1/(b-c)^2+1/(c-a)^2+1/(a-b)^2
Answers
The simplified form of the expression is:
(2a⁴ - 8a³b + 12a²b² - 8ab³ + 2b⁴ + b⁴ - 4b³c + 6b²c² - 4bc³ + c⁴) / ( (b - c)² x (c - a)² x (a - b)²)
We have,
To simplify the expression 1/(b - c)² + 1/(c - a)² + 1/(a - b)², we can start by finding a common denominator for the three fractions.
The common denominator will be the square of the product of the differences between the variables in the denominators.
Denominator = (b - c)² x (c - a)² x (a - b)²
Now, we can rewrite each fraction with the common denominator:
1/(b - c)² = ( (c - a)² x (a - b)²) / ( (b - c)² x (c - a)² * (a - b)²)
1/(c - a)² = ( (b - c)² x (a - b)²) / ( (b - c)² x (c - a)² * (a - b)²)
1/(a - b)² = ( (b - c)² x (c - a)²) / ( (b - c)² x (c - a)² * (a - b)²)
Now, we can combine the fractions by adding the numerators:
( (c - a)² x (a - b)² + (b - c)² x (a - b)² + (b - c)² x (c - a)²) / ( (b - c)² x (c - a)² x
(a - b)²)
Next, we can simplify the numerator by expanding the squares:
( (c² - 2ac + a²) * (a² - 2ab + b²) + (b² - 2bc + c²) * (a² - 2ab + b²) + (b² - 2bc + c²) x (c² - 2ac + a²) ) / ( (b - c)² x (c - a)² x (a - b)²)
Now, we can further simplify the numerator by distributing and combining like terms:
( (a⁴ - 4a³b + 6a²b² - 4ab³ + b⁴) + (a⁴ - 4a³b + 6a²b² - 4ab³ + b⁴) + (b⁴ - 4b³c + 6b²c² - 4bc³ + c⁴) ) / ( (b - c)² x (c - a)² x (a - b)²)
Finally, we can combine the like terms in the numerator:
(2a⁴ - 8a³b + 12a²b² - 8ab³ + 2b⁴ + b⁴ - 4b³c + 6b²c² - 4bc³ + c⁴) / ( (b - c)² x (c - a)² x (a - b)²)
Thus,
The simplified form of the expression 1/(b - c)² + 1/(c - a)² + 1/(a - b)² is
(2a⁴ - 8a³b + 12a²b² - 8ab³ + 2b⁴ + b⁴ - 4b³c + 6b²c² - 4bc³ + c⁴) / ( (b - c)² x (c - a)² x (a - b)²)
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Related Questions
on a certain island there are two populations of deer. after years, the numbers of deer in the two populations are and . when is the total population smallest?
Answers
On a certain island there are two populations of deer. after years, the numbers of deer in the two populations is zero.
Let x be the population of the first group of deer and y be the population of the second group of deer.
The total population is given by x + y.
The numbers of deer in the two populations are x and y.
Suppose that the population of the first group increases at a rate of a per year, and the population of the second group increases at a rate of b per year.
Then the differential equations that describe the growth of the populations are as follows:
dx/dt = ax
dy/dt = by
The solution to these equations is
\(x(t) = x_0ert\\ y(t) = y_0ert\)
where \(x_0 \:and \: y_0\) are the initial populations of the first and second groups of deer, respectively.
The total population P(t) at time t is given by
\(P(t) = x(t) + y(t) \\P(t) = x_0ert + y_0ert\)
Taking the derivative with respect to t gives the rate of change of P(t) as follows:
\(dP/dt = x_0er + y_0er\)
This is a monotonically increasing function of t.
Therefore, the total population is smallest when the derivative is zero, that is, when er(\(x_0 + y_0\)) = 0.
This occurs when t = 0 or when \(x_0 + y_0 = 0.\)
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where A is the surface area of a cube with edge e. Find A if e = 12 cm. A=62
Answers
Answer:
surface area= 6l²
= 6×12²
= 164cm²
hope it helps
Convert DAD base16 to binary
Answers
Answer:
D = 01000100
A = 01100001
D = 01000100
B = 01000010
A = 01100001
S = 01110011
E = 01100101
1 = 00110001
6 = 00110110
how to chain rule formula
Answers
The chain rule is a formula used in calculus to find the derivative of a composition of functions. It is an important tool for solving problems in many areas of mathematics and science.
The chain rule formula can be stated as follows:
If y = f(g(x)), then the derivative of y with respect to x is given by:
dy/dx = (df/dg) * (dg/dx)
In other words, the derivative of y with respect to x is equal to the derivative of f with respect to g, multiplied by the derivative of g with respect to x.
Here, f and g are functions of x, and y is a function of g. The chain rule formula tells us how to find the derivative of y with respect to x, by taking into account the effect of both f and g on the function y.
The chain rule can be extended to more complex compositions of functions, by applying the formula repeatedly. For example, if y = f(g(h(x))), then the chain rule can be applied twice, as follows:
dy/dx = (df/dg) * (dg/dh) * (dh/dx)
This formula tells us how to find the derivative of y with respect to x, by taking into account the effects of all three functions f, g, and h on the function y.
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1. What number is 1.23 x 10^6 without scientific notation?
Answers
The number 1.23 x 10⁶ without scientific notation is 12,30,000.
Scientific Notations:Scientific notation is a way to display extremely big or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper.
We use positive exponents for base 10 when expressing any huge integers in scientific notation. For example:
500000 = 5 x 10⁵, where 5 is the positive exponent.
We use negative exponents for base 10 when expressing any small integers in scientific notation. For example:
0.00005 = 2 x 10⁻⁵, where -5 is the negative exponent.
Here we have
The number 1.23 x 10⁶
We need to write the given number without scientific notation
In the given number the exponent of 10 = 6 and positive
Then we need to move the decimal place 7 places to the right or multiply the given decimal number with 1000000
Therefore,
1.23 x 10⁶ = 1.23 × 1000000 = 12,30,000.
Hence,
The number 1.23 x 10⁶ without scientific notation is 12,30,000.
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okay okay so can anyone help me with this??
Answers
Answer:
30
Step-by-step explanation:
how many possible outcomes contain the same number of heads and tails if the coin is flipped 8 times?
Answers
There are 70 possible outcomes containing the same number of heads and tails when a coin is flipped 8 times.
To find out how many possible outcomes contain the same number of heads and tails when a coin is flipped 8 times, we can use combinations.
Identify the total number of flips (n) and the number of heads (or tails) required (k).
- In this case, n = 8 (total flips) and k = 4 (since we need equal numbers of heads and tails, which is half of the total flips).
Calculate the combinations using the formula:
- C(n, k) = n! / (k!(n-k)!)
- Where "C" is the number of combinations, "n" is the total number of flips, "k" is the number of heads, "!" denotes a factorial (e.g., 5! = 5 x 4 x 3 x 2 x 1), and "n - k" is the difference between the total number of flips and the number of heads.
Plug the values into the formula and calculate the result:
- C(8, 4) = 8! / (4!(8-4)!)
- C(8, 4) = 8! / (4!4!)
- C(8, 4) = (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / ((4 x 3 x 2 x 1) (4 x 3 x 2 x 1))
- C(8, 4) = 40,320 / (24 x 24)
- C(8, 4) = 40,320 / 576
- C(8, 4) = 70
So, there are 70 possible outcomes containing the same number of heads and tails when a coin is flipped 8 times.
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Cameron collects old books, and they convinced their friend Kenji to start collecting as well. Every month, they go to the store together, and they each buy a book. This table shows how many books they each have: Month 1 11 2 22 3 33 4 44 Kenji 1 11 2 22 3 33 4 44 Cameron 12 1212 13 1313 14 1414 15 1515 They both want an equation they can use to find how many books Cameron will have ( � cc) when Kenji has � kk books. Complete their equation. � = c=c, equals
Answers
The linear equation that describe the relationship between the book collection by Cameron, c and Kenji, c each month is represented as c = k - 11.
Linear equations are defined as the equations of degree one. It is represents equation for the straight line. The standard form of linear equation is written as, ax + by + c = 0, where a ≠ 0 and b ≠ 0. We have specify that Cameron collects and his friend Kenji start collecting the old books. The above table figure which contains data of books collected by both in different months. We have to determine the equation many books Cameron will have (c) when Kenji has k books. Let c and k denotes the books collected by Cameron and Kenji respectively. We see there is always increase in old book collection by one in case of both of them (Cameron and Kenji) each month. So, there exits a linear equation. Also, from the table, the Kenji's book collection is always 11 units less from Cameron's book collection. So, the required equation is written by c = k - 11 for each month. Hence, the required equation is equal to c = k - 11.
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Complete question:
The above figure complete the question.
Cameron collects old books, and they convinced their friend Kenji to start collecting as well. Every month, they go to the store together, and they each buy a book. This table shows how many books they each have: They both want an equation they can use to find how many books Cameron will have (c) when Kenji has k books. Complete their equation.
Answer:
c=k+11
Step-by-step explanation:
ow many groups of
1
5
5
1
start fraction, 1, divided by, 5, end fraction are in
4
44?
Answers
By the calculations below, there are 20 groups of 1/5 in 4.
Division of Fractions: Finding GroupsTo find out how many groups of 1/5 are in 4, we can use the concept of division of fractions.
Recall that dividing by a fraction is the same as multiplying by its reciprocal. So, we can rewrite the problem as:
4 ÷ 1/5
To find the reciprocal of 1/5, we flip the fraction:
1/5 → 5/1
Now, we can rewrite the division problem as multiplication:
4 ÷ 1/5 = 4 × 5/1
Multiplying across gives:
4 × 5/1 = 20
Therefore, there are 20 groups of 1/5 in 4.
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A group of two friends each receive 612s of a pound of candy how much candy did they received total
Answers
Answer:
1224
Step-by-step explanation:
group of 2 friends each receive 612
so you do 612 x 2 = 1224
Mr.david gave ross a number and asked him to divide it by 15. The quotient and remainder obtained by ross are 341 and 12 respectively. Find the number that teacher gave ross.
Answers
The number the teacher gave Ross is 5127
Word problems on linear equationsFrom the question, we are to determine the number that the teacher gave Ross
From the given information,
Mr. David gave Ross a number and asked him to divide it by 15.
Let the number be x
That is,
x/15
The quotient and remainder obtained by ross are 341 and 12 respectively
That is,
x/15 = 341 + 12/15
Now, we will solve the equation for x
x/15 = 341 + 12/15
Multiply through by 15
x = 15×341 + 12
x = 5115 + 12
x = 5127
Hence, the number the teacher gave Ross is 5127
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express -3/5 as a rational number with denominator of 20
Show full work !
Answers
Answer:
- \(\frac{12}{20}\)
Step-by-step explanation:
To obtain a denominator of 20 requires the numerator and denominator to be multiplied by 4 , that is
- \(\frac{3}{5}\) = - \(\frac{3(4)}{5(4)}\) = - \(\frac{12}{20}\)
PLEASE HELP ME ASAP!! MY CLASS IN 6 MINUTES!
At a gathering of 12 people, there are 5 people who all know each other and 7 people who know no one. People who do not know each other shake hands. How many handshakes occur?
Answers
Answer: someone told me its 35 so...
Step-by-step explanation:
Answer:
Step-by-step explanation: Since there are 7 people who shake hands with everybody including the people who know each other, we can add 11+10+9+8+7+6+5, because each handshake counts once, but the other five can't be counted because they are the people who already know each other and if you add 11+10+9+8+7+6+5, you will also get 16*3 +8 which equals to 56.
Kevin has $500 in his savings account and he deposits $25 each week. Janet has $250 in her savings account and she deposits $50 each week.
(a) Write a system of equations that represents the scenario
(b) Solve the system to determine after how many weeks Kevin and Janet will have the same amount of savings. What will that amount be?
Answers
Answer:
(a) Let x be the number of weeks and let y be the total amount in their savings accounts. Then, the system of equations that represents the scenario is:
Kevin: y = 25x + 500
Janet: y = 50x + 250
(b) To determine after how many weeks Kevin and Janet will have the same amount of savings, we need to solve the system of equations by setting them equal to each other:
25x + 500 = 50x + 250
Subtracting 25x and 250 from both sides, we get:
250 = 25x
Dividing both sides by 25, we get:
x = 10
Therefore, Kevin and Janet will have the same amount of savings after 10 weeks. To find out what that amount is, we can substitute x = 10 into either equation:
y = 25x + 500
y = 25(10) + 500
y = 750
So after 10 weeks, both Kevin and Janet will have $750 in their savings accounts.
Step-by-step explanation: explained it in the answer
Anyone else have a bully and your bully makes fun of you because your adopted?
I do but I tell them "Well, my parents chose me. Your parents are stuck with you"
What should I do? Should I continue roasting them or should I just go with the fact that I'm adopted?
Answers
Answer:
TBH IF YOU WANT TO ROAST I GOT NO IDEA BUT THIS IS THE THING I DO
Step-by-step explanation:
Well to be honest I think you should just treat him the same say the same things you would normallily say when you didnt know he waS
Answer:
Go back to roasting them be the cool one
Step-by-step explanation:
Two cyclists begin from the same point and are traveling in opposite directions on a circular bike trail that is 5 miles long. Once cyclist travels at 12 miles per hour, and the other travels at a rate of 18 miles per hour. How far did cyclist A travel?
Answers
Answer:
three cytliys and six ka
Step-by-step explanation:
hope it hlp you
Statistics
Ethan repairs household appliances such as dishwashers and refrigerators. For each visit, he charges $25 plus $20 per hour of work. A linear equation that expresses the total amount of money Ethan earns per visit is y = 25 + 20x. What are the independent and dependent variables? What is the y-intercept, and what is the slope? Interpret them using complete sentences.
Answers
I WILL OPEN MY ALT AND COMENT AND GIVE YOU A BRINLIST OPEN IF YOU SHOWED YOUR WORK!!! OPEN THE IMAGE
Answers
Answer:
b = -3
Step-by-step explanation:
1. Rearrange Terms
-3(3 + 6b) = 36 - 3b
-3(6b + 3) = 36 - 3b
2. Distribute
-3(6b + 3) = 36 - 3b
-18b - 9 = 36 - 3b
3. Rearrange Terms
-18b - 9 = 36 - 3b
-18b - 9 = -3b + 36
4. Add 9 to both sides
-18b - 9 = -3b + 36
-18b - 9 + 9 = -3b + 36 + 9
5. Simplify
-18b - 9 + 9 = -3b + 36 + 9
-18b = -3b + 45
6. Add 3b to both sides
-18b = -3b + 45
-18b +3b = -3b + 45 + 3b
7. Simplify
-15b = 45
8. Divide both sides by the same factor
-15b = 45
\(\frac{-15b}{-15}\) = \(\frac{45}{-15}\)
9. Simplify
b = -3
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 10 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Answer:
WWWWWW
Step-by-step explanation:
Help me solve these equations by graphing please
Answers
Answer:
5, 6, and 8 don’t have solutions because they are parallel / have the same slope. 7 has a solution outside of the domain and range of this graph.
Step-by-step explanation:
I’m honestly not sure about 7, it seems like it should be parallel as well. tell me if I should redo it lol.
1
1. y=ax+1
y=-x-9
441
Answers
for a vector space v and a finite set of vectors s = {v1, · · · , vn} in v , copy down the definitions for a) span(
Answers
(a) Span (s) = {a₁v₁+a₂v₂+.........aₙvₙ} \(a_i\) ∈ field.
(b) A basic for V is linearly independent spanning set of V.
(c) A subset of V which its self is a vector space is called subspace of V.
Let V be a vector space and S be a set of vectors on i. e.
s{V₁,V₂,V₃..........Vₙ} then,
(a) Span (S) is set of all possible linear combinations of vector in S i.e.
Span (s) = {a₁v₁+a₂v₂+.........aₙvₙ} \(a_i\) ∈ field
i. e. \(a_i\) are scalars from field on which vector space V is defined.
(b) A basic for V is linearly independent spanning set of V i.e.
Let B be set of vectors in V. then B is a Basic of V if
(i) B is linearly independent set
(ii) Span (B) = V
(C) A subset of V which its self is a vector space is called subspace of V.
Therefore, Span (s) = {a₁v₁+a₂v₂+.........aₙvₙ} \(a_i\) ∈ field.
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Incomplete Question:
for a vector space v and a finite set of vectors s = {v1, · · · , vn} in v , copy down the definitions for
a) span(S).
b) a basis of b.
c) a subspace of V.
Which is the graph of f(x) = 1/4 (4)^x ?
Answers
Answer:
The only graph that is fully shown.
Step-by-step explanation:
I did the math and the points check out.
1.A race car drove around a circular track that was 0.5 mile. If 1 mile = 5,280 feet, what is the radius of the track, in feet? Use π = 3.14 and round to the nearest hundredth.
2.What is the circumference of a circle with a diameter of 28 cm? Approximate using pi equals 22/7.
3.A circle with a diameter of 36 inches is shown.
circle with diameter of 36 inches
What is the area of the circle using π = 3.14?
113.04 in2
452.16 in2
1,017.36 in2
4,069.44 in2
Answers
1. The radius of the track, in feet, is 420.04 ft.
2. The circumference of a circle with a diameter of 28 cm, using a pi of 22/7 is 88 cm.
3. The area of the circle with a diameter of 36 inches, using π = 3.14, is C. 1,017.36 in².
How the values are determined:1. Radius = circumference divided by (2 multiplied by pi).
r = c / (2 * π)
π = 3.14
Circumference = 0.5 miles
1 mile = 5,280 ft
Circumference in feet = 2,640 ft (5,280 x 0.5)
r = 2,640/(2 x 3.14)
r = 2,640/6.28
r = 420.04 ft
2. Diameter = 28 cm
Pi = 22/7
Therefore, Circumference = Diameter x π
= 28 x 22/7
= 88 cm.
3. Diameter = 36 inches
π = 3.14
Area = piR²
R = 1/2 diameter
= 18 inches
Area = 3.14 x 18²
= 3.14 x 324
= 1,017.36 in²
OR:
= A= 1/4πd²
= 1/4 x 3.14 x 36²
= 1/4 x 3.14 x 1,296
= 1,017.36 in²
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PLEASE HELP ME!!! ILL GIVE BRAINLIEST IF ITS RIGHT
Answers
Answer:
266.386
Step-by-step explanation:
im not shore if its right, i used a surface area calculator
Answer:
56ft
Step-by-step explanation:
Surface area is adding up all the sides multiplied by 2, so:
8 x 2 = 16ft
8 x 2 = 16ft
12 x 2 = 24ft
24ft + 16ft + 16ft = 56ft
given:• Square WJTSquare CBAZW is the midpoint of segment CZ• The perimeter of square WVJT is 12V2.BwThe measure of angle VWT isThe measure of angle CWV isThe length .cw isThe perimeter of square CBAZ is
Answers
All four interior angles of a square are 90°
Therefore,
The measure of ∠VWT will be
\(\angle VWT=90^0\)Hence,
∠VWT = 90°
Step2:measure the angle CWV
Sum of angles in a triangle is
\(=180^0\)Therefore,
\(\begin{gathered} \angle CWV+\angle CVW+WCV=180^0 \\ \theta+\theta+90^0=180^0(isosceles\text{ triangle)} \\ 2\theta=180^0-90^0 \\ 2\theta=90^0 \\ \text{Divide both sides by 2} \\ \frac{2\theta}{2}=\frac{90^0}{2} \\ \theta=45^0 \end{gathered}\)Hence,
∠ CWV = 45°
Since the perimeter of the square WVJT
\(=12\sqrt[]{2}\)Then
\(VW+WT+TJ+JV=12\sqrt[]{2}\)All sides of a square are equal, therefore,
\(VW=WT=TJ=JV=x\)Hence, we will have that
\(\begin{gathered} x+x+x+x=12\sqrt[]{2} \\ 4x=12\sqrt[]{2} \\ \text{divide both sides by 4} \\ \frac{4x}{4}=\frac{12\sqrt[]{2\text{ }}}{4} \\ x=3\sqrt[]{2} \end{gathered}\)\(\begin{gathered} CW=y=\text{ADJACENT} \\ CV=y=\text{OPPOSITE} \\ VW=3\sqrt[]{2}=\text{HYPOTENUS} \end{gathered}\)Using the Pythagoras theorem,we will have
\(\begin{gathered} \text{hypotenus}^2=\text{opposite}^2+\text{adjacent}^2 \\ (3\sqrt[]{2)}^2=y^2+y^2 \\ 2y^2=9\times2 \\ 2y^2=18 \\ \text{diveide both sides by 2} \\ \frac{2y^2}{2}=\frac{18}{2} \\ y^2=9 \\ \text{squareroot both sides } \\ y=\sqrt[]{9} \\ y=3 \end{gathered}\)Therefore,
Length CW = 3
The perimeter of CBAZ IS
\(\text{PERIMTER}=\text{ CB+BA+AZ+ZC}\)\(\begin{gathered} ZC=CW+ZW \\ \text{But CW=ZW=3} \\ \text{Therefore} \\ ZC=3+3 \\ ZC=6 \end{gathered}\)Recall, that all sides of a square are equal,
Hence,
\(ZC=CB=BA=AZ=6\)Therefore, perimeter of CBAZ will be
\(\begin{gathered} \text{Perimeter of CBAZ=6+6+6+6} \\ \text{PERIMETER =24} \end{gathered}\)Hence,
Perimeter of CBAZ =24
50 points and brainliest to first correct answer :/
The figure below shows a quadrilateral ABCD. Sides AB and DC are congruent and parallel:
A quadrilateral ABCD is shown with the opposite sides AB and DC shown parallel and equal.
A student wrote the following sentences to prove that quadrilateral ABCD is a parallelogram:
Side AB is parallel to side DC, so the alternate interior angles, angle ABD and angle CDB, are congruent. Side AB is equal to side DC, and DB is the side common to triangles ABD and BCD. Therefore, the triangles ABD and CDB are congruent by SSS postulate. By CPCTC, angles DBC and BDA are congruent and sides AD and BC are congruent. Angle DBC and angle BDA form a pair of alternate interior angles. Therefore, AD is congruent and parallel to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel.
Which statement best describes a flaw in the student's proof?
Question 11 options:
Angle DBC and angle BDA form a pair of vertical angles, not a pair of alternate interior angles, which are congruent.
Triangles ABD and CDB are congruent by the SAS postulate instead of the SSS postulate.
Triangles ABD and BCD are congruent by the AAS postulate instead of the SSS postulate.
Angle DBC and angle BDA form a pair of corresponding angles, not a pair of alternate interior angles, which are congruent.
Answers
Answer: Where is the figure??
"The figure below shows a quadrilateral ABCD. Sides AB and DC are congruent and parallel:"Answer:
I think it this one but picture would help...
Angle DBC and angle BDA form a pair of vertical angles, not a pair of alternate interior angles, which are congruent.
(1) An architect firm uses an average of 60 boxes of copier paper a day. The fim operates 280 days a year. Storage and handling costs for the paper are $30 a year per box, and its costs approximately $60 to order and receive a shipment of paper. (a) What quantity order size would minimize the total annual inventory cost? (b) Determine the minimum total annual inventory cost. (c) The office manager is currently using an order size of 300 boxes. The partners of the firm expect the office to be managed "in a cost-efficient manner." Would you recommend the manager to use your quantity from part (a) rather than 300 boxes? Justify your answer (by determining the total annual inventory cost for 300 boxes):
Answers
Part a: What quantity order size would minimize the total annual inventory cost? Total Annual Inventory Cost = Annual Ordering Cost + Annual Carrying Cost At minimum Total Annual Inventory Cost, the formula for the Economic Order Quantity (EOQ) is used. EOQ formula is given below: EOQ = sqrt((2DS)/H)Where, D = Annual DemandS = Ordering cost
The company should place an order for 168 boxes at a time in order to minimize the total annual inventory cost.Part b: Determine the minimum total annual inventory cost.Using the EOQ, the company can calculate the minimum total annual inventory cost. The Total Annual Inventory Cost formula is:Total Annual Inventory Cost = Annual Ordering Cost + Annual Carrying CostAnnual Ordering Cost = (D/EOQ) × S = (16,800/168) × $60 = $6,000Annual Carrying Cost = (EOQ/2) × H = (168/2) × $30 = $2,520Total Annual Inventory Cost = $6,000 + $2,520 = $8,520Therefore, the minimum Total Annual Inventory Cost would be $8,520.Part c: Would you recommend the manager to use your quantity from part (a) rather than 300 boxes? Justify your answer (by determining the total annual inventory cost for 300 boxes)
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Solve the equation for x. If necessary round to the nearest tenth.
x² = 17
X=
+
Answers
Answer:
x = 4.1 & x = −4.1
Step-by-step explanation:
\(x^2 = 17\\\)
x = ±√17
x = √17, −√17
x = 4.1 & x = −4.1
How many
months would it take for 25 rabbits
to grow to 1000 if they are growing at a rate of
50% each month?
A.7.95
B.11.31
C.9.10
D.227.15
Answers
The correct answer is option B. it would take approximately 11.31 months for 25 rabbits to grow to 1000 at a rate of 50% each month.
To find out how many months it would take for 25 rabbits to grow to 1000 at a rate of percentage of 50% each month, we can use the formula for compound interest:
A = P(1+r)^t
where A is the final amount, P is the initial amount, r is the growth rate (in decimal form), and t is the time (in months).
In this case, we have:
A = 1000
P = 25
r = 0.5 (since the rabbits are growing at a rate of 50% each month)
Plugging these values into the formula, we get:
1000 = 25(1+0.5)^t
Simplifying:
40 = (1.5)^t
Taking the logarithm of both sides:
log(40) = t*log(1.5)
Solving for t:
t = log(40)/log(1.5)
Using a calculator, we get:
t ≈ 11.31
Therefore, it would take approximately 11.31 months for 25 rabbits to grow to 1000 at a rate of 50% each month.
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I need help with these problems from #33 to #40 can someone please help me with them ASAP please and thank you.. can you show step by step please and thank you
Answers
#33
\(\\ \sf\longmapsto \dfrac{300(300+1)}{2}\)
\(\\ \sf\longmapsto \dfrac{300(301)}{2}\)
\(\\ \sf\longmapsto 150(301)=45150\)
#34
\(\\ \sf\longmapsto \dfrac{500(500+1)}{2}\)
\(\\ \sf\longmapsto 250(501)\)
\(\\ \sf\longmapsto 125250\)
#35
\(\\ \sf\longmapsto \dfrac{675(675+1)}{2}\)
\(\\ \sf\longmapsto dfrac{675(676)}{2}\)
\(\\ \sf\longmapsto 675(338)\)
\(\\ \sf\longmapsto 228150\)
#36
\(\\ \sf\longmapsto \dfrac{825(825+1)}{2}\)
\(\\ \sf\longmapsto \dfrac{825(826)}{2}\)
\(\\ \sf\longmapsto \dfrac{825(413)}{1}\)
\(\\ \sf\longmapsto 340725\)
#37
n=102/2=51
\(\\ \sf\longmapsto n^2\)
\(\\ \sf\longmapsto 51^2\)
\(\\ \sf\longmapsto 2621\)
#38
n=49+1/2=50/2=25
\(\\ \sf\longmapsto n^2\)
\(\\ \sf\longmapsto 25^2\)
\(\\ \sf\longmapsto 625\)
#39
n=999+1/2=1000/2=500
\(\\ \sf\longmapsto n^2\)
\(\\ \sf\longmapsto 500^2\)
\(\\ \sf\longmapsto 250000\)