Answers
Solution
Step 1:
A finite discontinuity exists when the two-sided limit does not exist, but the two one-sided limits are both finite, yet not equal to each other. The graph of a function having this feature will show a vertical gap between the two branches of the function.
Related Questions
For what value of k are the graphs of 8y = 12x + 6 and 4y = k(3x + 10)
parallel? perpendicular?
Answers
The value of k when the graphs are parallel = 2 and when the graphs are perpendicular = 36/32 or 1.125
What is the slope-intercept form?
the slope-intercept for of a line is, y=mx+c, where m is the slope.
we are given the two equations 8y = 12x + 6 and 4y = k(3x + 10)
PARALLEL CONDITION
if they are parallel, their slopes will be equal,
hence,
y=mx+c
where m is the slope
converting both the equations in the slope-intercept form
8y = 12x + 6
= y= 12x/8 + 3/4
and for equation
4y = k(3x + 10)
4y = k3x+ 10k
y = k 3x/4 + 10k/4
comparing the slopes
12/8 = k3/4
12 * 4 = 3k * 8
48 = 24k
k= 48/24
k = 2
therefore when both the lines are parallel, the value of k is 2.
PERPENDICULAR CONDITION
if the two lines are perpendicular the product of their slope will be 1
so,
12/8 * 3k/4 = 1
36k/32 =1
36k = 32
k = 32/36
or
k = 1.125
therefore when they both are perpendicular, the value of k is 1.125 or 36/32.
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This expression 12(1.0515)t models the population of elephants in a wildlife refuge after years since 1975 is the population of elephants increasing or decreasing?
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The function for an exponential growth/decay is given as follows;
[tex]f(x)=a(1+r)^x[/tex]Where,
[tex]\begin{gathered} x=\text{Number of years} \\ a=\text{initial value} \\ r=\text{rate of growth} \end{gathered}[/tex]Observe that from the equation provided, the rate is 1.015. This means there is a growth. If there was a decay(decrease), the rate would be less than 1 because, the formula then would be;
[tex]f(x)=a(1-r)^x[/tex]ANSWER:
Therefore, the population of elephants is INCREASING.
the perimeter of a rectangle room is 60 feet. let x be the width of the room (in feet) and let y be the length of the room (in feet). select all of the questions below that could modle this situation
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Given that,
The perimeter of a rectangle is 60.
The perimeter is generally defined as the length of the outline of the shape.
So, in rectangle having four sides, the perimeter would be sum of all the sides.
Length1 + length2 + length3 + length4 = perimeter
Here, length1 and length3 are equal, that are the lengths (y),
Similarly,
Length2 and length4 are equal, that is width (x).
Hence, the equation becomes,
x + y + x + y = perimeter
or
2x + 2y = 60
or
2 (x + y) = 60
Hence, the first two options are correct.
Using the translation that maps (3,-4) to its image (1,0), what is the image of any point (x,y)?A. (x+2,y+4)B. (x−2,y−4)C. (x+2,y−4)D. (x−2,y+4)
Answers
Explanation
Given (3,-4), its image (1,0) can be produced below;
[tex]\left(3,-4\right)\Rightarrow\left(x−2,y+4\right)\Rightarrow\left(1,0\right)[/tex]Answer: Option D
Solve x² + 6x + 7 = 0.x = -1 and x = -5 3+ √2-3+√2-3 ± √22
Answers
ANSWER
[tex]x=-3\pm\sqrt{2}[/tex]EXPLANATION
We want to solve for x in the equation:
[tex]x^2+6x+7=0[/tex]To do this, apply the quadratic formula:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]where a = 1, b = 6, c = 7
Therefore, substituting the values of a, b, and c into the formula and solve:
[tex]\begin{gathered} x=\frac{-6\pm\sqrt{6^2-4(1)(7)}}{2(1)}=\frac{-6\pm\sqrt{36-28}}{2} \\ \\ x=\frac{-6\pm\sqrt{8}}{2}=\frac{-6\pm2\sqrt{2}}{2} \\ \\ x=-3\pm\sqrt{2} \end{gathered}[/tex]That is the solution for x.
Part #1: Find the solution of the inequality.[tex]n - 6 \ \textgreater \ 10[/tex]Part #2: describe the solution
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so the solution is all the numbers that are greater than 16
Please help me name this figure, find the lateral surface area, and the total surface area. You can ignore the work I've done as it is incorrect.
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Answer:
• (,a)Triangular Prism
,• (b)Lateral Surface Area= 36 cm²
,• (c)Total Surface Area= 48 cm²
Explanation:
(a)The figure has a triangle as its uniform cross-section. Thus, it is a triangular prism.
(b)Lateral Surface Area
The lateral surface area is the area of the sides of the prism, i.e. excluding the uniform top and base.
The sides of the triangular prism consist of the three rectangles.
[tex]\begin{gathered} \text{Lateral Surface Area}=\text{Area of Rect. 1+Area of Rect. 2+Area of Rect. 3} \\ =(3\times4)+(3\times3)+(3\times5) \\ =12+9+15 \\ =36\;cm^2 \end{gathered}[/tex]The lateral surface area is 36 cm squared.
(c)Total Surface Area
To find the total surface area, add the area of the top and base to the lateral surface area.
The top and base are the two right-triangles with a base of 3 cm and a height of 4cm.
[tex]\begin{gathered} \text{ Total Surface Area=Lateral Surface Area+2\lparen Area of Triangles\rparen} \\ =36+2(\frac{1}{2}\times3\times4) \\ =36+12 \\ =48\;cm^2 \end{gathered}[/tex]The total surface area is 48 cm squared.
Members of the football team hold a fundraising dinner to raise money for their annual trip. They must sell tickets to the event at a price that will earn them more money than the cost of food.Here's a formula for this scenario:t = n (p - c)wheret = total profit made from the eventn = number of tickets soldp = price charged for each dinnerC = cost for food per plate The team hopes to sell 100 tickets. The cost for food per plate is $1.75 and they hope to charge $11.75 for each dinner. How much profit should they receive from the event?Enter the correct answer.
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t = n(p-c)
t=100(11.75 - 1.75)
t = 100(10)
t=$1000
total profit received = $1000
To which subsets of numbers does 1/3 belong?
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1/3 is a rational number, which written as a decimal is an infinite period decimal.
Solve: 9/14 + 2/6 = ?
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We have to solve the expression:
[tex]\frac{9}{14}+\frac{2}{6}[/tex]We have to find a common denominator for the fractions and then solve it.
We can start by simplifying the fractions that can be simplified, like 2/6.
[tex]\frac{9}{14}+\frac{2}{6}=\frac{9}{14}+\frac{1}{3}[/tex]Then, the common denominator between 14 and 3 is 14*3=42, so we end with:
[tex]\frac{9\cdot3}{14\cdot3}+\frac{1\cdot14}{3\cdot14}=\frac{27}{42}+\frac{14}{42}=\frac{27+14}{42}=\frac{41}{42}[/tex]Answer: 41/42
There are 396 students who are enrolled in an introductory engineering course. If there are four boys to every seven girls, how many boys are in the course?
Answers
Solution
For this case we know that the total of students are 396 so we can do this:
x + y = 396
Where:
x= number of girls
y = number of boys
Then we have the following condition:
4x = 7y
Then solving for x we got:
x = 7/4 y
Replacing in the first equation we got:
7/4 y + y = 396
11/4 y= 396
y= 396*4/11 = 144
And x= 7/4 * 144 = 252
Then the answer would be:
252 girls and 144 boys
scientific notation5.1x10⁶ x 2.3x10⁶
Answers
The given expression is
5.1 x 10^6 x 2.3 x 10^6
We would apply the law of exponents which is expressed as
a^b x a^c = a^(b + c)
By applying this, we have
5.1 x 2.3 x 10^6 x 10^6
= 11.73 x 10^(6 + 6)
= 11.73 x 10^12
What is the measure of the "Central Angle" for the 20% section?
Answers
The sum of all central angle is 360.
Determine 20% of 360 to obtain central angle for 20% section.
[tex]\begin{gathered} \frac{20}{100}\times360^{\circ}=36^{\circ}\cdot2 \\ =72^{\circ} \end{gathered}[/tex]So answer is 72 degrees.
1. if m∠6 =50° , then find m∠112. m∠2= 70°, then find m∠63. if m∠ 1=130°, then find m∠5
Answers
Answer:
1. m∠11=130°
2. m∠6= 70°
3. m∠5=130°
Explanation:
Part 1
Angles 6 and 11 are the same-side interior angles. We know that same side interior angles add up to 180 degrees, therefore:
m∠6+m∠11=180°
50°+m∠11=180°
m∠11=180°-50°
m∠11=130°
Part 2
Lines a and b are parallel lines. Therefore, angles 2 and 6 form a Z-Shape.
They are Alternate angles.
m∠2 = m∠6
Since m∠2= 70°
m∠6= 70°
Part 3
Angles 1 and 3 are Corresponding angles, this means that they are equal.
• m∠1=m∠3
Likewise, angles 3 and 5 form an X-shape, they are vertical angles and also equal.
• m∠5=m∠3
Combining the two, we have that:
m∠1=m∠3=m∠5
If m∠1=130°, then:
m∠5=130°
If a1 = 8 and an = 3an-1 then find the value of a4.
Answers
a_4= 216
1) Given that we have the first term and the Recursive Formula, let's find the fourth term of that Sequence
2) Let's find the second, the third to find the fourth since a Recursive formula depends on the prior term.
[tex]\begin{gathered} a_1=8 \\ a_n=3a_{n-1} \\ a_2=3(8)\text{ =24} \\ a_3=3(24)=72 \\ a_4=3(72)\text{ =216} \end{gathered}[/tex]3) Hence, the sequence is 8, 24, 72, 216 and the fourth term is 216
Every surface of the block shown will be painted, except for one of the bases. How many square units will be painted? 3.2 cm 3.2 cm 3.2 cm
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As given that the every surface of the block shown will be painted, except for one of the bases.
And a block have 6 surface but one is not painted so there are 5 surface that are painted so:
The area of the painted surface is:
[tex]A=5a^2[/tex]Where a is 3.2 cm
[tex]\begin{gathered} A=5(3.2)^2 \\ A=5\times10.24 \\ A=51.2cm^2 \end{gathered}[/tex]The area of painted surface is 51.2 square cm
This is a maze where you find the answer starting from where it says start, and as you find the answer you highlight it along the way! Pls help I’m really bad at this
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The start figure has two chords in the circle.
By theorem of internal division of chords it follows:
[tex]\begin{gathered} 21x=18\times14 \\ x=\frac{18\times14}{21} \\ x=12 \end{gathered}[/tex]Hence the value of x is 12.
A girl has scored 72, 76, 74, and 75 on her algebra tests.a. Use an inequality to find the score she must make on the final test to pass the course with an average of 78 or higher, given that the final exam counts three testsb. Explain the meaning of the answer to part (a)
Answers
Part A.
We know that the final exam counts 3 test. Let x be the score of this final exam, then we can write,
[tex]\frac{72+76+74+75+3\times x}{7}\ge78[/tex]the denominator is 7 because there are 7 scores: 72,76,74,75 and 3 times x (which is the final test). This average must be greater or equal to 78 in order to pass the course.
Then, by adding the numerator terms we get,
[tex]\frac{297+3\times x}{7}\ge78[/tex]and by moving 7 to the right hand side, we have
[tex]\begin{gathered} 297+3x\ge78\times7 \\ or\text{ equivalently} \\ 297+3x\ge546 \end{gathered}[/tex]by moving 297 to the right hand side, we obtain
[tex]\begin{gathered} 3x\ge546-297 \\ 3x\ge249 \end{gathered}[/tex]then, the score of the final exam must be
[tex]\begin{gathered} x\ge\frac{249}{3} \\ x\ge83 \end{gathered}[/tex]that is, at least greater or equal to 83.
Part B.
The last result means that our girls must obtain at least 83 points in the final test in order to pass Algebra.
Use the system of equations below to solve for z.7x+3y+2z-4w=184w+5x-3y-2z=6-2w-3x+y+z=-52z+3w+4y-8x=11253
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Equations:
[tex]\begin{gathered} 7x+3y+2z-4w=18\text{ \lparen1\rparen} \\ 5x-3y-2z+4w=6\text{ \lparen2\rparen} \\ -3x+y+z-2w=-5\text{ \lparen3\rparen} \\ -8x+4y+2z+3w=11\text{ \lparen4\rparen} \end{gathered}[/tex]Sum (1)+ (2):
[tex]\begin{gathered} 7x+3y+2z-4w=18\text{ }\operatorname{\lparen}\text{1}\operatorname{\rparen} \\ + \\ 5x-3y-2z+4w=6\text{ }\operatorname{\lparen}\text{2}\operatorname{\rparen} \\ 5x+7x+3y-3y+2z-2z-4w+4w=18+6 \\ 12x=24 \\ x=\frac{24}{12}=2 \end{gathered}[/tex]x=2
Now, we are going to sum (3)*2+(2).
[tex]\begin{gathered} 5x-3y-2z+4w=6\text{ }\operatorname{\lparen}\text{2}\operatorname{\rparen} \\ + \\ 2*(-3x+y+z-2w)=-5*2\text{ }\operatorname{\lparen}\text{3}\operatorname{\rparen} \\ 5x-6x-3y+2y-2z+2z+4w-4w=6-10 \\ -x-y=-4 \\ -2-y=-4 \\ y=-2+4=2 \end{gathered}[/tex]y=2.
Replacing y and x in (4) and (3):
[tex]\begin{gathered} -3(2)+2+z-2w=-5\text{ }\operatorname{\lparen}\text{3}\operatorname{\rparen} \\ -8(2)+4(2)+2z+3w=11\text{ }\operatorname{\lparen}\text{4}\operatorname{\rparen} \end{gathered}[/tex][tex]\begin{gathered} -6+2+z-2w=-5 \\ z-2w=-5+6-2 \\ z-2w=-1\text{ \lparen5\rparen} \end{gathered}[/tex][tex]\begin{gathered} -16+8+2z+3w=11 \\ 2z+3w=11+16-8 \\ 2z+3w=19\text{ \lparen6\rparen} \end{gathered}[/tex]Isolating w in (5) ans replacing in (6):
[tex]\begin{gathered} 2w=-1-z \\ w=\frac{-1-z}{2} \end{gathered}[/tex][tex]\begin{gathered} 2z+3(\frac{-1-z}{2})=19 \\ \frac{4z-3-3z}{2}=19 \\ z-3=19*2 \\ z=38-3=35 \end{gathered}[/tex]Answer: z=35.
Zappo’s has marked down rain boots 25% during its spring sale. What is the sale price of a pair of boots with a regular price of $149.99?
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Substract the 25% of the price to the regular price:
1. Find the 25% of the price: Multiply by 0.25 the price:
[tex]149,99\cdot0.25\approx37.50[/tex]2. Substract the result in step 1 (amount marked down) from the regular price:
[tex]149,99-37,50=112.49[/tex]Then, the sale price of the pair of boots is $112.49miguel saves the same amount of money into a bank account each week. the bank account started with some money in it. after 3 weeks, the bank account contained $250. after 10 weeks the bank account contained $600.write an equation that cqn be used to model tbe number of dollars, y,iguel saves in x weeks.exain what slope and y intercept of youre equation mean in the context of the aituation.enter your equation and your explanations in tbe space provided.
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Answer:
An equation that can be used to model the number of dollars, y, Miguel saves in x weeks is;
[tex]y=50x+100[/tex]The slope of the equation in the context is the amount of money Miguel saves in the bank account each week. So, Miguel saves $50 each week.
The y-intercept of the equation in the context is the amount of money Miguel initially have in the bank account. So, the initial amount of money in the bank account is $100.
Explanation:
Given that Miguel saves the same amount of money into a bank account each week.
Let y represent the amount of money in the account after x weeks;
[tex]y=mx+b[/tex]After 3 weeks, the bank account contained $250;
[tex]\begin{gathered} 250=m(3)+b \\ 3m+b=250 \end{gathered}[/tex]After 10 weeks the bank account contained $600;
[tex]\begin{gathered} 600=m(10)+b \\ 10m+b=600 \end{gathered}[/tex]Solving for m and b;
subtract the first equation from the second.
[tex]\begin{gathered} 10m-3m+b-b=600-250 \\ 7m=350 \\ m=\frac{350}{7} \\ m=50 \end{gathered}[/tex]substituting the value of m into the first equation;
[tex]\begin{gathered} 3m+b=250 \\ 3(50)+b=250 \\ 150+b=250 \\ b=250-150 \\ b=100 \end{gathered}[/tex]Therefore, an equation that can be used to model the number of dollars, y, Miguel saves in x weeks is;
[tex]y=50x+100[/tex]From the equation above, the slope m of the equation is;
[tex]m=50[/tex]and the y-intercept b of the equation is;
[tex]b=100[/tex]The slope of the equation in the context is the amount of money Miguel saves in the bank account each week. So, Miguel saves $50 each week.
The y-intercept of the equation in the context is the amount of money Miguel initially have in the bank account. So, the initial amount of money in the bank account is $100.
The blank of a line is the x-coordinate of the point where the line crosses the x-axis. It occurs when y = 0.
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Answer
The x-intercept of a line is the x-coordinate of the point where the line crosses the x-axis. It occurs when y = 0.
Hope this Helps!!!
Select the correct answer.6cis5pi/6Convert57to rectangular form.OA. 3V3 + 31O B. –313 + 3iO C. 373 – 3iOD. -3V3 – 31O E. 3 – 3731
Answers
Answer:
Choice B.
Explanation:
The equation can be rewritten as
[tex]6\text{cis}\frac{5\pi}{6}=6\cos \frac{5\pi}{6}+i\sin \frac{5\pi}{6}[/tex]Now since
[tex]6\cos \frac{5\pi}{6}=-3\sqrt[]{3}[/tex]and
[tex]6\sin \frac{5\pi}{6}=3[/tex]the expression becomes
[tex]-3\sqrt[]{3}+3i[/tex]Hence, choice B is the correct answer since it matches the answer we got above.
5. An expression is shown. 78 - 14 Between which two consecutive whole numbers does this value lie? Enter your numbers in the box. Between and
Answers
78 divide by 14
First, divide the numbers
78/14 = 5.57
5.57 lies between 5 and 6
1.At 8:30am, Student Life had served 37 meals at their pancake breakfast. By 10:15am, thetotal served had reached 77. Find the serving rate, in number of meals per minute. Keep youranswer as a reduced fraction.
Answers
We have to estimate a serving rate, with units of "number of meals per minute".
To solve this we have to calculate how many meals have been served in a certain time frame, and estimate a mean service rate.
The time interval we are taking is from 8:30 am to 10:15 am. That is 30 minutes to 9 am, plus 60 minutes to 10 am, plus 15 minutes to 10:15 am.
This is a total of 30+60+15=105 minutes.
The total served at 10:15 am is 77 meals. If we substract the meals that have been already served by 8:30 am, we get that in our time interval 77-37=40 meals have been served.
So we can calculate the serving rate as:
[tex]s=\frac{\text{ \#meals}}{\text{time}}=\frac{40\text{ meals}}{105\text{ min}}=\frac{8}{21}\text{ meals/min}[/tex]The serving rate, expressed as a reduced fraction (we divide both numerator and denominator by 5), is 8/21 meals per minute.
The weekly revenue for a product is given by R(x)=307.8x−0.045x2, and the weekly cost is C(x)=10,000+153.9x−0.09x2+0.00003x3, where x is the number of units produced and sold.(a) How many units will give the maximum profit?(b) What is the maximum possible profit?
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Answer:
The number of units that will give the maximum profit is;
[tex]1900\text{ units}[/tex]The maximum possible profit is;
[tex]\text{ \$}239,090[/tex]Explanation:
Given that the weekly revenue for a product is given by ;
[tex]R(x)=307.8x-0.045x^2[/tex]and the weekly cost is ;
[tex]C(x)=10,000+153.9x-0.09x^2+0.00003x^3[/tex]Recall that
Profit = Revenue - Cost
[tex]P(x)=R(x)-C(x)[/tex][tex]\begin{gathered} P(x)=307.8x-0.045x^2-(10,000+153.9x-0.09x^2+0.00003x^3) \\ P(x)=307.8x-0.045x^2-10,000-153.9x+0.09x^2-0.00003x^3 \\ P(x)=153.9x+0.045x^2-0.00003x^3-10,000 \end{gathered}[/tex]Using graph to derive the maximum point on the function;
Therefore, the maximum point is at the point;
[tex](1900,239090)[/tex]So;
The number of units that will give the maximum profit is;
[tex]1900\text{ units}[/tex]The maximum possible profit is;
[tex]\text{ \$}239,090[/tex]A product initially with a value of $21,800 has been depreciating at 8.1% p.a over 8 years. What is it's current value?
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we get that:
[tex]v=21800\cdot(0.919)^8=11091.25[/tex]its current value is $11091.25
Examine the following graph of the system of inequalities y≤x2−4x−3 and y<−2x+4. A is the area below the line and the parabola. B is the area below the line but above the parabola. C is the area above the line and the parabola. D is the area below the parabola but above the line.© 2018 StrongMind. Created using GeoGebra. Which section of the graph represents the solution set to the system of inequalities?
Answers
The solution set to a system of inequalities represents the area that contains points that satisfy both inequalities.
The best way to answer the question is to choose one point from each area and check if they satisfy both.
Let's start by selecting a point in area A. Let's use (-6, 0).
[tex]\begin{gathered} 0\leq(-6)^2-4(-6)-3 \\ 0\leq36+24-3 \\ 0\leq57\text{ TRUE} \\ \\ 0<-2(-6)+4 \\ 0<12+4 \\ 0<16\text{ TRUE} \end{gathered}[/tex]Because out test point (-6, 0) satisfies both inequalities, then the entire area that contains it is the solution. We no longer have to test other points.
The answer is A.
The solution set is also the intersection of the graphs of the two inequalities. So you may refer to the shaded regions and you'll see that area A is shaded red and blue at the same time.
Rosa sells cosmetics. She is paid a commission of 3.16% of her first 1500 in sales during the week and 11% on all sales over 1500. What is her commission in a week during which she sells 2137.38 worth of cosmetics? Express your answer as a dollar amount and round to the nearest cent
Answers
ANSWER:
$ 117.51
STEP-BY-STEP EXPLANATION:
The commissions are divided into two payments, the first payment of the first $ 1500 with a commission of 3.16% and a second payment with a commission of 11% of all the remaining money of the first $ 1500.
Therefore, we calculate it as follows:
[tex]\begin{gathered} p_T=p_1+p_2 \\ p_1=1500\cdot\frac{3.16}{100}=47.4 \\ p_2=(2137.38-1500)\cdot\frac{11}{100}=637.38\cdot0.11=70.11 \\ p_T=47.4+70.11 \\ p_T=117.51 \end{gathered}[/tex]The total commission is $ 117.51
What is the radius of a circle whose circumference is 36pi?
Answers
The circumference of a circle of radius r is given by:
[tex]C=2\pi r[/tex]For this question we simply need to take C=36π and solve for r:
[tex]36\pi=2\pi r[/tex]If we divide both sides by 2π we get:
[tex]\begin{gathered} 36\pi=2\pi r \\ \frac{36\pi}{2\pi}=\frac{2\pi r}{2\pi}=\frac{2\pi}{2\pi}\cdot r \\ 18=r \end{gathered}[/tex]Then the answer is option A, 18.