The spherical coordinates for the given rectangular coordinates (4,1,4) can be calculated using formulas for the transformation. They approximately yield (sqrt(33), 0.505, 1.540).
Explanation:In mathematics, we can convert rectangular coordinates to spherical coordinates using given formulas. Here, we have the rectangular coordinates (4,1,4). The transformation from rectangular to spherical involves three-step calculations:
First, calculate the radial coordinate, r, which is the distance from the origin to the point. It is given by r = sqrt(x^2 + y^2 + z^2).Second, find the polar angle, theta, measured relative to the vertical z-axis. It is given by cos(theta) = z/r.Lastly, find the azimuthal angle, phi, measured relative to the x-axis. It is given by cos(phi) = x/(r*sin(theta)).
Applying the formulas, we get: r = sqrt(4^2 + 1^2 + 4^2) = sqrt(33), theta = cos^-1(4/sqrt(33)) which is approximately 0.505, and phi = cos^-1(4/sqrt(33)*sin(0.505)) which is approximately 1.540.
So, the spherical coordinates of the point whose rectangular coordinates are (4,1,4) are approximately (sqrt(33), 0.505, 1.540).
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Is 1 fifth of 186 the same as 25% of 186
1/5 = 0.20
25% = 0.25
therefore 1/5 is not the same as 25%
Which is a ppssible number of distinct real roots for a cubic function select all that apply.
0
1
3
4
Try graphing y=x^3. It crosses the x-axis at (0,0), and this point represents the one and only real root.
Every form of a cubic function has a graph that crosses the x-axis in 1 or 3 places.
Thus, the correct answers to this particular problem are B and C.
Additionally, certain cubic function forms have graphs that cross the x-axis in one unique place, but which touch (but do not cross) the x-axis. Here you have one unique real root plus one repeated (duplicated) real root, for a total of 3 roots.
Using these facts, decide which of the four given answers are correct.
The value of a car decreases by 20% per year Mr. Singh for purchase is a $22,000 automobile what is the value of the car the end of the second year
Answer: the answer is $26,400
Step-by-step explanation:
Aurora earns a salary of $25,000 per year. Her benefits are equal in value to 30 percent of her salary. What is the value of Aurora's benefits?
Value of Aurora's benefits as 30percent of her salary is equals to $7500.
What is percentage?" Percentage is defined as the hundredth part of the given whole number."
According to the question,
Salary amount of Aurora = $25,000
Benefit value = 30 percent of ( $25,000)
Therefore,
30 percent of ( $25,000) = 30% of 25,000
= [tex]\frac{(30) * (25,000)}{100}[/tex]
= $7,500
Hence, value of Aurora's benefits as 30percent of her salary is equals to $7500.
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(08.03 MC)
A system of equations is shown below:
y = 3x – 7
y = 2x + 1
What is the solution to the system of equations? (1 point)
A. (8, 17)
B. (–8, 17)
C. (–8, –17)
D. (8, –17)
Answer:
(8, 17)
Step-by-step explanation:
Here you have two functions equalling y.
To find x, we set these two functions equal to one another, which eliminates y:
3x - 7 = 2x + 1.
Find x. To do this, subtract 2x from both sides, obtaining x - 7 = 1.
Next, add 7 to both sides: x = 8.
Finally, find y. Do this by subbing 8 for x in either of the two given equations.
Working with the 2nd equation: y = 2(8) + 1 = 17
Thus, the solution is (8, 17).
I believe the answer is (8 , 17)
A square with an area of 169 cm^2 is rotated to form a cylinder. What is the height of the cylinder?
Answer:
13 cm
Step-by-step explanation:
Area of the square is [tex]169 \:\:cm^{2}[/tex]
The square is rotated to form a cylinder. Now, we first need to find the side of the square, the cylinder is formed by rotating along its side.
Now area of square [tex]169 \:\:cm^{2}[/tex]
We know that area of square is [tex]\text{side}\times\text{side}[/tex]
So, [tex]\text{side}\times\text{side}=169[/tex]
[tex]\text{side}\times \text{side}=13\times13[/tex]
[tex]\text{side}=13 \:\text{cm}[/tex]
Now, as the cylinder is formed by rotating along its length, and we know that all the sides of a square is equal.
So, one side becomes the height of the cylinder and the other becomes the circumference.
Hence, the height of the cylinder is 13 cm.
Angle θ is in standard position. If (8, -15) is on the terminal ray of angle θ, find the values of the trigonometric functions.
Answer with explanation:
It is given that, Angle θ is in standard position.
A line from origin O to point , P(8,-15) is joined and then perpendicular to x and y axis, is drawn cutting X axis at Point M and Y axis at point N.
OM= 8 units
ON=P M=15 units
By Pythagorean Theorem
[tex]OM^2 + PM^2=OP^2\\\\ 8^2 +15^2=OP^2\\\\ OP^2=64 +225\\\\OP^2=289\\\\OP^2=17^2\\\\OP=17\\\\ Sin (\theta)=\frac{\text{Perpendicular}}{\text{Hypotenuse}}=\frac{-15}{17}\\\\Cos(\theta)=\frac{\text{Base}}{Hypotenuse}=\frac{8}{17}\\\\Tan(\theta)=\frac{\text{Perpendicular}}{Base}=\frac{-15}{8}\\\\ Cosec(\theta)=\frac{1}{Sin(\theta)}=\frac{-17}{15}\\\\ Sec(\theta)=\frac{1}{Cos(\theta)}=\frac{17}{8}\\\\ Cot (\theta)=\frac{1}{Tan(\theta)}=\frac{-8}{15}[/tex]
Point(8,-15), lies in Quadrant four. In Quadrant four Cosine and Secant Function are positive and all other trigonometric functions, Sine,Cosecant, Tangent,and Cotangent are Negative.
Divide the decimal numbers 12.012÷6
"4. Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x= 12. y = -10 when x = 2 "
Answer:
5/ 2 x
Step-by-step explanation:
Rita attends school 180 days out of the 365 days in a year. For what fraction of the year is Rita in school? Write your answer in simplest form.
the fraction is 180/365
this can get reduced to 36/73
What is the largest possible value of y, if y = - | 3 - x | + 5
Can anyone please solve the attached file?
If prices Increase at a monthly rate of 1.4
%, by what percentage do they increase in a year?
Car mart pays $110,000 rent each year for its two-story building. the space in this building is occupied by five departments as specified here. paint department 1,575 square feet of first-floor space engine department 2,925 square feet of first-floor space window department 1,845 square feet of second-floor space electrical department 765 square feet of second-floor space accessory department 1,890 square feet of second-floor space the company allocates 70% of total rent expense to the first floor and 30% to the second floor, and then allocates rent expense for each floor to the departments occupying that floor on the basis of space occupied. determine the rent expense to be allocated to each department.
First floor:
paint department 1,575 square feet
space engine department 2,925 square feet
Total = 4,500 square feet
Second floor:
space window department 1,845 square feet
electrical department 765 square feet
accessory department 1,890 square feet
Total = 4,500 square feet
Since 70% is allocated to the 1st floor, therefore the floor is receiving:
First floor expense = $110,000 * 0.70 = $77,000
Second floor expense = $110,000 - $77,000 = $33,000
The expense for each department is the proportion on the total expense per floor.
First floor:
paint department = (1575/4500) * 77,000 = $26,950
space engine department = 77,000 – 26,950 = $50,050
Second floor:
space window department = (1845/4500) * 33,000 = $13,530
electrical department = (765/4500) * 33,000 = $5,610
accessory department = 33,000 – 13530 – 5610 = $13,860
(05.02 MC)
Trevor solved the system of equations below. What mistake did he make in his work?
2x + y = 5
x − 2y = 10
y = 5 − 2x
x − 2(5 − 2x) = 10
x − 10 + 4x = 10
5x − 10 = 10
5x = 0
x = 0
2(0) + y = 5
y = 5
His work should have looked like this.
2x + y = 5
x − 2y = 10
y = 5 − 2x
x − 2(5 − 2x) = 10
x − 10 + 4x = 10
5x − 10 = 10 When he added in both sides, he subtracted 10 from 10,
5x = 20 instead of adding 10 from 10 to make 20.
x = 4
2(4) + y = 5
8 + y = 5
y = -3
Jane noticed as she was doing her morning run that a 12 m flagpole cast a 18 m shadow. A tree was casting a 36 m shadow. The tree was __? ___ m tall.
The price of a calculator dropped from $32.88 to $25.95. What was the percent decrease in price
An isosceles triangle with angles b and c having the same measure is shown. Find the measure of each angle whose degree measure is represented with variables. A= x+ 7y+41,B= 2y+13,C=6x+15
Answer:
A = 114°, B = C = 33°
Step-by-step explanation:
The triangle relationships let you write two equations:
A+B+C = 180
B=C
Substituting the expressions for A, B, and C, you have ...
(x+7y+41) +(2y+13) +(6x+15) = 180
7x +9y +69 = 180
7x +9y = 111
And the second equation gives ...
(2y+13) = (6x+15)
6x -2y =-2
3x -y = -1
Now, we can add 9 times this second equation to the first to eliminate the y-variable.
(7x +9y) +9(3x -y) = (111) +9(-1)
34x = 102
x = 3
Then the angle measures are ..
B = C = 6·3+15 = 33
A = 180 -2·33 = 114
The angles in the triangle are (A, B, C) = (114°, 33°, 33°).
Solve l=14j+3k for j.
To solve the equation l = 14j + 3k for j, subtract 3k from both sides and then divide by 14, giving j = (l - 3k) / 14.
Explanation:To solve the equation l=14j+3k for j, you need to isolate j on one side of the equation. Here's how it is done step by step:
Start with the original equation: l = 14j + 3k Subtract 3k from both sides of the equation to isolate the term with j in it: l - 3k = 14j Divide both sides of the equation by 14 to solve for j: j = (l - 3k) / 14Therefore, the solution to the equation for j is: j = (l - 3k) / 14.
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Josh estimates the height of his desk. Which is the best estimate?
Mr. Pham wrote the equation below on the board. 18 - 7x = -20.5 What is the value of x?
Answer: The answer should be D(x=5 1/2)
Step-by-step explanation:
Trust me I did the equation and work.
Samantha loves to download new music. She originally had 52 songs but plans to purchase 2 new songs each week. She wants to know how many songs she will have after 93 weeks. Which equation should she use
what's 6 3/4 divided by 1 7/8
The value of 6 (3/4) divided by 1 (7/8) is 3 (3/5).
What is a fraction?A fraction is a part of the whole represented by a/b, where a and b are any integers
The given numbers are 6 (3/4) and 1 (7/8).
Simplify the mixed fractions:
6(3/4) = 27/4 and 1 (7/8) = 15/8
Now, divide 27/4 by 15/8:
27/4 ÷ 15/8
= 27/4 × 8/15
= 18/5
= 3 (3/5)
Hence, The value of 6 (3/4) divided by 1 (7/8) is 3 (3/5).
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A drill instructor recorded the time in which each of 11 recruits completed an obstacle course both before and after basic training. to test whether any improvement occurred, the instructor would use a t distribution with 11 degrees of freedom.
In this problem, it is TRUE that the instructor would need to use a t distribution with 10 degrees of freedom to be able to test whether any improved occurred.
In order to check for its correctness, we need to measure the absolute difference between the mean value in two groups in a clinical trial by using the mean difference. Next, we check for the degrees of freedom. The degrees of freedom are the number of independent pieces of information that went into calculating the estimate.
You have to subtract 1 from
the number of items to be able to get the df for the estimate. Let’s check this
scenario:
Let’s say you need to find the mean weight loss for a low carbohydrate diet.
You can use 4 people and giving 3 degrees of freedom (4 -1 = 3), in turn, you
can also use 100 people with a df of = 99.
Jim has three times as many comic books as Charles Charles has two thirds as many as Bob Bob has 27 books how many comic books does Jim have
Charles has 2/3 of bob
bob has 27
so 2/3*27 = 27 *2 = 54/3 = 18
Charles has 18
Jim has 3 times as many as Charles so he has 3 x 18 = 54
jim has 54 comic books
The Panthers, a high school basketball team, charges $6 for adult tickets and $3 for children’s tickets. If 120 people went to the most recent game, and the total earnings for ticket sales was $612, how many children went to the game?
There were 36 children at the game.
There were 50 children at the game.
There were 84 children at the game.
There were 108 children at the game.
Answer:
The answer is 36 children
Step-by-step explanation:
There were 36 children at the game
The number of children who went to the game was 36
What is Linear Equation in 2 variables?
An equation is said to be linear equation in two variables if it is written in the form of ax + by + c = 0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.
Given data ,
Let the number of children be = x
Let the number of adults be = y
Cost of ticket for 1 child = $ 3
Cost of ticket for 1 adult = $ 6
Total number of people who went to the game = 120
So , x + y = 120
Total earnings for the ticket sales = $ 612
Total earnings =
( Cost of one child x Number of children ) + ( Cost of one adult x Number of adult)
Total earnings = 3x + 6y
Now , we have 2 equations to solve
x + y = 120 be equation (1)
3x + 6y = 612 be equation (2)
Multiply equation (1) by 3 , we get
3x + 3y = 360 be equation (3)
Subtract equation (3) from equation (2)
3x + 6y - ( 3x + 3y ) = 612 - 360
3y = 252
Divide by 3 on both sides , we get
y = 84
So , the number of children who went to the game will be
x + y = 120
x + 84 = 120
Subtract 84 on both sides , we get
x = 36
Hence , the number of children who were at the game was 36
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how to say 119,000,003 in two other ways?
You want to have $25,000 saved 6 years from now to buy a house. how much less do you have to deposit today to reach this goal if you can earn 5.5 percent rather than 5 percent on your savings? today's deposit is the only deposit you will make to this savings account this problem requires solving for
By moving from a 5% interest rate to a 5.5% interest rate, you would need to deposit $372.84 less today for your savings goal of $25,000 in 6 years.
Explanation:When planning for a savings goal, we use the formula for the future value of a single amount which is FV = PV * [tex](1 + r)^n[/tex], where PV is the present value or the amount you need to deposit today, FV is the future value or the goal of $25,000, r is the interest rate, and n is the number of years.
First, let's calculate how much you need to deposit today with an interest rate of 5% (r = 0.05), the formula will be rearranged to solve for PV which is PV = FV / [tex](1 + r)^n[/tex]:
PV = 25000 / [tex](1 + 0.05)^6[/tex] = $18724.08
Next, calculate the deposit for an interest rate of 5.5% (r = 0.055) using the same formula:
PV = 25000 / [tex](1 + 0.055)^6[/tex] = $18351.24
The difference between these two amounts is $18724.08 - $18351.24 = $372.84.
So, with an interest rate of 5.5% rather than 5%, you would need to deposit $372.84 less today to reach your goal of $25,000 in 6 years.
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Using the formula in model 1, choose the correct answers for the new balance and amount of interest earned in the following compound interest problem. $1,050 at 6%, for 25 years, compounded annually. Total Amount = $ Interest Amount =$
Name the properties that were used to derive the properties of logarithms.
The properties that were used to derive the properties of logarithms are the properties of exponent because logarithms are exponents. The properties of exponents are: product of powers, power to a power, quotient of powers, power f a product and power of a quotient.
As an example, the log property log(a^k) = k log (a) can be derived from the exponential property (b^a)^k = b^(ak).
Likewise,
log (ab) = log (a) + log (b) comes from c^(a+b) = c^a*c^b
Proof:
Let x = c^a and y=c^b
Then,
log (x) = a and log (y) =
b (base c)
log (xy) = log (c^a * c^b) = log (c^(a+b)) = a+b = log(x) + log (y)