a) An exponential equation in the form of y = a(b)ˣ that can model the amount of money (future value) in Patrick's account, y, x years after starting the account is y = 894(1.02)ˣ.
b) If Patrick makes no other deposits or withdrawals, after 5 years or approximately 6 years his account will have more than $1,000 (future value).
What is an exponential equation?An exponential equation is a mathematical function, written in the form of y = a(b)ˣ, where y is the ending value, a is the initial value, b is the growth or decay rate, and x is the exponent or number of years.
Thus, there are two types of exponential functions: exponential growth and exponential decay functions.
y = 894(1.02)^6
1,000 ≤ 894(1.02)ˣ
I/Y (Interest per year) = 2%
Present Value = $894
FV (Future Value) ≥ $-1,000
Results:
x = 5.658
x ≈ 6 years
= $1,006.79
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Complete Question:Patrick spent last summer working in construction with his dad, and he put $894 of his earnings into a new high-yield savings account. The money in this savings account will increase by 2% each year.
a) Write an exponential equation in the form of y = a(b)ˣ that can model the amount of money in Patrick's account, y, x years after starting the account. Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =
b) If Patrick makes no other deposits or withdrawals, after how many years will his account have more than $1,000?
у
3
Solve for y.
27
31>
=
y
30
y
y = [? ] v
Enter answer
y^2 = 90
y = √90 = 3√10
that's it
The function h(t) = 4 + 64t – 16t2 models the height h, in feet, of a ball thrown in the air, after t seconds.
Part A
What is the vertex of the graph of the function, (t, h(t))?
(
,
)
Part B
What does the t-coordinate of the vertex represent?
A. the ball's maximum height
B. the time it takes for the ball to reach its maximum height
C. the time it takes for the ball to hit the ground
D. the height the ball was thrown from
Part C
What does the h(t)-coordinate of the vertex represent?
A. the ball's maximum height
B. the time it takes for the ball to reach its maximum height
C. the time it takes for the ball to hit the ground
D. the height the ball was thrown from
Part A) The vertex of the graph of the function, (t, h(t)) is (2, 68).
Part B) The t-coordinate of the vertex represent is the time it takes for the ball to reach its maximum height (option b)
Part C) The h(t)-coordinate of the vertex represent is the ball's maximum height (option a).
Part A asks for the vertex of the graph of the function, which is the point where the function reaches its maximum or minimum value. To find the vertex of a quadratic function like
=> h(t) = 4 + 64t – 16t²,
we can use the formula
=> t = -b/2a,
where a, b, and c are the coefficients of the quadratic equation ax² + bx + c and t is the input variable (in this case, the time).
The t-coordinate of the vertex is simply the value we get when we plug this formula into our equation.
So, for
=> h(t) = 4 + 64t – 16t²,
we have a = -16, b = 64, and c = 4.
Plugging these values into the formula
=> t = -b/2a,
we get
=> t = -64/(2*(-16)) = 2.
The t-coordinate of the vertex is therefore 2.
To find the h(t)-coordinate of the vertex, we can simply plug t = 2 into the function h(t) = 4 + 64t – 16t² and evaluate it.
This gives us
=> h(2) = 4 + 64(2) – 16(2²) = 68.
Therefore, the vertex of the graph of h(t) is (2, 68).
Part B asks what the t-coordinate of the vertex represents. We know that the t-coordinate is the time at which the ball reaches its maximum height.
Therefore, the correct answer is B: the time it takes for the ball to reach its maximum height.
Part C asks what the h(t)-coordinate of the vertex represents. We just found that the h(t)-coordinate of the vertex is the maximum height of the ball.
Therefore, the correct answer is A: the ball's maximum height.
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(x^2-1)^3=64(X^2-1)^2
Answer:
x = ±1, ±√65
Step-by-step explanation:
You want the solution to (x² -1)³ = 64(x² -1)².
SolutionSubtracting the right side, we have ...
(x² -1)³ -64(x² -1) = 0
(x² -1)²(x² -1 -64) = 0
Zero product ruleThe solutions make the factors zero:
x² -1 = 0 ⇒ x = ±1
x² -65 = 0 ⇒ x = ±√65
Solutions are x = ±1 and x = ±√65.
__
Additional comment
The solutions ±1 are each multiplicity 2.
The cubic polynomial shown below has zeroes at x=-1and x= only and has a relative maximum at (3,8). Which of the following is its y-value when x=5?
The cubic polynomial is given as y = 0.25(x³ - 12x + 16). Then the value of y when x = 6 will be 40.
Therefore the option C is correct.
What is polynomial?A polynomial expression is described as an algebraic expression with variables and coefficients.
If the zeroes of the polynomial are negative 4, 2, and 2.
Then the factors will be (x + 4), (x - 2), and (x - 2).
Then the cubic polynomial will be
→ (x + 4) (x - 2) (x - 2)→ (x + 4) (x² - 4x + 4)→ (x³ - 12x + 16)we can write the polynomial equation as:
y = C(x³ - 12x + 16)
Then the polynomial is maximum at (-2, 8) then the value of C will be 0.25.
y = 0.25 (x³ - 12x + 16)
y = 0.25 (6³ - 12 × 6 + 16)
y = 0.25 (216 - 72 + 16)
y = 0.25 (160)
y = 40
Note that there was no diagram provides, i solved a similar question
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sin negative-1 (-3sqrt/2) in radians
The given trigonometric expression sin⁻¹(-3√(2)/2) in radians is approximately -2.2143 radians.
As we know that sin⁻¹(x) = -cos⁻¹(x) + π/2, which is the angle in the fourth quadrant whose cosine is 3sqrt(2)/2.
We have:
cos²θ + sin²θ = 1
Since sine is negative and cosine is positive, we know that:
sinθ = -sqrt(1 - cos²θ)
Substituting cosθ = 3√(2)/2, we get:
sinθ = -√(1 - (3√(2)/2)²) = -√(1 - 9/8) = -√(1/8) = -√(2)/2
Therefore, sin^(-1)(-3sqrt(2)/2) = -cos^(-1)(3sqrt(2)/2) + π/2.
Since cosine is positive in the fourth quadrant, we have:
cos⁻¹(3√(2)/2) = π/4
Substituting this value, we get:
sin⁻¹(-3√(2)/2) = -π/4 + π/2 = π/4
Therefore, sin⁻¹(-3√(2)/2) in radians is approximately -2.2143 radians.
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An annual depreciation rate is the percent that the value of an item decreases each year. A company purchases technology for $5,000. The company uses the function $r=1-\sqrt[3]{\frac{S}{5000}}$
to relate the annual depreciation rate $r$ (in decimal form) and the value $S$ (in dollars) of the technology after 3 years. Find $S$ when $r=0.15$ .
3. Rochelle helped in the garden 7 days during the last 4 weeks. Use the
numbers in the box to complete the sentences comparing her time in
the garden.
Numbers can be used more than once. Write each number in the
appropriate box.
For every day(s) Rochelle helped, she did not help
For every
day(s).
1 3 4 7 28
day(s).
day(s) Rochelle did not help, she helped
For every 3 days Rochelle helped, she did not help for 1 day.
For every 4 days Rochelle helped, she did not help for 1 day.
For every 7 days Rochelle helped, she did not help for 6 days.
For every 28 days Rochelle helped, she did not help for 21 days.
Let's use the terms provided to complete the sentences comparing Rochelle's time in the garden.
Since Rochelle helped in the garden for 7 days during the last 4 weeks, we can calculate the total number of days in 4 weeks and then find the number of days she did not help.
There are 7 days in a week, so in 4 weeks, there are 4 x 7 = 28 days.
Rochelle helped for 7 days, so she did not help for 28 - 7 = 21 days.
Now, let's complete the sentences:
For every 1 day(s) Rochelle helped, she did not help for 3 day(s).
For every 3 day(s) Rochelle did not help, she helped 1 day(s).
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Please help fast. Thanks! (:
The value of variable y from the system of vertical angles is equal to 125.
How to find the values of a variable associated with system of vertical anglesIn this problem we need to determine by algebra properties the value of a variable y from a system of two pairs of vertical angles. The system is represented by the following expression:
x + 20 = 3 · x - 50
2 · x = 70
x = 35
Then, by definition of supplementary angles:
(x + 20) + y = 180
55 + y = 180
y = 125
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What is the equation of a parabola with a vertical axis, vertex (h, k), and directrix y = k – p, where p is a nonzero real number? How can the equation be simplified if the vertex is at the origin?
The equation of a parabola with a vertical axis and vertex (h, k) is given by:
(x - h)² = 4p(y - k)
How to explain the equationIn the equation, where p is the distance from the vertex to the focus (and also the distance from the vertex to the directrix).
If the vertex is at the origin (h=0, k=0), then the equation simplifies to:
x² = 4py
where p is still the distance from the vertex to the focus (and also the distance from the vertex to the directrix).
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I don’t know how to do this question if anyone does please put the steps thank you.
If the third term is 31, then let's get the second term. We have to use the rule we were given and work backwards. So, we will add three and then divide by 2.
31 + 3 = 34
34 / 2 = 17
17 is the second term. Let's do the same thing we just did to find the first term: add three, divide by 2.
17 + 3 = 20
20 / 2 = 10
Answer: the first term is 10
Hope this helps!
Question 7(Multiple Choice Worth 1 points)
(07.04 HC)
Right triangle ABC is located at A (-1, -2), B (-1, 1), and C (-5, 1) on a coordinate plan
O (x + 1)2 + (y + 2)² = 9
O (x + 5)² + (1)² = 16
O(x + 1)2 + (y + 2)² = 25
O(x + 5)² + (y-1)² = 25
Answer:
O (x + 1)2 + (y + 2)² = 9
Step-by-step explanation:
This is because the distance between points A and B is 3 units, and the distance between points B and C is 4 units, making the triangle a 3-4-5 right triangle. Point B is located at (-1, 1), which is 3 units away from point A (-1, -2) and 4 units away from point C (-5, 1). Therefore, the circle with center (-1, -2) and radius 3 would pass through point B, and its equation would be:
(x + 1)2 + (y + 2)² = 3²
(x + 1)2 + (y + 2)² = 9
A can of soda is placed inside a cooler. As the soda cools its temperature C (t) in degrees Celsius after t minutes is given by the following exponential function.
C(t)=18(0.91)t
The initial temperature of the soda is 18 degrees Celsius.
Its temperature after 20 minutes is 2.73 degrees Celsius.
What is an exponential function?In Mathematics, an exponential function can be modeled by using this mathematical expression:
f(x) = a(b)^x
Where:
a represents the base value, initial value, or y-intercept.x represents time.b represents the rate of change.When time, t = 0, the initial value can be calculated as follows;
[tex]C(t)=18(0.91)^{t}\\\\C(0)=18(0.91)^{0}[/tex]
C(0) = 18(1)
C(0) = 18 degrees Celsius.
When time, t = 0 = 20, the temperature can be calculated as follows;
[tex]C(t)=18(0.91)^{t}\\\\C(20)=18(0.91)^{20}[/tex]
C(20) = 2.73 degrees Celsius.
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Complete Question:
A can of soda is placed inside a cooler. As the soda cools its temperature C (t) in degrees Celsius after t minutes is given by the following exponential function.
[tex]C(t)=18(0.91)^{t}[/tex]
Find the initial temperature of the soda and its temperature after 20 minutes?
The formula for the volume of a prism is V = area of base x height. What is the volume and surface area of each of these prisms? Show your thinking
The volume of the prism is V = 4000 cm³
Given data ,
Let the volume of the prism be represented as V
Now , the value of V is
Let the height of the prism be h = 10 cm
Let the width of the prism be w = 20 cm
Let the length of the prism be l = 20 cm
So , the base area of prism = l x w
Base area = 400 cm²
Now , the volume of the prism is V = 400 x 10
V = 4000 cm³
Hence , the volume of prism is V = 4000 cm³
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What linear function equation is represented by this graph?
ANSWER: 1
3
x−4 just took the test
Answer:
The linear function is y = (1/3)x - 4.
Step-by-step explanation:
The y-intercept is -4. Starting at (0, -4), go up 1 unit and then right 3 units. You will end at (3, -1). So the slope of this line is 1/3, and it follows that the function is
y = (1/3)x - 4.
From the observation deck of a skyscraper, Brandon
The horizontal distance from the base of the skyscraper out to the ship will be 1140 feet.
How to solveGiven that:-
The angle is = 45
The height of the skyscraper is 1140 feet.
The horizontal distance will be calculated by applying the angle property in the right angle triangle.
tan45 = ( P / B )
B = P / tan45
B = P Since ( tan45 =1 )
B = 1140 feet.
Therefore the horizontal distance from the base of the skyscraper out to the ship will be 1140 feet.
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From the observation deck of a skyscraper, Brandon measures a 45^{\circ} ∘ angle of depression to a ship in the harbor below. If the observation deck is 1140 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest tenth of a foot if necessary.
Given that X is a normal random variable with a mean of 40 and a standard deviation of 8 what is P (34
The probability is given as follows:
P(34 < X < 46) = 0.5468 = 54.68%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 40, \sigma = 8[/tex]
The probability is the p-value of Z when X = 46 subtracted by the p-value of Z when X = 34, hence:
Z = (46 - 40)/8
Z = 0.75
Z = 0.75 has a p-value of 0.7734.
Z = (34 - 40)/8
Z = -0.75
Z = -0.75 has a p-value of 0.2266.
Hence:
0.7734 - 0.2266 = 0.5468 = 54.68%.
Missing InformationThe probability is:
P(34 < X < 46).
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Please help if I don't finish this today my parents gonna take my phone away
Find the slope to solve the problem.
Sue drives 200 miles by 1:00 pm. She drives 350 miles by 4:00 pm if she continues at the same rate, how far will she drive by 5:00 pm?
To find the slope in this problem, we can use the formula for calculating slope, which is change in distance divided by change in time. In this case, the change in distance is 350 miles - 200 miles = 150 miles, and the change in time is 4:00 pm - 1:00 pm = 3 hours.
So, the slope (rate of driving) is 150 miles / 3 hours = 50 miles per hour.
Now, to find how far Sue will drive by 5:00 pm, we can use the slope and the additional time of 1 hour (from 4:00 pm to 5:00 pm).Distance driven by 5:00 pm = Slope * Time = 50 miles per hour * 1 hour = 50 miles.Therefore, Sue will drive an additional 50 miles by 5:00 pm, making her total distance driven by 5:00 pm 200 miles + 150 miles + 50 miles = 400 miles. So, Sue will drive 400 miles by 5:00 pm if she continues at the same rate. Note that in this problem, we are assuming that Sue maintains a constant speed throughout her drive. If her speed changes, the solution may be different.
You deposit $300 each month into an account earning 2% interest compounded
monthly.
a) How much will you have in the account in 30 years?
b) How much total money will you put into the account?
c) How much total interest will you earn?
a) The future value of the account after 30 years can be calculated using the formula:
FV = P * ((1 + r/n)^(n*t))
where P is the monthly deposit, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, P = $300, r = 0.02, n = 12 (monthly compounding), and t = 30. Plugging these values into the formula, we get:
FV = $300 * ((1 + 0.02/12)^(12*30)) = $150,505.60
So you will have $150,505.60 in the account after 30 years.
b) The total amount of money you will put into the account is simply the monthly deposit multiplied by the number of months in 30 years, which is 30*12 = 360 months. So the total amount of money you will put into the account is:
$300 * 360 = $108,000
c) The total interest earned can be calculated by subtracting the total amount deposited from the future value of the account. So the total interest earned is:
$150,505.60 - $108,000 = $42,505.60
Answer:
a) you will have approximately $133,381.85 in the account in 30 years.
b) a total of $108,000 into the account over 30 years.
c) a total of $25,381.85 in interest over 30 years.
Step-by-step explanation:
PLS HELP ASAP PLSSSSSS
Answer:
a) |x -8| = 6
b) |x -15| = 0
Step-by-step explanation:
You want the values of 'b' and 'c' for the cases where the solutions to the equation |x -b| = c are ...
2 and 1415SolutionsThe solutions to |x -b| = c are the solutions to ...
x -b = c ⇒ x = b +c
x -b = -c ⇒ x = b -c
ParametersGiven the two solutions P and Q, the values of 'b' and 'c' can be found from ...
P = b +c
Q = b -c
Adding these two equations gives ...
P +Q = 2b ⇒ b = (P +Q)/2
Subtracting the second equation from the first gives ...
P -Q = 2c ⇒ c = (P -Q)/2
a) Solutions 2 and 14b = (2 +14)/2 = 8
c = (14 -2)/2 = 6
The equation is ...
|x -8| = 6
b) Solutions 15 and 15b = (15 +15)/2 = 15
c = (15 -15)/2 = 0
The equation is ...
|x -15| = 0
Can anyone help with this part of my geometry notes ?
From the interior angle theorem:
m∠1 = ¹/₂(m∠AD + m∠BC)m∠2 = 180 - m∠1m∠AED = 77°m∠AEB = 103°m∠LK = 50°What is the interior angle theorem?The Interior Angle Theorem states that if two secants or chords intersect inside a circle, then the measure of the angle formed is equal to half the sum of the measures of the intercepted arcs.
Considering the given circles:
m∠AED = ¹/₂(45 + 109)
m∠AED = 77°
m∠AEB = 180 - 77
m∠AEB = 103°
m∠LK = (2 * 62) - 74)
m∠LK = 50°
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Help pleaseeeee I would appreciate it
(1) The result of the row operation R₂ ↔ R₃ is [ -5 1 0 8]
[ 8 8 -7 5 ]
[ 2 2 6 -5]
(2) The result of the row operation 3R₁ ↔ R₁ is [24 - 27 -21 - 18]
[8 9 -4 -5]
[2 2 -7 -8]
What is the result of the row operation?
The result of the row operation in the matrix is calculated as follows;
R₂ ↔ R₃, implies changing row 2 and row, and the result would be;
[ -5 1 0 8]
[ 8 8 -7 5 ]
[ 2 2 6 -5]
The result of obtained from 3R₁;
3R₁ = [24 - 27 -21 - 18]
3R₁ ↔ R₁ is determined as; (the row interchange)
[24 - 27 -21 - 18]
[8 9 -4 -5]
[2 2 -7 -8]
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La distancia entre Bay Town y Oak Glen es de 175 millas. Si la ecuación y = -x +175 representa la distancia que queda por recorrer hasta Oak Glen, ¿qué representa el dominio? ¿Qué es el dominio?
The correct answer is: D) distance traveled since leaving Bay Town; x ≥ 0
How to solveThe equation y = -x + 175 represents the distance left to travel to Oak Glen.
In this equation, x is the distance traveled since leaving Bay Town, and y is the distance left to reach Oak Glen.
The domain represents the possible values of x, which is the distance traveled since leaving Bay Town.
Since distance traveled cannot be negative, the domain is x ≥ 0. Therefore, the correct answer is:
D) distance traveled since leaving Bay Town; x ≥ 0
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The question in English is:
The distance between Bay Town and Oak Glen is 175 miles. If the equation y = -x +175 represents the distance to go to Oak Glen, what does the domain represent? What is the domain?
Find a pair of integers whose difference gives zero.
A)8 and 1
B)8 and 2
C)8 and 3
D)-8 and -8
Answer:
Answer is D.
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an expression that is equivelent to 12x-3x
Answer:
it would be 9x
Step-by-step explanation:
because subtract 3 from 12 and leave the x
Carson is organizing textbooks on his bookshelf. He has a Spanish textbook, a math textbook, a history textbook, and a health textbook. How many different ways can he line the textbooks up on his bookshelf?
Carson can line up his textbooks on his bookshelf in 24 different ways
What is Permutation?
Permutations are a way to count the number of ways that a set of objects can be arranged in a particular order. A permutation is an ordered arrangement of objects.
What is Combination?
The combination is a way to count the number of ways that a set of objects can be selected without regard to order. A combination is an unordered selection of objects.
According to the given information:
Carson has four textbooks that he wants to line up on his bookshelf. The number of different ways that he can do this is given by the permutation formula:
n! / (n - r)!
where n is the total number of objects (in this case, 4 textbooks), and r is the number of objects that he wants to arrange in a particular order (in this case, all 4 textbooks).
On substituting the values in the formula,
4! / (4 - 4)! = 4! / 0! = 4 x 3 x 2 x 1 / 1 = 24
Therefore, Carson can line up his textbooks on his bookshelf in 24 different ways.
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A group of 7 friends is planning a hike. Each friend will need of a gallon of water to drink during the hike. How many gallons of water will the group need for the hike?
to manufacturing floor
T
30 in.
72 in.
to loading dock
D
48 in.
36 in.
g) What is the longest rod that can be carried to the loading dock? Round to
the nearest tenth of an inch.
Answer:
To determine the longest rod that can be carried to the loading dock, we want to find the shortest distance from point T to line segment CD. We can use the Pythagorean theorem for this.
First, we need to find the equation of the line containing segment CD. We can find the slope of the line CD as:
m = (y2 - y1) / (x2 - x1) = (36 - 48) / (48 - 0) = -12/48 = -1/4
where (x1, y1) = (0, 48) and (x2, y2) = (48, 36).
Using point-slope form, we get the equation of the line CD as:
y - 48 = (-1/4)(x - 0)
y = (-1/4)x + 48
Now, we can find the perpendicular distance from point T to the line CD as follows:
d = |(-1/4)(30) + 72 - 48| / sqrt((-1/4)^2 + 1)
d = 42 / sqrt(17) ≈ 10.21
Therefore, the longest rod that can be carried to the loading dock is approximately 10.2 inches long (rounded to the nearest tenth of an inch).
Harrold is a dog walker. He walks 13 different dogs for the same distance around Greenpoint Park everyday. The park is a perfect square in shape. Harrold takes each dog for 1 full lap around the park. In one day Harrold will walk 6, 396ft all together. What is the length of 1 side of the park in yards.
Answer:
123 feet/41 yards
Step-by-step explanation:
When solving problems like this, we need to understand and note down what we already know to make our lives easier.
- He walks 13 different dogs
- the park is a perfect square
- he takes each dog for one full lap
- That day, he walked 6396ft
- He takes each dog the same distance
Now, let's find the unit value (how much ft does he walk if he takes JUST ONE dog around Greenpoint Park?)
Just divide: 6396 / 13 = 492 ft
Meaning, that when Harrold takes JUST ONE dog around the park, which is a perfect square, he walks 492 feet.
One full lap around the square shaped park is just 4 sides of the square.
So, he walks 492 ft every 4 sides.
However, the question specifically asked for one side.
Just divide again to get your answer:
492 / 4 = 123 ft
Therfore, the length of one side of the park is 123 feet, which is 41 yards.
PLEASE HURRY
Let u = - 4i + 2j , v = 3i - j and w = - 6j
Find the specified scalar or vector
5u(3v - 4w)
The specified scalar or vector 5u(3v - 4w) is equal to -420i + 250j.
We can begin by distributing the scalar 5 to the vector 3v - 4w:
5u(3v - 4w) = 5u(3v) - 5u(4w)
Next, we can find the scalar multiples:
5u(3v) = 5(-4i + 2j)(3(3i - j)) = 5(-36i + 10j)
5u(4w) = 5(-4i + 2j)(4(-6j)) = 5(48i - 40j)
Now we can substitute these values back into the original expression:
5u(3v - 4w) = 5(-36i + 10j) - 5(48i - 40j)
Simplifying:
5u(3v - 4w) = -420i + 250j
Therefore, 5u(3v - 4w) = -420i + 250j.
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if a clock shows it is 3 o'clock, how could you describe the smaller angle made my the two hands of the clock? solve this problem any way you choose
The smaller angle made by the two hands of the clock at 3 o'clock is 90 degrees.
What is an angle?A figure known as an angle is created by two rays or line segments that meet at a place known as the vertex of the angle. The sides or legs of the angle are other names for the rays or line segments.
According to question:To determine the smaller angle made by the two hands of a clock when it is 3 o'clock, we can use the following formula:
angle = |(11/2) * m - 30h|
where:
m is the number of minutes past the hour (in this case, since it is 3 o'clock, m = 0)
h is the hour (in this case, h = 3)
By using this formula, we get:
angle = |(11/2) * 0 - 30(3)| = |0 - 90| = 90
Therefore, the smaller angle made by the two hands of the clock at 3 o'clock is 90 degrees.
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