By the equations according to the cylindrical system of coordinates, the equation for a helix are x = 8 · cos (2π · t /T), y = 8 · sin (2π · t /T) and z = 6 · (t/T).
How to derive the equations of a helix in cylindrical form
According to the cylindrical system of coordinates, helix can be described by the following equations:
Radius
x = r · cos (2π · t /T) (1)
y = r · sin (2π · t /T) (2)
Height
z = H · (t/T) (3)
Where T is the period of one complete revolution.
If we know that r = 8 and H = 6, then the equations for the helix is:
x = 8 · cos (2π · t /T)
y = 8 · sin (2π · t /T)
z = 6 · (t/T)
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Need the answer for number 3 please!!
Answer: No
Step-by-step explanation:
The graph is increasing, yet as p increases, the value of 100/p decreases, meaning that the graph should be decreasing.
What is the point-slope form of a line with slope 3/2 that contains the point
(-1, 2)?
A.y+2=(x + 1)
B. y-2-(x-1)
C. y+2=(x-1)
D. y-2-(x+1)
Answer:
[tex]\boldsymbol{\rm{y-2=\dfrac{3}{2}(x+1)}}[/tex], or DStep-by-step explanation:
Hello
If a line's equation has the form [tex]\boldsymbol{\rm{y-y1=m(x-x1)}}[/tex], then it's considered to be in point-slope form.
In that formula,
[tex]\boldsymbol{\rm{y1}}[/tex] is the y co-ordinate (2nd co-ordinate) of the point (here it's given as 2)[tex]\boldsymbol{\rm{m}}[/tex] is the slope, here it's 3/2[tex]\boldsymbol{\rm {x1}}[/tex] is the x co-ordinate (the first co-ordinate) of the point.Now you know why this equation is called point-slope form!
Now that we're familiar with the equation, let's plug in the information that's given to us...
[tex]\boldsymbol{\rm{y-2=\displaystyle\frac{3}{2}(x-(-1)}}[/tex] | simplify
[tex]\boldsymbol{\rm{y-2=\displaystyle\frac{3}{2}(x+1)}}[/tex]
[tex]\pmb{\tt{done~!!}}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
Two bikers meet at a park. Biker A needs to stop at the store that is 12 miles east of the park. Biker B heads southeast at a 61° angle at the same time for 24 miles. Once biker A leaves the store he heads southwest at an angle of 89° for 21 miles. Do NOT use the law of cosines, use your knowledge from the content of this course.
Two bikers meet at a park at A
The triangle is geometric shape which includes 3 sides and sum of interior angle should not grater than 180°
Biker A needs to stop at the store that is 12 miles east of the park. Biker B heads southeast at a 61° angle at the same time for 24 miles. Once biker A leaves the store he heads southwest at an angle of 89° for 21 miles.
By following of the above statement the triangle is formed shown in the image attached below.
Thus, without using cosine formula, by drawing the triangle according to
the statement. At point A both the bikers were meet
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Participants in a darts tournament get 4 points
if they hit the red circle, 1 point if they hit the
blue circle, and no points if they miss both
circles. Each participant has 4 darts. How
many different scores are possible if everyone
gets at least one point?
Using the Fundamental Counting Theorem, it is found that 80 different scores are possible if everyone gets at least one point.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
There are 4 darts, and for each dart 3 possible scores, hence:
[tex]n_1 = n_2 = n_3 = n_4 = 3[/tex]
Hence the number of possible scores, removing the one score with zero points on all four rounds, is:
N = 3 x 3 x 3 x 3 - 1 = 80.
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Determine the amount of interest the principal in each account had earned. (From Example 2)
3. On March 3, Raul Avila deposited $10,000 in a savings account that pays 5.5% interest compounded daily until June 21.
4. On March 26, Samuel Griffin deposited $20,000 in a savings account that pays 5.5% interest compounded daily until July 24.
The amount of interest that the principal in each account had earned is as follows:
Raul Avila = $167.12
Samuel Griffin = $364.91
How is compound interest computed?The compound interests can be calculated using the compound interest formula:
A = P(1 + \frac{r}{n})^{nt}
Where:
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
It can also be computed using an online finance calculator as follows:
Data and Calculations:Raul Avila:N (# of periods) = 110 days
I/Y (Interest per year) = 5.5%
PV (Present Value) = $10,000
PMT (Periodic Payment) = $0
Results:
FV = $10,167.12
Total Interest = $167.12
Samuel Griffin:N (# of periods) = 120 days
I/Y (Interest per year) = 5.5%
PV (Present Value) = $20,000
PMT (Periodic Payment) = $0
Results:
FV = $20,364.91
Total Interest = $364.91
Thus, using the online finance calculator, the compound interest for each principal has been computed as $167.12 and $364.91, respectively.
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Somebody help please
Answer:
Emily raised $37.50
Justin raised $57.50
Step-by-step explanation:
(Step 1)
Say "x" equals the amount of money Emily made and "y" equals the amount of money Justin made. You can set up an equation with both of these variables because we know that they made a combined $95.
x = Emily's earnings
y = Justin's earnings
Emily + Justin = 95
x + y = 95
(Step 2)
The fact that there are two variables makes it difficult to find how much each person made individually. However, we can eliminate the "y" variable when we remember that Justin made $20 more than Emily. Now, we can substitute "x + 20" in for "y".
x + 20 = y
x + y = 95
x + (x + 20) = 95
(Step 3)
Finally, we can solve for the "x" variable.
x + (x + 20) = 95
2x + 20 = 95 <------ Combine like terms
2x = 75 <------ Subtract 20 from both sides
x = 37.5 <------- Divide both sides by 2
(Step 4)
Since we know the value of "x", we can plug it into one of the equations to find the value of "y".
x + 20 = y
37.5 + 20 = y
y = 57.5
Answer:
Emily raised $37.5 and justin raised $57.5
Which of the following is the best strategy to support children in learning about shapes?
a. Purchase a complete, wooden collection of two-and three- dimensional shapes from educational supply catalog.
b. Plan opportunities for children to talk about what is and what is not a shape and identify attribo les that define shapes.
C. Provide multiple worksheets with pictures of the basic shapes for children to color.
The best option is C. Provide multiple worksheets with pictures of the basic shapes for children to colour.
What does the learning process in children involve?The process of learning has often been described to include all but not limited to the following:
gaining new understanding, learning new behaviours,skills,values, attitudes, andpreferences.Children according to experts learn faster and easily remember what they see. Hence, providing multiple worksheets with pictures of the basic shapes for children to colour is the most cost-efficient strategy to support children in learning about shapes.
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Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Based on the triangle sum theorem, exterior angle theorem, the true statements are:
m∠5 + m∠6 = 180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
What is the Triangle Sum Theorem and the Exterior Angle Theorem?According to the triangle sum theorem, m∠2 + m∠3 + m∠5 = 180°.
Also, based on the exterior angle theorem, m∠2 + m∠3 = m∠6.
∠5 and ∠6 are a pair of linear angles, therefore: m∠5 + m∠6 = 180°.
In summary, the true statements about the diagram given are:
m∠5 + m∠6 = 180°m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°Learn more about the triangle sum theorem on:
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Una empresa embotelladora de gaseosas lanzará su propia bebida "Delicia" de un litro a un costo variable de S/ 2.50 por unidad, los costos fijos son S/ 18,500. Cada unidad tiene un precio de venta de S/ 4.50. Entonces, determine el número de botellas de un litro que deben venderse para que la empresa obtenga utilidades de S/ 30 000.
Por la ecuación de utilidad, necesitamos una producción de 7,667 botellas de un litro de capacidad para obtener un total de utilidades de S/ 30.000.
¿Cómo determinar las utilidades por la venta de bebidas gaseosas?
Las utilidades (U') se obtienen de sustraer los costes de producción (Cp) a las utilidades netas (U). Los costes de producción (Cp) son la suma de costes variables (C') y costes fijos (C). y la utilidades netas proceden de la venta de botellas. En consecuencia, tenemos la siguiente expresión:
U' = U - Cp
U' = U - C' - C
A continuación, desarrollamos y resolvemos la ecuación resultante:
30000 = 4.50 · x - 2.50 · x - 18500
1.50 · x = 11500
x = 7667
Por la ecuación de utilidad, necesitamos una producción de 7,667 botellas de un litro de capacidad para obtener un total de utilidades de S/ 30.000.
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What is 11 3/8 divided in half
Answer:
in fraction form it is : 5 11/16
Decimal form it is : 5.6875
Step-by-step explanation:
convert the mixed number into improper fractions: 11 3/8 = 91/8
= 91/8 / 8/2
Apollyon the fraction rule: a/b / c = a / b * c
= 91/8 * 2
Multiply the numbers: 8 * 2 = 16
= 91/15
convert the improper fractions into mixed numbers: 91/16 = 5 11/16
Final answer of:
= 5 11/16
The graph of a line has a slope of 3 and passes through the point (–4, –5).
What is the equation of the line in point-slope form?
y – 5 = 3(x – 4)
y – 4 = 3(x – 5)
y + 5 = 3(x + 4)
y + 4 = 3(x + 5)
Answer
(C) y +5 =3(x+4)
We will use the point-slope formula to solve this problem.
We will use the point-slope formula to solve this problem.(y+5)=3(x+4)
)Explanation:
)Explanation:We can use the point slope formula to solve this problem.
)Explanation:We can use the point slope formula to solve this problem.The point-slope formula states: (y−y1)=m(x−x1)
)Explanation:We can use the point slope formula to solve this problem.The point-slope formula states: (y−y1)=m(x−x1)Where m is the slope and (x1y1) is a point the line passes through.
)Explanation:We can use the point slope formula to solve this problem.The point-slope formula states: (y−y1)=m(x−x1)Where m is the slope and (x1y1) is a point the line passes through.We can substitute the slope and point we were given into this formula to produce the equation we are looking for:
)Explanation:We can use the point slope formula to solve this problem.The point-slope formula states: (y−y1)=m(x−x1)Where m is the slope and (x1y1) is a point the line passes through.We can substitute the slope and point we were given into this formula to produce the equation we are looking for:(y−(−5))=3(x--(4))
=> (y+5)=3(x+4)
Graph the function on the interval [-5, 2).
g(x) = [[x+4]]
4
Answer:
x=2 , y=6
Given: the interval (-5, 2) The graph are given that;
•°• g(x) = [ [ x +4 ] ]
g(-5) = [[ -5+4]]
= -1 (imposible)
g(2) = [[2+4]] = 6
x = 2
Let g(x) = y
= [[ x+4]]
y = 6
g(x) = 6 ✔
•°• x + 4 = 6
x = 2
g(y) = [[ y+4]] = 10
y + 4 = 10
y = 6
x = 2 , y = 6 ✔✔✔✔
What is the slope of the line shown below?
Answer:
(1/2)
Step-by-step explanation:
From one point, if you go up one and over 2 you will get exactly one block up than from your initial point. And since the graph is pointing down on left side, that means it's positive.
60°
X
x
60°
x = [ ? ]
Ingresar
Answer: 30
Step-by-step explanation:
Since there are two angles that measure [tex]60^{\circ}[/tex], the triangle is equilateral. This means that the angle bisector of the third angle is an altitude, and thus we have two right triangles with acute angles [tex]60^{\circ}[/tex] and [tex]x[/tex]. It follows that x=30.
PLEASE HELP !!! URGENT!!!
What is the range of f(x)?
O {f(x)
O {f(x)|-∞
O {f(x)|4
O {f(x)|0sf(x)<∞}
Answer:
best ans is { f(x)| –∞ < f(x) ≤ 4}
Step-by-step explanation:
usually to find the range of a fn, u need to see what the value can be. the graph show only a small range of x values. but u can see f(x) is definitely < 4. so the ans is { f(x)| –∞ < f(x) ≤ 4}
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[tex]\displaystyle \rm \int_{1 - \sqrt{\pi x} \large \frac{ {d}^{ {1/2 }} }{ {dx}^{1/2} } \small(1) }^{ \sum \limits_{n = 1}^ \infty \frac{4}{4 {n}^{2} - 1 } } \frac{arctan( \frac{2 - x}{1 + 2x}) }{ {x}^{2} - 4x - 1} dx[/tex]
There's nothing particularly tricky about the limits of integration. The upper limit is a telescoping series converging to 2,
[tex]\displaystyle \sum_{n=1}^\infty \frac4{4n^2-1} = 2 \sum_{n=1}^\infty \left(\frac1{2n-1} - \frac1{2n+1}\right) \\\\ ~~~~~~~~ = 2 \left(\left(1-\frac13\right)+\left(\frac13-\frac15\right) + \left(\frac15 - \frac17\right) + \cdots\right)[/tex]
The lower limit reduces to 0 using the Riemann-Liouville definition of the fractional derivative. For [tex]q\in\Bbb Q[/tex], let
[tex]\displaystyle \frac{d^q}{dx^q} f(x) = \frac1{\Gamma(\lceil q\rceil-q)} \frac{d^{\lceil q\rceil}}{dx^{\lceil q\rceil}} \int_a^x (x-t)^{\lceil q\rceil-q-1} f(t) \, dt[/tex]
With [tex]a=0[/tex], [tex]q=\frac12[/tex] and [tex]\lceil q\rceil=1[/tex], it follows that
[tex]\displaystyle \frac{d^{1/2}}{dx^{1/2}} 1 = \frac1{\Gamma\left(\frac12\right)} \frac d{dx} \int_0^x (x-t)^{-1/2} \, dt = \frac1{\sqrt{\pi x}}[/tex]
Let
[tex]\displaystyle I = \int_0^2 \frac{\tan^{-1}\left(\frac{2-x}{1+2x}\right)}{x^2-4x-1} \, dx[/tex]
Observe that
[tex]f(x) = \dfrac{2-x}{1+2x} = f^{-1}(x)[/tex]
is its own inverse, so by substituting [tex]\frac{2-x}{1+2x}\mapsto x[/tex], we get the equivalent integral
[tex]\displaystyle \int_0^2 \frac{\tan^{-1}(x)}{x^2-4x-1} \, dx[/tex]
We have the identity
[tex]\tan^{-1}(x) + \tan^{-1}\left(\dfrac{2-x}{1+2x}\right) = \tan^{-1}(2)[/tex]
so that
[tex]\displaystyle I + I = \int_0^2 \frac{\tan^{-1}\left(\frac{2-x}{1+2x}\right) + \tan^{-1}(x)}{x^2-4x-1} \, dx[/tex]
[tex]\implies \displaystyle I = \frac{\tan^{-1}(2)}2 \int_0^2 \frac{dx}{(x-2)^2-5}[/tex]
The remaining integral is trivial,
[tex]\displaystyle \int_0^2 \frac{dx}{(x-2)^2-5} = \int_{-2}^0 \frac{dx}{x^2-5} \\\\ ~~~~~~~~ = \frac1{2\sqrt5} \int_{-2}^0 \left(\frac1{x-\sqrt5} - \frac1{x+\sqrt5}\right) \, dx \\\\ ~~~~~~~~= -\frac{\ln(2+\sqrt5)}{2\sqrt5} \\\\ ~~~~~~~~ = -\frac1{\sqrt5} \tanh^{-1}\left(\dfrac2{\sqrt5}\right)[/tex]
Then the integral we want is
[tex]I = \displaystyle \int_0^2 \frac{\tan^{-1}\left(\frac{2-x}{1+2x}\right)}{x^2-4x-1} \, dx = \boxed{-\frac1{2\sqrt5} \tan^{-1}(2) \, \tanh^{-1}\left(\dfrac2{\sqrt5}\right)} \approx -0.357395[/tex]
Find y
please please please help
Answer: [tex]y=26^{\circ}[/tex]
Step-by-step explanation:
Using linear pairs, we can determine the two angles in the picture attached.
Thus, as angles in a triangle add to [tex]180^{\circ}[/tex], [tex]y=26^{\circ}[/tex]
Find the amount and compound interest on 1 (a) Rs. 16000 for 2+1/3 years at 15% per annum. 3
The amount and compound interest are Rs22169.11 and Rs6169.11 respectively
Compound interestThe formula for calculating the compound interest is expressed as:
P(t) = P0(1+r)^t
Substitute the given parameters
P(7/3) = 16000(1+0.15)^7/3
P(7/3) = 16000(1.15)^7/3
P(7/3) = 22169.11
For the interest
Interest = 22169.11 - 16000
Interest = 6169.11
Hence the amount and compound interest are Rs22169.11 and Rs6169.11 respectively
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100 POINTS!!! In one area, the lowest angle of elevation of the sun in winter is 21° Find the distance x that a plant needing full sun can be placed from a fence that is 10.5 feet high. Round your answer to the tenths place when necessary.
To find the length of the missing side x, use Tan trigonometric formula
Tan: [tex]\frac{opposite}{Adjacent}[/tex]
Tan 21 = [tex]\frac{10.5}{x}[/tex]
Tan 21 × [tex]\frac{1}{10.5}[/tex] = [tex]\frac{10.5}{x}[/tex]×[tex]\frac{1}{10.5}[/tex]
[tex]\frac{10.5}{Tan 21}=x[/tex]
x=27.4
X= 27.4 ft
Hope it helps!
Answer:
x = 27.4 ft
Step-by-step explanation:
Here given:
opposite side: 10.5 ftadjacent side: x ftto that angle: 21°So, use tan rule:
[tex]\sf tan(\theta) = \dfrac{opposite}{adjacent}[/tex]
insert values
[tex]\sf tan(21) = \dfrac{10.5}{x}[/tex]
make 'x' subject
[tex]\sf x= \dfrac{10.5}{tan(21) }[/tex]
calculate value
[tex]\sf x = 27.35343...[/tex]
rounded to nearest tenth
[tex]\sf x = 27.4 \ ft[/tex]
A line passes through the point (-3,4) and has a slope of -5. Find an equation of this line
Answer:
y = -5x - 11
Step-by-step explanation:
We are given that a line passes through the point (-3,4) and also has a slope of -5.
We want to write an equation of this line.
The equation of the line can be written in 3 different ways:
Slope-intercept form, which is written as y=mx+b, where m is the slope and b is the y intercept.Standard form, which is written as ax+by=c, where a, b, and c are free integer coefficients (but a and b cannot be 0, and a cannot be negative). Slope-point form, which is written as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope, and [tex](x_1, y_1)[/tex] is a pointSince the question did not specify, any of these 3 options will be valid, however, the most common way to write the equation of the line is in slope-intercept form, so let's do it that way.
Because we are already given the value of the slope, we can immediately plug that into the equation.
Replace m with -5.
y = -5x + b
Now we need to find b.
As the equation passes through the point (-3, 4), we can use its values to help solve for b.
Substitute -3 as x and 4 as y.
4 = -5(-3) + b
Multiply
4 = 15 + b
Subtract 15 from both sides.
-11 = b
Substitute -11 as b in the equation.
y = -5x - 11
Topic: finding the equation of the line
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Need help now due in 5 minutes pls help quick now pls pls pls pls pls
Answer: A and D
Step-by-step explanation:
- Career A's spread is more concentrated while Career B's spread is more dispersed or spread out
- Career A's median is 25 and Career B's median is 30
- Therefore A and D are the correct answers
hope this helps :)
Need the answer for number 3 please!!!
Answer:
Step-by-step explanation:
From a group of 6 men and 4 women, how many committees of 2 men and 3 women can be formed?
The number of ways committees of 2 men and 3 women can be formed is 60.
What is Permutation and Combination ?The method of arranging objects in order is called Permutation and the method of selecting things from a group of objects such that the order doesn't matter is called Combination.
Total Men = 6
Total Women = 4
Committee should consists of 2 men and 3 women
2 men from 6 men can be selected in [tex]\rm ^6 C _2[/tex] ways
3 women from 4 women can be selected in [tex]\rm ^4C_3[/tex] ways
The number of ways committees of 2 men and 3 women can be formed can be determined by Multiplication Principle
[tex]\rm ^6 C _2[/tex] * [tex]\rm ^4C_3[/tex]
15 * 4
= 60 ways
Therefore the number of ways committees of 2 men and 3 women can be formed is 60.
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A triangle has squares on its three sides as shown below. What is the value of x? 3 cm U x cm 4 cm 3 centimeters 4 centimeters 5 centimeters 07 centimeters A triangle has squares on its three sides as shown below . What is the value of x ? 3 cm U x cm 4 cm 3 centimeters 4 centimeters 5 centimeters 07 centimeters
The value of x is 10 centimeters
How to solve for x?The complete question is in the image
The value of x is calculated using the following Pythagoras theorem
x^2 = 6^2 + 8^2
Evaluate the sum of exponents
x^2 = 100
Take the square roots
x = 10
Hence, the value of x is 10 centimeters
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5. In a high school, 60% of the students live east of the school and 40% live west of the school. Among the students who live east of the school, 30% are in the math club, and among the students who live west of the school, 20% are in the math club. a. Find the probability that a randomly selected student is from east of the school and in the math club. b. Given that a student is from west of the school, what is the probability that he or she is in the math club? c. Is participation in the math club independent from whether a student lives east or west of the school? Justify your answer.
The probability for part (a) is 0.18, for part (b) is 0.08, and for part (c) is 0.26.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
a. Find the probability that a randomly selected student is from east of the school and in the math club:
P(east ∩ math club) = 0.6×0.3 = 0.18
b. Given that a student is from west of the school, what is the probability that he or she is in the math club?
P(west ∩ math club) = 0.4×0.2 = 0.08
c. Is participation in the math club independent of whether a student lives east or west of the school?
P(math club) = P(east ∩ math club) + P(west ∩ math club)
= 0.18 + 0.08
= 0.26
Thus, the probability for part (a) is 0.18, for part (b) is 0.08, and for part (c) is 0.26.
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The table shows all possible outcomes for rolling two sixed numbers cubes
The probability of rolling an even number first and an odd number second is 1/4.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability of rolling an even number first and an odd number second = (numbers that have the even number first and odd number second / total sample space)
9/36 = 1/4
Here is the complete question:
The table below shows all of the possible outcomes for rolling two six-sided number cubes. What is the probability of rolling an even number first and an odd number second?
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Why is it important to use the correct units of measurement when working with conversions? Explain by converting 5 feet into inches.
It is important to use the correct units of measurement when working with conversions because errors may occur. 5 feet = 60 inches.
What is conversion?Conversion means to convert the same thing into different units.
It is important to use the correct units of measurement when working with conversions because errors may occur.
1 foot = 12 inches
Then we have
5 feet = 60 inches
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The area of each circle is exactly
0.56π square inches.
There are 2 identical circles in the cylinder.
So the total area of all the circles is ??? π square inches.
Total area of the circle is 1.12π square inches.
What is Area of circle?The Area of circle is π times the square of the radius.
i.e., A = πr²
Given:
Area of one circle = 0.56π
As the second circle is also identical then the area will be same.
So, the total area of circle is
=2* 0.56π
=1.12π square inches.
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what is the strategy when figuring out the IQR and the 5-number summary for the data
The strategy when figuring out the IQR and the 5-number summary for the data include arrangement from lowest to highest.
What is 5-number summary?This is used to summarize distribution of data obtained or given in a sample and they include:
First quartile(Q1) valueMedianThird quartile(Q3) valueMinimumMaximum.Proper arrangement of the data ensures accuracy in the results/values thereby making the most appropriate choice.
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5. In 2011, Manitoba progressive income tax rates were 10.8% on the first $31,000, 12.75% on the next $36,000, anc
17.4% on any additional income. If your gross taxable earnings for the year were $85,000, what percentage of your
earnings did you pay in taxes?
Step-by-step explanation:
0 <= income <= 31000 : 10.8%
31000 < income <= 31000+36000 = 67000 : 12.75%
67000 < income < anything above 67000 : 17.4%
the total income is
$85,000
the taxes paid are
10.8% of 31000 = $3348
12.75% of 67000 - 31000 = 12.75% of 36000 = $4590
17.4% of 85000 - 67000 = 17.4% of 18000 = $3132
so, out of $85000 you paid
3348
4590
3132
----------
$11,070
taxes
100% = 85000
1% = 100%/100 = 85000/100 = 850
how many % are 11070 ?
well, as many as how often 1% fits into that amount :
11070 / 850 = 13.02352941...% ≈ 13.02%