pick a region of your choice. write out the integrals needed to find the volume of the region using a triple integral with rectangular, cylindrical and spherical coordinates. (you must use all three types coordinates on the same region - choose wisely!). setup but do not evaluate the integrals.
The volume integral for f(x,y,z) = 1 over the region E : x² + y² + z² ≤ 4,
1) In spherical coordinates system is
[tex]V = {\int_{0}^{2π} \int_{0}^{π} \int}_{0}^{2} \rho^{2} \sin( \phi) \: d\rho d\phi d\theta[/tex]
2) In cylinderical coordinates system is
[tex]V = \int_{0}^{2π} \int_{0}^{2} (\int_{-\sqrt {4 - x² - y²}}^{\sqrt{ 4 - x² - y²}} dz) rdr d \theta \\ [/tex]
3) In rectangular coordinates syatm is
[tex]V = \int_{0}^{2}\int_{-\sqrt {4 - x²}}^{\sqrt{4 - x²}} \int_{ - \sqrt{ 4 - x² - y²}}^{ \sqrt{4 - {x}^{2} - {y}^{2} } } \: dz dy dx \\ [/tex]
We pick a region E : x² + y² + z² ≤ 4 and determine volume over the region E for function, f(x,y,z ) = 1 .
Use of Spherical coordinates (ρ,θ, φ), Volume can be written as[tex]V = {\int \int \int}_{E} f(x,y,z) dV[/tex]
In spherical coordinates system we plug,
[tex]x = \rho sin \phi cos \theta[/tex]
[tex]y = \rho sin \phi sin \theta[/tex]
[tex]z = \rho cos \phi [/tex]
[tex]dV = dx dy dz = |J| d\rho d\phi d\theta [/tex]
where, [tex]|J| = \rho² sin \phi[/tex]
=> [tex]dx dy dz = \rho² sin \rho d\rho d\phi d\theta[/tex]
So, [tex]V = {\int \int \int}_{x² + y² + z² ≤ 4} 1 \: dxdy dz[/tex]
Now, [tex]V = {\int_{0}^{2π} \int_{0}^{π} \int}_{0}^{2} \rho^{2} \sin( \phi) \: d\rho d\phi d\theta[/tex]
Using Cylindrical coordinates (r,θ,z)Region , E : x² + y² + z² ≤ 4
=> z² ≤ 4 - x² - y²
=> z ≤ ± √4 - x² - y²
[tex]V = {\int \int_{ x² + y² ≤ 4} \int}_{ - \sqrt{ 4 - x² - y²}}^{ \sqrt{4 - {x}^{2} - {y}^{2} } } 1 \: dz dx dy \\ [/tex]
here, r∈[0, 2], θ∈[0,2π]
[tex]V = \int_{0}^{2π} \int_{0}^{2} (\int_{-\sqrt {4 - x² - y²}}^{\sqrt{ 4 - x² - y²}} dz) rdr d \theta \\ [/tex]
Using rectangular coordinates (x,y,z), Volume integral can be written as :[tex]V = {\int \int \int}_{E} f(x,y,z) dV[/tex]
[tex]V = {\int \int_{ x² + y² ≤ 4} \int}_{ - \sqrt{ 4 - x² - y²}}^{ \sqrt{4 - {x}^{2} - {y}^{2} } } 1 \: dz dx dy \\ [/tex]
Here, y² ≤ 4 - x²
=> y = ± √4 - x² and x∈ [0,2], So,
[tex]V = \int_{0}^{2}\int_{ -\sqrt {4 - x²}}^{\sqrt{4 - x²}} \int_{ - \sqrt{ 4 - x² - y²}}^{ \sqrt{4 - {x}^{2} - {y}^{2} } } \: dz dy dx \\ [/tex]
Hence, in above we determined the volume integral for region, E in all three coordinates systems.
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Question 4 options:
Quadrilateral WXYZ is inscribed in a circle with m∠W=55° and m∠X=117°. What is the measurement of angle Y?
What is the measurement of angle Z?
Angle Y measures 125 degrees and angle Z measures 63 degrees.
what is a circle?
A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. It can also be defined as the set of points that are a fixed distance (called the radius) away from the center point. The distance around the circle is called its circumference, and the distance across the circle passing through the center is called its diameter.
Since quadrilateral WXYZ is inscribed in a circle, we know that opposite angles add up to 180 degrees. Therefore:
m∠Y + m∠W = 180 degrees ...(1)
m∠Z + m∠X = 180 degrees ...(2)
We are given that m∠W = 55 degrees and m∠X = 117 degrees, so we can substitute those values into equations (1) and (2):
m∠Y + 55 = 180 ...(1)
m∠Z + 117 = 180 ...(2)
Solving for m∠Y and m∠Z, we get:
m∠Y = 125 degrees
m∠Z = 63 degrees
Therefore, angle Y measures 125 degrees and angle Z measures 63 degrees.
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In an Australian netball competition, these teams are tipped to win Round 1 by three experts:
Expert A: NSW, Queensland, WA, Tasmania
Expert B: SA, Victoria, Queensland, WA Expert C: NSW, ACT, WA, Victoria No one tipped the Northern Territory to win. Which team did Victoria play?
Answer:
undetermined or most likely Tasmania
Step-by-step explanation:
Based on the choices of experts in the first round of the Australian netball competition, we can conclude that Victoria played against WA. This is because, out of the common tips, WA was tipped by an expert who also tipped Victoria and didn't tip Queensland. Therefore, WA is the likely team that Victoria played against.
Explanation:To identify which team Victoria played in the Australian netball competition we can reason through our experts' tips. The experts' tips overlap at Queensland and WA as indicated by Expert A and Expert B. However, Expert C tipped Victoria, and they did not tip Queensland which tells us that Victoria did not play against Queensland, leaving us with WA. Hence Victoria must've played against WA.
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Choose the equation that represents the line that passes through the point (6, -3) and has a slope of
1
-İN
2
O
O
y=-x+6
O
y=-x-6
|_y=-x-3
2
|_y=-x+3
Answer:y=-x+6
Step-by-step explanation:
6×y^2=240in^2
Solve for Y
Answer:
[tex]y=40\sqrt{\frac{6}{x} }[/tex]
[tex]y=-40\sqrt{\frac{6}{x} } ,x > 0[/tex]
Step-by-step explanation:
pls tell me if wrong have a good night/day
find the length of the diagonal of the box below. Round to the nearest hundredth (you have to do pythagorean theorem twice)
Answer:
12.5
Step-by-step explanation:
9.6² + 2.8² = 10²
10² + 7.5² = 12.5²
7. The ride length of a roller coaster is 314
minutes. Every ride starts as soon as the
previous ride ends. How many rides take place
in 28 minutes?
Answer: To find out how many rides take place in 28 minutes, we need to divide the total ride length by the length of one side, and then round down to the nearest whole number.
The length of one ride can be calculated by dividing the total ride length by the number of rides. Since we don't know the number of rides, let's call it "n":
length of one ride = total ride length / n
314 minutes / n
Now we can set up an equation to solve for "n":
28 minutes = length of one ride * number of rides
28 minutes = (314 minutes / n) * number of rides
We can simplify this equation by multiplying both sides by "n":
28 minutes * n = 314 minutes * number of rides
Dividing both sides by 314 minutes, we get:
n = (28 minutes * number of rides) / 314 minutes
Multiplying both sides by 314 minutes and dividing by 28 minutes, we get:
number of rides = (n * 314 minutes) / 28 minutes
number of rides = 11.21
Rounding down to the nearest whole number, we get:
number of rides = 11
Therefore, in 28 minutes, 11 rides take place.
Step-by-step explanation:
Erin wants to buy a new car. To do this, she takes out a loan of $24,000. The loan is to be repaired in seven years with an interest of 12% per annum. What is the total amount of interest she pays?
Drag a statement or reason to each box to complete this proof
Drag the following statement, equation or reason to each box to complete this proof accordingly:
2. Multiplication Property of Equality
3. x-2 = 8
4. Addition Property of Equality
5. x = 10 Simplifying
How to complete the proof of the equation with reason?An equation is a mathematical statement that expresses the equality between two expressions. It contains an equal sign "=" that separates the two expressions.
The proof of the equation with reason can be completed as follow:
(x-2)/4 = 2 Given
4(x-2)/4 = 4 * 2 Multiplication Property of Equality
x-2 = 8 Simplifying
x - 2+ 2 = 8 + 2 Addition Property of Equality
x = 10 Simplifying
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Solve the following system by substitution. CHECK the solution.
3y = 2x + 12
y + 3x = -7
We can use substitution to solve this system of equations. We can solve the first equation for y and get:
y = (2x + 12)/3
We can then substitute this expression for y into the second equation:
(2x + 12)/3 + 3x = -7
Multiplying both sides of this equation by 3 to eliminate the denominator, we get:
2x + 12 + 9x = -21
Simplifying this equation gives:
11x = -33
Dividing both sides by 11, we get:
x = -3
We can then substitute this value of x back into either of the two original equations to find y. Using the first equation, we get:
3y = 2(-3) + 12
3y = 6
y = 2
Therefore, the solution to the system of equations is x = -3 and y = 2.
To check the solution, we substitute these values back into both equations:
3y = 2x + 12 3(2) = 2(-3) + 12 6 = 6
This equation is true, so the solution (x = -3, y = 2) checks out.
IF I A LIQUID IS AT A TEMPERATURE OF 16.9 AND RISES AT A RATE OF 2.3 AND A SOLID IS AT A TEMPERATURE OF 30.7 AND DECREASES AT A RATE OF 6.9 how long will it take for them to be at the same temperature in minutes
Answer:
The number of minutes it will take for a liquid and a solid to reach the same temperature is 3 minutes.
Step-by-step explanation:
You know that the temperature of liquid at 16.9°C is decreasing at a rate of 2.3°C per minute. Then, the temperature of the liquid after t minutes, as its value decreases, will be the difference between the initial temperature of 16.9 ° C and the temperature after t minutes. So:
temperature of the liquid= 16.9°C - 2.3 °C/minute * t
On the other side, you know that the temperature of a solid at 30.7°C is decreasing at a rate of 6.9°C per minute. Then, the temperature of the solid after t minutes, as its value decreases, will be the difference between the initial temperature of 30.7°C and the temperature after t minutes. So:
temperature of the solid= 30.7°C - 6.9 °C/minute * t
You want to calculate the number of minutes it will take for a liquid and a solid to reach the same temperature. This is:
temperature of the liquid= temperature of the solid
16.9°C - 2.3 °C/minute * t= 30.7°C - 6.9 °C/minute * t
Solving:
- 2.3 °C/minute * t= 30.7°C - 6.9 °C/minute * t - 16.9°C
- 2.3 °C/minute * t + 6.9 °C/minute *t= 30.7°C - 16.9°C
4.6 °C/minute * t = 13.8 °C
t=3 minutes
So the number of minutes it will take for a liquid and a solid to reach the same temperature is 3 minutes.
What is the area of this composite figure? Use 3.14 for pi. Round to the nearest hundredth. Show ALL work.
The composite figure compromising of a sector, a triangle and a trapezoid have a total area calculated to be 15.9 square units.
How to find the area of the composite figureWe can observe from the figure that it is a combination of a sector, a triangle and a trapezoid, so we shall calculate the area of each shape and add their result to get the area of the composite figure as follows:
area of the sector = 135°/360° × 22/7 × 2 × 2
area of the sector = 33/7
area of the sector = 4.7 square units
area of triangle = 2.6 × 1
area of the triangle = 2.6 square units
area of the trapezoid = 1/2 × (2.6 + 6) × 2
area of the trapezoid = 8.6 square units
area of the composite figure = 4.7 + 2.6 + 8.6
area of the composite figure = 15.9 square units
In conclusion, the composite figure compromising of a sector, a triangle and a trapezoid have a total area calculated to be 15.9 square units.
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A submarine is passing by a solar station, located al (0,0), that can detect objects that
are as far away as 5km in any direction. A swiss submarine is traveling along a trajectory defined by y= -2/3x +26/3 where x and y represent distances measured in kilometers. Determine algebraically whether the sonar station will detect the submitline.
Answer:
The sonar station will not detect the submarine.
Step-by-step explanation:
The area that the sonar station can detect can be modelled as a circle with center (0, 0) and radius 5 km.
The equation of a circle formula is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.
Therefore, the equation of the circle modelling the perimeter of the sonar station detection area is:
[tex]\implies (x-0)^2+(y-0)^2=5^2[/tex]
[tex]\implies x^2+y^2=25[/tex]
To determine whether the sonar station will detect a swiss submarine traveling along a trajectory defined by y = -2/3x + 26/3, substitute the equation of the trajectory into the found equation of the circle.
[tex]\implies x^2+\left(-\dfrac{2}{3}x+\dfrac{26}{3}\right)^2=25[/tex]
Simplify:
[tex]\implies x^2+\dfrac{4}{9}x^2-\dfrac{104}{9}x+\dfrac{676}{9}=25[/tex]
[tex]\implies 9x^2+4x^2-104x+676=225[/tex]
[tex]\implies 13x^2-104x+451=0[/tex]
Solve the equation for x using the quadratic formula:
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
[tex]\implies x=\dfrac{-(-104) \pm \sqrt{(-104)^2-4(13)(451)}}{2(13)}[/tex]
[tex]\implies x=\dfrac{104 \pm \sqrt{-12636}}{26}[/tex]
[tex]\implies x=\dfrac{104 \pm 18\sqrt{39}\:i}{26}[/tex]
[tex]\implies x=4 \pm \dfrac{9\sqrt{39}}{13}\:i[/tex]
As the solutions are complex numbers, this means that the linear trajectory of the submarine will not intersect the detection area of the sonar station. Therefore, the sonar station will not detect the submarine.
The weight of 4 hummingbirds is recorded below. The weight of each
1
hummingbird has been rounded to the nearest gram.
2
2
2/1/2
3 31/1 4 4/ 5
Weights of birds (grams)
10
What is the weight of all 4 hummingbirds combined?
grams
Answer: The total amount of the hummingbirds' weight is 15 grams.
Step-by-step explanation:
As it is shown in the dot graph, the four hummingbirds' weigh is recorded to the nearest gram.
Hummingbird 1 - 2 1/2
Hummingbird 2 - 3
Hummingbird 3 - 4 1/2
Hummingbird 4 - 5
2 1/2 + 4 1/2 = 7
3 + 5 = 8
Seven plus eight equals to fifteen. Therefore, the total weight of all four hummingbirds is 15.
Hope this helps coralasting123!Solve the inequality of 2(x-6)<-3(x-1)
Answer: 2(x-6) < -3(x-1) is x < 3.
Step-by-step explanation:
2(x-6) < -3(x-1)
Expanding the brackets, we get:
2x - 12 < -3x + 3
Adding 3x to both sides, we get:
5x - 12 < 3
Adding 12 to both sides, we get:
5x < 15
Dividing both sides by 5, we get:
x < 3
Answer:
x>12
Step-by-step explanation:
1/3(x-6)>2
distribute 1/3
1/3x-2>2
add 2 to both sides
1/3x>4
multiply both sides by 3
x>12
The sum of the ages of two brothers Kofi and Kwaku is 35. Kofi age is 2/3 of Kwaku's age. find their ages.
2/3 of 35 is 23. Kofi is 23.
i need help with finding y and x
Answer: x= 24 and y= 73
Step-by-step explanation:
we know
The opposite interior angles are equal and
The angles on the same side of the transversal are supplementary, that means they add up to 180 degrees.
the sum of the interior angles of a parallelogram is 360 degrees.
So 107 + y = 180
180 - 107 = 73
Y = 73
y is equal to its opposite angle so
X can be found by 73 = 3x + 1
Subtract 1 from both sides
73 - 1 = 3x +1 -1
Simplify
72 = 3x
Divide both sides by 3 to solve for x
72/3 = 3/3x
x=24
Check your work by adding the 4 angles together to equal 360
107 + 107 + 73 + 73 = 360
360 = 360
They equal so your solution is correct
since 1961 there has been a total of 6688 peace corp volunteers from the university of California Berkeley and the university of Wisconsin. the number of volunteers from the university of California is 464 more than the number of volunteers from the university Wisconsin. find the number of peace Corp volunteers from each university.
show work
The wheels on a car have a diameter of 2 ft. How many full revolutions will the wheels need to make to travel 220 feet? Round to the nearest whole number.
Using the circumference formula the number of full revolutions the wheels need to make to travel 220 feet is obtained as 35.
What is circumference?
The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area.
The distance traveled by the car in one full revolution of the wheel is equal to the circumference of the wheel.
The circumference of a circle is given by the formula -
C = 2πr
where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.
Since the diameter of the wheel is 2 feet, the radius is half of that, or 1 foot.
Therefore, the circumference of the wheel is -
C = 2π(1 foot) = 2π feet
To find how many full revolutions the wheel needs to make to travel 220 feet, we can divide the distance traveled by the circumference of the wheel -
Number of revolutions = distance traveled / circumference of the wheel
Number of revolutions = 220 feet / (2π feet) ≈ 35.03
Therefore, the wheels need to make 35 full revolutions to travel 220 feet.
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6 foot tall adult casts, a shadow that is 15 feet long estimate the height of a child who cast a 10 foot shadow
By similarity of triangle the height of a children will be 4ft.
What is similarity of triangle?Similar triangles are that kind of triangles that have the same shape, but different sizes. examples of similar objects are All equilateral triangles, squares of any side lengths. In another words, if two triangles having their corresponding angles are congruent and corresponding sides are in equal proportion then two triangles are said to be similar. It is denoted by ‘~’ symbol.
We can use the property of similar triangles to estimate the height of the child:
The ratio of the height of the adult to the length of their shadow is the same as the ratio of the height of the child to the length of their shadow:
height of adult / length of adult shadow = height of child / length of child shadow
Plugging in the values we know:
6 / 15 = height of child / 10
Solving for the height of the child:
height of child = (6 / 15) * 10 = 4 feet
Therefore, the estimated height of the child is 4 feet.
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Carolyn's hair grew 2.45 centimeters since her last haircut. Delia's hair grew 2.03 centimeters since her last haircut. Whose hair grew less since her last haircut? Explain.
Answer:
Delia's hair grew less since her last haircut
Step-by-step explanation:
2.45 centimeters is a higher number then 2.03, making Delia's hair shorter than Carolyn's.
Answer:
Delia's hair grew less.
Step-by-step explanation:
2.45 - 2.03 = 0.42
Deila's hair is 0.42 less than Carolyn's hair.
Please help step by step :)
Answer: √698 or 26.42 (2 d.p.)
Step-by-step explanation:
Pythagoras' Threorem is a² + b² = c²
Substitute 13 for a and 23 for b
13² + 23² = x²
169 + 529 = x²
698 = x²
x = √698 = 26.42 (2 d.p.)
Suppose the die has been “loaded” so that P(1)=1∕12, P(6)=3∕12, and the remaining four outcomes are equally likely with one another. Now find the probability that the number rolled is both even and greater than two
The "loading" of the die makes P(1)=112, P(6)=312, and the following four outcomes equally likely. A roll with an even number larger than two has a 50% probability of occurring.
The probability of rolling an even number is 1/2 since there are three even numbers (2, 4, 6) and six possible outcomes in total.
The probability of rolling a number greater than two is 5/6 since there are five outcomes (3, 4, 5, 6) greater than two and six possible outcomes in total.
To find the probability that the number rolled is both even and greater than two, we need to find the probability of rolling a 4 or a 6 since these are even numbers that are greater than two.
The probability of rolling a 4 is P(4) = 1/12 + 1/6 = 1/4 since the die is loaded to favour a 6 over the other numbers, but all other outcomes are equally likely.
The probability of rolling a 6 is P(6) = 3/12 = 1/4 since the probability of rolling a 6 is given as 3/12.
Therefore, the probability of rolling an even number that is greater than two is:
P(even and greater than two) = P(4 or 6) = P(4) + P(6) = 1/4 + 1/4 = 1/2.
So the probability of rolling an even number that is greater than two is 1/2.
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True or false. When you use multiple adjectives in a sentence, you do not have to put them in a certain order. True False
Answer:
False.
Step-by-step explanation:
When using multiple adjectives in a sentence, there is a general order that native English speakers tend to follow: opinion, size, age, shape, color, origin, material, purpose. This is known as the "OSASCOMP" order. However, this order is not always strictly followed, and there can be exceptions depending on the specific context or style of writing.
Answer:
It is False
Step-by-step explanation:
A right triangle is drawn on the coordinate plane. Apply a dilation with a scale factor of one over three to this triangle in draw the new triangle on the coordinate plane.
The image of the triangle is attached with coordinates
(0, 0)
(0. 3)
(3, 3)
What is a scale factor?In mathematics, a scale factor is a constant that multiplies every length of an object, changing its size while preserving its shape. In the context of dilation, which is a type of transformation that changes the size of a shape, the scale factor determines the amount by which the shape is enlarged or reduced.
When a shape is dilated with a scale factor greater than 1, the resulting shape is larger than the original. Conversely, when a shape is dilated with a scale factor between 0 and 1, the resulting shape is smaller than the original. If the scale factor is exactly 1, then the shape remains the same size.
In the problem the image is dilated with a scale factor less than one hence the resulting image is lesser
The new coordinates are gotten as follows
(0, 0) * 1/3 = (0, 0)
(0. 9) * 1/3 = (0. 3)
(9, 9) * 1/3 = (3. 3)
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Help me please. for 65 points and brainly
Answer:
Answer 3
Step-by-step explanation:
Answer: 3
Step-by-step explanation:
does anyone know how to solve this problem. (image attached)
The rectangle's area is growing at a pace of 138 [tex]\frac{cm^{2} }{s}[/tex] when its length is 10 cm and its width is 6 cm, this is the case.
What is the rate of change?One quantity's rate of change with regard to another quantity is known as the rate of change function. In order to calculate the rate of change, one simply divides the amount of change in one item by the equivalent amount of change in another.
Let L and W represent the length and breadth of the rectangle, respectively, and A represents the area of the rectangle. Next, we have:
A = L * W
When L = 10 cm and W = 6 cm, we are interested in determining the rate of increase of the rectangle's area with regard to time, or dA/dt.
We can begin by finding the derivative of A = L * W with regard to time t for both sides of the equation:
Derivate the equation by both sides with respective t.
[tex]\frac{d}{dt} (L * W) = \frac{dA}{dt}[/tex]
Using the principle of product rule of derivative, we arrive at:
[tex]L * W + L * \frac{dw}{dt} = \frac{dA}{dt}[/tex]
To determine dA/dt when L = 10 cm and W = 6 cm, we are provided that [tex]\frac{dL}{dt}[/tex] = 8 cm/s and [tex]\frac{dw}{dt}[/tex]= 9 cm/s. Therefore, we replace these numbers in the previous equation to obtain:
[tex]\frac{dA}{dt}[/tex] = (8 [tex]\frac{cm}{s}[/tex]) * (6 cm) + (10 cm * 9 [tex]\frac{cm}{s}[/tex]).
[tex]\frac{dA}{dt} = 48 \frac{cm^{2}}{s} + 90 \frac{cm^{2}}{s} \\[/tex]
[tex]138 \frac{cm^{2} }{s} = \frac{dA}{dt}[/tex]
Since the rectangle's area is growing at a pace of 138 [tex]\frac{cm^{2} }{s}[/tex]when its length is 10 cm and its width is 6 cm, this is the case.
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What value of x will make the triangles similar by the SSS similarity theorem? Show your work.
Answer:
x = 24
Step-by-step explanation:
by the similarity theorem
the ratios of corresponding sides are in proportion , that is
[tex]\frac{x}{9}[/tex] = [tex]\frac{16}{6}[/tex] ( cross- multiply )
6x = 9 × 16 = 144 ( divide both sides by 6 )
x = 24
James starts from point A along the pentagonal path A to B, B to C, C to D,
D to E and finally returns to point A. The distance of side
of pentagon is 8 m .He takes 16
from A to A along the path as said earlier. Write:
Distance covered by him
Displacement
Speed
Answer:
a) Distance is 40m b)0 c)2.5m/min
Step-by-step explanation:
a)8*5=40 b)He went from A to A c)16 min s=d/t 40/16
Progress!
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What is the image point of (-9,-5) after the transformation T-5,00 D₂?
attempt 11 out of 20/problem 1 out of ma
C
Thus, following the transformation T-5,00 D2, the image point of (-9,-5) is (-8,-10). Hence, choice C is the right response.
What is transformation ?The term "transformations" refers to the movements or adjustments that can be made to a geometric shape or object, such as turning, reflecting, translating, processes in an organization, or resizing. With these procedures, the original form or object can retain its geometry, angles, and other geometric attributes while changing its position, size, and orientation. Geometry, photography, and other disciplines frequently employ transformations to manipulate and examine patterns and shapes.
given
Applying the translation T-5,00 to the point (-9,-5) first yields (-9-(-5),-5+0) =, which we can use to determine the image point of (-9,-5) following the transformation T-5,00 D2 (-4,-5).
Then, we dilate the point (-4, -5) using the formula (2(-4,2(-5)) = (-8,-10).
Thus, following the transformation T-5,00 D2, the image point of (-9,-5) is (-8,-10). Hence, choice C is the right response.
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