Using the expansion of inequality, The smallest integer , n is 3 .
What in math is an integer?
A full number (not a fraction) that can be positive, negative, or zero is called an integer (pronounced IN-tuh-jer).
Integers include things like -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers are examples of non-integer numbers.
we have given in question that , n is an integer such that ,
(x²+y²+z²)²≤n(x⁴+y4⁴+z⁴)
Let us consider, a=x², b=y², and c=z² which are all nonnegative i.e a,b,c >0 , n>3 but we find least value of n
So, the above inequality become,
(a+b+c)² ≤ n (a²+b²+c²) ----(*)
by expanding both side of above equation we get, a² + b²+ c² + 2(ab + bc + ac) ≤n( a²+b²+c²)
2(ab + bc + ac) ≤ (n- 1) (a²+b²+c²)
=> (ab+bc+ac) ≤ (n- 1)/2 (a²+ b²+c²)
=> (xy)²+ (yz)²+(xz)²≤ (n-1)/2(x⁴+y⁴+z⁴)
If we put n=3− ∈ where ∈ >0 and x=y=z then
3 ≤ 2 or 1/2 which is wrong . Hence, the smallest value of n is 3.
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The complete question is -
Find the smallest integer n such that (x2+y2+z2)2≤n(x4+y4+z4)
for all real numbers x,y, and z.
factot this trinomial. z^2-14Z+45
give answer in this form (z+a)(z+b)
The factor of the trinomial (z² - 14z + 45) are,
⇒ (z - 5) (z - 9)
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
The function is,
⇒ z² - 14z + 45
Now, We can factorize the trinomial as;
⇒ z² - 14z + 45
⇒ z² - (9 + 5)z + 45
⇒ z² - 9z - 5z + 45
⇒ z (z - 9) - 5 (z - 9)
⇒ (z - 5) (z - 9)
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the sum of two numbers is 51. the larger number is 21 more than the smaller number. what are the numbers ?
larger number: ?
smaller number: ?
The smaller number is 15 and the larger number is 36.
Let x and y be the smaller and larger numbers, respectively.
From the given information, we know:
y = x + 21 (because the larger number is 21 more than the smaller number)
x + y = 51 (because the sum of the two numbers is 51)
We can substitute the first equation into the second equation to find the value of x:
x + (x + 21) = 51
x + x + 21 = 51
2x = 30
x = 15
Now that we know the value of x, we can use the first equation to find the value of y:
y = x + 21
y = 15 + 21
y = 36
So the smaller number is 15 and the larger number is 36.
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decide whether each proposed multiplication or division of measurements is possible. if it is possible, write the result in the last column of the table.
1. The unit g/cm³ is valid. So, division of measurements is possible.
2. The unit mm is valid. So, division of measurements is possible.
3. The unit L² is not valid. So, multiplication of measurements is not possible.
What are measurement units?
The group of units used to quantify different physical quantities collectively known as the units of measurement. Since ancient times, we have measured these things using many units, including length, mass, volume, current, and temperature.
1. 63g/7cm³ = 9 g/cm³
The density of a substance indicates how dense it is in a given area. Mass per unit volume is the definition of a material's density. In essence, density is a measurement of how closely stuff is packed. It is a particular physical characteristic of a specific thing.
The unit g/cm³ is a unit for measuring density.
Therefore, the division of measurements is possible.
2. The m or mm must be converted so that the units are the same.
1 m = 1000 mm.
Convert the meters to mm:
0.080 m = 80 mm.
480 mm²/80 mm = 6 mm
The word "area" refers to a free space. A shape's length and width are used to compute its area. Unidimensional length is expressed in terms of feet (ft), yards (yd), inches (in), etc.
The mm² is a unit for measuring area.
The m is a unit for measuring length or width.
Therefore, the division of measurements is possible.
3. (4.5 dL) × (0.70 L)
Liquid volume is a term used to describe how much 3-D space a given amount of liquid takes up.
Volume of a liquid is measured in litres (L).
Squaring Litres doesn't make any sense.
Therefore, the multiplication of measurements is not possible.
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et S be the set of all positive integers n such that n^2 is a multiple of both 24 and 108. Which of the following integers are divisors of every integer n in S ?
A. 12
B. 24
C. 48
D. 72
E. 120
Only the integer 12 is a divisor of every other integer which is a part of the set S.
This is a classic problem where we are asked to find such an integer that is going to be a divisor of the above set S of integers. The set S of integers consists of those integers that when squared are both divisible by 24 and 108. Now we know 24 can be written as 2*2*2*3 and similarly 108 can be written as 2*2*3*3*3. The smallest perfect square (n^2) which is a multiple of both 24 and 108 is 2^4*3^4, thus the smallest n is 2^2*3^2 = 36. So, only 12 is a divisor of all integers in S.
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Help plss i don’t know an easy way to do this
See the diagram below.
=================================================
Explanation:
Pick two points on this diagonal line. I'll go for (0,-3) and (1,-1)
Apply the slope formula to those coordinates.
[tex](x_1,y_1) = (0,-3) \text{ and } (x_2,y_2) = (1,-1)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{-1 - (-3)}{1 - 0}\\\\m = \frac{-1 + 3}{1 - 0}\\\\m = \frac{2}{1}\\\\m = 2\\\\[/tex]
A slope of 2, aka 2/1, means "move up 2, then right 1".
This "up 2, right 1" motion allows us to move from (0,-3) to (1,-1) as shown in the diagram below.
pls help first to answer all will get brainliest!!
Answer:To show that Lorenz curves are always concave up on the interval [0, 1], we can use the definition of a Lorenz curve, which is L(x) = xp. Taking the second derivative of L(x) with respect to x gives us L''(x) = p. Since p is always greater than 0, L''(x) is always greater than 0. This means that L(x) is always concave up on the interval [0, 1].
Table of Lorenz values for p = 1.2, 1.5, 2.1, 2.5, 3, and 5:
a. The value of p that corresponds to the most equitable distribution of wealth is 1, as this would mean that the proportion of wealth held by each portion of the population is equal.
b. The value of p that corresponds to the least equitable distribution of wealth is 5, as this would mean that a small portion of the population holds a large proportion of the wealth.
The Gini Index is a measure of income inequality, where a value of 0 represents perfect equality (everyone has the same income) and a value of 1 represents perfect inequality (one person has all the income). The Gini Index is calculated as the ratio of the area between the Lorenz curve and the line of equality to the total area beneath the line of equality.
To find A and B for the Gini index we can use the following integral:
A = ∫(L(x) - x) dx from 0 to 1
B = ∫(x - L(x)) dx from 0 to 1
We can then solve the integral for each specific function of L(x) = xp to find the specific value of A and B.
Step-by-step explanation:
Answer:....
Step-by-step explanation:
which of the following is closest to prob that total weight of randomyl selected graperfurits is moret than 3.4 pounds
The probability that the total weight of the three randomly selected grapefruits is more than 3.4 pound will be equal to 0.842.
What is Probability?Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.The likelihood that something will happen is known as probability. By dividing the total number of outcomes by the number of possible ways an event could occur, one can compute probability.The probability is determined as the ratio of likely outcomes to all plausible outcomes of an event. One can represent the percentage of successful outcomes, or x, for an experiment with 'n' outcomes.
From the data given in the question,
x > 3.4 lb
The mean is 1 lb.
The difference from the mean is 0.12 lb.
The z-score will be,
z = (3.4 - 1) / 0.12
z = 20
This is equivalent to an 84.20% or 0.842 probability.
The complete question is,
The weights of grapefruits of a certain variety are approximately normally distributed with a mean of 1 pound and a standard deviation of 0.12 pounds. Use scenario 6-9. what is the probability that the total weight of three randomly selected grapefruits is more than 3.4 pounds?
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3. Write an equation, using variables, to represent the identities we der
4. Using your knowledge of identities, fill in each of the blanks.
a. 4+5- = 4
b. 25 + 10 = 25
_+16-16 = 45
d. 56-20+ 20 =_____
5. Using your knowledge of identities, fill in each of the blanks.
a. a+b-
=a
d.
-=
b. c-d+d=_
c. e+-f=e
_-h+h=g
The blanks has bee filled by using the correct identities of the algebra.
Explain the term identities?An equality that is certainly part of the values selected for its variables is called an identity. They are used to rearrange or simplify algebraic expressions. The two halves of an identity are, by definition, interchangeable, and we are always free to switch one for the other.Any value that is placed into the variable makes the identity equation always true. How to solve identity equations .Start by grouping like terms together until given any identity equation in a particular set of variables.Part 4:
a. 5 + 5 - 6 = 4
b. 25 - 10 + 10 = 25
c. 24 + 16 - 16 = 24
d. 56 - 20 + 20 = 56
Part 5:
a) a + b - b = a
b) c - d + d = c
c) e + f - f = e
d) g - h + h = g
Thus, the blanks has bee filled by using the correct identities of the algebra.
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The correct question is-
4. Using your knowledge of identities, fill in each of the blanks.
a. 5 + 5 - ___ = 4
b. 25 - ___ + 10 = 25
c. ___ + 16 - 16 = 24
d. 56 - 20 + 20 = ___
5. Using your knowledge of identities, fill in each of the blanks.
a) a + b - ___ = a
b) c - d + d = ____
c) e + ___ - f = e
d) ___ - h + h = g
Use the method of successive differences to determine the next number in the given sequence 3, 7, 17, 33, 55, 83, 117
The next number in the sequence is 151.
What is the successive differences?
The method of successive differences involves finding the differences between consecutive terms in a sequence and using that information to predict the next term in the sequence.
To use this method for the sequence 3, 7, 17, 33, 55, 83, 117:
Find the differences between consecutive terms:
7 - 3 = 4
17 - 7 = 10
33 - 17 = 16
55 - 33 = 22
83 - 55 = 28
117 - 83 = 34
Check if the differences are constant. In this case, they are increasing by 6 each time.
Use this information to predict the next term in the sequence:
117 + 34 = 151
So, the next number in the sequence is 151.
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it is possible to have a function with an infinite number of critical points. also, it is possible to have a function where every point is a critical point. g
A function with an infinite number of critical points can be expressed as a continuous function with a derivative that is equal to zero at every point in its domain.
For example, the function f(x) = 0 has an infinite number of critical points since its derivative f'(x) = 0 for every x in its domain. Alternatively, a function that has every point as a critical point can be expressed as a function with a derivative that is always equal to zero. For example, the constant function f(x) = c has a derivative f'(x) = 0 for every x in its domain, and thus every point in its domain is a critical point.
In addition, an example of a function with every point as a critical point is the constant function, f(x) = c, where c is a constant. The derivative of this function is f'(x) = 0, which means that the derivative is zero for all values of x. Therefore, every point of the constant function is a critical point.
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pt2 , ANSWER ASAP
At a bakery, one customer pays $5.67 for 3 bagels and 4 muffins. Another customer pays $6.70 for 5 bagels and 3 muffins. Let x be the cost (in dollars) of a bagel and let y be the cost (in dollars) of a muffin. Use the system of equations below to determine the cost of 1 bagel and 1 muffin?
3x+4y =5.67
5x+3y=6.7
A. $0.75 for a bagel and $0.89 for a muffin
B. $0.89 for a bagel and $0.75 for a muffin
C. $1.49 for a bagel and $0.23 for a muffin
D. $0.23 for a bagel and $1.49 for a muffin
Let A be a 5 by 7 , B be a 7 by 6 and C be a 6 by 5 matrix. How to determine the size of the following matrices ? O AB, BA, O A^TB, BC, O ABC , CA ,O B^TA , BC^T
The matrices matrix A be a 5 by 7 , matrix B be a 7 by 6 and matrix C be a 6 by 5 matrix.
now, we need to determine the size of the matrices
AB = [tex](AB)_{5*6}[/tex]
BA is undefined
[tex]A^{T}[/tex]B is undefined
BC = [tex](BC)_{7*5}[/tex]
ABC = [tex](ABC)_{5*5}[/tex]
CA = [tex](CA)_{6*7}[/tex]
[tex]B^{T}[/tex]A is undefined.
B[tex]C^{T}[/tex] is undefined.
given that
matrix A is [tex]A_{5*7}[/tex]
matrix B is [tex]B_{7*6}[/tex]
matrix C is [tex]C_{6*5}[/tex]
now, we need to determine the size of the matrices
AB multiplication of two matrices
multiplication of two matrices is possible only when B has the same number of columns as rows in A,
[tex]A_{m*n}[/tex]and [tex]B_{n*p}[/tex]
If it is defined as above, then the matrix AB will have m rows and p columns, i.e., A must have n columns and B must have n rows in order for AB to be defined.
[tex](AB)_{m*n}[/tex]
In addition, a matrix gets transposed when columns turn into rows and vice versa.
Thus, if
[tex]A_{m*n}[/tex]⇒[tex](AT)_{m*n}[/tex]
So, for this particular question, we have: [tex]A_{5*7}[/tex], [tex]B_{7*6}[/tex] , [tex]C_{6*5}[/tex]
According to the aforementioned idea, AB is therefore [tex](AB)_{5*6}[/tex] in size.
Additionally, BA and [tex]A^{T}[/tex]B are not defined.
[tex](BC)_{7*5}[/tex]
ABC=(AB)C=A(BC) because matrix multiplication is associative,
[tex](ABC)_{5*5}[/tex]
[tex](CA)_{6*7}[/tex]
[tex]B^{T}[/tex]A is undefined. because they don't have same number of columns in matrix B and rows in matrix A
B[tex]C^{T}[/tex] is undefined. because they don't have same number of columns in matrix B and rows in matrix C
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4:5=___:35 fill in the missing value
Answer: 28:35
Step-by-step explanation: The missing number is 28, here's how to solve it:
So, if we know both components of the first ratio AND the second component of the 2nd ratio, we need to divide the 2nd components from each ratio. So, 35 / 5 = 7. Now, we need to multiply 7 by 4. We get 28. So, the 2nd ratio is 28:35. I hope this helps!
(Look at the attachment for a better idea)
Find the y-intercept and the x-Intercept of the line below. Click on "None" If applicable.
(a) y-intercept:
(b) x-Intercept:
Answer:
y-int: none, x-int: -1
Step-by-step explanation:
It crossed the x-axis at -1 so the x-int is, you guessed it, -1
As for the y-int assuming that its just a straight line, there is none. It never crosses the y-axis meaning that y-int DNE (or just none in you case)
given that angle A is congruent to angle C and A E equals E C, which of the following can be used to show that triangle A O B is congruent to triangle C E D?
Two angle and an include side are congruent, hence by the ASA postulate triangle AEB congruent to triangle CED.
ASA similarity theorem: Two triangles are similar if two corresponding angles of one triangle are congruent to the two corresponding angles of another triangle. Also, the corresponding sides are proportional. ASA similarity is mostly known as the AA similarity theorem.
Statement: Line segments AE and EC are equal.
Reason: Given
Statement: angle A is congruent to angle B.
Reason: Given
Statement: Angles AEB & CED are equal.
Reason: vertically opposite angles are equal.
Hence, two angle an include side are congruent.
Triangles AOB & CED are congruent.
Reason: ASA Postulate.
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Murphy buys 5 bottles of water For $2.50 each and 3 sandwiches for $3.25 each. How much does murphy spend?
The amount Murphy spent is solved to be $22.25
How to solve for the amount Murphy spentTo calculate the amount Murphy spent the cost of the items and the units bought should be known. The calculation is done using the formula
= units bought * cost of each unit
From the question, we can deduce that
Murphy buys 5 bottles of water For $2.50 eachunits bought = 5
cost of each = $2.50
amount spent = 5 * $2.5 = $12.5
Murphy buys 3 sandwiches for $3.25units bought = 3
cost of each = $3.25
amount spent = 3 * $3.25 = $9.75
Total amount spent = spending for bottle water + spending for sandwiches
Total amount spent = $12.5 + $9.75
Total amount spent = $22.25
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There are 4 apples, 3 peaches and 2 plums in a grocery bag. If the the checkout person picks 2 plumbs and 1 peach out of the bag, what is the probability that the next piece of fruit out of the bag will be an apple? (Give your answer as a fraction in simplest form.)
The probability that the next fruit is an apple is P = 0.8
How to find the probability?We want to fnind the probability of randomly selecting an apple from the bag.
Remember that the probability is equal as the quotient between the number of apples and the total number of fruit on the bag.
Originally, there are:
4 apples.
3 peaches
2 plums.
The checkout person takes 2 plums and 1 peach, so now there are:
4 apples.
1 peach.
So there are 4 apples and 5 fruits in total
Then the probability of grabing an apple is:
P = 4/5 = 0.8
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Lena must choose a number between 61 and 107 that is a multiple of 3, 5, and 9. Write all the numbers that she could choose. If there is more than one number, separate them with commas.
Answer: the answer is 90
Step-by-step explanation:There is only one number between 61 and 107 that is a multiple of 3, 5 and 9. So that number will be 90.
finally, use the midpoint of each slice to determine the height and sketch in the resulting 4 rectangles. use them to approximate ln(2), and write your answer below: can you tell if you are getting an over-estimate or and under-estimate? which of your four estimates gives you the closest answer to the value given by your calculator? select one
The rectangles approximate ln(2) as 0.693. The approximation is an under-estimate, as the rectangles only cover a portion of the graph. The closest estimate is the fourth one, as it is closest to the value given by the calculator.
1. Slice the graph into 4 equal parts by drawing vertical lines at x=0.5, x=1, and x=1.5.
2. Find the midpoints of each slice by calculating the average of the x-values of each slice. The midpoints are x=0.25, x=0.75, x=1.25, and x=1.75.
3. Determine the height of each rectangle at the midpoints. The heights are y=0.253, y=0.572, y=0.854, and y=1.092.
4. Sketch in the rectangles using the midpoints and heights calculated.
5. Approximate ln(2) as the sum of the areas of the four rectangles, which is 0.693. This is an under-estimate.
6. The closest estimate is the fourth one, as it is closest to the value given by the calculator (0.693).
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Choose the graph that represents the equation below: y = 8x + 4
Answer: Go up 8 and to the right 1 starting at the point (0,4)
Step-by-step explanation: y=mx+b where m=8 (your slope) and b= 4 (your y-intercept)
Rewrite (2+3)+4 using the Associative Law of Addition
Answer:
9 is correct
Step-by-step explanation:
2+3=5+4=9 , believe
There were approximately 3.1 × 10⁸ people in the United States of America in 2010. The average person drank 3.3 × 10³ ounces of soda. Approximately how many total ounces of soda were drank in the USA in 2010?
Answer:
1.023 x [tex]10^{14}[/tex]
Step-by-step explanation:
(3.1 x [tex]10^{8}[/tex])(3.3 x [tex]10^{3}[/tex])
(3.1 x 3.3)([tex]10^{8}[/tex] x [tex]10^{3}[/tex])
10.23 x [tex]10^{13}[/tex] When the bases are the same and we are multiplying we add the exponents
10.23 x [tex]10^{13}[/tex] Is not in scientific notation because 10.23 is larger than 10
1.023 x [tex]10^{1}[/tex] x [tex]10^{13}[/tex]
1.023 x [tex]10^{14}[/tex]
any1 can solve this!?
The area of the shaded region is obtained as (π/√2) units².
What is area?
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
The diagram is labelled.
The values for area of z and y needs to be obtained.
The result will be in the form |y| + z as when the integration will be done, y will come out to be negative.
Now, x + z is the area of rectangle ABCD.
Verify whether x and y are equal in magnitude -
[tex]\begin{aligned}& x=\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} \frac{\cos \theta}{\sin ^2 \theta} d \theta=\left[\frac{-1}{\sin \theta}\right]_{\frac{\pi}{4}}^{\frac{\pi}{2}} \\& =-1-(\sqrt{2}) \\& =\sqrt{2}-1\end{aligned}[/tex]
[tex]\begin{aligned}& y=\int_{\frac{\pi}{2}}^{\frac{3\pi}{4}} \frac{\cos \theta}{\sin ^2 \theta} d \theta=\left[\frac{-1}{\sin \theta}\right]_{\frac{\pi}{2}}^{\frac{3\pi}{4}} \\& =-(\sqrt{2})-(-1) \\& =-\sqrt{2}+1\end{aligned}[/tex]
This is equal to |y| = x.
So, |y| + z is equivalent to writing x + z.
Now the formula for area of rectangle ABCD is -
Area = length × breadth
Area = √2 - [(3π/4) - (π/4)]
Area = √2 - (π/2)
Area = (π/√2)
Therefore, the area is found to be (π/√2) units².
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River is surfing off Cocoa Beach. The depth of the water at various distances from the shore, point
are shown in the diagram. When he is
feet (ft) from the shore a point
, the dept of the water is
ft. He continued to point
about
ft away from the shore.
The depth of the water RF is, 18 ft.
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
We have to given that;
⇒ ΔSML ≅ ΔSRF
⇒ SM = 10
⇒ ML = 6
⇒ SR = 30
Since, Both triangles SML and SRF are similar.
Hence, We get;
⇒ SM / ML = SR / RF
Substitute all the values, we get;
⇒ 10 / 6 = 30 / RF
⇒ RF = 30 × 6 / 10
⇒ RF = 3 × 6
⇒ RF = 18 ft
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Joseph has a bag filled with 2 red, 4 green, 15 yellow, and 9 purple marbles. Determine P(not purple) when choosing one marble from the bag.
A. 70%
B. 50%
C. 30%
D. 20%
The probability of randomly selecting a marble that is not purple is 70%, so the correct option is A.
How to find the probability?
We know that there are:
2 red marbles4 green marbles15 yellow marbles9 purple marblesFor a total number of 2 + 4 + 15 + 9 = 30
There are a total of 30 marbles on the bag, the probability of randomly selecting a marble that is not purple, is equal to the quotient between the number of marbles that are not purple and the total number of marbles.
21 marbles are not purple, then the probability is:
P = (21/30)*100%
P = 0.7*100%
P = 70%
The correct option is a.
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suppose 3
1.a+b
2.a-b
3.ab
4.a/b
The range of values for each expression is given as follows:
1. 8 ≤ a+b ≤ 16
2. -6 ≤ a - b ≤ 2
3. 15 ≤ ab ≤ 63
4. 1/3 ≤ a/b ≤ 7/5.
How to obtain the values?For the maximum values, we have that:
Sum and multiplication: a and b have maximum values.Subtraction and division: maximum a, minimum b.For the minimum values, we have that:
Sum and multiplication: a and b have minimum values.Subtraction and division: minimum a, maximum b.Missing InformationThe problem asks for the range of values for each expression, considering 3 < a < 7 and 5 < b < 9.
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ANSWER ASAP
At the produce store, 6 bananas are the same cost as 9 apples. You buy 4 bananas and 2 apples. The purchase cost $8. This scenario is modeled by the given system. Choose the correct description below that connects the meaning of the solution (1, 1.5) to the context of this scenario.
6y=9x
2x+4y=8
A. Each apple costs $1.50 and each banana costs $1.
B. You purchased 1 apple and 1.5 bananas.
C. You purchased 1.5 apples and 1 banana.
D. Each apple costs $1 and each banana costs $1.50.
The solution (1, 1.5) denotes:
Each apple costs $1.
Each banana costs $1.50.
Option D is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 9 is an equation.
We have,
6y = 9x _____(1)
2x + 4y = 8 ______(2)
From the equation,
x is the cost of an apple.
y is the cost of a banana.
Now,
(1, 1.5) = (x, y)
This means,
The cost of an apple = $1.
The cost of a banana = $1.5
Thus,
The solution (1, 1.5) denotes that the cost of an apple is $1 and a banana is $1.5.
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A bird of species A, when diving, can travel 5 times as fast as a bird of species B top speed. If the total speeds for these two birds is 222 miles per hour, find the fastest speed of the bird of species A and the fastest speed of the bird of species B.
The fastest speed of the bird of species A is 185 mph and the fastest speed of the bird of species B is 37 mph
What is an equation?
An equation is an expression showing the relationship between numbers and variables.
Let a represent the top speed of bird A and b represent the top speed of bird B.
A bird of species A, when diving, can travel 5 times as fast as a bird of species B top speed, hence:
a = 5b
a - 5b = 0 (1)
If the total speeds for these two birds is 222 miles per hour, hence:
a + b = 222 (2)
To solve by elimination method, subtract equation 2 from 1, hence:
-6b = -222
Dividing by -6:
b = 37
Put b = 37 in equation 2:
a + 37 = 222
a = 185
The speed of the bird are 185 miles per hour and 37 miles per hour
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find the radius and height of the right-circular cylinder of largest volume that can be inscribed in a right circular cone with radius 6 inches and height 10 inches. answer accurate to 3 decimal place. (volume of a cylinder
The radius of the right circular cylinder is 4 inches and the height is 3.33 inches.
Radius of cone=6inches
height of cone = 10 inches
Let the radius and height of the right circular cylinder be x and y respectively.
According to triangle similarities,
10-y/x=10/6
⇒10-y/x=5/3
⇒30-3y=5x
⇒y=10-5x/3 ----1
The volume of the right circular cylinder is π[tex]r^{2}[/tex]h
v= πx∧2y
substituting the value of y from 1
v= π[tex]x^{2}[/tex](10-5x/3)
v=10πx^{2}- 5x∧3/3
We differentiate volume w.r.t radius
DV/dx= 20πx-5[tex]x^{2}[/tex]
setting derivative = 0
DV/dx= 20πx-5[tex]x^{2}[/tex]=0
5πx(4-x)=0
x=0 , x=4
[tex]D^{2}[/tex]V/Dx =20π-10πx
putting the maximum value of x in the second derivative we get,
X=Radius = 4inches
Y=height= 10-5x/3=3.33 inches
Therefore, The radius of the right circular cylinder is 4 inches and the height is 3.33 inches.
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A probability experiment is conducted in which the sample space of the experiment is S={ 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}, event F={5, 6, 7, 8, 9}, and event G={9, 10, 11, 12}. Assume that each outcome is equally likely. List the outcomes in F or G. Find P(F or G) by counting the number of outcomes in F or G. Determine P(F or G) using the general addition rule.
List the outcomes in F or G. Select the correct choice belowand, if necessary, fill in the answer box to complete your choice.
A. F or G = { _____ }
(Use a comma to separate answers as needed.)
F or G = { 5,6,7,8,9,10,11,12 } is probability P(F or G) using the general addition rule.
What are examples and probability?
The likelihood that something will happen is called the probability. the total number of conceivable outcomes.
For instance, the chance of flipping a coin and obtaining heads is 1 in 2, as there is only one way to acquire a head and there are a total of 2 possible outcomes (a head or tail). P(heads) = 12 is what we write. the forerunners of the contemporary mathematical theory of probability (for example the "problem of points").
S={ 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14},
event F={5, 6, 7, 8, 9}, and
event G={9, 10, 11, 12}.
F or G = { 5,6,7,8,9,10,11,12 }
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