By assuming that the item we wish to prove is false and then demonstrating that the results of this are not feasible, we can prove something by contradiction.
What is meant by contradiction?3a + b = 1 6 . This is contradictory because 3a + b is an integer according to the closure properties, but 1/6 is not. It follows that there aren't any integers a and b for which 18a + 6b = 1. Each of the following claims can be demonstrated using contradiction. The foundation of the evidence by contradiction approach is the contradiction rule. Simple logic dictates that one should assume the falsity of any given premise or assertion. The supplied assertion must be true if this assumption results in a contradiction.When two angles of a triangle are equal, the sides that are on the other side of the equal angles are likewise equal. The evidence moves forward with the presumption that the opposing angles are not equal and creates a contradiction.To learn more about contradiction, refer to:
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Two equal ide of a triangle are each 4m le than three time the third ide. Write down the dimenion of the triangle, if it perimeter i 55m
9 m, 23 m, and 23 m are the triangle's measurements.
What is meant by triangle's measurement?The total of a triangle's three inner angles is always 1800. Any two sides of a triangle can have a sum of lengths that is always greater than the length of the third side. Half of a triangle's area is equal to the sum of its base and height. Any triangle's three angles add up to a whole 180 degrees.Wisconsin University's Brian McCall A 45° 45° 90° triangle is a particular kind of isosceles right triangle in which the two legs are congruent and the non-right angles are both 45°. The hypotenuse or missing legs of 45 45 90 triangles can frequently be determined using the Pythagorean theorem.To learn more about triangle's measurement, refer to:
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Molly uses 9.3 pints of blue paint and white paint to paint her bedroom walls.
2
5
of this amount is blue paint, and the rest is white paint. How many pints of white paint did she use to paint her bedroom walls?
The white paint did she use to paint her bedroom walls will be 6.975 pints.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that Molly uses 9.3 pints of blue paint and white paint to paint her bedroom walls 25% of this amount is blue paint.
The amount of white paint will be calculated as:-
Amount = [ 9.3 x ( 100 - 25 )%]
Amount = [ ( 9.3 x 0.75 ) ]
Amount = 6.975 pints.
Hence, the amount of white paint used for painting is 6.975 pints.
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Here is a tile game with two colors, say red and blue. On a turn, a person can either take any number of tiles of one color or they can take the same number of red and blue tiles. The last one to take a tile WINS. For example, if you start with 5 red and 7 blue tiles, taking 4 blue tiles is a legal move, taking 2 red tiles is a legal move, and taking 3 red and 3 blue tiles is a legal move, but taking 4 blue and 2 red tiles is not allowed. Describe a strategy for winning this game for all cases with 40 or fewer total tiles. Describe patterns you see in the numbers involved in your solution, and justify what you can
This strategy works for all cases with 40 or fewer total tiles. The pattern observed here is that XORing pattern.
If there are 5 red tiles and 7 blue tiles, the binary representation of these numbers is 101 and 111, respectively. Taking the bitwise XOR of these numbers gives 010, which is 2. Hence, the player should take 2 tiles of either color, leaving 3 tiles of one color and 5 tiles of the other color. This leaves the other player in a losing position.
The pattern observed here is that XORing all the numbers together effectively cancels out all the common bits, leaving only the unique bits. The player should then take a number of tiles such that the unique bits become 0.
Unique bits refer to the concept of binary representation of numbers in mathematics. The binary system is a base-2 numeral system where each digit can either be 0 or 1. Unique bits refers to the distinct and non-repeating number of binary digits used to represent a number. It is a measure of the number of bits needed to represent a unique number.
The unique bits in mathematics is a concept that is widely used in computer science, information theory and cryptography. The more unique bits used, the greater the number of unique combinations that can be produced and hence, the greater the accuracy in representation. For example, using 8 unique bits in binary representation can result in up to 256 unique combinations, compared to using only 7 unique bits, which can only result in 128 unique combinations. Unique bits plays a crucial role in ensuring the accuracy and efficiency of information representation and transmission.
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Please use R.
Write a function called by_type() that takes an atomic vector as input and an optional argument ‘sort’ with default value FALSE. The function looks at each element in the atomic vector and sees if it can coerce them into integer or floating-point values. The function outputs a list that has separated the values into a list with integers, doubles, and character values. If the optional argument sort is TRUE, then it will sort the results of each vector.
Atomic vectors typically come in four different types: logical, integer, double, and character. Complex and raw are the two less common varieties.
An atomic vector can have any properties, with the exception of a dimension attribute, and is either logical, integer, numeric, complex, character, or raw (like matrices). For example, a matrix or NULL are not atomic vectors, but a factor is. This is, in essence, the same as is. atomic. Using the built-in int function, one can transform texts in Python into integers. Any Python data type can be sent to the int() function to be transformed into an integer.
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Six friends went to a movie and spent $9 per ticket. They also purchased a small bag of popcorn each. If the friends spend a total of $82.50, how much does each small bag of popcorn cost?
Hello!
If six friends went to a movie and spent $9 per each ticket and also purchased a small bag of popcorn each with them spending a total of $82.50, the cost of each small bag of popcorn costs $4.75.
Step-by-step explanation:
[tex]6[/tex] × [tex]9=54[/tex]
[tex]82.50-54=28.50[/tex]
[tex]28.50[/tex] ÷ [tex]6=4.75[/tex]
Hope this helps!
Select the correct answer. A parabola declines through (negative 2, 4), (negative 1 point 5, 2), (negative 1, 1), (0, 0) and rises through (1, 1), (1 point 5, 2) and (2, 4) on the x y coordinate plane. The function f(x) = x2 is graphed above. Which of the graphs below represents the function g(x) = (x + 1)2? A parabola declines through (negative 2, 5), (negative 1 point 5, 3), (negative 1, 2), (0, 1) and rises through (1, 2), (1 point 5, 3) and (2, 5) on the x y coordinate plane. W. A parabola declines through (negative 2, 3), (negative 1 point 5, 1), (1, 0), (0, negative 1) and rises through (1, 1), (1 point 5, 1) and (2, 2) on the x y coordinate plane. X. A parabola declines through (negative 3, 4), (negative 2 point 5, 2), (negative 2, 1), (negative 1, 0), (0, 1), (0 point 5, 2) and (1, 4) on the x y coordinate plane. Y. A parabola declines through (negative 1, 4), (negative 0 point 5, 2), (0, 1) and (1, 0) and rises through (2, 1), (2 point 5, 2) and (3, 4) on the x y coordinate plane. Z. A. W B. X C. Y D. Z Reset Next
The parabola function has a minimum value of -4.
How to determine the maximum or the minimum?The given parameters are:
Declines through (-5,-2), (-3,-4)
Rises through (-2, -3), (-1, -2), (0, 0), (0, 2) and (1, 4)
Because the parabola declines before it rises, it means that the function has a minimum
From the point of decline;
-4 is less than -2
Hence, the parabola function has a minimum value of -4.
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Find the ratio of the areas in the following sets or similar triangles with corresponding sides labeled.
The ratios of the areas in the following sets or similar triangles are:
1. 9:1, 2. 4:1, 3. 25:9,
4. 46:9, 5. 9:4, 6. 4:1,
7. 25:4, 8.9:4, 9. 9:1.
What are triangles?Having three edges and three vertices, a triangle is a three-sided polygon. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.
Given a set of triangles is similar,
for similar triangles the ratio of their corresponding sides is equal,
so A/a = B/b = C/c
where A, B, and C are sides of larger triangles and a, b, and c are sides of small triangles.
area of small triangle = 1/2*b*h
here b =base and h = height
area of large triangle = 1/2*B*H
here B =base and H = height
the ratio of areas = area of the large triangle/area of the small triangle
the ratio of areas = [1/2*B*H]/[1/2*b*h]
the ratio of areas = BH/bh
since the triangles are similar, B/b = H/h
the ratio of areas = B²/b²
or the ratio of areas = (SIDE)²/(side)²
1. given side of large triangle = 3
side of small triangle = 1
ratio of areas = 3²/1²
ratio of areas = 9/1 = 9:1
2. given side of large triangle = 4
side of small triangle = 2
ratio of areas = 4²/2²
ratio of areas = 16/4 = 4:1
3. given side of large triangle = 5
side of small triangle = 3
ratio of areas = 5²/3²
ratio of areas = 25/9 = 25:9
similarly for other questions,
4.ratio of areas = 16/9 = 16:9
5. ratio of areas = 9/4 = 9:4
6. ratio of areas = 64/16 = 4:1
7. ratio of areas = 25/4 = 25:4
8. ratio of areas = 36/16 = 9:4
9. ratio of areas = 4/1 = 4:1
Hence the ratios are as possible.
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Question content area top Part 1 Given the following functions, find the indicated values f(x)=4-9x (a) f(-8) (b) f(0) (c) f(9)
Answer:
Step-by-step explanation:
Given the function f(x) = 4 - 9x, the indicated values are:
(a) f(-8) = 4 - 9(-8) = 4 + 72 = 76
(b) f(0) = 4 - 9(0) = 4
(c) f(9) = 4 - 9(9) = 4 - 81 = -77
So, the values of f(-8), f(0), and f(9) are 76, 4, and -77, respectively.
The surface area of a sphere is found using the formula SA=4², where r is the radius. If the surface area of a
sphere is 144π square feet, what is the radius, in feet?
A. 6
B. 12
C. 18
D. 36
Answer:
A
Step-by-step explanation:
Surface area of sphere is 4 pi r^2
144 pi = 4 pi r^2
144 pi / (4 pi) = r^2
36 = r^2
r = 6 ft
determine whether the sequence converges or diverges. if it converges, find the limit. (if an answer does not exist, enter dne.) an = n 2 sin(2/n) lim n→[infinity] an = incorrect: your answer is incorrect.
The given sequence is convergent and the limit is 1.
What is a sequence?
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members. The number of elements is called the length of the sequence.
Here, we have
Given: aₙ = (n/2) sin(2/n)
First, we will find the limit of a given sequence.
aₙ = [tex]\lim_{n \to \infty} (n/2)sin(2/n)[/tex]
We apply L'hospital's rule here and we get
aₙ = [tex]\lim_{n \to \infty} {cos(2/n)(-2/n^2)}/(-2/n^2)[/tex]
aₙ = [tex]\lim_{n \to \infty} cos(2/n)[/tex]
aₙ = 1
We concluded that the given series is convergent.
Hence, the given sequence is convergent and the limit is 1.
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what is the value of the expression below when z =4
The solution of the expression ( 10z - 3 ) is equal to 37.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the expression is 10z - 3. The value of the expression at z = 4 will be calculated below,
Evaluate for z = 4,
E = 10x - 3
E = (10)(4)−3
E = (10)(4)−3
E = 37
Therefore, the solution for the expression is 37.
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pls help it urgent ty
Answer: A. 2/5 or 0.4 and B. 5/2 or 2.5 or 2 1/2
Step-by-step explanation: I'm a personal math calculator
Teresa was offered two jobs one job pay with $400 a week plus $200 Signing bonus the other job paid 420 week with no signing bonus how many weeks would she have to work orders for the total amount earned from the job to be equal
Teresa would need to work 10 weeks in order to earn the same total amount as the second job.
Assuming Teresa takes the first job, she would need to work for 10 weeks in order to earn the same total amount as the alternate job. The total amount earned from the first job can be calculated by (400 x 10) + 200 = 6000. The total amount earned from the second job can be calculated by (420 x 10) = 4200. Thus, in order to earn the same amount from the total of both jobs, Teresa would need to work 10 weeks at the first job. This can be expressed by the following formula: (400 x n) + 200 = 420 x n, working for n is the number of weeks. Solving for n gives n = 10.
Thus, Teresa would need to work 10 weeks in order to earn the same total amount as the second job.
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PLEASE PLEASE HELP whats the origin of the number zero (pls give me interesting info its for a math project)
Please Brainliest
The origin of the number zero is believed to be ancient India, where it was invented as a placeholder in the decimal system around the 5th century CE. The concept of zero as a number in its own right was a revolutionary idea that greatly advanced mathematical understanding and allowed for much more efficient mathematical calculation. From India, the use of zero spread to the Islamic world and eventually to the West. The modern representation of zero as a circle or a digit was introduced in the 13th century in India.
for what value of k is y-x^k a solution to the differential equation x^2y'y''
For k =3, y = [tex]x^k[/tex] is a solution to the differential equation [tex]x^2[/tex]y'y'' - 4yy' = 6[tex]x^5[/tex].
The differential equation is [tex]x^2[/tex]y'y'' - 4yy' = 6[tex]x^5[/tex].
Let y = [tex]x^k[/tex] is a solution to the differential equation [tex]x^2[/tex]y'y'' - 4yy' = 6[tex]x^5[/tex].
So y' = k[tex]x^{k-1}[/tex]
y'' = k(k-1)[tex]x^{k-2}[/tex]
Now putting the value of y, y' and y'' in the differential equation.
[tex]x^2[/tex](k[tex]x^{k-1}[/tex])(k(k-1)[tex]x^{k-2}[/tex]) - 4[tex]x^k[/tex](k[tex]x^{k-1}[/tex]) = 6[tex]x^5[/tex]
Now simplifying the equation.
[tex]k^2(k-1)x^2x^{k-1}x^{k-2} - 4kx^kx^{k-1}[/tex] = 6[tex]x^5[/tex]
As we know that the power gets add in the multiplication so
[tex]k^2(k-1)x^{(2+k-1+k-2)} - 4kx^{(k+k-1)}[/tex] = 6[tex]x^5[/tex]
[tex](k^3-k^2)x^{2k-1} - 4kx^{2k-1}[/tex] = 6[tex]x^5[/tex]
[tex]k^3x^{2k-1}-k^2x^{2k-1} - 4kx^{2k-1}[/tex] = 6[tex]x^5[/tex]
Taking common [tex]kx^{2k-1}[/tex]
[tex]kx^{2k-1}(k^2-k - 4)[/tex] = 6[tex]x^5[/tex]
On comparing
2k-1 = 5
Add 1 on both side, we get
2k = 6
Divide by 2 on both side, we get
k = 3
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The complete question is:
For what value of k is y = [tex]x^k[/tex] a solution to the differential equation [tex]x^2[/tex]y'y'' - 4yy' = 6[tex]x^5[/tex]?
How do you solve a spring equation?
Hooke's Law states that when a spring is extended, the force is proportional to how much longer it is than its equilibrium length. The spring constant can be calculated using the formula k = -F/x.
What is a spring equation?Hooke aimed to show how a spring's elasticity and the forces acting on it are related.
According to Hooke's Law, a spring's extension is proportional to the load placed on it.
As long as the load does not exceed the material's elastic limit, a variety of materials will adhere to this rule.
F = k(x - x0), where x represents the spring's displacement from equilibrium and k is the spring constant.
The negative sign indicates that the force represented by the spring is a restorative force and operates in the opposite direction.
According to Hooke's Law, when a spring is stretched, the force applied is proportional to the lengthening from the equilibrium length.
The formula k = -F/x, where k is the spring constant, can be used to get the spring constant. F stands for force, and x is for the variation in spring length.
Therefore, Hooke's Law states that when a spring is extended, the force is proportional to how much longer it is than its equilibrium length. The spring constant can be calculated using the formula k = -F/x.
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You are trying to raise money for college. You have $1000 right now to invest into an account. You have two options for accounts:
Option 1: An account that pays 12% interest compounded quarterly.
Option 2: An account that pays 6% interest compounded continuously.
Which option will give you the most money after 2 years? Use numerical calculations and words to justify your answer.
The option that will give you the most money after 2 years is option (a)
Which option will give you the most money after 2 yearsOption (a)
Here, we have
Principal, P = $1000
Rate, r = 12% = 0.12
Number of times, n = 4
Time, t = 2
The formula of amount is
A = P * (1 + r/n)^(nt)
So, we have
A = 1000 * (1 + (0.12/4))^(4 *2)
A = 1266.77
Option (b)
Here, we have
Principal, P = $1000
Rate, r = 6% = 0.06
Time, t = 2
The formula of amount is
A = P * e^(rt)
So, we have
A = 1000 * e^(0.06 * 2)
A = 1127.50
1266.77 is greater than 1127.50
Hence, the option is option (a)
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The sum of two numbers is 25 the difference between three times the larger one and two times the smaller one is 55
Answer:
(21, 4)
Step-by-step explanation:
x+y=25
3x-2y=55
3x+3y=75
3x-2y=55
5y=20
y=4
x+4=25
x=21
The sum of 11 and three-fourths of a number is less than 112. What are all the possible values of the number? Write an inequality that could be used to solve this problem. Use the letter x as the variable, and write the inequality so that the x term comes first. Where necessary, write numbers as fractions (rather than decimals).
The required inequality that shows the possible value of x is x < 404/3
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Let's call the number we're trying to find "x". Then, the inequality can be written as:
11 + (3/4)x < 112
To solve for x, we'll isolate x on one side of the inequality. First, we'll subtract 11 from both sides.
(3/4)x < 101
Next, we'll divide both sides by (3/4).
x < (4/3) * 101 = 404/3
So, all values of x that are less than 404/3 satisfy the inequality. The possible values of x are all numbers less than 404/3.
x < 404/3
or written as an interval:
x ∈ (-∞, 404/3)
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Sandy used a virtual coin toss app to show the results of flipping a coin 100 times, 500 times, and 1,000 times. Explain what most likely happened in Sandy's experiment.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 100 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 500 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 1,000 flips.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 100 flips.
Explanation:
In Sandy's experiment, she used a virtual coin toss app to simulate the results of flipping a coin 100 times, 500 times, and 1,000 times. The experimental probability is the probability obtained from the observed outcomes of the experiment, while the theoretical probability is the probability calculated based on mathematical principles and assumptions.
Based on the information given, it is stated that Sandy's experimental probability was closest to the theoretical probability in the experiment with 100 flips. This suggests that the observed outcomes of the 100 flips aligned more closely with the expected outcomes based on the theoretical probability.
It is important to note that experimental probability tends to converge towards theoretical probability as the number of trials increases. Therefore, it is expected that the experimental probability would be closer to the theoretical probability in the experiment with 1,000 flips compared to the experiment with 500 flips.
Without further information, it is not possible to determine whether Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments. However, based on the given statement, it can be concluded that Sandy's experimental probability was closest to the theoretical probability in the experiment with 100 flips.
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In Sandy's experiment, the experimental probability was closest to the theoretical probability in the experiment with 100 flips.
Explanation:
In Sandy's experiment, she used a virtual coin toss app to simulate the results of flipping a coin 100 times, 500 times, and 1,000 times. The experimental probability is the probability obtained from the observed outcomes of the experiment, while the theoretical probability is the probability calculated based on mathematical principles and assumptions.
Based on the information given, it is stated that Sandy's experimental probability was closest to the theoretical probability in the experiment with 100 flips. This suggests that the observed outcomes of the 100 flips aligned more closely with the expected outcomes based on the theoretical probability.
It is important to note that experimental probability tends to converge towards theoretical probability as the number of trials increases. Therefore, it is expected that the experimental probability would be closer to the theoretical probability in the experiment with 1,000 flips compared to the experiment with 500 flips.
Without further information, it is not possible to determine whether Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments. However, based on the given statement, it can be inferred that the experimental probability was closest to the theoretical probability in the experiment with 100 flips.
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A walkway forms one diagonal of a square playground. The walkway is 32m long. How long is a side of the playground
Answer:14 meters
Step-by-step explanation:
Can someone PLEASE help? I will give brainliest if possible and lots of points
Click on the image to see questions
Answer:
A) <5 and <6 are commentary
B) 72
C < 4 = 22
<3 = 68
Step-by-step explanation:
A) The square drawn over the 2 angles shows that the angles together measure 90 degrees
B) 90 - 18 = 72
C) 4x -10 + 5x + 28 = 90 Combine like terms
9x + 18 = 90 Subtract 18 from both sides
9x = 72 Divide both sides by 9
x = 8
<4
4x - 10
4(8) - 10
32 - 10
<4 = 22
<3
5x + 28
5(8) + 28
40 + 28
68
<3 = 68
Answer:
Part A: Yes, ∠5 and ∠6 are complementary angles because they add up to 90°.
Part B: If the measure of ∠6 is 18°, then the measure of ∠5 is 72° because ∠6+∠5=90° so 90°-18°=72°.
Part C: ∠4+∠3=90°
(4x-10)°+(5x+28)°=90°
add 10 to both sides
4x+5x+28=100
subtract 28 from both sides
4x+5x=72
combine like terms
9x=72
divide both sides by 9
x=8
now plug 8 in for x
∠4=(4(8)-10)°
∠4=22°
∠3=(5(8)+28)
∠3=68°
22°+68°=90°
Guess the value of the limit (if it exists) by evaluating the function at the given numbers.
lim x→−5
x2 − 5x
x2 − 25
,
x = −4.5, −4.9, −4.95, −4.99, −4.999, −4.9999, −5.5, −5.1, −5.05, −5.01, −5.001, −5.0001
The value of the limit for the given function [tex]\lim_{x \to 5} \frac{x^2 - 5x}{x^2 - 25}[/tex] = 1/2.
What is L'hospital rule?A general technique for assessing indeterminate forms like 0/0 or / is the L'Hospital rule. L'Hospital's rule is applied to calculate the limits of indeterminate forms for calculus derivatives. It is possible to use the L Hospital rule many times. This rule is still valid after being applied, and it will take any indefinite form. L'Hospital's Rule cannot be applied if the issue is not of the indeterminate types.
The given function is:
[tex]\lim_{x \to 5} \frac{x^2 - 5x}{x^2 - 25}[/tex]
Substituting the value of limit we can see that the function is of the indeterminate form 0/0.
Using the L'Hospital rule we have:
[tex]\lim_{x \to 5} \frac{x^2 - 5x}{x^2 - 25}\\\\\lim_{x \to 5} \frac{2x - 5}{2x}\\[/tex]
Substitute the value of limits:
[tex]=\frac{2(5) - 5}{2(5)}\\ \\=\frac{1}{2}[/tex]
Hence, the value of the limit for the given function [tex]\lim_{x \to 5} \frac{x^2 - 5x}{x^2 - 25}[/tex] = 1/2.
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If you cannot show the triangles are congruent from the given information leave the triangle's name black and write CNBD for Cannot be Determined in place of the rule.
BOY=???
Step-by-step explanation:
triangle BOY is congruent with triangle MAN by ASA (angle-side-angle) : 2 angles are the same and the side between them has the same length.
that is sufficient to declare the triangles congruent.
Suppose consumer incomes increase. How will this affect the demand, supply, price, and quantity of potatoes (an inferior good) in the market?
An increase in consumer incomes would lead to a decrease in the demand and price of potatoes, and an increase in supply and quantity.
When consumer incomes increase, the demand for inferior goods such as potatoes usually decreases. This is because as people's incomes rise, they tend to switch to buying more superior goods, which are generally more expensive than inferior goods.
At the same time, the supply of potatoes may also increase as farmers respond to the potential for higher prices by growing more potatoes.
With both a decrease in demand and an increase in supply, the market price for potatoes is likely to fall. The quantity of potatoes supplied will likely increase as well, as the lower price attracts both consumers and producers.
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two less than a number times four
Answer:
is equal to the number minus six.
Write exponential growth/decay equation and solve for each problem
A savings account balance is compounded annually. If the interest rate is 2% per year and the current balance is $1,460.00, what will the balance be 8 years from now?
Answer:
The equation is y = 1,460e^(2%)x, and the balance will be $2,067.54 in 8 years
What is the extreme value theorem example?
The function is continuous on [−2,2], and its derivative is f′(x)=4 x 3−9 x 2. Because x=9/4 is not in the interval [−2,2], the only critical point occurs at x = 0 which is (0,−1).
What is meant by function ?
Having or performing a utilitarian function; being able to fulfil its intended function: useful furniture; architectural design that serves a purpose.I dropped the flashlight, yet it still worked. The computer network is working properly.Both sorts of access can be granted to a user using the functional usage model.You can grant a user only one kind of access, such as permission to utilise but not modify a specific feature, element, or object.All biological activities, including respiration, excretion, and nourishment, can be performed by a cell. It is therefore referred to as the functional unit of life. The lowest unit of life is the cell, and cells make up every living thing.To the complete questions is;
Find the maximum and minimum values of f(x)= x 4−3 x 3−1 on [−2,2].
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In this figure, h = 3, and r = 4.
What is the exact surface area of the cone?
Enter your answer in the box.
units²
The exact surface area of the cone having height 3 unit and radius 4 unit, 113.09734 unit²
What is the area?An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².
Given that,
A Cone having,
Radius r = 4 unit
Height h = 3 unit
Surface Area = ?
Formula for the Cone,
Surface Area of Cone = πrl + πr²
where, l = [tex]\sqrt{h^{2}+r^{2} }[/tex]
Surface Area of Cone = πr([tex]\sqrt{h^{2}+r^{2} }[/tex]) + πr²
= πr([tex]\sqrt{h^{2}+r^{2} }[/tex] + r)
= 4π([tex]\sqrt{3^{2}+4^{2} }[/tex] + 4)
= 4π(5 + 4)
= 20π
≈ 113.09734
Thus, the surface area of cone is 113.09734 unit²
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Adriana is 8 more than twice the height of her little brother in inches. Adriana is at least 60 inches tall. What is the minimum height of her brother?
Applying inequality, the minimum height of her brother is: 26 inches.
How to Apply Inequality?An inequality is a mathematical statement that shows the relationship between two values or expressions, where one value is either greater than, less than, greater than or equal to, or less than or equal to the other value. It is represented using symbols such as ">", "<", "≥", or "≤".
Let's call the height of Adriana's little brother "x".
So Adriana's height is 2x + 8 inches.
And because Adriana is at least 60 inches tall, we can write the following inequality:
2x + 8 ≥ 60
Subtracting 8 from both sides:
2x ≥ 52
Dividing both sides by 2:
x ≥ 26
So the minimum height of Adriana's little brother is 26 inches.
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