Answers
The coordinates of the triangle after translation would be A'(-2,3), B'(-1,1), and C'(-4,0).
To translate the triangle by a shifting factor of [-5,3], we need to move each point of the triangle horizontally by 5 units to the left (subtract 5 from the x-coordinate) and vertically by 3 units upwards (add 3 to the y-coordinate).
Let's take the point A(3,0) as an example. To obtain the new coordinates A', we need to subtract 5 from the x-coordinate and add 3 to the y-coordinate
A' = (3 - 5, 0 + 3) = (-2, 3)
Similarly, for point B(4,-2), we get
B' = (4 - 5, -2 + 3) = (-1, 1)
For point C(1,-3), we get
C' = (1 - 5, -3 + 3) = (-4, 0)
Therefore, the new coordinates of the triangle would be A'(-2,3), B'(-1,1), and C'(-4,0).
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Related Questions
A family has a unique pattern in their tile flooring on the patio. An image of one of the tiles is shown.
A quadrilateral with a line segment drawn from the bottom vertex and perpendicular to the top that is 5 centimeters. The right vertical side is labeled 3 centimeters. The portion of the top from the left vertex to the perpendicular segment is 5 centimeters. There is a horizontal segment from the left side that intersects the perpendicular vertical line segment and is labeled 6 centimeters.
What is the area of the tile shown?
53 cm2
45.5 cm2
42.5 cm2
36.5 cm2
Answers
To find the area of the tile, we need to first find the length of the top horizontal side.
Using the Pythagorean theorem, we can find the length of the diagonal:
d² = 3² + (5+6)²
d² = 9 + 121
d = √130
Now we can use the fact that the diagonal cuts the rectangle into two right triangles to find the length of the top horizontal side:
5x = 3(6)
x = 18/5
Therefore, the length of the top horizontal side is 18/5 centimeters.
Now we can find the area of the tile:
A = (3 + 18/5) * 5/2
A = 15 + 27/5
A = 102/5
Rounding to one decimal place, we get:
A ≈ 20.4 cm²
Therefore, the closest option to the area of the tile shown is 42.5 cm².
which probability distribution should be used to solve the following problem?affirmative action commitments by many organizations have led to an increase in the number of women in executive positions. satellite office systems has vacancies for two executives that it will fill from among four women and six men. what is the probability that at least one woman is selected?
Answers
The probability distribution to use in this problem is the binomial distribution and the probability of success is the probability of selecting a woman, which is 4/10.
The probability distribution that should be used to solve the problem of selecting at least one woman from a group of four women and six men for two executive vacancies is the binomial distribution.
The binomial distribution formula is used to calculate the probability of getting a certain number of successes in a fixed number of trials, given the probability of success in each trial. In this case, the probability of success is the probability of selecting a woman, which is 4/10.
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per the central limit theorem the standard deviation of the sampling distribution of the sample mean is equal to the population: a. standard deviation divided by n b. standard deviation divided by the square root of n c. mean d. standard deviation
Answers
The correct option is D, Per the Central Limit Theorem the mean of the sampling distribution of the sample mean is equal to the population Mean.
The Central Limit Theorem (CLT) is a fundamental concept in probability theory and statistics. It states that if you take repeated random samples of a population, the sample means will follow a normal distribution, regardless of the shape of the population distribution, provided the sample size is large enough. This means that as the sample size increases, the sample mean becomes more and more normally distributed.
The CLT is important because it helps us to understand the properties of large samples, even when the population is not normally distributed. It is used in many areas of research, including social sciences, finance, engineering, and more. The theorem provides a powerful tool for estimating population parameters, such as the mean or variance, and for testing hypotheses about them. It also helps to explain why the normal distribution is so commonly observed in real-world data, and why it is often used as a model for statistical analysis.
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Complete Question:-
Per the Central Limit Theorem the mean of the sampling distribution of the sample mean is equal to the population:
a. Standard deviation divided by n
b. Mean divided by n
c. Standard Deviation divided by the square root of n
d. Mean
PLEASE HELP WILL MARK BRANLIEST!!!
Answers
Answer:
x^2 - x + 6 = 0
x = (-(-1) + √((-1)^2 - 4(1)(6)))/(2 × 1)
= (1 + √(1 - 24))/2
= (1 + √-23)/2
So there are no real solutions to this equation--we have the empty (null) set.
{ }
In the diagram below AB = BC and BCD = 110 find A with justification
Answers
Result:
A (is an angle) = 70°.
How to calculate angle A?Based on the provided information:
AB = BC
BCD = 110
We can use the information to find the value of A.
Since AB = BC, we can assume that triangle ABC is an isosceles triangle, where AB and BC are the two equal sides. For an isosceles triangle, the angles opposite to the equal sides are also equal.
So, ∠ABC = ∠BCA (opposite angles of an isosceles triangle are equal).
Since BCD = 110, we can deduce that ∠BCA + ∠ BCD = 180 (sum of angles in a triangle equals 180 degrees).
Substituting the values, we get:
∠BCA + 110 = 180
Subtracting 110 from both sides, we get:
∠BCA = 180 - 110
∠BCA = 70
Now, since ∠ABC = ∠BCA, we have:
∠ABC = 70°
Therefore, A = 70 degrees.
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Antonia is a 75% free throw shooter which means that on average she makes 3 out of 4 free throw attempts. The table shows the results of 10 trials of a simulation where "Y" represents a made free throw and "N" represents a missed free throw. According to the results of the simulation, what is the experimental probability that Antonia makes both of her next 2 free throw attempts?
Answers
Antonia's probability of making a free throw is 0.75, and the probability of her missing a free throw is 0.25. Based on the results of a simulation of 10 trials, the experimental probability that Antonia makes both of her next two free throw attempts is 0.6 or 60%.
Using the given information, we know that Antonia's probability of making a free throw is 75%, which is equivalent to 0.75. Therefore, the probability of her missing a free throw is 25%, which is equivalent to 0.25.
Looking at the table of results from the simulation, we can see that there are 6 instances where Antonia made both of her next two free throw attempts (YY), out of a total of 10 trials. Therefore, the experimental probability of Antonia making both of her next two free throw attempts is
Experimental probability = Number of trials where Antonia made both of her next two free throws / Total number of trials
Experimental probability = 6/10
Experimental probability = 0.6
Therefore, based on the results of the simulation, the experimental probability of Antonia making both of her next two free throw attempts is 0.6 or 60%.
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help me please there are two equations.
Answers
The number of 2-pointers and 3-pointers are 11 and 4, respectively
How many of determine the number of 2-pointers and 3-pointersGiven that the pointers are 2 and 3 where
Let x = 2 pointers
Let y = 3 pointers
Using the above as a guide, we have the following:
2x + 3y = 34
x + y = 15
Multiply the second equation by 2
So, we have
2x + 3y = 34
2x + 2y = 30
Subtract the equations
y = 4
Recall that
x + y = 15
So, we have
x + 4 = 15
Evaluate
x = 11
Hence, the number of 2-pointers is 11
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i am thinking of a two digit square number
its digits add up to a prime number
write down a square number that i could be thinking of
Answers
Answer:
25
Step-by-step explanation:
25 sqrt= 5
2+5=7; 7 is a prime number
Simplify each of the following expressions:
(√5-√12)²
(√12+√11)²
(√6+√7) (√6-√7)
Rationalize
1/√8
1/√7-√1
1√8+3
Answers
Simplifying each of the following expressions:
a) (√5-√12)²:
First, we can simplify the square of each term using the formula (a-b)² = a² - 2ab + b²:
(√5-√12)² = (√5)² - 2(√5)(√12) + (√12)²
= 5 - 2√60 + 12
Next, we can simplify √60 by factoring out its largest perfect square factor, which is 4:
5 - 2√60 + 12 = 17 - 2√(4*15) = 17 - 4√15
Therefore, (√5-√12)² = 17 - 4√15.
b) (√12+√11)²:
We can simplify this expression using the same formula as before:
(√12+√11)² = (√12)² + 2(√12)(√11) + (√11)²
= 12 + 2√132 + 11
Next, we can simplify √132 by factoring out its largest perfect square factor, which is 4:
12 + 2√132 + 11 = 23 + 2√(4*33) = 23 + 2√132
Therefore, (√12+√11)² = 23 + 2√132.
c) (√6+√7) (√6-√7):
This expression can be simplified using the difference of squares formula, (a-b)(a+b) = a² - b²:
(√6+√7) (√6-√7) = (√6)² - (√7)²
= 6 - 7
= -1
Therefore, (√6+√7) (√6-√7) = -1.
Rationalizing each of the following expressions:
a) 1/√8:
To rationalize the denominator, we can multiply both the numerator and denominator by √8:
1/√8 = (1/√8) * (√8/√8) = √8/8
Therefore, 1/√8 = √8/8.
b) 1/√7-√1:
To rationalize the denominator, we can multiply both the numerator and denominator by the conjugate of the denominator, which is √7+√1:
1/√7-√1 = (1/√7-√1) * (√7+√1)/(√7+√1) = (√7+√1)/(7-1)
= (√7+√1)/6
Therefore, 1/√7-√1 = (√7+√1)/6.
c) 1/√8+3:
To rationalize the denominator, we can multiply both the numerator and denominator by the conjugate of the denominator, which is √8-3:
1/√8+3 = (1/√8+3) * (√8-3)/(√8-3) = (√8-3)/(8-9)
= -(√8-3)
Next, we can simplify √8 by factoring out its largest perfect square factor, which is 4:
-(√8-3) = -
a house is built by 20 workers in 30 days. how many workers will be needed to complete the work in 15 days?
Answers
Therefore, we need 40 workers to complete the work in 15 days.
Let's assume that the amount of work required to build the house is the same, regardless of the number of workers. This means that the number of workers and the time required to complete the work are inversely proportional to each other. We can use the following formula:
n1 × d1 = n2 × d2
where n1 is the initial number of workers, d1 is the initial number of days, n2 is the new number of workers, and d2 is the new number of days.
Substituting the given values, we get:
20 × 30 = n2 × 15
Simplifying the equation, we get:
n2 = (20 × 30) ÷ 15
n2 = 40
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Solve for x.
5x – 10 > 20 or 5x – 10 ≤ –15
Answers
The required simplified value of x is x > 6 or x ≤ -1.
We have two inequalities here:
5x - 10 > 20 or 5x - 10 ≤ -15
We can start by solving the first inequality:
5x - 10 > 20
5x > 30
x > 6
So x is greater than 6 for the first inequality to hold.
Next, we can solve the second inequality:
5x - 10 ≤ -15
5x ≤ -5
x ≤ -1
So x is less than or equal to -1 for the second inequality to hold.
Putting it all together, the solution to the system of inequalities is:
x > 6 or x ≤ -1
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What is the value of x?
please answer
Answers
Answer: 5
Step-by-step explanation:
You will use Pythagorean theorem for this problem (a²+b²=c²)
This will be 13² - 12² = a
13² - 12² = 25
you must square root your answer
√25 = 5
x=5
10) An airplane can travel 1716 feet in 3 seconds. Find the speed of the plane in miles per hour.
Answers
First, we need to convert feet to miles and seconds to hours.
1 mile is equal to 5280 feet.
So, 1716 feet is equal to (1716/5280) miles or 0.325 miles.
1 hour is equal to 3600 seconds.
So, 3 seconds is equal to (3/3600) hours or 0.00083333 hours.
Now we can calculate the speed of the plane in miles per hour by using the formula:
Speed (in miles per hour) = Distance (in miles) / Time (in hours)
Speed = 0.325 miles / 0.00083333 hours
Speed = 390 miles per hour (rounded to the nearest whole number)
Therefore, the speed of the plane is 390 miles per hour.
brainliest, 100 points, and multiple choice!! i appreciate it thanks so much!!
Answers
No because RS and LM are not corresponding sides.
You can see that the shapes are “similar” and that the tick marks designate corresponding sides. The tick marks are different between RS and LM, showing that they do not correspond.
a college professor notices that the greater the distance students sit from the front of the room, the worse their grades in the course seem to be. what type of correlation is this? note: distance is increasing, whereas grades are decreasing.
Answers
The correlation between the distance a student sits from the front of the room and their grades in the course is a negative correlation.
Negative correlation is a type of correlation where one variable increases while the other variable decreases. In this case, as the distance of a student in the class increasing, the grades of the student in decreasing.
This shows that distance and grades may not correlate favorably. The professor's discovery of a negative association may therefore reflect the reality that students become less attentive as they grow farther away from their teachers.
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choosing the pivot row by requiring that the ratio associated with that row be the smallest non-negative number ensures that the iteration will not take us from a feasible point to a non-feasible point.
Answers
Answer:
This statement is true.
In the simplex method, choosing the pivot row involves selecting a row with a negative value in the right-hand column and dividing the elements in the last column by the corresponding elements in the selected row to obtain the ratios. The row with the smallest non-negative ratio is then chosen as the pivot row.
By choosing the pivot row in this way, we ensure that the new solution will still be feasible, meaning that all the constraints will still be satisfied. This is because choosing the smallest non-negative ratio ensures that the new solution will not violate any of the non-negativity constraints.
Therefore, requiring that the ratio associated with the pivot row be the smallest non-negative number is an important step in the simplex method to ensure that the iteration will not take us from a feasible point to a non-feasible point.
Step-by-step explanation:
This statement is true when using the simplex method to solve a linear programming problem.
In the simplex method, we start with a feasible solution and iteratively improve it until we reach an optimal solution. At each iteration, we choose a pivot row and a pivot column to pivot around. The pivot row is chosen based on the ratio of the right-hand side value to the coefficient of the entering variable in that row. This ratio is called the pivot ratio.
Choosing the pivot row with the smallest non-negative pivot ratio ensures that we pivot to a new feasible solution. This is because the pivot row represents a constraint in the linear programming problem, and the pivot ratio represents how much we can increase the value of the entering variable while still satisfying that constraint. If the pivot ratio is negative, it means that increasing the entering variable would violate the corresponding constraint, and so we cannot pivot in that direction.
Therefore, by choosing the pivot row with the smallest non-negative pivot ratio, we ensure that we pivot in a direction that preserves feasibility and does not take us to a non-feasible point.
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The corresponding angles of similar triangles are equal. always sometimes never
Answers
This is one of the fundamental properties of similar triangles. If two triangles are similar, then their corresponding angles are equal. This means that if we have two triangles that are similar, we can compare the angles of the two triangles by pairing up the corresponding angles and comparing them.
For example, if we have two similar triangles ABC and DEF, where angle A is corresponding to angle D, angle B is corresponding to angle E, and angle C is corresponding to angle F, then we know that angle A is equal to angle D, angle B is equal to angle E, and angle C is equal to angle F.
This property is also used in solving problems involving similar triangles, such as finding the lengths of sides or the measures of angles in one triangle given the corresponding measures in another similar triangle.
Answer: Always True
Step-by-step explanation:
Graph the given data set and describe what kind of model best describes the data. Then write a function that models
the data..
X y
-2,-1
-1,-2
0,-1
1,2
2,7
Answers
The linear equation that models the data based on the information is y = 2.2x + 0.6.
What is an equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.
In conclusion, the linear equation that models the data based on the information is y = 2.2x + 0.6.
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Calcula la cantidad de malla que necesitaremos para construir un colador en forma de cono de 22cm de diámetro y 48cm de generatriz. ¿Cuál es su volumen?
Answers
The amount of mesh required is: 1686.24cm²
The volume is: 5934.66cm³cm³
To calculate the amount of mesh we say
L = πrℓ
where r is the radius of the base, ℓ is the generatrix, and π is approximately 3.14.
Given the diameter of the cone, we can calculate the radius as follows
r = d/2 = 22/2 = 11 cm
We are also given that the generatrix ℓ is 48 cm.
Therefore, the lateral surface area of the cone i is
L = πrℓ = 3.14 x 11 x 48 = 1657.92cm²
To find the volume of the cone, we can use the formula
V = (1/3)πr²h
where h is the height of the cone.
We can use the Pythagorn theorem to find the height of the cone as shown below
h² = ℓ² - r²
h² = 48² - 11²
h² = 2197
h = √2197
h ≈ 46.86 cm
Now we can find the volume of the cone whic is
V = (1/3)πr²h = (1/3) x 3.14 x 11² x 46.86 ≈ 5934.66cm³
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Translation:
Calculate the amount of mesh we will need to build a cone-shaped strainer with a diameter of 22cm and a generatrix of 48cm. What is its volume?
Frank buys a commemorative plate for $375, plus 6% sales tax. He pays an
additional $6.50 to have the plate shipped to him, but he does not pay sales tax
on the shipping charge. Three years later, he sells the plate for 10% more than
the total he paid for the plate, including taxes and shipping charges. What is his
net profit?
Answers
Answer:
$39.75
Step-by-step explanation:
First, you find the tax by dividing the cost of the plate by 100, and then multiplying your answer by the tax, 6.:
375/100 = 3.75
3.75*6 = 22.5.
Then add the shipping charges, 375 + 22.5 = 397.5. This is the total cost. SInce Frank sold the plate three years later for 10% more than the total cost, you find 10% of the total cost, and then add that 10% to $397.5
397.5/100 = 3.975
3.975*10 = 39.75
39.75 + 397.5 = 437.25.
To find the profit, subtract 397.5 from $437.25:
437.25 - 397.5 = 39.75.
The total profit is $39.75
Find the perimeter of this semi-circle with diameter,
d= 26cm.
Give your answer rounded to 1 DP.
Answers
The perimeter of the semicircle is approximately 66.8 cm.
The diameter of the semicircle is given as d = 26cm.
r = d/2 = 26/2 = 13cm
The circumference of a full circle with radius r is given by:
C = 2πr
Therefore, the circumference of the semicircle is:
C/2 = πr
Substituting the value of r, we get:
πr = π(13) = 13π
The perimeter of the semicircle is therefore:
P = d + C/2 = 26 + 13π
Using the value of π = 3.14, we can approximate the perimeter as:
P = 26 + 13(3.14)
= 26 + 40.82
= 66.82 cm
Rounding to 1 dp
= 66.8 cm
Therefore, the perimeter of the semicircle is approximately 66.8 cm.
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A spinner with nine equal-sized sections numbered one to nine is spun once. What is the probability that the spinner will land on a number that is not a multiple of three?
A. 1/3
B. 2/3
C. 7/9
D. 5’9
Answers
Answer:
2/3.
Step-by-step explanation:
Total number of possible outcomes on one spin = 9.
Total of non multiples of 3:
1, 2, 4, 5,7 and 8
= 6
Answer is 6/9 = 2/3.
Answer:
B. 2/3
Step-by-step explanation:
Probability is written like a fraction where on the bottom you have ALL the possibilities. There's 9 numbers on the spinner, so there's a total of 9 different ways for it to land.
9 ways total. That goes on the bottom of the fraction.
On top of the fraction you put however many number of ways the event in question can happen. That goes on top.
A multiple of three is 3, 6, 9. There are 3 ways the spinner can land on a multiple of three. So there are 6 ways to land on NOT a multiple of three (1, 2, 4, 5, 7, 8) 6 ways, so 6 goes on top.
6/9 is the answer. But always simplify fractions first, like you do.
6/9 simplifies to 2/3
The answer is
B. 2/3
What are two numbers in the ratio 7:3 that have the difference of 20 between them?
Answers
Answer:
The answer for
x=35
y=15
Step-by-step explanation:
let the first number be x
" second number " be y
x:y=7:3
x-y=20
x=20+y
x:y=7:3
20+y/y=7/3
7y=3(20+y)
7y=60+3y
7y-3y=60
4y=60
divide both sides by 4
y=15
x=20+y
x=20+15
x=35
A, B & C form the vertices of a triangle. ∠ CAB = 90°, ∠ ABC = 64° and AC = 9.1. Calculate the length of AB rounded to 3 SF.
Answers
Answer:
Since ∠CAB = 90°, we know that AC is the hypotenuse of the right triangle ABC. Let's use the sine function to find the length of BC:
sin(∠ABC) = BC/AC
sin(64°) = BC/9.1
BC = 9.1 * sin(64°)
Now, using the Pythagorean theorem, we can find the length of AB:
AB = sqrt(AC^2 - BC^2)
AB = sqrt(9.1^2 - (9.1*sin(64°))^2)
AB ≈ 5.222
Rounding this to 3 significant figures, we get:
AB ≈ 5.22
Therefore, the length of AB rounded to 3 significant figures is approximately 5.22 units.
Last year, The Cedarburg Times had a total of 6,100 subscribers. This year, after the paper was bought out, it had 6,832 subscribers. What is the percent of increase in the number of subscribers? %
Answers
The percent increase in the number of subscribers this year as compare to last year is equal to 12%.
Total number of subscribers last year = 6,100
Total number of subscribers this year = 6,832
The percent increase in the number of subscribers,
= Difference between number of subscribers this year and last year / number of subscribers last year multiply by 100
The difference between this year's and last year's subscribers is equal to
= 6,832 - 6,100
= 732
The percent increase in the subscribers this year compare to last year is,
= (732 / 6,100) x 100
= 0.12 x 100
= 12%
Therefore, the percent increase in the number of subscribers is 12%.
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Help urgent
A construction worker on the ground tosses an apple to a fellow worker who is 20. ft. above
the ground. The starting height of the apple is 5 ft. Its initial upward velocity is 32 ft/s. At
what time(s) will the apple be at the same height as the worker? (h=-16t+ vt +c, where h
is the height, v is the initial velocity and c is the starting height.)
Answers
The apple will be at the same height of 20ft as the construction worker at t = 3/4sec and t = 5/4sec.
It is given that h = -16t^2 + vt +c
v = 32ft/sec , c = 5ft , h =20ft
So plugging in these values into the formula we have
20 = -16t^2 + 32t + 5
[tex]$\Rightarrow 16t^2 -32t + 15 =0[/tex]
[tex]$\Rightarrow 16t^2 -20t - 12t + 15 =0[/tex]
[tex]$\Rightarrow 4t(4t - 5) -3(4t - 5) = 0[/tex][tex]$\,\,\,\Rightarrow (4t-3)(4t-5) = 0[/tex][tex]$\Rightarrow 4t-3 =0 \Rightarrow t = 3/4\,\,\textrm{ and } \,\, 4t-5 =0 \Rightarrow t = 5/4[/tex]
So t = 3/4 and at t = 5/4 are two times when the apple will be at an elevation of h = 20ft.
What is projectile motionThe motion of an object launched into free motion under gravity is called projectile motion. During this motion, the only force acting on the object is gravity, whose value is -32ft/sec^2. During this motion, the y coordinate is given by [tex]y = u_yt -(1/2)gt^2 + y_0 = u_yt - 16t^2 + y_0[/tex]. here [tex]u_y[/tex] is the vertical component of the initial velocity and [tex]y_0[/tex] is the initial y coordinate. The value of the x coordinate is given by [tex]x = u_xt[/tex], where [tex]u_x[/tex] is the horizontal component of the initial velocity.
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Helppppppp meee please
Answers
Answer:
x=36 y=71
Step-by-step explanation:
for x use the Z alternate angle
for y use 180 -73-36=71
Find the volume of the cylinder. Use 3.14 for π. Round to the tenths if necessary.
Answers
Answer:
577.76
Step-by-step explanation:
we know formula for volumne of cylinder
pie × square of radius × height
that is = 3.14× 8^2 × 23
that is = 577.76
Enhanced - with Hints and Feedback At 100°C the rms speed of nitrogen molecules is 576 m/s. Nitrogen at 100°C and a pressure of 2.4 atm is held in a container with a 13 cm x 13 cm square wall.
Answers
At 100°C, the nitrogen molecules in the container have an rms speed of 576 m/s. The pressure inside the container,
which is at a pressure of 2.4 atm, is a result of the collisions of these fast-moving molecules with the walls of the container. The area of the wall is 13 cm x 13 cm, which means there is a total surface area of 169 cm^2.
The collisions of the nitrogen molecules with this surface area will result in a force on the wall, which is what creates the pressure.
Overall, the properties of the nitrogen molecules, including their speed and number, contribute to the overall pressure inside the container.
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what is the angle between the z-axis and the vector: r with rightwards arrow on top space equals space minus 2 space i with hat on top space plus space 3 j with hat on top space plus space 7 k with hat on top ? please give your answer in proper angle notation and do not include units.
Answers
The angle between the z-axis and the given vector r with rightwards arrow on top is 33.69 degrees.
The x-component of the vector is -2, which means that the vector has a component that points in the negative x-direction. The y-component of the vector is 3, which means that the vector has a component that points in the positive y-direction. We can use these components to find the magnitude of the projection of the vector onto the xy-plane, which is given by the Pythagorean theorem:
|proj_r| = √((-2)² + 3²) = √(13)
Next, we need to find the angle between the projection of the vector onto the xy-plane and the positive x-axis. We can do this by taking the arctan of the y-component over the x-component:
theta = arctan(3/-2) = -56.31 degrees
Note that we get a negative angle because the projection of the vector lies in the third quadrant of the xy-plane, which is opposite to the positive x-axis.
Finally, we can find the angle between the z-axis and the vector by subtracting the angle between the projection of the vector onto the xy-plane and the positive x-axis from 90 degrees:
phi = 90 - 56.31 = 33.69 degrees
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