given conditions, we need to construct a matrix that satisfies each condition individually.
Condition (i) requires that all entries below the main diagonal of A are zero. This condition can easily be satisfied by constructing a matrix with zeros in the appropriate positions.
Condition (ii) states that a18, the entry in the first row and eighth column, must be non-zero. By assigning a non-zero value to this entry, we can fulfill this condition.
Condition (iii) requires that the matrix A is diagonalizable. This condition means that A must have a complete set of linearly independent eigenvectors. If we can find eigenvectors corresponding to distinct eigenvalues that span the entire 8-dimensional space, then A is diagonalizable.
If we are able to construct such a matrix that satisfies all three conditions, we can provide it as an example and prove that it fulfills the given conditions. However, if it is not possible to construct such a matrix, we can prove that no such matrix exists by showing that the conditions are mutually exclusive and cannot be satisfied simultaneously.
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Finance Name: This project has two problems centered around finance - one question about the mathematical explosion of compound interest and the other about the stock market. Problem 1 1. Let's use mathematics to see why time is so important when it comes to saving for retirement. Suppose you have $10,000 to invest in a mutual fund that averages a 12% annual return. a) After 5 years, what is the value of the fund? Explain or show your work. b) After 10 years, what is the value of the fund? Explain or show your work. c) After 20 years, what is the value of the fund? Explain or show your work. d) it looks like time doubles in parts b) and c) from 10 to 20 years. Does the account value also double? if not, why not?
The value of the funds are A) $5,674.27 b) $3219.73 c) $1036.37
What Net Present Value?Rerecall that Net Present Value (NPV) is the difference between the present value of cash inflows and outflows over a period of time. It is used in capital budgeting and investment planning to analyze the profitability of a projected investment or project.
Cost of investment = $10,000
averages a 12% annual return.
a) After 5 years,
The value of the fund PV = FV/(1 + r)ⁿ
PV = 10,000/1+0.12)⁵
PV = 10000/(1.12)⁵
PV = 10000/1.762341683
PV = 5,674.27
The net present value of the investment after 5 years is $5674.27
b) After 10 years,
The value of the fund is PV = 10,000/1+0.12)¹⁰
PV = 10000/(1.12)¹⁰
PV = 10000/3.105848208
PV = 3219.73
The net present value of the investment after 5 years is $3219.73
c) After 20 years
The value of the fund is PV = 10,000/1+0.12)²⁰
PV = 10000/(1.12)²⁰
PV = 10000/9.646293093
PV = 1036.37
The net present value of the investment after 5 years is $1036.37
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HELP PLS MARKING BRAINLIEST SHOW WORK IF YOU CAN IF NOT ITS COMPLETELY FINE JUST DO IT
Answer:
1824 in.
Step-by-step explanation:
First find the area of the two shapes you split that are the rectangle and triangle:
Rectangle Area:
48 * 32 = 1536
Area- 1536 in.
Triangle Area:
48 * 12 * 1/2
or
48 * 12 divided by 2
= 288 in.
Now add the two areas up:
1536 + 288 = 1824 in.
Answer:
1824
Step-by-step explanation:
I assume you want to find the area of the shape. So in order to find the area of the triangle it is height times base than divide it by 2 which looks like this
(12*48)/2 which equals 576
than to find the area of the rectangle it is height times width which is
48*32 which equals 1536
add them together and you get 1824
A brine solution of salt flows at a constant rate of 8 min into a large tank that initially held 100 L of brine solution in which was dissolved o 3 kg of sall . The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the brine entering the tank is 003 kg/l determine the mass of salt in the tank after I min When will the concentration of salt in the tank reach 0.01 kg/L?
After 1 minute, the mass of salt in the tank will be 3.072 kg. The concentration of salt in the tank will reach 0.01 kg/L after approximately 31 minutes.
To determine the mass of salt in the tank after 1 minute, we need to consider the inflow and outflow of the brine solution. The rate of inflow is 8 L/min, and the initial concentration of salt in the solution is 0.03 kg/L. Therefore, after 1 minute, 8 L of brine solution with a concentration of 0.03 kg/L will enter the tank, resulting in an additional mass of salt of 0.24 kg (8 L * 0.03 kg/L).
Since the solution inside the tank is well stirred and flows out at the same rate, the outflow rate is also 8 L/min. Thus, after 1 minute, 8 L of the brine solution will leave the tank, taking away 0.24 kg of salt.Considering the initial mass of salt in the tank (3 kg) and the change in mass due to the inflow and outflow after 1 minute, the mass of salt in the tank after 1 minute will be 3 kg + 0.24 kg - 0.24 kg = 3.0 kg.
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You randomly choose a marble from a jar. The jar contains 4 red marbles, 10 blue marbles, 7 green marbles, and 6 yellow marbles. Find the probability of the event. Not choosing a blue marble.
Answer:
17/27
Step-by-step explanation:
Since there are 10 blue marbles, and 27 total marbles, the probability of not choosing a blue marble is 17/27 because you subtract the amount of blue marbles (10) from the amount of total marbles (27).
The probability of not choosing a blue marble is 17/27.
What is probability?
Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.
For the given situation,
Number of red marbles = 4
Number of blue marbles = 10
Number of green marbles = 7
Number of yellow marbles = 6
The event is the probability of not choosing a blue marble is
⇒ [tex]\frac{red+green+yellow}{Total marbles}[/tex]
⇒ [tex]\frac{4+7+6}{27}[/tex]
⇒ [tex]\frac{17}{27}[/tex]
Hence we can conclude that the the probability of not choosing a blue marble is 17/27.
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Which is greater 52,800 cm or 1 km?
Answer:
1 km
Step-by-step explanation:
According to the unit of conversion in every 1 kilometer, there is a total of 100 000 centimeters. Now, the given value of centimeters is equals to 52 800 => 1 km = 100 000 cm => 52 800 cm is less than the value of 100 000 cm which is equivalent to 1 km. Thus, the given is not correct.
help pleaseee!! i’ll give u most brianliest
Which one is true
1
2
3
4
Triangle triangle A^ prime B^ prime C^ prime is the image of triangle ABC under a dilation What is the scale factor of the dilation
The scale factor of a dilation is the ratio of the corresponding side lengths of the image triangle to the original triangle. In this case, the image triangle is triangle A' B' C' and the original triangle is triangle ABC.
To find the scale factor, we can compare the corresponding side lengths of the two triangles. Let's denote the lengths of the corresponding sides as follows:
Side AB corresponds to side A'B'
Side BC corresponds to side B'C'
Side CA corresponds to side C'A'
The scale factor is then given by:
Scale factor = Length of corresponding side in image triangle / Length of corresponding side in original triangle
To find the scale factor, you can calculate the ratio of the corresponding side lengths. For example, if the length of AB is 4 units and the length of A'B' is 8 units, then the scale factor would be 8/4 = 2.
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Marcus asked 10 people at a juggling festival what age they were when they started to juggle
Question
Marcus asked 10 people at a juggling festival what age they were when they started to juggle. Which interval contains the median age?
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]n = 10[/tex]
Required
The median interval
The question is incomplete, as the required data is not given.
To solve this question, I will use the following assumed dataset.
[tex]Age:17\ 17\ 18\ 20\ 21\ 22\ 22\ 24\ 28\ 28[/tex]
First, calculate the median position.
[tex]Median = \frac{n+1}{2}\ th[/tex]
[tex]Median = \frac{10+1}{2}\ th[/tex]
[tex]Median = 5.5\ th[/tex]
This implies that the median is the mean of the 5th and 6th data
So, we have the interval to be.
[tex]Median = [5th, 6th][/tex]
[tex]Median=[21,22][/tex]
Generally, the median of 10 data set is located at interval 5 to 6
Dot plot A is the top plot. Dot plot B is the bottom plot.
According to the dot plots, which statement is true?
The mean of the data in dot plot A is less than the
mean of the data in data plot B.
The median of the data in dot plot A is greater than the
median of the data in dot plot B.
The mode of the data in dot plot A is less than the
mode of the data in dot plot B.
The range of the data in dot plot A is greater than the
range of the data in dot plot B.
Please help I’m giving BRAINLIEST
Answer:
The median of plot A is greater that the median of plot B
Step-by-step explanation: the median on plot A is 45 and the median on plot B is 15
1)The mean of the data in plot A is greater than the
mean of the data in plot B.
2) The median of the data in plot A is greater than the
median of the data in dot plot B.
3) The range of the data in plot A is greater than the
range of the data in plot B.
What is the median?
The median is the middle number in a sorted, ascending, or descending, list of numbers.
Let us arrange the data of plot A in ascending order:
30,35,35,40,40,40,40,45,45,45,45,50,55,55,60
Number of observations = 15
Mean of the plot A = 44
Median will be the middle observation i.e. 8th observation i.e. 45
Let us arrange the data of plot A in ascending order:
5,5,5,10,10,10,10,15,15,15,20,20,25,30,35
Number of observations = 15
Mean of the plot B = 15.33
Median will be the middle observation i.e. 8th observation i.e. 15
Therefore,1)The mean of the data in plot A is greater than the
mean of the data in plot B.
2) The median of the data in plot A is greater than the
median of the data in dot plot B.
3) The range of the data in plot A is greater than the
range of the data in plot B.
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A recent stocktake measured the price of BBQs at a large hardware store. From the stocktake, it was determined that the price was normally distributed with a mean of 450 dollars and a standard deviation of 30 dollars. 20 per cent of the BBQs would cost more than what price? Select from the answers below.
(a)424.8 (b)475.2 (c)430 (d)492
Answer: (a) $424.8
Step-by-step explanation:
Consider the system of equations below. Explain how you could use multiplication to help eliminate one of the variables.
x−5y=13
4x−3y=1
Answer:you cross multiply
Step-by-step explanation:
i hate tacos
PLz hlep will mark brain list
Answer:
20
Step-by-step explanation:
Find the difference of the smallest value and the largest value.
Answer:
30 minus 10 then the range is 20
find the surface area to the nearest tenth
Step-by-step explanation:
Surface Area of Figure = Area of 4 triangular sides + Area of Base
=
[tex]4 \times ( \frac{1}{2} \times base \times height) + (length \: \times \: width) \\ = 4 \times ( \frac{1}{2} \times 10 \times 12.1) + (10 \times 10) \\ = 4 \times 60.5 + 100 \\ = 242 + 100 \\ = 342 {yd}^{2} [/tex]
The larger of two numbers is 6 more than the smaller integer. Their sum is 52, What are the numbers?
Find an equation of the line through (2,6) and parallel to y=2x+3
Step-by-step explanation:
We first Find the Slope of the line y=2x+3
The Slope Intercept Form of the equation of a given line is:
y=mx+c
where m is the Slope of that line, and c is the Y intercept.
For this line, the Slope is 2
So the Slope of the line PARALLEL to y=2x+3 will also be 2. And we are given that it passes through the point (2,6)
The Point-Slope form of the Equation of a Straight Line is:
(y−k)=m⋅(x−h)
m is the Slope of the Line
(h,k) are the co-ordinates of any point on that Line.
Here, we have been given the coordinates (h,k) of 1 point on that line as (2,6)
And the Slope m is 2
Substituting the values of h,k and m in the Point-Slope form, we get
(y−2)=(2)⋅(x−6)
(y−2)=2⋅(x-6)
y−2=2x -12
y=2x -12 +2
y=2x-10
The graph will look like
graph{y=2x -10 10 [10, -10, 5, - 5]}
Prove or disprove, using any method, that if /25 Q, then it is the case that 25 – 17 € Q.
The statement if /[tex]\sqrt{25}[/tex]∉Q, then it is the case that [tex]\sqrt{25}[/tex] – [tex]\sqrt{17}[/tex] ∈ Q is false.
To disprove the statement, we need to provide a counter example where [tex]\sqrt{25}[/tex] ∉ Q (irrational) and [tex]\sqrt{25}[/tex] – [tex]\sqrt{17}[/tex] ∉ Q (also irrational).
Let's consider [tex]\sqrt{25}[/tex] = 5, which is a rational number since it can be expressed as a ratio of two integers (5/1).
In this case, [tex]\sqrt{25}[/tex] ∉ Q is false since it is a rational number.
Furthermore, [tex]\sqrt{25}[/tex] – [tex]\sqrt{17}[/tex] = 5 - [tex]\sqrt{17}[/tex] is also irrational since it cannot be expressed as a ratio of two integers.
Therefore, we have found a counterexample that disproves the statement, showing that if [tex]\sqrt{25}[/tex] ∉ Q, then it is not necessarily the case that [tex]\sqrt{25}[/tex] – [tex]\sqrt{17}[/tex] ∈ Q.
Hence, the statement is false.
Question: Prove or disprove, using any method, that if /[tex]\sqrt{25}[/tex]∉Q, then it is the case that [tex]\sqrt{25}[/tex] – [tex]\sqrt{17}[/tex] ∈ Q.
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