1. a) The price is 5 dollars. b) The rate of change of demand with respect to price, p, when x = 4 is 5/6 thousands of units per dollar. c) The elasticity of demand when x = 4 is 25/24.
2. a) The price is 2*sqrt(3) dollars. b) The rate of change of demand with respect to price, p, when x = 10 is - (3 * sqrt(3))/(7) thousands of units per dollar. c) The elasticity of demand when x = 10 is -6/7.
3. Demand is increasing at -23.30 thousands of units per week.
4. If the daily production is 800 cases, then revenue is decreasing at a rate of -1200 dollars per day.
5. Supply is rising at a rate of 150.90 thousands of styluses per week.
1)
(a) Compute the price, p, when x = 4.
Price, p = −3(4)^2 − 4(4) + 69 = -48 -16 + 69 = 5 dollars
(b) Use implicit differentiation to compute the rate of change of demand with respect to price, p, when x = 4.
Rate of change of demand, x' = - (2 * -3 * x + 4)/(-3 * 2 * x) = -(-24 + 4)/(-24) = 20/24 = 5/6 thousands of units per dollar
(c) Compute the elasticity of demand when x = 4.
The elasticity of Demand = (x'/x) * (p) = (5/6)/(4) * (5) = 25/24
2)
(a) Compute the price, p, when x = 10.
Price, p = sqrt((216 - 10^2 - 8*10)/3) = sqrt((216 - 100 - 80)/3) = sqrt(12) = 2*sqrt(3) dollars
(b) Use implicit differentiation to compute the rate of change of demand with respect to price, p, when x = 10.
Rate of change of demand, x' = - (2 * 3 * p)/(2 * x + 8) = - (6 * 2 * sqrt(3))/(20 + 8) = - (12 * sqrt(3))/(28) = - (3 * sqrt(3))/(7) thousands of units per dollar
(c) Compute the elasticity of demand when x = 10.
Elasticity of Demand = (x'/x) * (p) = (- (3 * sqrt(3))/(7))/(10) * (2*sqrt(3)) = -6/7
3)
The weekly demand equation is given by p + x + 3xp = 53,
where x is the number of thousands of units demanded weekly and p is in dollars. If the price p is decreasing at a rate of 70 cents per week when the level of demand is 5000 units, then demand is increasing at a rate of (53 - 5000 - 70)/(3*70 + 1) = -4917/211 = -23.30 thousands of units per week.
4)
A company is decreasing production of math-brain protein bars at a rate of 100 cases per day. All cases produced can be sold. The daily demand function is given by p(x) = 20 − x/200,
where x is the number of cases produced and sold, and p is in dollars.
If the daily production is 800 cases, then revenue is decreasing at a rate of (20 - 800/200) * (-100) + (800) * (-1/200) * (-100) = (20 - 4) * (-100) + (800) * (1/2) = -1600 + 400 = -1200 dollars per day.
5)
The wholesale price p of e-tablet writing styluses in dollars is related to the supply x in thousands of units by 400p^2 − x^2 = 14375,
If 5,000 styluses are available at the beginning of a week, and the price is falling at 30 cents per week, then supply is rising at a rate of (2 * 400 * p * (-0.30) - 2 * x * x')/(2 * -1 * x) = (800 * p * (-0.30) - 0)/(2 * -5000) = (800 * sqrt(14375 + 5000^2)/400 * (-0.30) - 0)/(2 * -5000) = (800 * sqrt(14375 + 25000000)/400 * (-0.30))/(2 * -5000) = (2 * sqrt(14375 + 25000000) * (-0.30))/(-5000) = 0.012 * sqrt(14375 + 25000000) = 150.90 thousands of styluses per week.
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1.Solve log2x=log218 showing steps as done in the exam 2. 2.Solve log2×2=log2(4x−4) showing steps as done in the 3. Solve logb(x2−56)=logbx showing steps as done in the e
x = 2logb(x2 + 56)/2
1. log2x = log218
log2x = 3
x = 23 = 8
2. log2×2 = log2(4x−4)
log2×2 = log2(4x)−log2(4)
log2×2 = log2(4x)−2
log2×2 + 2 = log2(4x)
log2(2×2) + 2 = log2(4x)
log2(4) + 2 = log2(4x)
4 + 2 = log2(4x)
6 = log2(4x)
26 = 4x
x = 23 = 8
3. logb(x2−56)=logbx
logb(x2−56) = logbx
logb(x2)−logb(56) = logbx
logbx2−logb56 = logbx
logbx2−logb56 + logbx = logbx + logbx
2logbx = logbx2 + logb56
2logbx − logbx2 = logb56
2logbx − logb(x2−56) = logb56
2logbx − logb(x2) + logb(56) = logb56
2logbx−logbx2 + logb(56) = logb56
2logbx = logb(x2 + 56)
2logbx = logb(x2 + 56)
logbx = logb(x2 + 56)/2
x = 2logb(x2 + 56)/2
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al numbers that could be zeros of the polynomial accordir P(v)=14v^(5)+6v^(4)+5v^(3)-4v^(2)+2v
The only possible rational zero of the polynomial is 0
The possible zeros of the polynomial P(v) = 14v^5 + 6v^4 + 5v^3 - 4v^2 + 2v can be found by using the Rational Root Theorem. This theorem states that if a polynomial has rational zeros, they will be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
In this case, the constant term is 0 and the leading coefficient is 14. The factors of 0 are just 0, and the factors of 14 are 1, 2, 7, and 14. Therefore, the possible rational zeros of the polynomial are 0/1, 0/2, 0/7, and 0/14, which all simplify to just 0.
This means that the only possible rational zero of the polynomial is 0. However, there may also be irrational or complex zeros. To find these, we would need to use other methods, such as synthetic division or the quadratic formula.
In conclusion, the possible zeros of the polynomial P(v) = 14v^5 + 6v^4 + 5v^3 - 4v^2 + 2v are 0 and any irrational or complex numbers that satisfy the equation.
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Consider the expression |x+3|5x-2|-(x+3)(4x+3)| a. Rewrite the expression in the form (x+3)|ax+b|
The expression |x+3|5x-2|-(x+3)(4x+3)| can be rewritten as (x+3)|x-5|.
Consider the expression |x+3|5x-2|-(x+3)(4x+3)|. To rewrite this expression in the form (x+3)|ax+b|, we will need to use the distributive property and combine like terms.
First, let's distribute the (x+3) term:
|x+3|5x-2| - (x+3)(4x+3) = |5x^2 + 13x - 2| - |4x^2 + 15x + 9|
Next, let's combine like terms:
|5x^2 + 13x - 2| - |4x^2 + 15x + 9| = |x^2 - 2x - 11|
Now, we can factor the expression inside the absolute value:
|x^2 - 2x - 11| = |(x+3)(x-5)|
Finally, we can rewrite the expression in the form (x+3)|ax+b|:
|(x+3)(x-5)| = (x+3)|x-5|
So, the expression |x+3|5x-2|-(x+3)(4x+3)| can be rewritten as (x+3)|x-5|.
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Big ideas 7.5 question
None of the options are sufficient to prove that ABCD quadrilateral is a kite.
what are quadrilaterals ?
Quadrilaterals are closed two-dimensional shapes with four straight sides and four angles. The word "quadrilateral" comes from the Latin words "quadri" which means "four" and "latus" which means "side". Some common examples of quadrilaterals include squares, rectangles, parallelograms, rhombuses, and trapezoids.
Each type of quadrilateral has its own unique set of properties and characteristics. For example, a rectangle has four right angles and opposite sides that are parallel and congruent. A parallelogram has opposite sides that are parallel and congruent, and opposite angles that are congruent. A rhombus has four congruent sides and opposite angles that are congruent.
According to the question:
Option A: OBC and DC being congruent only tells us that OBDC is a parallelogram, but it does not tell us anything about the other pair of adjacent sides, AB and BC.
Option B: OAC and DC being congruent only tells us that OACD is an isosceles trapezoid, but it does not tell us anything about the other pair of adjacent sides, AB and BC.
Option C: OAC and BC being congruent only tells us that OABC is a kite, but it does not tell us anything about the other pair of adjacent sides, AD and DC.
None of the options given are sufficient to prove that ABCD is a kite. To prove that ABCD is a kite that we need to show that two pairs of adjacent sides are congruent.
Therefore, none of the options are sufficient to prove that ABCD is a kite.
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What is the exact value of x?
Answer:
x= 6[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Write a formula for a linear function f(x) that models the situation, where x is the number of years after. In 2006 the average adult ate 56 pounds of chicken. This amount will increase by 0. 6 pounds per year until 2011
The required linear function is (f(x) = 0.6(x - 2006) + 56) and this can be determined by using the arithmetic operations.
Given :
In 2006 the average grownup ate fifty-six kilos of birds.
the amount will increase by means of zero.6 pounds in step with yr till 2011.
To determine the linear feature f(x) following steps can be used
Let 'x' be the number of years.
Then the total number of years since 2006 will be:
= x - 2006
The amount boom in kilos in line with 12 months could be:
= 0.6(x - 2006)
Now, add 56 to the above equation.
= 0.6(x - 2006) + 56
It is a type of function that has a constant rate of change between the independent variable (usually denoted as x) and the dependent variable (usually denoted as y). The general form of a linear function is y = mx + b, where m is the slope or the rate of change, and b is the y-intercept.
Linear functions are commonly used in mathematics, economics, physics, and engineering to model real-world phenomena that have a linear relationship between two variables. For example, the cost of producing a certain number of units of a product may be modeled by a linear function, where the slope represents the cost per unit and the y-intercept represents the fixed costs.
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A road map is drawn to a scale of 1mm : 50m calculate:
i) The distance on the map which represents 20km on the road
ii) The distance on the road which correspond to 228 on the map
The ratio used to depict the relationship between the dimensions of a model or scaled figure and the corresponding dimensions of the real figure or object is called the scale. On the other hand, a scale factor is a value that is used to multiply all of an object's parts in order to produce an expanded or decreased figure.
Given, A road map is drawn to a scale of 1mm: 50m
i) To find the distance on the map which represents 20 km on the road, we need to use the scale of the map.
Since 1 mm on the map represents 50 m on the road, we can set up a proportion:
1 mm / 50 m = x mm / 20,000 m
Cross-multiplying and solving for x, we get:
x = (1 mm / 50 m) * 20,000 m = 400 mm
Therefore, the distance on the map which represents 20 km on the road is 400 mm.
ii) To find the distance on the road which corresponds to 228 on the map, we can again use the scale of the map.
Since 1 mm on the map represents 50 m on the road, we can set up a proportion:
1 mm / 50 m = 228 mm / x m
Cross-multiplying and solving for x, we get:
x = (228 mm / 1) / (50 m / 1) = 4.56 km
Therefore, the distance on the road which corresponds to 228 on the map is 4.56 km.
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A large wooden prism will be covered with spray paint for a prop in a school play. The prop must be painted on all sides. A can of spray paint costs $4.00 and will cover 40 square feet. What is the cost to paint the box ?
Part A: how many full cans of spray paint need to be purchased?
Part B What is the cost to paint the box
(a) The number of cans of spray paint that needs to be purchased is 3.
(b) The cost to paint the wooden prism is $12.00.
What is the cost of the painting?
To determine the cost of painting the wooden prism, we need to calculate the surface area of the prism and then divide it by the coverage of each can of spray paint.
Let's assume the wooden prism has dimensions of 6 feet by 4 feet by 3 feet.
Part A:
The surface area of the prism can be calculated as follows:
The top and bottom faces have an area of 6 ft x 4 ft = 24 ft² each
The two side faces have an area of 6 ft x 3 ft = 18 ft² each
The front and back faces have an area of 4 ft x 3 ft = 12 ft² each
Therefore, the total surface area of the prism is:
2(24 ft²) + 2(18 ft²) + 2(12 ft²) = 96 ft²
Since each can of spray paint covers 40 ft², we need:
96 ft² ÷ 40 ft²/can = 2.4 cans
We can't purchase a partial can of spray paint, so we need to round up to the nearest whole can.
Therefore, we need to purchase 3 cans of spray paint.
Part B:
The cost of painting the box will be the number of cans required multiplied by the cost per can.
Since we need to purchase 3 cans, the cost will be:
3 cans x $4.00/can = $12.00
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Match the number in scientific notation to the same number in standard notation.
Answer:
Step-by-step explanation:
from top to bottom:
1,200
0.012
120
0.00012
If the exponent is positive, move the decimal to the RIGHT the number of spaces equal to the exponent.
If the exponent is negative, move the decimal to the LEFT the number of spaces equal to the exponent.
Use the relationships in the diagrams below to solve for the given variable. Justify your solution with a definition or theorem.
In the parallelogram given the value for the variable x is deduced as 25°.
What is a parallelogram?
A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.
According to the properties of a parallelogram, the vertically opposite angles of a parallelogram is always equation.
The first angle measures 2x + 50°.
The second angle measures 3x + 25°.
They both are placed vertically opposite to each other.
So, the equation will be -
2x + 50° = 3x + 25°
Collect the like terms -
2x - 3x = 25° - 50°
- x = - 25°
x = 25°
Therefore, the value of x is obtained as 25°.
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Tangents. of a circle
The required,
19. AB is tangent to circle C.
20. AB is not tangent.
In a right-angled triangle, its sides, such as the hypotenuse, are perpendicular and the base is Pythagorean triplets.
Here,
Form figure 19.
Applying the Pythagorean theorem,
BS² = AS² + AB²
Substitute the value in the above expression.
12² = 7.2² + [2*4.8]² [radius = diameter /2]
144 = 51.84+92.16
144 = 144
Thus, the required AB is tangent to circle C.
Similarly,
In figure 20 AB is not tangent because,
BC² ≠ AB² + AC²
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What is the y-intercept
Answer:
y-intercept: 3
equation: y = -x + 3
Step-by-step explanation:
For problem #6: (-2,5) and (2,1)
Slope m = (y2 - y1)/(x2 - x1)
=>m = (1 - 5)/(2 - -2) = -4/4 = -1
Slope-intercept form is y = mx + b
Given m = -1, y = 1, x = 2
=> 1 = -1(2) + b
=> 1 = -2 + b
=> b = 1 + 2 = 3
equation: y = -x + 3
since b is the y-intercept => 3
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
What type of polynomial is: −2/3b*3
A. quadratic
B. linear
C. quartic
D. cubic
The type of polynomial that - 2 / 3 x b³ is D. Cubic polynomial.
What is a cubic polynomial ?A cubic polynomial is a type of polynomial function in algebra that has a degree of three. Cubic polynomials can take many different forms and can have multiple real roots, complex roots, or no real roots at all.
A quadratic polynomial contains a degree of 2, a linear polynomial contains a degree of 1, and a quartic polynomial contains a degree of 4. In this case, the highest degree of the variable b is 3, which makes it a cubic polynomial.
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I neeeed help plssssssssssssssssssssssss
Answer:
I AINT SOLVING ALL THAT
Rearrange the equation y - 4 = x into slope intercept form
The answer is y=x+4
You would had the 4 to the side with the x on it.
Answer:
Below
Step-by-step explanation:
Slope-intercept form is : y = mx + b
y - 4 = x add 4 to each side of the equation
y = x + 4 Done.
Liam opens a savings account with $400 deposit and a simple interest rate of 7. 5%. Of the balance of the account is not $760 and there were no deposits or withdrawals, how long ago did he open the account?
Liam opened the savings account 4 years ago based on the given condition of a $400 deposit.
The formula for simple interest is I = Prt, where I is the interest earned, P is the principal amount, r is the interest rate per year, and t is the time in years.
We are given that Liam deposited $400 and the interest rate is 7.5%. Let's first calculate the interest earned:
I = Prt = 4000.075t = 30t
After some time t, the balance of the account is $760, which means the total amount in the account is the principal plus the interest earned:
400 + 30t = 760
Simplifying this equation, we get:
30t = 360
t = 12
Therefore, Liam opened the savings account 12/3 = 4 years ago.
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A recipe uses 2 cups of milk to make 6 servings. If the same amount of milk is used for each serving, how many servings can be made from one gallon?
1 gallon
=
1 gallon=
4 quarts
4 quarts
1 quart
=
1 quart=
2 pints
2 pints
1 pint
=
1 pint=
2 cups
2 cups
1 cup
=
1 cup=
8 fluid ounces
8 fluid ounces
Before you try that problem, answer the question below.
How many cups will you need to find the number of servings for?
Answer:
48 servings
Step-by-step explanation:
since there are 16 cups in a gallon and 2 cups makes 6 servings, then to find the number of servings a gallon makes we divide the amount of cups in a gallon (16) by how many you need to make the recipe (2), and 16/2=8 so now we multiply how many times we can make the recipe with a gallon (8) by how many servings the recipe makes (6) to get 8x6=48 servings
pls help due today plesh
Answer:
£67.78
Step-by-step explanation:
Given that rolls come in a package of 20 for £2.87 and ham slices come in a package of 30 for £6.32, you want the minimum cost of enough packs for more than 90 sandwiches, each of which uses 1 roll and 2 ham slices.
RatiosOne package of 20 bread rolls is enough for 20 sandwiches. One package of 30 ham slices is enough for 15 sandwiches. The least common multiple of these numbers is the number of sandwiches that will use a whole number of each of the kinds of packages:
LCM(20, 15) = 60 = 3·20 = 4·15
PackagesWe want to make a number of sandwiches that is more than 90. The least multiple of 60 that is more than 90 is 120.
120 sandwiches will require 120/20 = 6 packages of bread rolls, and 120/15 = 8 packages of ham slices.
CostThe cost of 6 packages of bread rolls and 8 packages of ham slices is ...
6×£2.87 +8×£6.32 = £17.22 +50.56 = £67.78
The least Tina can spend on packs of bread and ham is £67.78.
An L-shaped polygon is shown on the coordinate grid. Draw the dilation
of this polygon after multiplying each coordinate by 3. Upload your
picture. (I need help with finding out the original coordinates so I can multiply it by 3 and draw the dilation)
Answer:
Step-by-step explanation:
ypi ,tfr
A principle ideal is an ideal generated by a single
element. That is I is a principle
ideal if there exists an element a of I such that
I = (a) = {ar : r ∈ I}.
This means that there exists an element a of the ideal I, such that all other elements in the ideal can be written as a multiple of a. In other words, the ideal I can be written as I = (a) = {ar : r ∈ I}, where r is any element of the ideal I.
A principle ideal is an ideal that is generated by a single element. This means that there exists an element a of the ideal I, such that all other elements in the ideal can be written as a multiple of a. In other words, the ideal I can be written as I = (a) = {ar : r ∈ I}, where r is any element of the ideal I. This is an important concept in the study of rings and algebraic structures, as it allows us to understand how ideals are generated and how they relate to other ideals in the same ring.
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HELP ASAP i would really appreciate it. GIVING 50POINTS please no wrong answers or guesses.
Answer:
D. x > 0, x ≤ 4, y ≥ 1 and y < 4
given the growth population model 12000/3+e^-.02(t), what is the initial population and what is the maximum population?
The initial population for this model is 12,000 and the maximum population is 24,000. The equation 12000/3+e^-.02(t) is used to model population growth.
The initial population and maximum population can be found by examining the growth population model.
The initial population is represented by the term before the exponential function, which in this case is 12000/3. This means that the initial population is 4000.
The maximum population is represented by the term in the denominator of the fraction with the exponential function. In this case, the maximum population is 3. This means that the population will never exceed 3, even as time (t) increases.
In conclusion, the initial population is 4000 and the maximum population is 3 according to the given growth population model.
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The isosceles trapezoid ABDE is part of an isosceles triangle ACE. Find the measure of the vertex angle of triangle ACE.
The measure of the vertex angle of triangle ACE is 50°. The solution has been obtained by using properties of angles.
What is an angle?
An angle is a figure in plane geometry that is created when two rays or lines share an endpoint.
We are given an isosceles triangle ACE which means that AC = CE.
We are given ∠BDE = 115°
Since, angles on a straight line form a linear pair, therefore
⇒∠BDE + ∠BDC = 180°
⇒115° + ∠BDC = 180°
⇒∠BDC = 65°
Since, BD║AE so,
∠BDC = ∠AEC
So, ∠AEC = 65°
Since, AC = CE so,
∠AEC = ∠CAE
So, ∠CAE = 65°
Now, using angle sum property, we get
⇒∠AEC + ∠CAE + ∠ACE = 180°
⇒65° + 65° + ∠ACE = 180°
⇒130° + ∠ACE = 180°
⇒∠ACE = 50°
Hence, the measure of the vertex angle of triangle ACE is 50°.
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-2(-3)+27÷ (-3) +3=calculate without using a calculator
the value of the expression is 0.
To solve this expression, we can use the PEMDAS order of operations:
since there are no Parentheses and Exponents we move to multiplication and division
-2(-3) + 27 ÷ (-3) + 3 = 6 + (-9) + 3
6 + (-9) + 3 = 0
As a result, the equation has a value of 0.
What are equations?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.
Here,
5 and 13 are expressions for 2x.
These two expressions are joined together by the sign "=".
Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality. The two most well-known groups of equations in algebra are linear equations and polynomial equations. P(x) = 0 can be used to represent polynomial equations with a single variable. P is a polynomial, and axe + b = 0 is the standard form for linear equations. Here, are the parameters a and b.
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Alex draws the scale model shown as a plan for a large wall mosaic. He will use 2 cm square tiles to make his mosaic. How many tiles will he need? Explain how you found your answer.
Alex will need 150 tiles to make his mosaic.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the tiles in a two-dimensional plane is called the area of the tiles.
To determine the number of tiles needed to create the mosaic, we need to find out the area of the wall mosaic and then divide it by the area of each tile.
First, let's find the area of the wall mosaic. We can do this by counting the number of squares within the rectangular shape, which is the plan for the mosaic.
By counting, we can see that there are 30 squares in the horizontal direction and 20 squares in the vertical direction. Therefore, the area of the wall mosaic is:
Area of wall mosaic = 30 x 20 = 600 square cm
Now, let's find the area of each tile. The problem tells us that each tile is a square with a side length of 2 cm. Therefore, the area of each tile is:
Area of each tile = 2 x 2 = 4 square cm
Finally, we can find the number of tiles needed by dividing the area of the wall mosaic by the area of each tile:
Number of tiles needed = Area of wall mosaic ÷ Area of each tile
= 600 ÷ 4
= 150
Therefore, Alex will need 150 tiles to make his mosaic.
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WILL GIVE BRAINLIST TO BEST ANSWER
Given the recursive formula for a geometric sequence find the common ratio, the first five terms, the term named in the problem, and the explicit formula.
Show work
12) f(n) = f(n - 1) * (- 3)
f(1) = - 1
Find f(12)
[tex]f(n) = f(n - 1) * (- 3)[/tex]
[tex]f(2) = f(2 - 1) * (- 3) = \boxed{f(1) * (- 3)} = (-1)*(-3) = \bf 3\\[/tex]
[tex]f(3) = f(3 - 1) * (- 3) = f(2) * (- 3) = f(1) * (-3) * (- 3) = \boxed{f(1) * (-3)^{2}} = (-1)*3^{2} =-3^{2} = \bf -9\\[/tex]
[tex]f(4) = f(4 - 1) * (- 3) = f(3) * (- 3) = f(1) * (-3)^{2} * (- 3) = \boxed{f(1) * (-3)^{3}} = (-1)*(-3^{3}) = 3^{3} = \bf 27\\[/tex]
[tex]f(5) = f(5 - 1) * (- 3) = f(4) * (- 3) = f(1) * (-3)^{3} * (- 3) = \boxed{f(1) * (-3)^{4}} = (-1)*3^{4} =-3^{4} = \bf -64\\[/tex]
[tex]f(12) = f(12 - 1) * (- 3) = f(1) * (-3)^{10} * (- 3) = \boxed{f(1) * (-3)^{11}} = (-1)* (-3)^{11} = -(-3^{11}) = 3^{11} \\[/tex]
⇒
[tex]\boxed{f(n) = (-1)^{n} * 3^{n - 1}}[/tex]
SLOVE RN ITS DUE IN ONE HOUR
The part of the mural that Trevor has completed is 6/20 square meter.
The correct answer choice is option C.
What part of the mural has Trevor completed?Area of a rectangle is the measure of the extent of a surface. it is measured in square units.
Total area of the mural = 1 square meter
Rectangular part of the mural:
Length = 2/5 meter
Width = 3/4 meter
Area of the rectangular part of the mural = length × width
= 2/5 × 3/4
= 6/20 square meter
Ultimately, Trevor has completed 6/20 of the mural.
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Do not use L'Hospital's Rule.
Prove
A. show that 1(x) = {(sin(x) A. Show × EQ (x) XER-Q
X= zkπ, K 6 z
is continuous only at.
B. Prove that lim x=2 by & definition X-8
A. we can observe that 1(x) is continuous at x = kπ- for any integer k, and hence, it is continuous only at x = kπ, where k is an integer.
B. We have proved that limx → 2 (x2 - 1) = 3 using the definition of a limit.
How to proveA. To prove that 1(x) = {(sin(x) × EQ (x) XER-Q, X = zkπ, K 6 z is continuous only at x = kπ, where k is an integer without using L'Hospital's Rule, we can use the concept of limits.Let's consider the left limit of the function at x = kπ+ (where ε > 0 is a small value).
Here, we can observe that:
lim x → kπ+ 1(x) = lim x → kπ+ sin(x)/x > 0 since sin(x) > 0 when x is in (kπ, kπ + ε/2) and x is in (kπ - ε/2, kπ)
So, 1(x) = {(sin(x) × EQ (x) XER-Q, X = zkπ, K 6 z is continuous at x = kπ+ for any integer k.
Similarly, we can observe that 1(x) is continuous at x = kπ- for any integer k, and hence, it is continuous only at x = kπ, where k is an integer.
B. To prove that limx → 2 f(x) = 3, we can use the following definition of a limit:
For any ε > 0, there exists a δ > 0 such that |f(x) - 3| < ε for all 0 < |x - 2| < δ.
Here, f(x) = x2 - 1, and we need to prove that limx → 2 (x2 - 1) = 3.
Using algebraic manipulation, we can write x2 - 1 - 3 = (x + 2)(x - 2).Now, |(x + 2)(x - 2)| = |x + 2||x - 2|.
Therefore, we need to find δ such that |(x + 2)(x - 2)| < ε whenever 0 < |x - 2| < δ.
In order to ensure this, we can put an upper bound on |x + 2| and |x - 2|:|x + 2| < 4 (since x is close to 2)|x - 2| < δ
From the above inequalities, we can say that |(x + 2)(x - 2)| < 4δ.
Then, we can say that |(x2 - 1) - 3| = |(x + 2)(x - 2)| < 4δ < ε.
So, we can choose δ = ε/4.
Hence, we have proved that limx → 2 (x2 - 1) = 3 using the definition of a limit.
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Use the properties of equality to find the value of x, in the equation 12(5x-4. 5)=36
Step-by-step explanation:
12(5x - 4.5) = 36
if that is really correct, then we solve this first by dividing both sides by 12
5x - 4.5 = 3
then we add 4.5 to both sides
5x = 7.5
and finally we divide both sides by 5
x = 1.5
The Kennedy high school cross country running team ran the following distances in recent practices 3.5, miles 2.5, miles 4 miles 3.25 miles, 3 miles, 4 miles and 6 miles find the mean and median of the team's distances
The result is the mean of 3.9 miles and median of the team's distances is 3.5 miles.
What is mean and median?Mean and median are two ways to measure the center of a set of numbers. Mean is the average of all the numbers in the set, while median is the middle number in the set. Mean is more affected by extreme values, while median is not. Mean is generally used when data is normal, and median when data is skewed.
Mean and median are both measures of central tendency, or measures of the center of a data set. Both measures are used to summarize a data set, but the mean is more affected by outliers, or extreme values, while the median is not.
The mean of the team's distances is 3.9 miles, and the median is 3.5 miles. To calculate the mean, add all the distances together (3.5 + 2.5 + 4 + 3.25 + 3 + 4 + 6) and divide by the number of distances (7). The result is the mean of 3.9 miles. To calculate the median, first order the distances from least to greatest (2.5, 3, 3.25, 3.5, 4, 4, 6) and take the middle number (3.5). The median of the team's distances is 3.5 miles.
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