Answers
The general format of the exponential expression is given as follows:
[tex]a^{\frac{n}{m}}[/tex]
In which:
The base is given by a.The exponent is given by n.The radicand is given by m.The radical form is given as follows:
[tex]\sqrt[m]{a^n}[/tex]
Meaning that the equivalence relation is given as follows:
[tex]\sqrt[m]{a^n} = a^{\frac{n}{m}}[/tex]
That is:
The radicand is the numerator of the fraction in the exponent.The radical is the denominator of the fraction in the exponent.Hence the relation for the cube root of 21 is given as follows:
[tex]\sqrt[3]{21} = 21^{\frac{1}{3}}[/tex]
(applying the conversion of the fractional exponent to a radical expression).
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Related Questions
I need help with C! If sin = 7/10 theta , find the exact value of
Answers
The evaluation of the trigonometric identities can be presented as follows;
(a) cos(θ) = -√(51)/10
(b) sin(θ + π/76) = (7·√3 - √(51))/20
(c) cos(θ - π/3) = (7·√3 - √(51))/20
What are trigonometric identities?Trigonometric identities are equations involving trigonometric ratios, in which the values correct far all possible values of the input variable.
(a) The value of sin(θ) = 7/10
The location of the angle θ is quadrant II, therefore;
The adjacent side to the angle θ is -ve, therefore;
cos(θ) = (√10² - 7²)/10 = -√(51)/10
(b) sin(θ + π/6) = sin(θ) × cos(π/6) + sin(π/6) × cos(θ)
sin(θ + π/6) = 7/10 × √3/2 + 1/2 × (-√(51)/10) = 7/10 × √3/2 - 1/2 × √(51)/10
sin(θ + π/6) = (7·√3 - √(51))/(2 × 10) = (7·√3 - √(51))/(20)
(c) cos(θ - π/3) = cos(θ)·cos(π/3) + sin(θ)·sin(π/3)
Therefore;
cos(θ - π/3) = ((-√51)/10 )× (1/2) + (7/10) × √3/2
cos(θ - π/3) = ((-√51)/10 )× (1/2) + (7/10) × √3/2 = (7·√3 - √(51))/20
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a killer whale is 7.5 m long. Convert this length to feet and the nearest inch.
Answers
Answer:
24.6063 ft
Step-by-step explanation:
Select the correct answer. Solve for x. x2 + 4x - 21 = 0 A. -3, -7 B. -3, 7 C. 3, -7 D. 3, 7
Answers
Answer:
x=3
x=-7
Step-by-step explanation:
What is the area of this figure? 2 m 2 m 3 m 9 m 2 m 3 m 7 m 14 m Area of compound figures
Answers
The area of the compound figure is 41 square meters.
How to find the are of compound figure?We can subdivide the compound figure into smaller shapes and add the areas of each to determine its area.
The figure can first be divided into two rectangles:
The first rectangle has a surface area of 18 m2 with measurements of 2 m by 9 m.
The second rectangle is 3 m by 7 m in size, which equals a surface area of 21 m2.
Next, we can calculate the two triangles' areas:
The area of the first triangle is 1/2 x 2 m x 2 m, or 2 m2, because its base is 2 m and its height is 2 m.
The area of the second triangle is 1/2 x 3 m x 2 m = 3 m2, with a base of 3 m and a height of 2 m.
The overlap between the two rectangles can then be subtracted:
The overlap measures 2 m by 3 m, making it a rectangle whose size is 2 m by 3 m, or 6 m2.
We sum the areas of the two rectangles, the two triangles, then subtract the overlap between the rectangles to determine the total area of the compound figure:
(18 m2 + 21 m2) + (2 m2 + 3 m2) - 6 m2 = total area
Area total: 41 m2.
Hence, the compound's area is 41 square metres.
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Complete question:
Area of compound figures.
2 m
2 m
3 m
9 m
2 m
3 m
7 m
14 m
What is the area of this figure?
PLEASE HELP PLEASEEE
Answers
Answer: (4,9)
Step-by-step explanation: The X is going to flip signs as you mirror across the y axis.
HELPP! ITS DUE TODAY PLEASE
Answers
The total area of the exercise room is 160 square feet.
The number of square yards equivalent to this total area is 17. 78 square yards.
Since the rubber flooring is sold in whole square yards, Juan must purchase exactly 18 square yards.
How to find the area ?To find the area of the exercise room, you should divide it into two different rectangles and then add up their areas.
Rectangle 1 length = 16 ft
Rectangle 1 width = ( 13 - 6 ) = 7 ft
Rectangle 2 length = ( 16 - 8 ) = 8 ft
Rectangle 2 width = 6 ft
The area is therefore :
= ( 16 x 7 ) + ( 8 x 6 )
= 160 square feet
1 square yard is 9 square foot so 160 square foot is:
= 160 / 9
= 17. 78 square yards
The area of rubber flooring that Juan must purchase would then be the whole number of 18 square yards which is 17.78 rounded up.
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PLEASE HELP ME ON QUESTION D. THE answer is not Kite.
Answers
Which point is a relative minimum?
A. A
B. B
C. C
D. D
Answers
The relative minimum point is B. Option B is the correct option.
What is the relative minimum?
The function's graph makes it simple to locate relative minima. It is the pivotal point in the function's graph. Relative minima are locations where the function's graph shifts from decreasing to increasing. A point that is lower than the points to its left and right is said to be at its relative minima.
The points of the graph function are A, B, C, D.
The lowest point among the given points on the graph is B.
Thus the relative minimum point is B.
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What are the domain and range of the function f(x)= x^4-2x^2-4? domain: all real numbers range: all real numbers greater than or equal to –5 domain: all real numbers range: all real numbers greater than or equal to –4 domain: all real numbers between –2.5 and 2.5 range: all real numbers domain: all real numbers between –2.5 and 2.5 range: all real numbers greater than or equal to –5
Answers
Answer:
The correct answer is: domain: all real numbers, range: all real numbers greater than or equal to -5.
We can see that the function is a polynomial of degree 4, which means it is defined for all real numbers. Also, as x^4 is always non-negative, the minimum value of the function occurs when x=0, and it is f(0) = -4. Therefore, the range of the function is all real numbers greater than or equal to -4. However, since the function is increasing as we move away from 0, the range is actually all real numbers greater than or equal to the minimum value of -4 plus the vertical shift of -1, which is -5.
HELPP PLS ITS MY HOMEWORK
Answers
Answer:
x=16
Step-by-step explanation:
Mark as brainliest
Answer:
x = 16
Step-by-step explanation:
First find height (h) of the triangle:
15² = 9² + h²
h² = 15² - 9² = 144
h = √144 = 12
Now you can find the base angle Ф of the 12-9-15 triangle:
Ф = sin⁻¹(12/15) = 53.1°
Find the measure of the other base angle by knowing that the sum of the interior angles of a triangle = 180:
180 - 90 - 53.1 = 36.9°
Now you can find x:
tan(36.9) = 12/x
x = 12/tan(36.9) = 16
General Sherman, a tree located in Sequoia National Park, stands 275 feet tall. To see the top of the tree, Carlos looks up at a 15° angle of elevation. If Carlos is 6 feet tall, how far is he from the base of the tree to the nearest foot?General Sherman, a tree located in Sequoia National Park, stands 275 feet tall. To see the top of the tree, Carlos looks up at a 15° angle of elevation. If Carlos is 6 feet tall, how far is he from the base of the tree to the nearest foot?
Answers
We may calculate the distance from Carlos and the tree as [tex]D = 781.23[/tex] ft using trigonometric relationships.
Is calculus more difficult than trigonometry?Many functions in trigonometry offer excellent illustrations of how calculus may be used in practical situations. By the way, basic trigonometry primarily deals with the algebraic features of circular functions, therefore basic calculus is not always simpler than basic trigonometry. On the other hand, calculus is fundamentally non-algebraic in nature.
Trigonometry: SOH CAH TOA or not?The mnemonic SOHCAHTOA makes it simple for us to recall the three primary trigonometric ratios.
Then one of the cathetus of the triangle is equal to:
[tex]275ft - 6ft = 269ft[/tex]
That cathetus is the opposite cathetus to the angle of 19° (the elevation angle). And the adjacent cathetus is the distance between Carlos and the tree.
Then we can use the relation:
Where:
[tex]a=19^{0}[/tex]
opposite cathetus [tex]=269ft[/tex]
adjacent cathetus [tex]=D[/tex]
Replacing that, we get
[tex]tan(19^{0} ) = 269ft/D[/tex]
Solving for D, we get:
[tex]D = 269ft/tan(19^{0} ) = 781.2ft[/tex]
So we conclude that Carlos is at [tex]781.23[/tex] ft of the tree.
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Which statement is sometimes true? only one answer.
Question 2 options:
A square is a rhombus.
A trapezoid is a parallelogram.
A rectangle is a parallelogram.
A rectangle is a square.
Answers
Answer:
The statement that is sometimes true is C: A rectangle is a parallelogram.
Step-by-step explanation:
A parallelogram is a four-sided shape with opposite sides parallel. A rectangle is a specific type of parallelogram where all angles are right angles, and opposite sides have equal lengths. Therefore, a rectangle is considered a parallelogram. However, not all parallelograms are rectangles because other parallelograms may have angles that are not right angles.
HELPPPP!
You are washing cars for a fundraiser and have reservations for 30 cars to be washed. You realize that it will take 4 people 8 hours to wash all the cars. Exactly how long will it take 6 people to wash all the cars? If you only have 2 hours and 40 minutes to wash all the cars how many people will you need?
Answers
Answer:
How long will it take 6 people to wash all the cars? 5 hours 20 minutes
If you only have 2 hours and 40 minutes to wash all the cars how many people will you need? 12 people
Step-by-step explanation:
The important thing to realize here is that the time taken to wash x cars is inversely proportional to the number of people
That is represented mathematically as
y ∝ 1/x
The more the number of people, the less time it takes
We can write this as a proportionality equation:
y = k/x
where k is referred to as the constant of proportionality
We have the information: 4 people take 8 hours.
Plugging these two values into the equation
4 = k/8
k = 4 x 8 = 32 hours
So it takes 1 person 32 hours to wash all the cars
If there were 6 people instead
6 = 32/h where h is the time taken for 6 people to wash 30 cars
h = 32/6 = 16/3 hours = 5 1/3 hours
= 5 hours and 20 minutes
2 hours and 40 minutes = 2 40/60 hours = 2 2/3 hours
Converting to improper fraction
2 2/3 = (2 x 3 + 2)/3 = 8/3 hours
Plugging this value of x into the equation gives
y = 32/(8/3)
32 ÷ 8/3 is computed by flipping the fraction and multiplying
32 ÷ 8/3 = 32 x 3/8 = 12 people
Atul gets a pocket money allowance of Rs.120 per day. Thinking that this was rather less he asked his friends about their allowances and obtained the following data which includes his allowance also ( Amount I Rs.) 120, 180, 100, 50, 250, 200,200,220, 150, 100,100,150,130,200,180, 100, 150, 100, 180, 150, 120, 150, 100, 150, 100, 120, 180, 200, 50.
He presented this data to his father and asked for an increase in his allowance as he was getting less than average amount. His father, a statistician, countered pointing out that Atul's allowance was actually more than the average amount.
Answers
Atul's father is mistaken, and Atul's request for an increase in his allowance may be valid based on the information given.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
To determine whether Atul's allowance is above or below the average, we need to calculate the average allowance for all the friends, including Atul.
To do his, we add up all the amounts and divide by the total number of friends:
Average allowance = (120+180+100+50+250+200+200+220+150+100+100+150+130+200+180+100+150+100+180+150+120+150+100+150+100+120+180+200+50) / 29
Average allowance = 162.07
So, the average allowance for Atul's friends, including himself, is Rs. 162.07 per day.
Since Atul's allowance is Rs. 120 per day, we can see that his allowance is actually less than the average.
Therefore, Atul's father is mistaken, and Atul's request for an increase in his allowance may be valid based on the information given.
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Please help i need it!!!!!
A 6 N crate is lifted 2 meters. How much work is done?
A) 12 N/m
B) 4 N/m
C) 8 N/m
D) 3 N/m
Answers
The amount of work done is Option A) 12 N/m
What is work done?Work done is simply defined as the product of the magnitude of displacement, (d) and the component of the force that in the direction of displacement.
It measures energy transfer that occurs when an object is moved to a distance by an external force which is applied in the direction of the displacement.
Work done on a body is equivalent to the increase in the energy of the body, because it transfers energy to the body.
The formula for work done is;
W = fd
Where, 'f' is the applied force and d is the distance
Substitute the values
Work done = 6(2)
Work done = 12 N/m
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3. Solve this word problem:
Candice's wanted to paint the wall of her room with her favourite colour blue. Candice had
4 cans of blue paint stored in the garage. She used 2 - cans to paint her room.
3
How much blue paint did Candice have left over?
Answers
Answer:
Candice had 2 cans left over.
If using the method of completing the square to solve the quadratic equation
x
2
+
7
x
+
27
=
0
x
2
+7x+27=0, which number would have to be added to "complete the square"?
Answers
The number that was added to complete the square is (7/2)²
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
The given quadratic equation is x²+7x+27=0
Add and subtract (7/2)² = 49/4
x² + 7x + 27
= ( x² + 7x + 49/4) - 49/4 + 27=0
= (x + 7/2)² - 59/4
Now we can rewrite the original equation as:
(x + 7/2)² - 59/4 = 0
Adding 59/4 to both sides, we get:
(x + 7/2)² = 59/4
Taking the square root of both sides, we get:
x + 7/2 = ±√59/2
Solving for x, we get:
x = -7/2 ±√59/2
Therefore, the number that was added to complete the square is (7/2)²
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please help thankss
:) g
Answers
Answer:
origin
Step-by-step explanation:
the point (0,0) is called the origin
Answer:
The center of a coordinate plane, which is point (0,0) is called "the origin."
Step-by-step explanation:
two bakers make 30 loaves of bread every morning. assume all bakers work at the same rate. suppose two bakers make 30 loaves in one hour. how many hours would 3,5,6 and 15 bakers need to make 30 loaves.
Answers
Answer:
Step-by-step explanation:
If two bakers can make 30 loaves in 1 hour, then we can use proportionality to find how many hours it would take for 3, 5, 6, and 15 bakers to make 30 loaves.
Let h be the number of hours needed for a given number of bakers to make 30 loaves. Then we have:
2 bakers can make 30 loaves in 1 hour, so 1 baker can make 15 loaves in 1 hour.
Therefore:
3 bakers can make 45 loaves in h hours, so 45/3 = 15 loaves can be made in 1 hour. Thus, 3 bakers can make 30 loaves in 2 hours.
5 bakers can make 75 loaves in h hours, so 75/5 = 15 loaves can be made in 1 hour. Thus, 5 bakers can make 30 loaves in 2 hours.
6 bakers can make 90 loaves in h hours, so 90/6 = 15 loaves can be made in 1 hour. Thus, 6 bakers can make 30 loaves in 2 hours.
15 bakers can make 225 loaves in h hours, so 225/15 = 15 loaves can be made in 1 hour. Thus, 15 bakers can make 30 loaves in 2 hours.
Therefore, regardless of the number of bakers, it would take 2 hours to make 30 loaves of bread.
Select ALL the true equations.
(a) 5 + 0 = 0
(b) 15 ⋅ 0 = 0
(c) 1.4 + 2.7 = 4.1
(d) 2/3 ⋅ 5/9 = 7/12
(e) 4 & 2/3 = 5 − 1/3
Answers
Answer:
b,c,e
Step-by-step explanation: a: 5+0=5
b:15x0 =0
c: 1.4+2.7=4.1
d:2/3 x 5/9
e:4& 2/3 =5-1/3
In a normal distribution curve, the mean is equal to what?
Answers
In a normal distribution curve, the mean is equal to center of the curve
What is the mean equal to?In a normal distribution curve, the mean is equal to the center of the curve, also known as the peak, and is represented by the highest point on the curve.
The mean of a normal distribution is also the point around which the data points are symmetrically distributed, with an equal number of data points on both sides of the mean. This is why the mean is often referred to as the "average" of a normal distribution.
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Anyone please help me please anyone ???!! Thank you (((:!!!!
Answers
Answer:
23
Step-by-step explanation:
(16-12)×4+7
(4)×4+7
16+7
=23 I think
Find the surface area of the composite figure. Round your answer to the nearest whole
number.
6 ft
00
5 ft
12 ft
Hint: how many circles are part of your final surface area?
ft. 2
Answers
The surface area of the figure is 549.5 square ft
How to determine the surface area of the figureGiven that
The composite figure comprises of a cone and a cylinder of the following dimensions
Cone: Radius = 5 ft and Height = 12 ft
Cylinder: Radius = 5 ft and Height = 6 ft
The surface area of the figure is calculated as
Surface area = Cone + Cylinder - Circle
So, we have
Surface area = πr(r + √[h² + r²]) + 2πr(r + h) - πr²
Substitute the known values in the above equation, so, we have the following representation
Surface area = 3.14 * 5 * (5 + √[12² + 5²]) + 2 * 3.14 * 5 * (5 + 6) - 3.14 * 5²
Evaluate
Surface area = 549.5
Hence, the surface area is 549.5
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What happens after Lisa finishes
working on the car?
When Lisa's brothers see the car, they
are
But Lisa is
▼ what she did.
and thinks the car is
▼ her work
Answers
Lisa and her brothers share a mutual appreciation for the car, albeit for different reasons.
After finishing working on the car, Lisa's brothers are surprised by the changes she made to the car. They may compliment her on her work or express their appreciation for her efforts. On the other hand, Lisa is proud of her work and takes pride in the changes she made to the car. She may feel a sense of accomplishment and satisfaction in seeing the final result of her hard work. While her brothers may appreciate the car, Lisa feels a personal connection to it as she knows the effort and dedication she put into making it look and function better.
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Answer:
I have the answer
Step-by-step explanation:
1. Suprised by
2. Proud of
3. unique
Hope it helps, Have a good day!
The sides of a triangle are 63, 58, and 30. Use the Pythagorean
Theorem to determine if the triangle is right, acute, or obtuse.
Answers
Answer:
To use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse, we need to find the length of the longest side (also known as the hypotenuse) by squaring each side, adding the results, and taking the square root of the sum.
So,
63^2 = 3969
58^2 = 3364
30^2 = 900
Now, we add 3969 and 3364 to get 7333, and take the square root to get approximately 85.62.
Since 63, 58, and 30 are the lengths of the sides of the triangle, we can compare the length of the longest side (85.62) to the sum of the other two sides (63 + 58 = 121) to determine if the triangle is right, acute, or obtuse.
85.62^2 = 7326.23
121^2 = 14641
Since 7326.23 is less than 14641, the triangle is acute.
Quincy has a jewelry business in which he designs and sells bracelets. His daily profit, Q(x), can be modeled by the function Q(x) = 7.25x − 36.25, where x is the number of bracelets he sells. What is the value of Q(5), and what is its interpretation?
Q(5) = 0; If Quincy sells 0 bracelets, he will earn $5.
Q(5) = 0; If Quincy sells 5 bracelets, he will earn $0.
Q(5) = 5.69; If Quincy sells 5.69 bracelets, he will earn $5.
Q(5) = 5.69; If Quincy sells 5 bracelets, he will earn $5.69.
Answers
The function Q(x) = 7.25x 36.25 can be used to model daily profit, Q(x), making none of the proposed answers suitable.
what is function ?A function in mathematics is a relationship between a domain—a set of possible inputs—and a range—a set of potential outputs—with the property that each input is linked to precisely one output. Frequently, a mathematical expression, equation, or formula will be used to describe a function. They are a fundamental idea in calculus, algebra, and other branches of mathematics, used to explain how one quantity relies on another.
given
Let Q(x) = 7.25x 36.25 be a model for his daily earnings, where x is the quantity of bracelets he sells.
Q(5) = 23.5, which indicates that Quincy will make $23.50 if he sells 5 wristbands today.
The function Q(x) = 7.25x 36.25 can be used to model daily profit, Q(x), making none of the proposed answers suitable.
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What are the inputs of the following function?
((-3, 2), (-4, 2), (8, 3), (7, 1))
[1, 2, 3]
[1, 2, 3, 7, 8)
(-4,-3, 7, 8)
(4, -3, 1, 2, 3, 7, 8)
Answers
Answer:
(-4,-3,7,8)
Step-by-step explanation:
the inputs are the X values , the X values are the first number on the parenthesis (X , Y) , the outputs are the Y values
Yaritza has a collection of vintage action figures that is worth $320. If the collection
appreciates at a rate of 2% per year, which equation represents the value of the
collection after 5 years?
Answers
The end result of this equation is the value of the collection after 5 years. In this case, the total value would be V = 320(1.02)⁵ = 413.25.
What is exponential growth?Exponential growth is a pattern of growth that occurs when a base number is multiplied by a consistent number over a period of time. This type of growth is often seen in population growth, inflation, the money supply and other areas of mathematics. The growth rate of an exponential function increases over time, making it an important concept in mathematics, economics, and other fields.
This equation utilizes the concept of exponential growth, which is when a quantity increases at a rate which is proportional to its current value. In this case, the quantity is the value of the collection, and the rate of growth is 2% per year.
The equation can be broken down into its components in order to better understand what it is saying. The base value of the collection, 320, is represented by the first part of the equation, V = 320. The second part, (1.02)^5, represents the growth rate over 5 years. The 1.02 is the growth rate of 2% per year, and the 5 indicates that the growth rate will be compounded for 5 years. In other words, the rate of growth is applied to the original value, and then the resulting value is used as the new base for the growth rate to be applied again, and so on for 5 years.
The end result of this equation is the value of the collection after 5 years. In this case, the total value would be V = 320(1.02)⁵ = 413.25. This means that in 5 years, the collection would have appreciated to a total value of 413.25.
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CALC
PLEASE HELP!!
A chemical substance has a decay rate of 8.8% per day. The rate of change of an
dN
amount N of the chemical after t days is given by = -0.088N
dt
(i) Let No represent the amount of the substance present at to. Find the exponential function
that models the decay.
(ii) Suppose that 400g of the substance is present at to. How much will remain after 3 days?
(iii) What is the rate of change of the amount of the substance after 3 days?
(iv) After how many days will half of the original 400 g of the substance remain?
Answers
A function is a relationship between a few different inputs and an output, where each input can only lead to one possible outcome.
What is the chemical substance has a decay rate?(i) The exponential function that models the decay of the substance is given by:
[tex]N(t) = Noe^(-0.088t)[/tex]
(ii) If [tex]400g[/tex] of the substance is present at to, then [tex]No = 400g[/tex] . Therefore, the amount of the substance remaining after 3 days is:
[tex]N(3) = 400e^(-0.0883) = 309.21g[/tex] (rounded to two decimal places)
(iii) The rate of change of the amount of the substance after 3 days is given by:
[tex]dN/dt = -0.088N(3) = -0.088309.21 = -27.21 g/day[/tex] (rounded to two decimal places)
(iv) To find the number of days it takes for half of the original [tex]400g[/tex] of the substance to remain, we need to solve the equation:
[tex]N(t) = 0.5No[/tex]
[tex]0.5No = Noe^(-0.088t)[/tex]
[tex]0.5 = e^(-0.088t)[/tex]
[tex]ln(0.5) = -0.088t[/tex]
[tex]t = ln(0.5)/(-0.088) = 7.89 days[/tex] (rounded to two decimal places)
Therefore, after [tex]7.89[/tex] days, half of the original [tex]400g[/tex] of the substance will remain.
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Figure W is a dilation of figure V. Where is the center of dilation located?
A) inside figure V
B)outside figure V
C)on a vertex of figure V
Answers
The center of dilation is located inside figure V.
What is Dilation?Dilation is a type of transformation where the figure is enlarged or made smaller such that it preserves the shape but not size.
Every dilated image are similar figures to the original figure.
Center of dilation is defined as the point which is fixed on a plane. All the points are dilated about this point.
This can be situated inside or outside the preimage and image.
We can find the position of center of dilation by connecting corresponding vertices of the image and preimage and extend the line up to which all the lines intersect.
The intersecting point is the center of dilation.
Using this concept, here, the center of dilation is inside V.
Hence the center of dilation is located inside the figure V.
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