Convert from rectangular to polar coordinates (0,-1) (Give your answer in the form *) Express numbers in exact form: Use symbolic notation and fractions where needed )
(r,0) = (14-1)
Incorrect
(b) (3,V3) (Give your answer in the form (*, *) Express numbers in exact
form. Use symbolic notation and fractions where needed )
0)
Incorrect
(c) (2,-2) (Give your answer in the form '*) Express numbers in exact form: Use symbolic notation and fractions where needed )
(r,0)
Incorrect
(-1,V3)
(Give your answer in the form
Express numbers in exact form. Use symbolic notation and fractions where
needed )
Answers
The polar coordinates are (2, -\(\pi\)/3).
(a) For the point (0,-1), we have:
r = \(\sqrt{(x^2 + y^2)}\) = \(\sqrt{(0^2 + (-1)^2)}\) = 1
theta = arctan(y/x) = arctan(-1/0) = -\(\pi\)/2 (Note that x = 0, so we can't use arctan(y/x) directly. Instead, we use the fact that the point lies on the negative y-axis, so the angle is -\(\pi\)/2.)
Therefore, the polar coordinates are (1, -pi/2).
(b) For the point (3, \(\sqrt{(3)}\)), we have:
r = \(\sqrt{(x^2 + y^2)}\) = \(\sqrt{(3^2 + (\sqrt{(3)} )^2)}\) = 2\(\sqrt{(3)}\)
theta = arctan(y/x) = \(arctan(\sqrt{3)/3} )\)
Therefore, the polar coordinates are (2sqrt(3), arctan(sqrt(3)/3)).
(c) For point (2,-2), we have:
\(r = \sqrt{(x^2 + y^2)} = \sqrt{(2^2 + (-2)^2) } = 2\sqrt{(2)}\)
theta = arctan(y/x) = arctan(-2/2) = -\(\pi\)/4 (Note that x and y have opposite signs, so the angle is in the third quadrant.)
Therefore, the polar coordinates are (2\(\sqrt{(2)}\), -\(\pi\)/4).
(d) For the point (-1, \(\sqrt{(3)}\)), we have:
\(r = \sqrt{(x^2 + y^2)} = \sqrt{((-1)^2} + (\sqrt{(3))^2} ) = 2\)
theta = arctan(y/x) = arctan\(\sqrt{3}\)/-1) = -\(\pi\)/3 (Note that x and y have opposite signs, so the angle is in the fourth quadrant.)
Therefore, the polar coordinates are (2, -\(\pi\)/3).
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Related Questions
Show by base step and induction step, that will every triangle free planar graph will have 4 colorable? and give the example.
Answers
This theorem can also be verified using a computer. For example, if you look at the octahedral graph, which is a graph of the faces of a cube, you will see that it is a triangle-free planar graph that can be colored using four colors.
Base step: A graph without vertices can be colored with zero colors, which means it is 4-colorable.
Induction step: For a graph with n vertices, suppose that every planar graph with fewer than n vertices is 4-colorable. Remove a vertex v and all edges that are attached to it from the graph.
By induction hypothesis, the resulting planar graph can be colored using four colors. We'll now return v to the graph and think about the edges that we removed.
Since there is no triangle in the graph, any edge can be included between v and the remaining vertices, including the case where there are no edges from v.
This produces a graph with at most n-1 vertices, each of which is colored with one of four colors, and the neighboring vertices of v cannot both be colored with the same color.
This implies that there is at least one of the four colors that can be used to color v without any color problems occurring, completing the induction process. As a result, every triangle-free planar graph can be 4-colorable.
This theorem states that every planar graph without triangles can be 4-colored. The theorem is true, and the induction technique can be used to prove it.
This theorem can also be verified using a computer. For example, if you look at the octahedral graph, which is a graph of the faces of a cube, you will see that it is a triangle-free planar graph that can be colored using four colors.
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an individual has been driving a passenger vehicle to work, averaging 60 miles a week in a car that averages 22 miles per gallon. the individual plans to purchase a hybrid vehicle that averages 50 miles per gallon. if the individual drives to work 50 weeks a year, how much gas will they save if they switch to a hybrid vehicle for their commute? responses 28 gallons 28 gallons
Answers
If the individual drives to work 50 weeks a year, 76.36 gallons of gas would have been saved if they switch to a hybrid vehicle for their commute.
Assuming that the individual's work commute stays the same, driving an average of 60 miles per week for 50 weeks per year would mean that the individual drives a total of 3,000 miles per year to work.
If the individual switches from their current car, which averages 22 miles per gallon, to a hybrid vehicle that averages 50 miles per gallon, the individual would need (3,000 miles / 22 miles per gallon) = 136.36 gallons of gas for their current car per year.
However, if they switch to a hybrid vehicle that averages 50 miles per gallon, the individual would need (3,000 miles / 50 miles per gallon) = 60 gallons of gas for their new car per year.
Therefore, the individual would save (136.36 gallons - 60 gallons) = 76.36 gallons of gas per year by switching to a hybrid vehicle.
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answer all questions 9-13!!!!
Answers
Answer:
9) 3.7 in
10) 12 in²
11) 18 in³
12) V=432π cm³
TSA= 216π cm²
13)V=448π ft³
TSA=240π ft²
Step-by-step explanation:
9) Since all side of the trapezium are the same the height = perpendicular line which is 3.7 in
10) 3×4 (the quadrilateral at the bottom)
11)∵ A= Cross-sectional area× height
⇒A= Area of the trapezium × 4
∴ A=\(\frac{1}{2} \\\) (sum of the parallel sides) × 4
A=\(\frac{1}{2} \\\) (3+6) × 4
A= 18 in²
12) V=πr²h
V=π(6)²(12)
⇒V=432 cm³
TSA=2(πr²)+2πrh
TSA=2(π(6)²)+2π(6)(12)
⇒TSA=240π cm²
13. V=πr²h
V=π(8)²(7)
V=448π ft³
TSA=2(πr²)+2πrh
TSA=2(π(8)²)+2π(8)(7)
TSA=240π ft²
9) 3.7 in
10) 12 in²
11) 18 in³
12) V=432π cm³
TSA= 216π cm²
13)V=448π ft³
TSA=240π ft²
Let A={a,b,c} and B={a,b,d}. (a) List or draw the ordered pairs in A×A. (b) List or draw the ordered pairs in A×B. (c) List or draw the set {(x,y)∈A×B:x=y}.
Previous question
Answers
a. The ordered pairs in A×A, where A is the set {a, b, c}, can be listed as {(a, a), (a, b), (a, c), (b, a), (b, b), (b, c), (c, a), (c, b), (c, c)}.
b. The ordered pairs in A×B, where A is the set {a, b, c} and B is the set {a, b, d}, can be listed as {(a, a), (a, b), (a, d), (b, a), (b, b), (b, d), (c, a), (c, b), (c, d)}.
c. The set {(x, y) ∈ A×B: x = y} consists of the ordered pairs where the elements of A and B are the same, i.e., {(a, a), (b, b)}.
a. To find the ordered pairs in A×A, we take each element in set A and pair it with every other element in set A. In this case, A = {a, b, c}, so the resulting ordered pairs are {(a, a), (a, b), (a, c), (b, a), (b, b), (b, c), (c, a), (c, b), (c, c)}.
b. To find the ordered pairs in A×B, we take each element in set A and pair it with every element in set B. In this case, A = {a, b, c} and B = {a, b, d}, so the resulting ordered pairs are {(a, a), (a, b), (a, d), (b, a), (b, b), (b, d), (c, a), (c, b), (c, d)}.
c. The set {(x, y) ∈ A×B: x = y} consists of the ordered pairs where the elements of A and B are the same. In this case, the elements of A and B that are the same are 'a' and 'b'. Therefore, the set {(x, y) ∈ A×B: x = y} contains the ordered pairs {(a, a), (b, b)}.
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If you go on both rides, can you be confident that your wait time for Speed Slide will be longer than your wait time for Wave Machine? Yes. Every Speed Slide wait time is more than every Wave Machine wait time. No. There is a lot of overlap in the two data sets.
Answers
Answer:
No
Step-by-step explanation:
Hope this helps :)
Find the measure of the combined angle
Answers
Answer: 71°
Step-by-step explanation:
To find the measure of the combined angle, we will add the two parts of it together;
44° + 27° = 71°
Answer:
71
Step-by-step explanation:
الاجابه هي 71 فقط لاغير
Solve the following expression when
a = 4 and c = 3
4a + 12 – 2c + c
Order of operation
Answers
Answer:
19
Step-by-step explanation:
4×4= 16+12= 28
2×3= 6+3= 9
28-9= 19
28 - 9 = 19
△ABC∼△EFG.
Given m∠A=39° and m∠F=56°, what is m∠C?
Answers
Answer:
x=85
Step-by-step explanation:
let's angle c be x
39+56+x=180
95+x=180
x=180-95
x=85
Answer:
85 degrees
Step-by-step explanation:
In similar triangles, corresponding angles are congruent, or have the same measure.
Therefore, angle B must also be 56 degrees. In a triangle, there are 180 degrees.
A+b+c=180
39+56+c=180
c=85 degrees.
Find the factored form of x2 + 11x + 30.
» (x+6)(x-5)
» (x+6)(x+5)
» (x+10)(x+3)
» (x-10)(x-3)
irrelevant deleted
Answers
Answer:
2nd option
Step-by-step explanation:
x² + 11x + 30
Consider the factors of the constant term (+ 30) which sum to give the coefficient of the x- term (+ 11)
The factors are + 6 and + 5 , since
6 × 5 = 30 and 6 + 5 = 11 , then
x² + 11x + 30 = (x + 6)(x + 5) ← in factored form
Answer:
(x+6)(x+5)
because the sum of 6+5 is 11x
and the multiplication of 6·5 is 30
In which expression should the following exponents be multiplied?
2^9/2^7
Answers
A would be subtracting the exponents, while C & D are adding exponents
Find the radius of a circle which has a sector area of 9 pi whose central angle is 90 degrees.
Answers
Answer:360/90 = 4
Total area = 4 times that of the sector.
Step-by-step explanation:
A 90 deg sector has 1/4 the area of the circle.
Total circle area = 4*9pi = 36pi
Answer:
The area is A= 3/2π
Step-by-step explanation:
The area of whole circle is:
A
c
=
π
×
r
2
=
9
π
The central angle
60
o
is
1
6
of a full angle, so the area of the sector is:
A
s
=
1
6
A
c
=
1
6
×
9
π
=
9
6
π
=
3
2
π
What is the equation of the given line in standard form? use integer coefficients. y=-1.7x 8.5
Answers
The given equation, y = -1.7x + 8.5, is not in standard form with integer coefficients. The standard form of a linear equation is Ax + By = C, where A, B, and C are integers and A is positive.
To convert the given equation to standard form, we need to eliminate the decimal coefficient. We can do this by multiplying both sides of the equation by 10 to clear the decimal: 10y = -17x + 85 Next, we want the coefficient of x to be positive, so we can multiply both sides of the equation by -1: -10y = 17x - 85
Now, we can rearrange the terms to match the standard form: 17x - 10y = 85 So, the equation of the given line in standard form with integer coefficients is 17x - 10y = 85. To convert the given equation to standard form, we need to eliminate the decimal coefficient.
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Suppose that 25% of adults exercise regularly. If 11 adults randomly selected, what is the probability that four or less exercise regularly
Answers
The probability that four or less adults exercise regularly out of 11 randomly selected adults is approximately 0.9824.
This problem can be solved using the binomial distribution, since we are interested in the probability of a certain number of successes (adults who exercise regularly) in a fixed number of trials (selecting 11 adults randomly).
Let X be the number of adults who exercise regularly out of 11. Then X has a binomial distribution with parameters n = 11 and p = 0.25, since the probability of success (an adult who exercises regularly) is 0.25.
We want to find the probability that four or less adults exercise regularly, which is equivalent to finding the probability of X ≤ 4. We can use the binomial cumulative distribution function to calculate this probability:
P(X ≤ 4) = Σ P(X = k), for k = 0, 1, 2, 3, 4
Using a calculator, spreadsheet software, or a binomial probability table, we can find the probabilities for each value of k, and then add them up to get the cumulative probability:
P(X = 0) = (11 choose 0) * (0.25)^0 * (0.75)^11 = 0.0563
P(X = 1) = (11 choose 1) * (0.25)^1 * (0.75)^10 = 0.2015
P(X = 2) = (11 choose 2) * (0.25)^2 * (0.75)^9 = 0.3159
P(X = 3) = (11 choose 3) * (0.25)^3 * (0.75)^8 = 0.2747
P(X = 4) = (11 choose 4) * (0.25)^4 * (0.75)^7 = 0.1340
P(X ≤ 4) = 0.0563 + 0.2015 + 0.3159 + 0.2747 + 0.1340 = 0.9824
Therefore, the probability that four or less adults exercise regularly out of 11 randomly selected adults is approximately 0.9824.
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A patio is in the shape of a square, with a lengh of 35 feet. You wish to draw a black line down one diagonal.
a. Use the Pythagorean Theorem to find the lengh of the diagonal. Write your answer as a square root.
b. Find the two perfect squares that the lenght of the diagonal falls between.
c. Estimate the lenght of the diagonal to the nearest tenth.
Answers
Answer:
a) 35√2
b) between 25 and 36 (5² and 6²)
c) 49.5 ft
label the slope and y intercept
Answers
Slope is 3/2
Let P be some predicate. Check the box next to each scenario in which ∀n ∈ N, P(n) must be true.
a) For every natural number k > 0 , if P(i) holds for every natural number i < k, then P(k) holds.
b) P(0) holds and for every natural number k > 0, if P(i) does not hold, then there is some natural number i < k such that P(i) does not hold.
c) For every natural number k, if P(i) holds for every natural number i < k, then P(k) holds.
d) For every natural number k, if P(k) does not hold, then there is a smaller natural number i < k such that P(i) does not hold.
Answers
Answer:
A
Step-by-step explanation:
a) ✔️
This is the principle of mathematical induction. If P holds for the base case k=1 and we can show that if it holds for any arbitrary k (e.g. k=n) then it must also hold for the next value (e.g. k=n+1), then we have shown it holds for all natural numbers.
b) ❌
There is no guarantee that P holds for all natural numbers from the statement alone. It only guarantees that for any k where P does not hold, there exists a smaller number i where P does not hold.
c) ❌
This is the principle of weak mathematical induction. It only shows that if P holds for a given k and for all smaller values i then it must hold for k+1. It does not guarantee that P holds for all natural numbers.
d) ❌
This statement is the negation of the principle of mathematical induction. It is known as the "strong induction" principle, which assumes that if P does not hold for k, then there exists a smaller i where P does not hold. However, this principle is not sufficient to prove that P holds for all natural numbers k.
for this lesson, you will come up with your own challenging algorithm for other students to trace. it must contain at least 4 if statements, 1 else statement and use at least one and or or boolean condition. note: elif statements will not count - your statements must be if statements. each if statement should use a unique variable name. for this challenge, try reading 3 or 4 of your classmates' code as well. trace their code and predict what it will output, then check the code by running it to see if you got it right, and submit your work for a grade.
Answers
By using Python, you will come up with your own challenging algorithm for other students to trace.
What are If else Statements ?If a certain is true, the if/else expression triggers a sequence of instructions to run. Another piece of code may be run if the condition is false.
The if/else statement is a component of Python's "Conditional" Statements, which are used to carry out various operations based on various circumstances.
These conditional statements are available in Python:
If you want a block of code to run only if a certain condition is true, use the if statement.
If the same expression is false, use instead that to provide a set of instructions that should be run.
If the first expression is false, can use else if sentence to establish a comprehensive criterion to test.
To choose which of the several program code should be performed, use the switch.
How to write the code?
num = 100
if num < 20:
print('Less than 20')
if num < 30:
print('Less than 30')
if num < 40:
print('Less than 40')
if num < 50:
print('Less than 50')
if num > 100 or num == 100:
print('More than or equal to 100')
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Help me solve this problem please
Answers
Answer:
C. 16
Step-by-step explanation:
y^2-z^2
(-5)^2-(-3)^2
25-9
16
Answer:
Step-by-step explanation:
y = - 5
y^2 = (-5)^2
y^2 = 25
z = - 3
z^2 = (-3)^2
z^2 = 9
y^2 - z^2 = 25 - 9 = 16
Can someone please help me with this???
1.
Part A: If (26)x = 1, what is the value of x? Explain your answer. (5 points)
Part B: If (50)x = 1, what are the possible values of x? Explain your answer. (5 points)
Answers
Part A:
(26)x = 1
Solve for x by dividing both sides by 26:
X = 1/26
part B:
(50)x = 1
Solve for x by dividing both sides by 50:
X = 1/50
\(\\ \rm\Rrightarrow 26x=1\)
\(\\ \rm\Rrightarrow x=1/26\)
#B
\(\\ \rm\Rrightarrow 50x=1\)
\(\\ \rm\Rrightarrow x=1/50=0.02\)
Write an equation in slope-intercept form of the line that passes through (-1, 4) and (0,2).
y =
Answers
Answer:
y =( -1/2 )x + 2
Step-by-step explanation:
first step is to determine the slope of the line ( which is the rise over the run) or symbolically slope is defined as m= ∆x / ∆y, so plugging those values we get...
m= ∆x / ∆y = (-1 - 0) / (4 - 2) = -1 / 2
so next is to find the zero( y-intercept) of the function by ....
y = mx + b
y = ( -1/2)x + b (since m is equal to -1/2)
2 = ( -1/2)0 + b
2= b
solve the system of simultaneos equations using substitution method. 2/x-3/x=1 equation one 1/x-2/y= 2. equation two
Answers
Answer:
First solve the first one
2/x -3/x = 1
Multiply through by x
2/x×x -3/x×x = x
You will get
2 - 3 = x
x = - 1
Substitute x into the second Equation
1/x - 2/y = 2
x = 1
1/1 -2/y = 2
-2/y = 2-1
-2/y = 1
y = -2
Therefore x = - 1 and y = - 2
Hope this helps.
Sheila collect pokemon card. A of 2018, he ha a Mewtwo card that i twice a old a her Snorlax card. Two year ago, her rare Raichu card wa five time a old a the Snorlax card. If the Raichu card i even year older than the Mewtwo card in what year wa the Raichu card made?
Answers
The Raichu card was made 8 years ago.
To calculate this, we need to take into account the age of the Mewtwo card, the Snorlax card, and the Raichu card.
The Mewtwo card is twice as old as the Snorlax card, so the Mewtwo card is two years old. The Raichu card is five times as old as the Snorlax card, so it must be ten years old.
Since the Raichu card is two years older than the Mewtwo card, it must be eight years old. Therefore, the Raichu card was made eight years ago.
To summarise, the Mewtwo card is two years old, the Snorlax card is one year old, and the Raichu card is ten years old. Therefore, the Raichu card was made eight years ago.
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Worth 60 points for a rapid reply- find the area of each regular polygon. Answers are rounded to the nearest whole number.
Answers
The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.
How to calculate for the area of the polygonArea of regular polygon = 1/2 × apothem × perimeter
perimeter = (s)side length of octagon × (n)number of side.
apothem = s/[2tan(180/n)].
11 = s/[2tan(180/12)]
s = 11 × 2tan15
s = 5.8949
perimeter = 5.8949 × 12 = 70.7388
Area of dodecagon = 1/2 × 11 × 70.7388
Area of dodecagon = 389.0634 in²
Area of pentagon = 1/2 × 5.23 × 7.6
Area of pentagon = 19.874 in²
Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.
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In a survey, a group of students were asked their favorite sport. Eighteen students chose “other” sports.
Answers
Answer:
22.5% Hope this helps
Step-by-step explanation:
Answer:
22.5%
Step-by-step explanation:
a study of 1000 randomly selected flights of a major airline showed that 769 of the flights arrived on time. what is the probability of a flight will not arrive on time?
Answers
The probability of a flight will not arrive on time is 231/1000
What is probability?Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.
Probability requested is equivalent to:
Flights arrive on time= 769
Total flights = 1000
P(arrive on time) = Flights arrive on time / Total flights
P(arrive on time) = 769/1000
P (not arrive on time) = 1 - 769/1000
P (not arrive on time) = (1000 - 769)/1000
P (not arrive on time) = 231/1000
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MIGHT GIVE BRAINLIEST.
Calculator What is the surface area of the square pyramid?
Answers
Answer:
I need to know the dimensions to solve
need answer plz help Which function is equivalent to y=2(x+5)2−7?
y = 2x² + 20x + 43
y = 2x² + 10x + 13
y = 2x² + 18
y = 2x² + 20x + 36
Answers
Answer:
y = 2x^2 +20x + 43
Step-by-step explanation:
simplify e equation to:
y= 2(x^2 + 5x + 5x + 25) -7
y 2x^2 + 20x +50 - 7
y = 2x^2 +20x +43
convert the following decimals to an equivalent fraction: 0.666= [answer1] 0.1875 = [answer2] 0.240 = [answer3] 1.75 = [answer4] 0.3125 = [answer5] 0.60 = [answer6] 0.56 = [answer7] 1.50 = [answer8]
Answers
Answer 1: 0.666 can be expressed as the fraction 2/3.
Answer 2: 0.1875 can be expressed as the fraction 3/16.
Answer 3: 0.240 can be expressed as the fraction 6/25.
Answer 4: 1.75 can be expressed as the fraction 7/4.
Answer 5: 0.3125 can be expressed as the fraction 5/16.
Answer 6: 0.60 can be expressed as the fraction 3/5.
Answer 7: 0.56 can be expressed as the fraction 14/25.
Answer 8: 1.50 can be expressed as the fraction 3/2.
In decimal to fraction conversion, the first step is to identify the place value of the last digit.
For example, in 0.666, the last digit is in the thousandths place.
To convert it to a fraction, we write the digits as the numerator and the place value as the denominator. So, 0.666 becomes 666/1000, which simplifies to 2/3.
Similarly, in 0.1875, the last digit is in the ten thousandths place. So, we write it as 1875/10000, which simplifies to 3/16.
This process is repeated for each decimal, identifying the place value and expressing it as a fraction.
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Find the area of the regular pentagon with radius 19 mm.
Answers
Answer:
621.09 mm²
Step-by-step explanation:
Area of pentagon = \(\frac{(perimeter) (apothem)}{2}\)
Let's solve
\(\frac{(5 times 19) times 13.08}{2}\) = 621.09 mm²
So, the answer is 621.09 mm²
Answer: 8.58 cm²
Step-by-step explanation:
The area of the central triangle bounded by each of the sides can be computed as ...
A = (1/2)r²sin(α) . . . . where α is the central angle, 360°/5 = 72°
There are 5 such triangles, so the area of the pentagon is
A = (5/2)(1.9 cm)²sin(72°) ≈ 8.58 cm²
Select the condition for which it is NOT possible to construct a triangle. A triangle with side lengths 4 cm, 5 cm, and 6 cm A triangle with side lengths 4 cm, 5 cm, and 15 cm A triangle with side lengths 4 cm and 5 cm and an included 50°angle A triangle with angle measures 30° and 60°, and an included 3 cm side length.
Answers
Answer:
Option B: A triangle with side lengths 4 cm, 5 cm, and 15 cm
Step-by-step explanation:
Since we are dealing here majorly with sides, one condition is that each side has to be shorter than the sum of the other two sides and longer than their difference meaning that if we have a, b and c
The a value has to be shorter than the sum of b and c - a < b+c and the a value also has to be longer than their difference - a > b-c
In this example,we have side lengths 4 cm, 5 cm, and 15 cm. Taking a, b and c as 4 cm, 5 cm, and 15 cm respectively.
The sum of 5 and 4 is 9 and the third side 15 is greater than 9 when it is supposed to be less to construct a triangle.