Answer:
[tex]5.8\text{ \%}\rightarrow\frac{29}{500}[/tex]Explanation: We have to write 5.8% In fraction in lowest terms:
This percent number essentially is:
[tex]5.8\text{ \%=}\frac{5.8}{100}[/tex]Therefore we can write it as:
[tex]\frac{5.8}{100}=\frac{5.8\times10}{100\times10}=\frac{58}{1000}[/tex]In lowest terms, this would be:
[tex]\frac{58}{1000}=\frac{29}{500}[/tex]The angle of elevation to the top of a Building in New York is found to be 11 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building. Round to the tenths. Hint: 1 mile = 5280 feet
Your answer is __________ feet.
The height of the building is given as 1026.43 feet
What is angle of elevation?This is the term that is used to refer to the angle that is usually formed from the horizontal line to the angle of sight of a person.
We have to make use of the trig function that tells us that
tan(∅) = opposite length /adjacent length.
where ∅ = 11 degrees
adjacent length = 1
opposite length = x
When we put these values in the formula we would have
tan 11 = x / 1
0.1944 = x /1
we have to cross multiply to get x
x = 0.1944 x 1
= 0.1944
Then the height of the building would be 0.1944 x 5280 feet
= 1026.43 feet
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Identify the type of polar graph for the equation: r = 3-5cos θ aLimacon with inner loop bCardioid cDimpled limacon dConvex limacon eRose Curve fCircle gLemniscate
Given the equation:
[tex]r=3-5\cos \theta[/tex]Let's identify the type of polar graph for the equation.
To identify the type of polar graph, use the formula below to get the Cartesian form:
[tex](x^2_{}+y^2)=r(\cos \theta,\sin \theta)[/tex]Thus, we have:
[tex](x^2+y^2)=3\sqrt[]{x^2+y^2}-5x[/tex]We have the graph of the equation below:
We can see the graph forms a Limacon with an inner loop.
Therefore, the type of polar graph for the given equation is a limacon with inner loop.
ANSWER:
Plot the point given by the following polar coordinates on the graph below. Each circular grid line is 0.5 units apart.230(2.5. -,
Solution:
Given:
[tex](2.5,-\frac{2\pi}{3})[/tex]a half cylinder with a diameter of 2 mm is 9n top of a rectangular prism. A second half cylinder with a diameter of 4 mm is on the side of the prism. All shapes are 5 mm long. What is the volume of the combined figures?
The volume will be given by:
The volume of the half cylinder on top, plus the volume of the rectangular prims, plus the volume of the half cylinder on the right:
so:
The volume of the half cylinder on top is:
[tex]\begin{gathered} V1=\frac{\pi r^2l}{2} \\ V1=\frac{\pi(1^2)5}{2}=\frac{5\pi}{2} \end{gathered}[/tex]The volume of the half cylinder on the right is:
[tex]\begin{gathered} V2=\frac{\pi r^2l}{2} \\ V2=\frac{\pi(2^2)\cdot5}{2}=10\pi \end{gathered}[/tex]The volume of the rectangular prism is:
[tex]\begin{gathered} V3=l\cdot w\cdot h \\ V3=4\cdot2\cdot5 \\ V3=40 \end{gathered}[/tex]Therefore, the total volume is:
[tex]\begin{gathered} Vt=V1+V2+V3 \\ Vt=\frac{5}{2}\pi+10\pi+40=79.3mm^3 \end{gathered}[/tex]What will be the coordinates of the vertex s of this parallelogram? Which answer choice should I pick A B C or D?
Answer:
A
Step-by-step explanation:
the opposite sides of a parallelogram are parallel
then QT is parallel to RS
Q → T has the translation
(x, y ) → (x + 2, y- 7 ) , so
R → S has the same translation from R (0, 3 )
S = (0 + 2, 3 - 7 ) → S (2, - 4 )
Can you please help me out with a question
Notice that the arc GH has the same measure as the angle GFH, which also has the same measure as the angle EFI since they are vertical angles.
On the other hand, EFI and IFS are adjacent angles, then:
[tex]m\angle EFI+m\angle IFS=m\angle EFS[/tex]Observe that the measure of the angle EFS is 90°. Since the measure of IFS is 20°, substitute those values into the equation to find the measure of EFI:
[tex]\begin{gathered} m\angle EFI+20=90 \\ \Rightarrow m\angle EFI=90-20 \\ \Rightarrow m\angle EFI=70 \end{gathered}[/tex]Thereore, the measure of GH is 70°.
Find the critical value z a/2 that corresponds to the confidence level 96%
To find the Z a/2 for the 96% confidence. We write the confidence level in decimal form, in this case 0.96.
Now:
[tex]\alpha=1-0.96=0.04[/tex]and then:
[tex]\frac{\alpha}{2}=0.02[/tex]Now we subtract this value to 0.5 to know the value we need to find in the Z table:
[tex]0.5-0.02=0.48[/tex]Now we look at the Z table for this value, by finding we notice that this happens when Z=2.05.
Therefore the Z a/2 value is 2.05
f(9) =
(Simplify your answer. Type an integer or a fraction.)
Answer:
9f
Step-by-step explanation:
f(9) = f * (9)
a) Multiply.
f * (9) = 9f
The graph shows the distance a car traveled, y, in x hours: What is the rise-over-run value for the relationship represented in the graph?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
point 1 (2 , 60) x1 = 2 y1 = 60
point 2 (4 , 120) x2 = 4 y2 = 120
Step 02:
slope formula
[tex]m\text{ = }\frac{y2-y1}{x2-x1}[/tex][tex]m\text{ = }\frac{120-60}{4-2}=\text{ }\frac{60}{2}=30[/tex]The answer is:
30
In ABC, B = 51°, b = 35, and a = 36. What are the two possible values for angle A to the nearest tenth of a degree?Select both correct answers.
Using the law of sines:
[tex]\frac{a}{\sin(A)}=\frac{b}{\sin (B)}[/tex]Solve for A using the data provided:
[tex]\begin{gathered} \sin (A)=\frac{\sin (B)\cdot a}{b} \\ A=\sin ^{-1}(\frac{\sin (51)36}{35}) \\ A\approx53.1 \\ or \\ A\approx126.9 \end{gathered}[/tex]65+ (blank) =180
11x + (blank)=180
11x =
x =
Answer:
sorry if this is wrong
I just answered it according to the question you gave not the pic
Step-by-step explanation:
x = 65
11x + x = 180
12x = 180
x = 180 ÷ 12
= 15
Clark and Lindsay Banks have agreed to purchase a home for $225,000. They made a down payment of 15%. They have obtained a mortgage loan at a 6.5% annual interest rate for 25 years. What is the mortgage total if they finance the closing costs?
SOLUTION
We will be using the annual compound interest formula to solve this question.
[tex]\begin{gathered} A=P(1+\frac{R}{100})^{mn} \\ \text{where m=1, n=25years, R=6.5,} \end{gathered}[/tex]After a down payment of 0.15 x $225,000 = $33750
The principal value will be $225,000 - $33750 = $191250
Put all these values into the compound interest formula above,
we will have:
[tex]\begin{gathered} A=191250(1+\frac{6.5}{100})^{1\times25} \\ A=191250(1+0.065)^{25} \end{gathered}[/tex][tex]\begin{gathered} A=191250(1.065)^{25} \\ \text{ = 191250}\times4.8277 \\ \text{ =923,297.63} \end{gathered}[/tex]The mortgage total if they finance the closing costs will be:
$923,297.63
Find the area to the right of x=71 under a normal distribution curve with the mean=53 and standard deviation=9
Answer:
[tex]Area=0.0228\text{ or 2.28\%}[/tex]Explanation:
We were given the following information:
This is a normal distribution curve
Mean = 53
Standard deviation = 9
We are to find the area right of x = 71
This is calculated as shown below:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ x=71 \\ \mu=53 \\ \sigma=9 \\ \text{Substitute these into the formula, we have:} \\ z=\frac{71-53}{9} \\ z=\frac{18}{9} \\ z=2 \end{gathered}[/tex]We will proceed to plot this on a graph as sown below:
The area to the right of x = 71 (highlighted in red above) is given by using a Standard z-score table:
[tex]\begin{gathered} =1-0.9772 \\ =0.0228 \\ =2.28\text{\%} \end{gathered}[/tex]Therefore, the area that lies to the right of x = 71 is 0.0228 or 2.28%
Consider the following quadratic function Part 3 of 6: Find the x-intercepts. Express it in ordered pairs.Part 4 of 6: Find the y-intercept. Express it in ordered pair.Part 5 of 6: Determine 2 points of the parabola other than the vertex and x, y intercepts.Part 6 of 6: Graph the function
Answer:
The line of symmetry is x = -3
Explanation:
Given a quadratic function, we know that the graph is a parabola. The general form of a parabola is:
[tex]y=ax^2+bx+c[/tex]The line of symmetry coincides with the x-axis of the vertex. To find the x-coordinate of the vertex, we can use the formula:
[tex]x_v=-\frac{b}{2a}[/tex]In this problem, we have:
[tex]y=-x^2-6x-13[/tex]Then:
a = -1
b = -6
We write now:
[tex]x_v=-\frac{-6}{2(-1)}=-\frac{-6}{-2}=-\frac{6}{2}=-3[/tex]Part 3:For this part, we need to find the x-intercepts. This is, when y = 0:
[tex]-x^2-6x-13=0[/tex]To solve this, we can use the quadratic formula:
[tex]x_{1,2}=\frac{-(-6)\pm\sqrt{(-6)^2-4\cdot(-1)\cdot(-13)}}{2(-1)}[/tex]And solve:
[tex]x_{1,2}=\frac{6\pm\sqrt{36-52}}{-2}[/tex][tex]x_{1,2}=\frac{-6\pm\sqrt{-16}}{2}[/tex]Since there is no solution to the square root of a negative number, the function does not have any x-intercept. The correct option is ZERO x-intercepts.
Part 4:
To find the y intercept, we need to find the value of y when x = 0:
[tex]y=-0^2-6\cdot0-13=-13[/tex]The y-intercept is at (0, -13)
Part 5:
Now we need to find two points in the parabola. Let-s evaluate the function when x = 1 and x = -1:
[tex]x=1\Rightarrow y=-1^2-6\cdot1-13=-1-6-13=-20[/tex][tex]x=-1\Rightarrow y=-(-1)^2-6\cdot(-1)-13=-1+6-13=-8[/tex]The two points are:
(1, -20)
(-1, -8)
Part 6:
Now, we can use 3 points to find the graph of the parabola.
We can locate (1, -20) and (-1, -8)
The third could be the vertex. We need to find the y-coordinate of the vertex. We know that the x-coordinate of the vertex is x = -3
Then, y-coordinate of the vertex is:
[tex]y=-(-3)^2-6(-3)-13=-9+18-13=-4[/tex]The third point we can use is (-3, -4)
Now we can locate them in the cartesian plane:
And that's enough to get the full graph:
The sum of two numbers is ten. One number is
twenty less than four times the other. Find the
numbers.
Note: List numbers with a comma separating
them, e.g. 5, 12.
By solving the equations, we can conclude that the two numbers are 4 and 6.
What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. As in 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, and others. The three primary forms of linear equations are point-slope, standard, and slope-intercept.So, the two numbers are:
Let the 2nd number be 'x'.Then, the 1st number will be '4x - 20'.The equation will be:
4x - 20 + x = 10Now, solve this equation for 'x' as follows:
4x - 20 + x = 105x = 10 + 205x = 30x = 6Now, 4x - 20:
4(6) - 2024 - 204Therefore, by solving the equations, we can conclude that the two numbers are 4 and 6.
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The local appliance store is advertising a 17% off sale on a new flat-screen TV. If the saleprice is $664, what was the original price of the flat-screen TV? Use X in the equation
Let's assume X is the original price of the flat-screen TV
The store is advertising a 17% off sale in that price, so the real sale price should be less than the original price
To calculate a % discount, we proceed as follows:
Compute the discount:
discount = 17% of X
Recall a percentage can be expressed as the number divided by 100, that is:
discount = 17 / 100 * X = 0.17X
Now we have the discount, we calculate the actual or sale price, which is the original price minus the discount:
sale price = original price - discount
sale price = X - 0.17X
We apply simple algebra to simplify the expression, just subtracting 1-0.17=0.83
sale price = 0.83X
We know the sale price is $664, thus:
0.83X = 664
Finally, we solve for X
[tex]X=\frac{664}{0.83}=800[/tex]This means that the original price of the TV was $800. Let's verify our result
What’s the correct answer asap for brainlist
Answer:
Step-by-step explanation:its a 69420 dum as
Line p is the perpendicular bisector of MN. Write the equation of line p in slope-intercept form.
Line p is perpendicular bisector of line MN. This means that it divides line MN equally. Thus, point B is the midpoint of line MN. Thus, we would find the midpoint of line MN by applying the midpoint formula which is expressed as
(x1 + x2)/2, (y1 + y2)/2
Looking at the given points of line MN,
x1 = - 5, y1 = 2
x2 = 7, y2 = - 1
Midpoint = (- 5 + 7)/2, (2 + - 1)/2
Midpoint = 2/2, 1/2
Midpoint = 1, 1/2
We would find the slope of line MN. The formula for finding slope is expressed as
m = (y2 - y1)/(x2 - x1)
Looking at the given points of line MN,
x1 = - 5, y1 = 2
x2 = 7, y2 = - 1
m = (- 1 - 2)/(7 - - 5) = - 3/(7 + 5) = - 3/12 = - 1/4
If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. This means that the slope of line p is 4/1 = 4
Thus, line p is passing through point (1, 1/2) and has a slope of 4
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept
To determine the equation of line p, we would substitute m = 4, x = 1 and y = 1/2 into the slope intercept equation. It becomes
1/2 = 4 * 1 + c
1/2 = 4 + c
c = 1/2 - 4
c = - 7/2
Substituting m = 4 and c = - 7/2 into the slope intercept equation, the equation of line p would be
y = 4x - 7/2
write a word problem in which you divide two fractions into mixed numbers or a mixed number and a fraction solve your word problem and show how you found the answer
Jade share 4 1/3 cups of chocolate by 1/3 among his friends
The mixed fraction = 4 1/3
Fraction = 1/3
[tex]\begin{gathered} \text{Firstly, we n}eed\text{ to convert the mixed fraction into an improper fraction} \\ 4\frac{1}{3}\text{ = }\frac{(3\text{ x 4) + 1}}{3} \\ 4\frac{1}{3}\text{ = }\frac{12\text{ + 1}}{3} \\ 4\frac{1}{3}\text{ = }\frac{13}{3} \\ \text{Divide }\frac{13}{3}\text{ by 1/3} \\ =\text{ }\frac{13}{3}\text{ / }\frac{1}{3} \\ \text{ According to mathematics, once the numerator and denominator of the LHS is interchanged then the order of operator changes from division to multiplication} \\ =\text{ }\frac{13}{3}\text{ x }\frac{3}{1} \\ =\text{ }\frac{13\text{ x 3}}{3} \\ \text{= }\frac{39}{3} \\ =\text{ 13} \end{gathered}[/tex]Therefore, the answer is 13
the client is to receive cimetidine 300mg by mouth every 6 hours. The medication is available as cimetidine 300mg/5ml. How many teaspoons should the nurse instruct the client to take?
Step 1
Given; The client is to receive cimetidine 300mg by mouth every 6 hours. The medication is available as cimetidine 300mg/5ml.
Required; How many teaspoons should the nurse instruct the client to take?
Step 2
[tex]\begin{gathered} 1\text{ teaspoon =5ml } \\ Patient\text{ takes 300mg/5ml or 300mg/teaspoon} \\ \frac{Required\text{ dosage in mg}}{Dosage\text{ in 1 teaspoon}}\times5ml \\ Required\text{ dosage in mg=300mg} \\ Dosage\text{ in 1 teaspoon=300mg} \\ \frac{300mg}{300mg}\times5ml=5ml \\ From\text{ the table 5ml is the equivalent of 1 teaspoon .} \end{gathered}[/tex]Thus, the client takes 300mg every six hours. This means that the nurse will instruct the client to take 1 teaspoon every 6 hours.
Answer;
[tex]1\text{ teaspoon every 6 hours}[/tex]A game uses a single 6-sided die. To play the game, the die is rolled one time, with the following results: Even number = lose $91 or 3 = win $25 = win $12What is the expected value of the game?
The expected value of the game is $1.83.
In a recent poll, 13% of all respondents said that they were afraid of heights. Suppose this percentage is true for allAmericans. Assume responses from different individuals are independent.
I need help with this practice problem If you can, show your work step by step so I can take helpful notes
The given geometric series is
[tex]120-80+\frac{160}{3}-\frac{320}{9}+\cdots[/tex]In a geometric series, there is a common ratio between consecutive terms defined as
[tex]r=\frac{-80_{}}{120_{}}=-\frac{2}{3}[/tex]The sum of the first n terms of a geometric series is given by
[tex]S_n=\frac{a(1-r^n)}{1-r},r<1[/tex]Where a is the first term.
From the given series
a = 120
Hence, the sum of the first 8 terms is
[tex]S_8=\frac{120(1-(-\frac{2}{3})^8)}{1-(-\frac{2}{3})}[/tex]Simplify the brackets
[tex]S_8=\frac{120(1-\frac{2^8}{3^8}^{})}{1+\frac{2}{3}}[/tex]Simplify further
[tex]\begin{gathered} S_8=\frac{120(1-\frac{256}{6561})}{\frac{3+2}{3}} \\ S_8=\frac{120(\frac{6561-256}{6561})}{\frac{5}{3}} \\ S_8=\frac{120(\frac{6305}{6561})}{\frac{5}{3}} \\ S_8=\frac{120\times6305}{6561}\div\frac{5}{3} \\ S_8=\frac{120\times6305}{6561}\times\frac{3}{5} \\ S_8=\frac{120\times6305}{6561}\times\frac{3}{5} \\ S_8=\frac{8\times6305}{729} \\ S_8=\frac{50440}{729} \end{gathered}[/tex]Therefore, the sum of the first 8 terms is
[tex]\frac{50440}{729}[/tex]the red line equation is y=0.5*2^xthe blue line equation is y=2x+25Compare and contrast this graph
In this question, we are given two lines.
1) y = 0.5*2^x
2) y = 2x + 25
The standard equation of a line is y = mx + b, where m is the slope and b is the y-intercept.
The positive slope moves the line upwards and the negative slope moves the line downwards.
If we compare both the equations, we see the 2nd equation maps with the standard line form. Hence, the second equation is a line with the slope equals to 2 and y-intercept equals 25. As the slope is positive, the line is moving upwards.
The standard equation of an exponential function is y = a*b^x, where b is the base, x is the exponent and a is the y-intercept.
The positive value of the base moves the function upwards and the negative value moves it downwards.
If we compare both the equations, we see the 1st equation maps with the standard exponential form. Hence, the 1st equation is an exponent form with the base to 2 and y-intercept equals 0.5. As the base is positive, the line is moving upwards.
When 6 is subtracted from the 5 times of a number the sum becomes 9 find the number
Let that unknown number be x
⇒Mathematically this is written as
[tex]5(x)-6=9\\5x-6=9\\5x=9+6\\5x=15\\\frac{5x}{5} =\frac{15}{5} \\x=3[/tex]
This just means that the unknown number is 3
GOODLUCK!!
Answer:
nine plus six
= 15 ÷ five
answer Three
A trail mix brand guarantees a peanut to raisin ratio of 5:2. If a bag of that trail mix contains 30 peanuts, how many raisins are in the bag?
Answer:
12
Explanation:
In the bag, the guaranteed ratio of peanut to raisin = 5:2
Number of peanuts = 30
Let the number of raisins =x
We therefore have that:
[tex]\begin{gathered} 5\colon2=30\colon x \\ \frac{5}{2}=\frac{30}{x} \\ 5x=30\times2 \\ x=\frac{30\times2}{5} \\ x=12 \end{gathered}[/tex]The number of raisins in the bag is 12.
I need help with the entire problem. The question is about a sketchy hotel.
Let d and s be the cost of a double and single- occupancy room, respectively. Since a double-occupancy room cost $20 more than a single room, we can write
[tex]d=s+20\ldots(A)[/tex]On the other hand, we know that 15 double-rooms and 26 single-rooms give $3088, then, we can write
[tex]15d+26s=3088\ldots(B)[/tex]Solving by substitution method.
In order to solve the above system, we can substitute equation (A) into equation (B) and get
[tex]15(s+20)+26s=3088[/tex]By distributing the number 15 into the parentheses, we have
[tex]15s+300+26s=3088[/tex]By collecting similar terms, it yields,
[tex]41s+300=3088[/tex]Now, by substracting 300 to both sides, we obtain
[tex]41s=2788[/tex]then, s is given by
[tex]s=\frac{2788}{41}=68[/tex]In order to find d, we can substitute the above result into equation (A) and get
[tex]\begin{gathered} d=68+20 \\ d=88 \end{gathered}[/tex]Therefore, the answer is:
[tex]\begin{gathered} \text{ double occupancy room costs: \$88} \\ \text{ single occupancy room costs: \$68} \end{gathered}[/tex]The following table shows a company's annual income over a 6-year period. The equation y=60000(1.2)x describes the curve of best fit for the company's annual income (y). Let x represent the number of years since 2001.
Given that the annual income of a company over a 6-year period is described by the equation:
[tex]\begin{gathered} y=60000(1.2)^x \\ \text{where} \\ x\text{ is the number of years since 2001} \end{gathered}[/tex]The annual income at the end of each year since 2001 is as shown in the table below:
Required: To evaluate the company's approximate annual income in 2009.
Solution:
Given the annual income described as
[tex]y=60000(1.2)^x[/tex]The number of years between 2001 and 2009 is evaluated as
[tex]x\text{ = 2009 -2001 = 8 years}[/tex]thus, it's been 8 years since 2001.
The annual income in 2009 is thus evaluated by substituting 8 for the value of x in the annual income function.
This gives
[tex]\begin{gathered} y=60000(1.2)^x \\ x\text{ = 8} \\ \text{thus,} \\ y\text{ = 60000}\times(1.2)^8 \\ =\text{ 60000}\times4.29981696 \\ y=\text{ }257989.0176 \\ \Rightarrow y\approx258000 \end{gathered}[/tex]Hence, the company's approximate annual income in the year 2009 will be $ 258000.
The third option is the correct answer.
the drop down menus choices are: two imaginary solutionstwo real solutionsone real solution
Given a quadratic equation of the form:
[tex]ax^2+bx+c=0[/tex]The discriminant is:
[tex]D=b^2-4ac[/tex]And we can know the number of solutions with the value of the discriminant:
• If D < 0, the equation has 2 imaginary solutions.
,• If D = 0, the equation has 1 real solution
,• If D > 0, the equation has 2 real solutions.
Equation One:
[tex]x^2-4x+4=0[/tex]Then, we calculate the discriminant:
[tex]D=(-4)^2^-4\cdot1\cdot4=16-16=0[/tex]D = 0
There are 1 real solution.
Equation Two:
[tex]-5x^2+8x-9=0[/tex]
Calculate the discriminant:
[tex]D=8^2-4\cdot(-5)\cdot(-9)=64-20\cdot9=64-180=-116[/tex]D = -116
There are 2 imaginary solutions.
Equation Three:
[tex]7x^2+4x-3=0[/tex]
Calculate the discriminant:
[tex]D=4^2-4\cdot7\cdot(-3)=16+28\cdot3=16+84=100[/tex]D = 100
There are 2 real solutions.
Answers:
Equation 1: D = 0, One real solution.
Equation 2: D = -116, Two imaginary solutions.
Equation 3: D = 100, Two real solutions.
An 18-foot ribbon is attached to the top of a pole and is located on the ground 10 feet awayfrom the base of the pole. Suppose Mateo has a second ribbon that will be located anadditional 23 feet away past that point.Find the measure of the angle formed by Mateo's ribbon and the ground. Round the angle tothe nearest tenth of a degree.a10 ft18 ft23 ft8
To begin we need to find the value of a
We apply the Pythagorean theorem
[tex]\begin{gathered} 18^2=a^2+10^2 \\ a^2=18^2-10^2 \\ a=\sqrt{18^2-10^2} \\ a=4\sqrt{14} \end{gathered}[/tex]Now we find theta
Here we use the tangent that is the oppositive side over the adjacent side
[tex]\begin{gathered} \tan\theta=\frac{4\sqrt{14}}{33} \\ \\ \theta=\tan^{-1}(\frac{414}{33})=24.39\degree \end{gathered}[/tex]