The height of Cone Mountain, given the trail length and the radius, would be C. 2,520 feet
How to find the height ?
To find the height of Cone Mountain, we can use the properties of a right circular cone. The key relationship we'll use is the Pythagorean theorem :
[tex]l^2 = r^2 + h^2[/tex]
The slant height (l) is the length of the trail, which is 3,150 feet.
The radius (r) is 1,890 feet.
Pythagorean theorem:
[tex](3,150)^2 = (1,890)^2 + h^29,922,500 = 3,572,100 + h^2[/tex]
Make h the subject:
[tex]h^2 = 9,922,500 - 3,572,100\\h^2 = 6,350,400[/tex]
Take the square root of both sides to find h:
h = √(6,350,400)
h = 2,520 feet
What is the number in the * cell? 9 38 47 4 6 35 42 * 12 21 23 27?
The missing number can be found using Matrix rule. We have to apply addition and subtraction rule to find the missing number form given matrix.
The missing number is -5.
Given:
The given matrix is,
[tex]\left[\begin{array}{cccc}9&38&47&4\\6&35&42&x\\12&21&23&27\end{array}\right][/tex]
Let the missing number is [tex]x[/tex].
Apply the subtraction rule to subtract second row from first row.
[tex]\left[\begin{array}{cccc}9&38&47&4\\3&3&5&4-x\\12&21&23&27\end{array}\right][/tex]
The sum of first three number is equal to the sum of digits of the first three number in the third row,
[tex]1+2=3\\2+1=3\\2+3=5[/tex]
Now from the same pattern.
[tex]2+7=4-x\\x=-5[/tex]
Thus, the missing number is -5.
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Will mark brainliest, help!!
Triangle ABC has vertices at A(1, 2) B(4, 6) and C(4, 2) in the coordinate plane. The triangle will be reflected over the x-axis and then rotated 180 degrees about the origin to form ABC. What are the vertices of A'B'C'?
Answer:
The vertices of A'B'C are A'(-1,2), B'(-4,6) and C'(-4,2).
Step-by-step explanation:
Triangle ABC has vertices at A(1, 2) B(4, 6) and C(4, 2).
If a figure reflected over x-axis, then
[tex](x,y)\rightarrow (x,-y)[/tex]
Therefore the vertices of triangle ABC after reflection over x-axis are:
[tex]A(1,2)\rightarrow A'(1,-2)[/tex]
[tex]B(4,6)\rightarrow B'(4,-6)[/tex]
[tex]C(4,2)\rightarrow C'(4,-2)[/tex]
Rotation 180 degrees about the origin is defined as
[tex](x,y)\rightarrow (-x,-y)[/tex]
Therefore the vertices of triangle ABC after reflection over x-axis followed by rotated 180 degrees about the origin are:
[tex]A(1,-2)\rightarrow A'(-1,2)[/tex]
[tex]B(4,-6)\rightarrow B'(-4,6)[/tex]
[tex]C(4,-2)\rightarrow C'(-4,2)[/tex]
Therefore the vertices of A'B'C are A'(-1,2), B'(-4,6) and C'(-4,2).
Answer:
C
Step-by-step explanation:
If ur not trying to look at all that but you should
Write the standard form of the line that passes through the point (-2, 4) and is parallel to x - 2 y = 6.
x-2y=6
-2y=-x+6
2y=x-6
y=0.5x-3
Parallel=same slope
y=0.5x+5
Write the series -25-22-19+... for 14 terms using summation notation
Answer:
The correct answer option is a. 14∑1 (-28+3n)
Step-by-step explanation:
The summation notation for the given series is 14∑1 (-28+3n) where [tex]i[/tex] (the index of summation or the lower limit of summation) is 1 and [tex]n[/tex] (the upper limit of summation) is 14.
Putting in the values of the limit from 1 to 14 in the notation to get the first 14 terms of the series:
[tex]-28+3(1)=-25\\\\-28+3(2)=-22\\\\-28+3(3)=-19\\\\-28+3(4)=-16\\\\-28+3(5)=-13\\\\-28+3(6)=-10\\\\-28+3(7)=-7\\\\-28+3(8)=-4\\\\-28+3(9)=-1\\\\-28+3(10)=2\\\\-28+3(11)=5\\\\-28+3(12)=8\\\\-28+3(13)=11\\\\-28+3(14)=14\\[/tex]
Therefore, first option is the correct one.
Answer:
A is the correct one hope ive been of help
math help please!!!! will be marking brainly
The answer is C. 3/5
20 girls, 3 boys. 23/40 is about 60 percent, or 3/5.
I wrote the wrong answer on accident for whatever reason when I first sent this, I apologize.
Millie needs the average height of the plants she is buying to be at least 73 inches. She has selected three plants that are 70, 71 and 72 inches tall. Write and solve an inequality that Millie could use to determine the possible heights of her fourth plant
Answer:
[tex]\frac{70+71+72+x}{4}\geq 73[/tex]
[tex]x\geq 79[/tex]
Step-by-step explanation:
Let x be the height of 4th plant purchased by Millie.
We have been given that Millie needs the average height of the plants she is buying to be at least 73 inches. She has selected three plants that are 70, 71 and 72 inches tall.
So the average of 4 plants purchased by Millie will be: [tex]\frac{70+71+72+x}{4}[/tex]
We can represent this information in an inequality as: [tex]\frac{70+71+72+x}{4}\geq 73[/tex]
Therefore, our desired inequality will be [tex]\frac{70+71+72+x}{4}\geq 73[/tex].
Now let us solve our inequality by multiplying both sides of inequality by 4.
[tex]4*\frac{70+71+72+x}{4}\geq 4*73[/tex]
[tex]70+71+72+x\geq 292[/tex]
[tex]213+x\geq 292[/tex]
[tex]x\geq 292-213[/tex]
[tex]x\geq 79[/tex]
Therefore, the height of 4th plant purchased by Millie must be at least 79 inches.
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[tex]m < c = 36 \\ m < b = 123 \\ find \: \: \: m < cad[/tex]
Using exterior angle formula, you get that ∠CAD=36+123=159°
Exterior angle formula says that the angles facing CAB (ACB and ABC) sum to CAD.
Select all the names for a in the expression.
7ab+3
variable
expression
sum
constant
factor
coefficient
Answer:
It is a factor and a variable.
Step-by-step explanation:
Item 16 Evaluate 2x+6y when x=?45 and y=13. Write your answer as a fraction
Answer:
168
Step-by-step explanation:
2x45=90
6x13=78
78+90=168
In your lab, a substance's temperature has been observed to follow the function f(x) = (x − 1)3 + 9. The point at which the function changes curvature from concave down to concave up is where the substance changes from a solid to a liquid. What is the point where this function changes curvature from concave down to concave up?
Hint: The point is labeled in the picture.
Answer:
The point of change is the point (1,9)
Step-by-step explanation:
The first derivative of the function equated to zero will give you the point where the function changes.
Therefore, to solve this problem find the first derivative of f (x)
[tex]f '(x) = 3*3(x-1)^{3-1}\\\\f '(x) = 9(x-1)^2[/tex]
Now we equate the derivative to 0.
[tex]9 (x-1)^ 2 = 0\\\\x = 1[/tex]
Then the derivative of the function is equal to 0 when x = 1. This means that the concavity of the function changes in x = 1.
When [tex]x = 1, y = 3(1-1) ^ 3 +9\\\\x =1, y = 9.[/tex]
Then the point of change is the point (1,9)
Answer:
The point of inflection is (1,9)
Step-by-step explanation:
We have following given function
[tex]f(x)=(x-1)^{3} +9[/tex]
The point at which the function changes its curvature is defined by the point of inflection.
To find point of inflection we set 2nd derivative to 0
[tex]f''(x)= 0[/tex]
The first derivative is given by
[tex]f'(x)= \frac{d}{dx} [(x-1)^{3} +9][/tex]
[tex]f'(x)= 3(x-1)^{2}[/tex] ( using chain rule and derivative of constant is 0)
now again we take 2nd derivative
[tex]f''(x)=3(2(x-1))[/tex]
[tex]f''(x)=6(x-1)[/tex]
now we equate 2nd derivative to 0
[tex]6(x-1)=0\\x-1=0\\x=1[/tex]
hence point of inflection is at x=1
now we find y coordinate of point of inflection by plugging x=1 in f(x)
[tex]y=f(1)=(1-1)^{3} +9 =9[/tex]
Hence the point of inflection is (1,9)
plz help :)))))))))))
Given:
b1 = 17 ft
b2 = 20 ft
h = 13 ft
r = 17/2 = 8.5 ft
Area of the Semi-circle = 1/2 π r²
= 1/2 (22/7) (8.5²)
= (11/7) (72.25)
= 113.535 ft²
Area of the trapezium = (h) (b1 + b2) / 2
= (13)(17 + 20)/2
= 240.5 ft²
Total area of the amphitheater stage = Area of Semi-circle + Area of the trazezium = 113.535 + 240.5 = 354.035 ft²
The length of a rectangle is twice the with. If the perimeter of the rectangle is 60 units, find the area of the garden
w - width
2w - length
60 - perimeter
w + w + 2w + 2w = 6w - perimeter
The equation:
6w = 60 divide both sides by 6
w = 10 → 2w = 2 · 10 = 20
The area: A = width × length
A = (10)(20) = 200
Answer: The area of the garden is equal 200 square units.PLEASE HELP ASAP 25 POINTS
Answer:
Your answer is B!
Step-by-step explanation:
Payton leaves to go on an 8585 minute bike ride at 3{:}27\text{ p.M.}3:27 p.M. Payton's family eats dinner at 5{:}45\text{ p.M.}5:45 p.M. How much time will Payton have between finishing her bike ride and eating dinner?
Answer:
53 minutes.
Step-by-step explanation:
We have been given that Payton leaves to go on an 85 minute bike ride at 3:27 pm.
Let us find when Payton will finish biking by 85 minutes after 3:27 pm.
Since 85 minutes equals to 1 hour and 25 minutes. 1 hour after 3:27 pm will be 4:27 pm. Now let us add 25 minutes to 4:27 pm.
So Payton will finish biking at 4:(27+25) pm= 4:52 pm.
Payton's family eats dinner at 5:45 pm. Now let us find remaining time between dinner and 4:52 pm.
[tex]\text{Minutes between dinner and finishing bike ride}=5:45 pm- 4:52 pm[/tex]
[tex]\text{Minutes between dinner and finishing bike ride}=53[/tex]
Therefore, Payton have 53 minutes between finishing her bike ride and eating dinner.
Felipe and his mom bought some cookies for there party 23 people attended the party and each ate 3 cookies how manny cookies did they buy at the supermarket
Answer:
69
Step-by-step explanation:
23 times 3
A rectangle roof is 756 sguare inches the length is 108 how many inches wide is the roof The doll house is 954 square inches the length of the roof is 106 inches what is the width of the roof
Answer:
1. 756 / 108 = 7 inches (the width of the first roof);
2. 954 / 106 = 9 inches (the width of the second roof);
Step-by-step explanation:
Select the graph and the description of the end behavior of f(x) = −x3 + 2.
This is a cubic function. The end behavior of the graph will decrease to the right and increase to the left.
This is a cubic function. The end behavior of the graph will increase to the right and decrease to the left.
This is a cubic function. The end behavior of the graph will increase to the right and decrease to the left.
This is a cubic function. The end behavior of the graph will decrease to the right and increase to the left.
Answer: D
Step-by-step explanation:
End behavior is determined by two factor:
1. Coefficient - determines right side:
If the leading coefficient is POSITIVE, then right side goes to +∞If the leading coefficient is NEGATIVE, then right side goes to -∞2. Degree - determines left side:
If degree is EVEN, then left side is SAME as right sideIf degree is ODD, then left side is OPPOSITE of right side******************************************************************************************
-x³ + 2
Leading coefficient is NEGATIVE, so right side goes to -∞ (decreases)
Degree is ODD, so left side is opposite of right side → goes to +∞ (increases)
Points A and B are 200 mi apart. A cyclist started from point A and a motorcyclist started from point B, moving towards each other.The speed of the cyclist was 17 mph, the speed of motorcyclist was 83 mph. At what distance from point A will they meet?
Answer:
34 miles is the distance from point A will they meet.
Step-by-step explanation:
Proportion states that the two ratios or fractions are equal.
Given the statement:
Distance between point A and B (i.e AB) = 200 mi.
Let the cyclist speed be c, and motor- speed be m;
then;
c = 17 mph and m=83 mph
Let they meet at distance x miles from a point A.
By definition of proportion, we have;
[tex]\frac{x}{17} =\frac{200-x}{83}[/tex]
By cross multiply;
[tex]83x = 17(200-x)[/tex]
Using distributive property, [tex]a\cdot(b+c) =a\cdot b+ a\cdot c[/tex]
[tex]83x = 3400 - 17x[/tex]
Add 17x both sides we get;
[tex]83x+ 17x= 3400 - 17x +17x[/tex]
Simplify:
100x = 3400
Divide by 100 on both sides we get;
x = 34 miles
Therefore, the distance from point A will they meet is, 34 miles.
Answer:
Image
Step-by-step explanation:
Image
ok this is my question that my math tutor gave me to get the wifi password!!!
Answer:
The answer is π
Step-by-step explanation:
Not really an explanation, but you can type this in wolframalpha: integrate (x^3 cos x/2 + 1/2) sqrt(4-x^2) dx from x=-2 to 2
The given integral can be solved using numerical calculation methods. The integral by part formula also would be applicable in the given integral.
The value of the given integral is [tex]3.14\rm\: or\: \pi[/tex].
Given:
Write the given integral.
[tex]\int_{-2}^{2}\sqrt{4-x^2}\left(\cos\left(\dfrac{x}{2}\right)x^3+\dfrac{1}{2}\right)\\[/tex]
Write the formula for the integration by part formula.
[tex]\int u.v=u\int vdx-\int u'(\int vdx)dx[/tex]
Let,
[tex]u=\sqrt{4-x^2}[/tex]
[tex]v=\left (x^3\cos\dfrac{x}{2} +\dfrac{1}{2} \right)[/tex]
Now put the value in above formula and integrate.
[tex]\begin{aligned}\int_{-2}^{2}\sqrt{4-x^2}\left(\cos\left(\dfrac{x}{2}\right)x^3+\dfrac{1}{2}\right)&=\left [\dfrac{\frac{x\sqrt{4-x^2}}{2}+2\arcsin\left(\frac{x}{2}\right)}{2}\right]_{-2}^{2}\\&=\left [\dfrac{x\sqrt{4-x^2}}{4}+\arcsin\left(\dfrac{x}{2}\right)\right]_{-2}^{2}\\\end[/tex]
Now, further simplify the expression.
[tex]\int_{-2}^{2}\sqrt{4-x^2}\left(\cos\left(\dfrac{x}{2}\right)x^3+\dfrac{1}{2}\right)\\=\left [\dfrac{2\sqrt{4-2^2}}{4}+\arcsin\left(\dfrac{2}{2}\right)\right]-\left [\dfrac{2\sqrt{4-(-2)^2}}{4}+\arcsin\left(\dfrac{-2}{2}\right)\right]\\=1.57-(-1.57)\\=3.14[/tex]
The value of the given integral is [tex]3.14\rm\: or\: \pi[/tex].
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If A, B, and C are the interior angles of triangle ABC, prove that
4 sinA sinB sinC = sin2A + sin2B + sin2C
NOTES:
1)⇒ A + B + C = 180°
A + B + C = π
A + B = π - C
2)⇒⇒ sin (A + B) = sin (π - C)
= (sin π)(cos C) - (sin C)(cos π)
= (0)(cos C) - (sin C)(-1)
= 0 - (-sin C)
= sin C
3)⇒⇒⇒cos (A + B) = cos (π - c)
= (cos π)(cos C) + (sin π)(sin C)
= (-1)(cos C) + (0)(sin C)
= - cos C
4)⇒⇒⇒⇒ sin 2A + sin 2B = 2 sin (A + B) cos (A - B)
PROOF (from left side):
sin 2A + sin 2B + sin 2C = 4 sin A sin B sin C
2 sin (A + B) cos (A - B) + sin 2C refer to NOTE 4
2 sin (A + B) cos (A - B) + 2 sin C cos C double angle formula
2 sin C cos (A - B) + 2 sin C cos C refer to NOTE 2
2 sin C [cos (A - B) + cos C] factored out 2 sin C
2 sin C [cos (A - B) - (cos(A + B)] refer to NOTE 3
2 sin C [2 sin A sin B] sum/difference formula
4 sin A sin B sin C multiplied 2 sin C by 2 sin A sin B
Proof completed: 4 sin A sin B sin C = 4 sin A sin B sin C
Two numbers such that the greater number is 75 percent more than the lesser number
If x = the first number (equal to 1x) then the second number is 75% more than this.
This means the value of the bigger number is 100 + 75 (because 100 is the starting number and 75 is the percent bigger)
This can be shown with the following equation:
Amount * [tex]\frac{percentage}{100}[/tex]
x * [tex]\frac{175}{100}[/tex] = 1.75x
1.75x is the value of the bigger number.
Name the property of real numbers illustrated by the equation.
-3(x+4)=-3x-12
A. Distributive Property
B. Associative Property of Addition
C. Associative Property of Multiplication
D. Commutative Property of Addition
Answer:
A. Distributive Property
Step-by-step explanation:
I'm taking the exam right now. :)
Average movie prices in the United States are, in general, lower than in other countries. It would cost $80.26 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $76.69. How much does an average movie ticket cost in each of these countries?
Answer: weclome
Step-by-step explanation:
Average movie ticket prices in the united states are, in general, lower than other countries. It would cost in $77.87 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $73.83. How much does an average movie ticket cost in each of these countries?
Let ticket in japan cost x
Let ticket in Switzerland cost y
3x+2y=77.87 ------1
3y+2x=73.83------2
Subtract the equations
x-y= 4.04 ---4
3y+2x=73.83------5
Answer:
Step-by-step explanation:
Average movie ticket prices in the united states are, in general, lower than other countries. It would cost in $77.87 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $73.83. How much does an average movie ticket cost in each of these countries?
Let ticket in japan cost x
Let ticket in Switzerland cost y
3x+2y=77.87 ------1
3y+2x=73.83------2
Subtract the equations
x-y= 4.04 ---4
3y+2x=73.83------5
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What is an equation of the line that passes through the points (7,−6) and (3,−6)?
Answer:
The equation of this line would be y = -6
Step-by-step explanation:
In order to find this, we must first find the slope. For that we use the two points and the slope equation.
m(slope) = (y2 - y1)/(x2 - x1)
m = (-6 - -6)/(7 - 3)
m = 0/4
m = 0
Given that slope, we can use it along with a point in point slope form. From there we can solve for y and get the equation.
y - y1 = m(x - x1)
y + 6 = 0(x - 7)
y + 6 = 0
y = -6
Final answer:
To find the equation of a line passing through given points, calculate the slope, use the point-slope formula, and simplify to obtain the final equation. In this case, the line passing through (7,-6) and (3,-6) results in the equation y = -6.
Explanation:
To find the equation of the line passing through the points (7,-6) and (3,-6):
Calculate the slope (m) using the formula: m = (y₂ - y₁) / (x₂ - x₁)
Substitute one of the points and the slope into the point-slope formula: y - y₁ = m(x - x₁)
Simplify the equation to get the final answer: y = mx + b
The equation of the line passing through those two points is y = -6.
Taylor has $97.23 and her checking account she uses debit card to spend 29 .74 and then deposits 118.08 into her accounts what is Taylor's new balance
The swimsuit is on sale for 25% off its original price. If the original price was $58. What is the sale price?
Answer:
The sale price is $43.50.
Step-by-step explanation:
58 x .25 = 14.50 off the original price
58 - 14.50 = 43.50
If someone could help me out with this, I would greatly appreciate it!!
We are given that revenue of Tacos is given by the mathematical expression [tex]-7x^{2}+32x+240[/tex].
(A) The constant term in this revenue function is 240 and it represents the revenue when price per Taco is $4. That is, 240 dollars is the revenue without making any incremental increase in the price.
(B) Let us factor the given revenue expression.
[tex]-7x^{2}+32x+240=-7x^{2}+60x-28x+240\\-7x^{2}+32x+240=x(-7x+60)+4(-7x+60)\\-7x^{2}+32x+240=(-7x+60)(x+4)\\[/tex]
Therefore, correct option for part (B) is the third option.
(C) The factor (-7x+60) represents the number of Tacos sold per day after increasing the price x times. Factor (4+x) represents the new price after making x increments of 1 dollar.
(D) Writing the polynomial in factored form gives us the expression for new price as well as the expression for number of Tacos sold per day after making x increments of 1 dollar to the price.
(E) The table is attached.
Since revenue is maximum when price is 6 dollars. Therefore, optimal price is 6 dollars.
A stone is an Old English unit of weight and equal to 14 slug. How many kilograms are there in 6 stones? (1 slug = 14.59 kg) Answer in units of kg.
Answer:
1225.56 kg
Step-by-step explanation:
1 stone = 14 slugs
1 slug = 14.59 kg
[tex]\text{6 stones} ( \dfrac{14 slug}{1 stone})(\dfrac{14.59 kg}{1 slug})[/tex]
numerator 6 * 14 * 14.59 = 1225.56 kg
denominator = 1
Answer 1225.56 kg in 6 stones
Convert 4x + 2y = 25 from standard form to slope intercept form
Show your steps
Answer:
y = -2x + 25/2
Step-by-step explanation:
Slope intercept form is y = mx + b.
You must solve the equation for y.
4x + 2y = 25
Subtract 4x from both sides.
2y = -4x + 25
y = -2x + 25/2
Answer:
solution given:
4x+2y=25
we know that
slope intercept form is
y=mx+c
so
4x+2y=25
2y=-4x+25
y=-4/2 x+25/2
y=-2x+25/2 is a required answer.
A triangle has two sides of length 20 and 2. what is the smallest possible whole-number length for the third side?
The smallest possible whole number length for the third side of a triangle with sides of length 20 and 2, based on triangle inequalities, is 19.
Explanation:The subject of your question revolves around triangle inequalities, a fundamental concept in geometry. Triangle inequalities state that the length of any one side of a triangle must be less than the sum of the lengths of other two sides. In this case, you have two sides of lengths 20 and 2. This means the third side must be less than 22 but more than 18 (since it also needs to be more than the difference of two sides).
However, your question asks for the smallest whole-number length possible for the third side. Hence, the smallest possible whole number length for the third side of the triangle is 19.
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The smallest possible whole-number length for the third side of the triangle is 18.
To determine the smallest whole-number length for the third side of a triangle with sides of length 20 and 2, one must consider the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.Let's denote the lengths of the sides as [tex]\( a \), \( b \), and \( c \)[/tex] , where [tex]\( a = 20 \) and \( b = 2 \)[/tex] . We are looking for the smallest whole number [tex]\( c \)[/tex] that satisfies the triangle inequality theorem:
1. [tex]\( a + b > c \)2. \( a + c > b \)3. \( b + c > a \)[/tex] . Substituting the known values of [tex]\( a \) and \( b \), we get: 1. \( 20 + 2 > c \)[/tex]
2.[tex]\( 20 + c > 2 \)[/tex]
3. [tex]\( 2 + c > 20 \)[/tex] From inequality 1, we have: [tex]\( 22 > c \)[/tex] This means [tex]\( c \[/tex] must be less than 22.From inequality 2, we have:[tex]\( 20 + c > 2[/tex] Since [tex]\( c \)[/tex] is a positive number, this inequality will always hold true for any positive \( c \).From inequality 3, we have:[tex]\( 2 + c > 20 \)[/tex]. Solving for [tex]\( c[/tex] , we get: [tex]\( c > 18[/tex]) .Since [tex]\( c \)[/tex] must be a whole number and the smallest whole number greater than 18 is 19, one might initially think that the smallest possible length for [tex]\( c \)[/tex] is 19. However, we must also consider that [tex]\( c \)[/tex] must be less than the sum of the other two sides (inequality 1). The smallest whole number less than 22 is 21, but since [tex]\( c \)[/tex] cannot be equal to [tex]\( a \)[/tex] or [tex]\( b[/tex]) (as this would not form a triangle), the next smallest whole number is 20, which is also not possible as it would make two sides equal and the triangle degenerate. Therefore, the next smallest whole number is 19. However, we must also consider that for a valid non-degenerate triangle, the difference between the lengths of any two sides must be less than the length of the third side. Since [tex]\( a = 20 \) and \( b = 2 \)[/tex] , the difference between [tex]\( a \). and \( b \)[/tex] is 18, which means [tex]\( c \)[/tex] must be greater than 18 to satisfy this condition.Thus, the smallest possible whole-number length for the third side [tex]\( c \)[/tex] is 19, but since we are looking for the smallest whole number greater than 18, the correct answer is actually 18, as it is the smallest whole number that satisfies all the conditions of the triangle inequality theorem and the condition that the difference between the lengths of any two sides must be less than the length of the third side.