the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{(-3)}}} \implies \cfrac{-4}{3 +3} \implies \cfrac{ -4 }{ 6 } \implies - \cfrac{2}{3}[/tex]
Joaquin is buying bags of tortilla chips to make a nacho platter for a party. He can buy the 13-oz bags for $2. 99 each or the 18-oz bags for $3. 42 each. Which is the better value? Explain
To determine which is the better value, we need to compare the cost per ounce of each bag of tortilla chips.
Joaquin should buy the 18-oz bags of tortilla chips to make his nacho platter.
How to get the best valueFor the 13-oz bag at $2.99, the cost per ounce is:
2.99 / 13 ≈ $0.23 per ounce
For the 18-oz bag at $3.42, the cost per ounce is:
3.42 / 18 ≈ $0.19 per ounce
Therefore, the 18-oz bag is the better value, as it has a lower cost per ounce than the 13-oz bag. Joaquin should buy the 18-oz bags of tortilla chips to make his nacho platter.
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0.1(-90 + 50a) in distributive property
Given:
[tex]0.1(-90 + 50a)[/tex]
Apply the distributive law: [tex]a(b+c)=ab+ac[/tex]
[tex]0.1(-90 + 50a)=0.1(-90)+0.1\times50a[/tex]
[tex]=0.1(-90)+0.1\times50a[/tex]
Simplify [tex]0.1(-90)+0.1\times50a[/tex]:
[tex]\boxed{\bold{=-9+5a}}[/tex]
. I am a rectangular prism.
I am fewer than 3 cubes high.
• I am made of more than 5 cubes.
. My volume is fewer than 8 cubes.
• Who am I
The rectangular prism that has all the given qualities can be found to be Option D.
How to find the rectangular prism ?The shape is said to be a rectangular prism which means that it could be Options B, D, and F.
The shape is made up of more than 5 cubes which means that Option F is out as it is only made up of 4 cubes.
The volume of the rectangular prism is less than 8 cubes which means that it cannot be Option B as this has 8 cubes as its volume.
In conclusion, the rectangular prism described is Option D.
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before comparing means, we need to test the relationship of the population variances. what null hypothesis would you use to determine if the population variances differ? group of answer choices population variance 1 equals population variance 2 population variance 1 differs from population variance 2 population variance 1 is less than population variance 2 population variance 1 exceeds population variance 2
The correct option is B, The null hypothesis to test if the population variances differ is population variance 1 differs from population variance 2.
Variance is calculated as the average of the squared differences of each data point from the mean. In other words, variance measures how far the data points are from their average value. A high variance indicates that the data points are spread out over a wider range, while a low variance indicates that the data points are clustered more tightly around the mean.
Variance is an important concept in statistical analysis because it helps to assess the reliability of data and to make inferences about the population from a sample. It is also used in many areas of research, such as finance, economics, and engineering, to measure the risk or uncertainty associated with a set of data. Variance is closely related to other statistical measures such as standard deviation, covariance, and correlation, and is often used in conjunction with these measures to gain a deeper understanding of the data.
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Complete Question:-
Before comparing means, we need to test the relationship of the population variances. what null hypothesis would you use to determine if the population variances differ?
a. population variance 1 equals population variance 2
b. population variance 1 differs from population variance 2
c. population variance 1 is less than population variance 2
d. population variance 1 exceeds population variance 2
(e) The radius of the semi-circle centre O is 5 cm. A square is fitted into the semi-circle as shown in the diagram. Calculate the area of the square. (Hint: Let the length of the square equal x)
The length of the square is derived to be √20 using the Pythagoras rule and the area of the square is 20 cm²
What is the Pythagoras rule?The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let the length of the square be x, thus considering the triangle formed with the radius as the hypotenuse, x as the height and x/2 as the base, then By Pythagoras rule we can evaluate for x as follows:
x² + (x/2)² = 5²
(4x² + x²)/4 = 25
5x² = 100 {cross multiplication}
x² = 20
x = √20
Area of the square = (√20)²
Area of the square = 20 cm²
Therefore, the length of the square is derived to be √20 using the Pythagoras rule and the area of the square is 20 cm²
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Draw out the two triangles and state what triangle is congruent to what triangle and how we know.
a)ML congruent ZJ, LR congruent JB,Angle L congruent angle J
BRAINILEST 18 POINTS
Answer:
To draw the two triangles and state what triangle is congruent to what triangle and how we know, we start by drawing two triangles, one with vertices M, L, and R, and the other with vertices Z, J, and B. We are given that ML is congruent to ZJ, LR is congruent to JB, and angle L is congruent to angle J.
We can use the Side-Angle-Side (SAS) congruence criterion to show that the two triangles are congruent. This criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
In this case, we have ML congruent to ZJ, LR congruent to JB, and angle L congruent to angle J. Therefore, we can conclude that triangle MLR is congruent to triangle ZJB by the SAS criterion.
a teacher conducted a random survey of his students and found that 33% did not have a pet. to the nearest whole number, how many students would have a pet out of a population of 134? gaumath
The number of students who would have a pet out of a population of 134 is equal to 90.
Percent of students did not have pet = 33%
Total number of students = 134
Number of students who do not have a pet
= 33% × 134
= 0.33 × 134
= 44.22
Since we cannot have a fraction of a student.
Round 44.22 to the nearest whole number which is 44.
This means that 44 out of the 134 students surveyed did not have a pet.
The number of students who have a pet
= subtract the number of students who do not have a pet from the total number of students.
⇒ Number of students who have a pet = 134 - 44
⇒ Number of students who have a pet = 90
Therefore, approximately 90 students out of a population of 134 have a pet.
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The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 9 above 80 to 89, at 9 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Flower Town.
When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?
Mean, because Flower Town is symmetric
Mean, because Flower Town is skewed
Median, because Desert Landing is skewed
Median, because Desert Landing is symmetric
The answer is either A. IQR, because Sunny Town is symmetric or B. IQR, because Beach Town is skewed.
We know that,
A distribution refers to the pattern of how data is spread out or distributed across different values or intervals. It is a way to describe and analyze the shape, center, and spread of a set of data.
According to question:
To determine the location with the most consistent temperature, we need to measure the variability of the temperature data in both locations. The measure of variability that is appropriate for this purpose is the interquartile range (IQR), which measures the spread of the middle 50% of the data.
Therefore, the answer is either A. IQR, because Sunny Town is symmetric or B. IQR, because Beach Town is skewed, depending on the shape of the distributions. If the temperature data in Sunny Town is symmetric, then the IQR would be appropriate to measure the spread of the data. If the temperature data in Beach Town is skewed, then the IQR would also be appropriate to measure the spread of the data. However, if the temperature data in either location is not skewed, then the range would not be an appropriate measure of variability.
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I need the axis of symmetry and the vertex of the following y=x^2+6x+4
y=-2x^2+8x-5
y=x^2-2x
y=-x^2-8x-9
1. axis of symmetry = -3
vertex = ( -3,-5)
2. axis of symmetry = -2
vertex = ( -2,-13)
3. axis of symmetry = 1
vertex = ( 1,-1)
4. axis of symmetry = 4
vertex = (4,-5)
What is axis of symmetry and vertex?The vertex is the highest point if the parabola opens downward and the lowest point if the parabola opens upward.
The axis of symmetry is the line that cuts the parabola into 2 matching halves and the vertex lies on the axis of symmetry.
The vertex is calculated as -b/2a and we substitute the value in the equation to get the y axis. The equation must be in the form ax²+bx + c
The axis of symmetry is calculated as -b/2a
1. x²+6x+4
axis of symmetry = -6/2 = -3
the y cordinate vertex = -3)²+6(-3)+4 = 9-18+4 = -5
therefore the vertex = ( -3,-5)
2. 2x²+8x-5
axis of symmetry= -8/2(2) = -8/4 = -2
the y cordinate of vertex = 2(-2)² + 8(-2) -5
= 8-16-5 = -13
therefore the vertex = ( -2,-13)
3. x²-2x
axis of symmetry = -(-2)/2 = 2/2 = 1
the y cordinate of vertex = 1²-2(1) = 1-2 = -1
vertex = ( 1,-1)
4. x²-8x-9
axis of symmetry = -(-8)/2 = 8/2 = 4
the y cordinate of the vertex= 4²-8(4) -9 = 16-12-9 = -5
therefore the vertex = (4,-5)
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4. Write an equation for the quadratic below in VERTEX form and STANDARD form.
a) VERTEX form
y=-1 (1₁)
b) STANDARD form (Hint: expand the
vertex form above)
f(x) =
(-1,0)
(0, 3)
(1,4)
0
(3,0)
Help me please!!!!!!
The vertex form of the quadratic equation is:
y = -(x - 1)^2 + 4
The standard form is:
y = -x^2 + 2x + 3
How to find the equations for the parabola?If the leading coefficient is a and the vertex is (h, k), we can write:
y = a*(x - h)^2 + k
Here the vertex is at (1, 4), then:
y = a*(x - 1)^2 + 4
And it also passes through (0, 3), then we can write:
3 = a*(0 - 1)^2 + 4
3 = a + 4
3 - 4 = a
-1 = a
The vertex form is:
y = -(x - 1)^2 + 4
b) Now expand that, we will get:
y = -(x^2 - 2x + 1) + 4
y = -x^2 + 2x - 1 + 4
y = -x^2 + 2x + 3
That is the standard form.
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The sides of a triangle measure 5 meters and 8 meters. What are the possible side lengths for the third side?
Answer:
To determine the possible lengths of the third side of a triangle with sides measuring 5 meters and 8 meters, we can use the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side.
So in this case, let's call the length of the third side "x". According to the triangle inequality theorem:
5 + 8 > x
or
x < 13
8 + x > 5
or
x > -3
Since the length of a side cannot be negative, we can disregard the second inequality. Therefore, the possible lengths of the third side, "x", are:
- 5 < x < 13
So the third side can measure any length between 5 and 13 meters, exclusive of 5 and 13.
mark me brilliant
help asap thank youuu
Answer: D
Step-by-step explanation:
What is the
area in square
millimeters of
the triangle
outlined on the
origami figure?
b = 5 cm
h = 1.28 cm
The area of the triangle outlined on the origami figure is 3.2 square centimeters or 3200 square millimeters (since 1 cm = 10 mm).
What is area?Area is the measurement of the extent of a two-dimensional surface or shape, typically measured in square units such as square meters or square feet.
What is origami figures?Origami is a Japanese art form of paper folding where intricate and beautiful designs are created by folding a single piece of paper without cutting or gluing it.
According to the given information:
the area of a triangle using base (b) and height (h) measurements. The formula is:
Area = (1/2) x b x h
To convert this area into square millimeters, you would need to ensure that the base and height measurements are also in millimeters. If the base is 5 cm, this would be equivalent to 50 mm (since there are 10 millimeters in each centimeter). If the height is 1.28 cm, this would be equivalent to 12.8 mm.
Using these measurements in the formula, we get:
Area = (1/2) x 50 mm x 12.8 mm
Area = 320 mm²
Therefore, the area of the triangle outlined on the origami figure would be 320 square millimeters.
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A tree is struck by lightning and snaps off 34 feet above the ground. The top part of the tree, 117 feet long, rests with the tip on the ground, while the broken end rests on the top of the stump.
What angle does the top part of the tree make with the ground?
Given that a company lets you download songs for $0.99 each after you pay a $5 fee to be a member, evaluate f(4)
for the function of total cost for x songs.
Responses
3.96
21. 96
9.90
8.96
Question 2
Suppose that you want to design a set of four congruent square pyramids whose combined volume is the same as the volume of a single
rectangular pyramid. What values of land h for the four square pyramids and what values of I, w, and h for the rectangular pyramid will produce
Identical volumes? There is more than one correct answer.
The values of l and h for the four square pyramids and values of I, w, and h for the rectangular pyramid that will produce Identical volumes is w = 4l.
What is a square pyramid?In Mathematics and Geometry, a square pyramid can be defined as a type of pyramid that has a square base, four (4) triangular sides, five (5) vertices, and eight (8) edges.
In this scenario, the base areas of each geometric figures can be calculated as follows:
Square pyramid, A = L².
Rectangular pyramid, A = lw.
Where:
l represents the length of a rectangular prism.w represents the width of a rectangular prism.Since the four (4) congruent square pyramids has a combined volume that is the same as the volume of one rectangular pyramid, a relation for the dimension is given by:
4l²h/3 = lwh/3.
w = 4l.
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Answer:
Step-by-step explanation:
take a sheet of paper that is 0.1mm thick. amuse yourself by tearing it in half and putting both pieces together, and then tearing those in half. repeat the process until you have torn it in half twenty-five times. how high, in meters, is the stack of paper?
The stack of paper will be 3355.4432 meters high after stacking halves of it tearing up for 25 times by method of unit conversion from millimeters to meters.
A sheet of paper is 0.1 mm thick.
It is folded in halves for 25 times by tearing it.
The above information can be represented in an equation form as,
Height of the paper stack = (0.1)* ([tex]2^{n}[/tex]) in millimeters
where, n denotes the number of times paper is folded.
Thus, height of the paper stack after tearing it in halves for 25 times we get,
Height = (0.1)* ([tex]2^{25}[/tex]) in millimeters
= 3355443.2 millimeters
We can convert milimmillimeters in meters by the following way as,
1 millimeter = 0.001 meter
Therefore, 33355443.2 millimeters = (0.001)(3355443.2) meters
= 3355.4432 meters
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a new car is offered with eleven different optional packages. the dealer claims that there are more than 2,000 different combinations available. is this claim justified? explain. there are incorrect: your answer is incorrect. different ways to choose which of the packages you get, so the claim is changed: your submitted answer was incorrect. your current answer has not been submitted. justified.
The dealer's claim that there are "more than 1,000 different combinations" of the 10 optional packages available for the new car is justified, as there are actually 1024 possible combinations.
To determine whether the dealer's claim is justified, we need to calculate the total number of possible combinations of packages that can be selected.
Since there are 10 optional packages, there are 2^10 (or 1024) possible combinations of packages. This is because for each package, there are two possible choices: either it is selected or it is not selected.
Therefore, the dealer's claim that there are "more than 1,000 different combinations" is indeed justified. The actual number of possible combinations is 1024, which is greater than 1,000.
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Factor the following expressions completely. Show and check all work on your own paper.
x^4 - 16
thx so much I will give brainiest
Answer:
(x² + 4)(x + 2)(x - 2)------------------------------
Factor the given expression, using the difference of squares identity:
a² - b² = (a + b)(a - b)Factoring in below steps:
x⁴ - 16 = (x²)² - 4² = (x² + 4)(x² - 4) = (x² + 4)(x² - 2²) = (x² + 4)(x + 2)(x - 2)HELPP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
[tex]\cos(18^o )=\cfrac{\stackrel{adjacent}{x}}{\underset{hypotenuse}{23}} \implies 23\cos(18^o)=x \implies 21.87\approx x[/tex]
Make sure your calculator is in Degree mode.
Surface of triangle is 305 inches and area of base is 55 inches. Each face has a base of 9 inches. What is the slant
Note that where the above is given, the slant is 18.52 inches
How is this so?Given the above, we can use the formula for the surface area of a triangular pyramid, which is given by...
Surface area = base area + (1/2) × perimeter × slant
where the perimeter is the sum of the lengths of the three sides of the base, and the slant is the height of each triangular face.
We are given that the base area is 55 square inches and the perimeter is 3 × 9 = 27 inches. We are also given that the total surface area is 305 square inches. Substituting we have
305 = 55 + (1/2) × 27 × slant
Simplifying and solving for the slant, we get:
250 = 13.5 × slant
slant = 18.52 inches
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The diagram shows a tree and a man.
#
The man is of average height.
The tree and the man are drawn to the same scale.
a) Write down an estimate for the real height, in metres, of the man.
b) Find an estimate for the real height, in metres, of the tree.
The requried estimate of the real height of the man is 1.7 meters and the height of the tree is 10.2 meters.
Since the man is of average height, we can assume he is about 1.7 meters tall.
From the diagram, the man is approximately 1/6 the height of the tree. Therefore, the tree is about 6 times taller than the man.
Thus, an estimate for the real height of the tree is 6 times the height of the man, which is 6 x 1.7 = 10.2 meters.
Therefore, the requried estimate of the real height of the man is 1.7 meters and the height of the tree is 10.2 meters.
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Dan weighs 14 kg more than Steve. Together they weigh less than 178 kg. What can Dans weight be
Dan's weight can be any value between 82 kg and 96 kg
Let's call Steve's weight "x".
According to the problem, Dan weighs 14 kg more than Steve, so Dan's weight would be x + 14.
Together, their weight would be the sum of their weights
x + (x + 14) = 2x + 14
We know that their combined weight is less than 178 kg, so the inequality will be
2x + 14 < 178
Subtracting 14 from both sides
2x < 164
Dividing by 2
x < 82
So Steve's weight is less than 82 kg.
To find the possible range of Dan's weight, we can substitute x + 14 for Dan's weight
(x + 14) < (178 - x)
Simplifying
2x < 164
x < 82
x + 14 < 96
So Dan's weight is less than 96 kg.
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ite the equation of the graph shown below in factored form.
Answer:
f(x) = (x + 1)((x - 1)^2)(x - 3)
On April 11, 2012, two earthquakes were measured off the northwest coast of Sumatra. The first had a magnitude of
8.6. The second had a magnitude of 8.2. By what approximate factor was the intensity of the first earthquake greater
than the intensity of the second earthquake?
M-log
M = the magnitude of an earthquake
/= the intensity of an earthquake
lo=
= the smallest seismic activity that can be measured, which is 1
Answer:
Step-by-step explanation:
The relationship between magnitude (M) and intensity (I) of an earthquake is given by:
I ~ 10^(1.5M + 4.8)
We can use this relationship to compare the intensities of the two earthquakes:
I1/I2 = (10^(1.5M1 + 4.8))/(10^(1.5M2 + 4.8))
= 10^(1.5(M1 - M2))
Substituting the given magnitudes, we get:
I1/I2 = 10^(1.5(8.6 - 8.2))
= 10^(1.5(0.4))
≈ 2.24
Therefore, the intensity of the first earthquake was approximately 2.24 times greater than the intensity of the second earthquake.
Simplify 3! A. 2 B. 5 C. 3 D. 6
3! = 6
In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers from 1 up to n. For example
1! = 1
2! = 2 x 1 = 2
4! = 4 x 3 x 2 x 1 = 24
The factorial function is defined only for non-negative integers, but it is often extended to other types of numbers, such as complex numbers or even some non-integer real numbers, using techniques from complex analysis.
Factorials are used in a variety of mathematical contexts, such as combinatorics, probability theory, and calculus. For example, in combinatorics, factorials are used to count the number of ways to arrange a set of objects, or the number of ways to choose a subset of objects from a larger set. In calculus, factorials appear in Taylor series, which are used to approximate functions as a sum of powers of x.
Hence, the correct option is D.
The expression 3! (read as "3 factorial") is a mathematical shorthand for the product of all positive integers from 1 to 3. It is written as
3! = 3 x 2 x 1
Evaluating this expression gives
3! = 6
Hence, the correct option is D.
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A car is purchased for $23,750 and it depreciates in value at a 9% rate every year. Write the equation for this exponential function and determine the worth of the vehicle in 3 years.
Answer:
f(3) = 23,750(0.09)^3 = 6412.5
Step-by-step explanation:
how many unique slip planes of the {110} type are in a bcc metal?how many unique slip planes of the {110} type are in a bcc metal?2468122448
As per the mentioned informations, there are 4 slip planes associated with each of the 3 unique <111> directions, giving a total of 12 unique {110} slip planes in a body-centered cubic (BCC) crystal
In a body-centered cubic (BCC) crystal, there are 12 slip systems of the {110} type. Each of these slip systems is associated with a unique slip plane.
To understand why there are 12 slip systems, consider that the {110} plane has two perpendicular <111> directions, which are the directions of maximum atomic density in a BCC crystal. Each of these <111> directions can be associated with four equivalent {110} slip planes, which intersect at a line that lies along the <111> direction.
Therefore, there are 4 slip planes associated with each of the 3 unique <111> directions, giving a total of 12 unique {110} slip planes in a BCC metal.
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Question 5 of 20
Euler's formula, V-E+F=2, relates the number of vertices V, the number of edges E, and the number of
faces F, of a polyhedron. Solve Euler's formula for E
O E=2-V+F
O E= -F-2+V
OE=V+F-2
O E=2+-F
The solution for E in the equation V - E + F = 2 is E = V + F - 2
Solving the Euler's formula for EFrom the question, we have the following parameters that can be used in our computation:
V - E + F = 2
The above equation relates the number of vertices V, the number of edges E, and the number of faces F, of a polyhedron.
It is called the Euler's formula
So, we have
V - E + F = 2
Add E to both sides
V + F = 2 + E
Subtract 2 from both sides
V + F - 2 = E
So, we have
E = V + F - 2
Hence, the solution for E is E = V + F - 2
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Determine t he minimum speed of a particle moving in 3-space with position function r(t) = t^2 i + 6t j + (t^2 - 24t) k. min speed = 19 units/sec min speed = 18 units/sec min speed = 16 units/sec min speed = 17 units/sec min speed = 20 units/sec
To determine the minimum speed of a particle moving in 3-space with position function r(t) = t^2 i + 6t j + (t^2 - 24t) k, we need to find the magnitude of the velocity vector, which is the derivative of the position vector with respect to time.
v(t) = r'(t) = 2ti + 6j + (2t - 24)k
The speed of the particle at any given time t is the magnitude of the velocity vector, which is:
|v(t)| = √(4t^2 + 36 + (2t - 24)^2) = √(4t^2 + 4t^2 - 96t + 576) = √(8t^2 - 96t + 576)
To find the minimum speed, we need to find the minimum value of |v(t)|. We can do this by finding the vertex of the parabolic function 8t^2 - 96t + 576, which corresponds to the minimum value of the function.
The vertex of a parabola of the form ax^2 + bx + c is at x = -b/2a. In this case, a = 8, b = -96, and c = 576, so the vertex is at t = -b/2a = 96/16 = 6.
So the minimum speed of the particle is:
|min speed| = |v(6)| = √(8(6)^2 - 96(6) + 576) = √(288) = 12√2
Therefore, the minimum speed of the particle moving in 3-space with position function r(t) = t^2 i + 6t j + (t^2 - 24t) k is approximately 16.97 units/sec (rounded to two decimal places). Option 4, min speed = 17 units/sec, is the closest answer.
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