According to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and 'a' is any real number, then, (x-a) is a factor of f(x), if f(a)=0.
The factor theorem states
[tex]$(x-a)$ is a factor of $f(x) \Leftrightarrow f(a)=0$[/tex]
f(x)=4 x^3-3 x^2-8 x+4
we have (x-2)[tex]\Rightarrow a=2[/tex]
& [tex]f(2)=4 \times 2^3-3 \times 2^2-8 \times 2+4 \\& f(2)=4 \times 8-3 \times 4-16+4 \\& f(2)=32-12-16+4 \\& f(2)=8 \neq 0\end{aligned}[/tex]
[tex]$\therefore x-2$ is not a factor of $4 x^3-3 x^2-8 x+4$[/tex]
however by the remainder theorem when
[tex]$f(x)=4 x^3-3 x^2-8 x+4$[/tex] is divided by [tex]$(x-2)$[/tex] the remainder is 8
the factor theorem being a special case of the remainder theorem
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Answer:
Step-by-step explanation:
Use the factor Theorem to determine whether x =3 is a factor of P (x)=x-2x2-6. Specifically, evaluate P at the proper value, and then determine whether X-3 is a factor. P (UI) - 0 P 0 1 - 3 is a factor of P (*) O +- 3 is not a factor of P (x) This problem has been solved!
How many pounds are in 2,600 ounces? Enter only a number. Do not enter units.
Answer: 162.5 Pounds
Given P(A) = 0.6, P(B) = 0.79 and
P(A and B) = 0.544, find the value of P(B|A),
rounding to the nearest thousandth, if necessary.
[tex]P(B|A) = \frac{P(AandB)}{P(A)}[/tex]
Answer:
0.3324
Step-by-step explanation:
a company's sales in year 1 were $330,000 and in year 2 were $367,500. using year 1 as the base year, the percent change for year 2 compared to the base year is:
Percentage change in company's sales is 11%
What is percentage?
In arithmetic, a proportion may be a range or magnitude relation expressed as a fraction of a hundred. it's usually denoted victimisation the percentage sign, "%", d. A proportion may be a dimensionless number; it's no unit of measuring.
Main body:
According to the question:
company's sales in year 1 = $330,000
company's sales in year 2 =$367,500
Change = $ 367500 – 330000 = $ 37,500
Percentage change = $ 37500 / $ 330000 = 0.11
Percentage change = 11%
Hence ,Percentage change in company's sales is 11%.
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Darren kept track of the number of e-mails he received from one of his customers each day for 14 days on the dot plot. A number line goes from 1 to 12. 1 dot is above 2. 2 dots are above 7. 3 dots are above 8. 1 dot is above 9. 3 dots are above 11. 4 dots are above 12. Which statement must be true according to the dot plot?
The customer sent Darren more than 12 e-mails over the 14-day period. The maximum number of emails represented in the dot plot is 12 + 4 = 16
The dot plot provides information about the number of emails he received from one customer over a 14-day period.
The number line goes from 1 to 12, but there are 4 dots above 12 which means that the customer sent him more than 12 emails over the 14-day period.
Therefore, the statement "The customer sent Darren more than 12 e-mails over the 14-day period" must be true according to the dot plot.The maximum number of emails represented in the dot plot is 12 + 4 = 16. Therefore, the customer sent Darren more than 12 emails over the 14-day period.
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Brad reads a scatterplot that displays the relationship between the number of cars owned per household and the average number of citizens who have health insurance in neighborhoods across the country. The plot shows a strong positive correlation.
Brad recalls that correlation does not imply causation. In this example, Brad sees that increasing the number of cars per household would not cause members of his community to purchase health insurance. Identify the lurking variable that is causing an increase in both the number of cars owned and the average number of citizens with health insurance.
Brad looks at a scatterplot that shows the correlation between the typical population's access to health insurance and the number of cars owned by each household in different parts of the country. A substantial positive association can be seen in the plot.
What are some examples of scatter plots?
The association between two sets of data is depicted by points on a scatter (XY) plot. Each dot in this illustration represents the weight and height of one individual. (The information is displayed as "Cartesian (x,y) Coordinates")
What is the purpose of a scatter plot?
Data points are plotted on a horizontal and vertical axis using scatter plots in an effort to demonstrate the degree to which one variable is influenced by another.
The values of the columns selected on the X and Y axes determine where each row in the data table is represented by a marker, whose position.
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select all that apply identify the steps involved in the six sigma approach. (check all that apply.)
the steps involved in the six sigma approach. -Define-Measure-Analyze-Improve-Control
-Define: Identify the problem and set objectives and goals
-Measure: Collect and analyze data related to the problem
-Analyze: Identify the root cause of the problem
-Improve: Develop and implement solutions to the problem
-Control: Monitor and maintain the improvements to ensure the problem does not recurrence are the steps involved in six sigma.
1. Define: Identify the problem, set objectives and goals, and develop a project plan.
2. Measure: Collect and analyze data related to the problem and determine the current process performance.
3. Analyze: Examine the data to identify the root cause of the problem.
4. Improve: Develop and implement solutions to improve the process.
5. Control: Monitor and maintain the improvements to ensure the problem does not recur.
6. Optimize: Continuously look for ways to make the process more efficient and effective.
the complete question is:
Select all that apply identify the steps involved in the six sigma approach. (check all that apply.)
-Define
-Measure
-Analyze
-Improve
-Control
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Please be legible and thorough. please be detailed with your explanations. thank you very much.
Q: Solve the infinite potential well problem for a symmetric well. That is, the potential energy function is given by the following:
-a CO r I 2 -a 2 V(r)={ 0 .rs ss > a CO < 2 Or graphically: KV(x) 1 III a/2
your solution should give the following: (a) normalized eigenfunctions (b) eigenvalues hints: follow the same procedure as done in the text, section 2.2 of griffiths. the only significant difference is the boundary conditions. you should also note that unlike the version in the text(called the asymmetric well) this well is symmetric about the origin and hence shows reflection symmetry: V(.x)=V(-x). As a result, your eigenfunctions must be either even or odd under the same reflection operation. This means you should have two sets of eigenfunctions, one even and the other odd under x inversion. Make sure you see this. X
As per the given inversion, the time independent Schrödinger equation in one dimension is [tex]\frac{-hx^{2}}{2m} \times\frac{d^{2}(x)}{dx^{2} } + U(x)f(x)=Ef(x)[/tex]
The term inversion in math refers a concept in discrete mathematics to measure how much a sequence is out of its natural order.
Here we have given that the potential energy function is given by the following: -a CO r I 2 -a 2 V(r)={ 0, s > a CO < 2}
And we need to find the eigenfunctions must be either even or odd under the same reflection operation.
While we looking into the given question, let us consider E is the total energy of the particle, and U (x) the potential energy function and ψ (x) the spatial part of the wavefunction.
Based on the the function can be written as,
=> [tex]\frac{-hx^{2}}{2m} \times\frac{d^{2}(x)}{dx^{2} } + U(x)f(x)=Ef(x)[/tex]
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a church window is bounded above by a parabola and below by the arc of a circle (see figure). find the surface area of the window. (round your answer to three decimal places.)
The surface area of a church window bounded above by a parabola and below by the arc of a circle is 2.750x^2, rounded to three decimal places.
Let x be the length of the window. The radius of the arc of a circle is x/2.
Surface area = [Area of parabola] + [Area of arc of a circle]
= (1/2)x^2 + (π/2)*(x/2)^2
= (1/2)x^2 + (π/4)x^2
= (π/4 + 1/2)x^2
= (1 + π/4)x^2
= 2.75x^2
Answer: 2.750
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5 + 2a = a - 9 what does a equal
a= -14.
Step-by-step explanation:1. Write the expression.[tex]5 + 2a = a - 9[/tex]
2. Subtract 5 from both sides of the equation.[tex]5 + 2a -5= a - 9-5\\ \\2a=a-14[/tex]
3. Subtract "a" from both sides of the equation.[tex]2a-a=a-14-a\\\\a=-14[/tex]
4. Verify.[tex]5 + 2(-14) = (-14) - 9\\ \\5-28=-23\\ \\-23=-23[/tex]
Both sides are equal to each other, hence a= -14 is the correct solution.
5. Conclude.a= -14.
-------------------------------------------------------------------------------------------------------
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TRUE OR FALSE the difference between timing diagrams and state diagrams is that timing diagrams show changes along the flow of time, whereas state diagrams show changes based on triggers received from other objects in or outside the system.
Therefore, the answer to this problem is that the statement is true.
What is state diagram?A state diagram is a particular kind of diagram used in computer science and related subjects to represent system behavior. A system must have a finite number of states in order to be represented by a state diagram; sometimes this is the case, and other times it is a valid abstraction.
Here,
Since,
Timing diagrams depict changes during the passage of time, whereas state diagrams depict changes as a result of triggers from other system objects or from external sources.
So ,the above statement is true
Therefore the answer to this problem is that the statement is true.
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PLS HELP QUICK! 20 POINTS
Can a triangle be formed with side lengths 5, 6, 12? Explain.
No, because 5 + 6 < 12
Yes, because 5 + 6 > 12
No, because 12 − 6 < 6
Yes, because 12 − 6 < 5
Answer:
No, because [tex]5+6<12[/tex]
Step-by-step explanation:
The side lengths do not satisfy the triangle inequality.
Which of the following points would fall on the line produced by the point-slope form equation y + 12 = 3(x - 4) when graphed
Answer:
where r the points??
Step-by-step explanation:
give them atleast to find the ans.
Determine which of these are linear homogeneous recurrence relations with constant coefficients. Also, find the degree of those that are:
a) an = 3an-1 + 4an-2 +5an-3
b) an = 2nan-1 + an-2
c) an = an-1 + an-4
A linear recurrence relation is homogeneous if f(n) = 0. The order of the recurrence relation is determined by k. We say a recurrence relation is of order k if an = f(an−1,...,an−k).
Given: a) an = 3an-1 + 4an-2 +5an-3
We note that the given recurrence relation is linear, because the right-hand side is a linear combination of previous terms. We note that the given recurrence relation is homogeneous, because the recurrence relation does not contain any constant terms. The degree of the recurrence relation is the largest value k for which are occurs in the recurrence relation.
k=3
Given: b) an = 2nan-1 + an-2
We note that the given recurrence relation is not linear, because the right-hand side is not a linear combination of previous terms (due to the
fact that 2n is not a constant). We note that the given recurrence relation is homogeneous, because the recurrence relation does not contain any constant terms.
Given: c) an = an-1 + an-4
Because the right-hand side is a linear combination of the prior terms, we observe that the provided recurrence relation is linear. Given that there are no constant terms in the recurrence relation, it is important to observe that it is homogenous. The biggest value k for which are k appears in the recurrence relation is the recurrence relation's degree.
Degree of linear homogeneous recurrence are k=3 .
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UX ≅ UY, YZ ≅ WX, TZ ≅ VW, and UV ≅ TU. Complete the proof that ∠W≅∠Z.
This is the first question I have seen with this type of two column proof, and i do not want to get it wrong as a large portion of my score will be taken from me.
(There may have to be another row(s) added, which can be done with the "Add line" button)
Geometry, Proofs involving SSS(and CPCTC)
https://www.ixl.com/math/geometry/proofs-involving-sss
You are just couple of steps away from completing the proof.
So far you have concluded that two sides of triangles ZTX and WVY are congruent. You need to complete it for the third side and prove the triangles are congruent. Then use it to complete the proof.
Missing statement and reasons given below.
Statement Reason
12. WY = XZ Transitive property13. ΔZTX ≅ ΔWVY SSS congruency14. ∠W ≅ ∠Z CPCTCI need help with this by tonight pls or I will not get an updated grade it's hard for me to understand this
Find the Sum, Difference, or Product
1. [tex]3x^2 + 4x -1 - 2x^2 -3x + 2 = x^2 + x + 1[/tex]
2. [tex]12x^5 - 3x^4 + 2x -5+8x^4-3x^3+4x+1 = 12x^5 +5x^4-3x^3+6x-4[/tex]
3. [tex]3x^3 - 2x^2 + 4x-8-5x^3-12x^2+3x+4 = -2x^3-14x^2+7x-4[/tex]
4. [tex]5x^6 - 2x^4 +9x^3+2x-4-7x^5+8x^4-2x+11 = 5x^6-7x^5+6x^4+9x^3+7[/tex]
5. [tex]x^3+3x^2-10x-24[/tex] (Multiply the first two factor, then multiply the product to the last factor)
6. [tex](7h+4)*(7h+4)= 49h^2+28h+28h+16 =49h^2+56h+16[/tex]
Factor the Sum or Difference of Cubes
Sum of Cubes Formula: [tex]a^3+b^3 = (a+b)(a^2-ab+b^2)\\[/tex]
Difference of Cubes Formula: [tex]a^3-b^3 = (a-b)(a^2+ab+b^2)\\[/tex]
Just apply it to the equations.
1. [tex]x^3 + 4^3 = (x+4) (x^2 - 4x+16)[/tex]
2. [tex]c^3 - 3^3 = (c-3) (c^2+3c+9)[/tex]
3. [tex](3d)^3 + 2^2 = (3d+2)((3d^)^2-(3d)(2)+4) = (3d+2)(9d^2-6d+4)[/tex]
4. [tex]5^3-(2b)^3= (5-2b)(5^2+(2b)(5)+(2b)^2) = (5-2b)(25+10b+4b^2)[/tex]
Factor the Polynomials Completely
Nt. I'm having a hard time with this one
1. [tex]x(x-6)(x+4)+24(x-1)[/tex]
2. [tex]2m^4 (m-4)(m-8)[/tex]
3. [tex](6v+7)(3v+2)[/tex]
4. [tex]4n^2(n^5-2)(n^5-6)[/tex]
5. [tex](9a^2-16b)(9a^2+16b)[/tex]
6. [tex](4z^2-25y)(4z^2+25y)[/tex]
in a certain quadrilateral, the three shortest sides are congruent and both diagonals are as long as the longest side. what is the degree measure of the largest angle of tihs quadrilateral
The measurement of the largest angle of the quadrilateral is 108°
Given,
Quadrilateral;
A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.
Here,
Three shortest sides of the quadrilateral are congruent.
Both diagonals are as long as the longest side.
That is,
Side 1 ≅ Side 2 ≅ Side 3
Side 4 = Diagonal 1 = Diagonal 2
Then,
The largest angles of the quadrilateral will be 108°
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Find the value of the variable. The sum of angle measures is 180°. Then find the angle measures of the polygon
Answer:
28° + 112° + 40° = 180°
Step-by-step explanation:
A Triangle has 3 angles that adds up to 180°
You are given 3 angles already so they must add up to 180°
Equation: n + 4n + 40° = 180°
Simple the equation.
Add the variable n together.
5n + 40° = 180°
Subtract 40 to both sides.
5n = 140°
Divide 5 to both side to solve for n.
n = 28°
Now plug n into our angles to have our angles in degree.
n = 28°
4n = 4×28° = 112°
40°
28° + 112° + 40° = 180°
Answer:
Step-by-step explanation:
The internal angles of a triangle sum 180°
n + 4n + 40 = 180
5n = 180 - 40
5n = 140
n = 140/5
n = 28
Check:
28 + 4*28 + 40 = 180
28 + 112 + 40 = 180
Answer:
variable n = 28°
∡n = 28°
∡4n = 4*28 = 112°
PLEASE HELP the question is in the picture
The required expression that can be simplified without the conversion of terms is 9.32 × 10 ⁻⁵ + 1.078 × 10⁻⁵. Option A is correct.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
In order to do, no needs to convert terms, so then expression with the same exponent of 10 is the required expression.
So,
= 9.32 × 10 ⁻⁵ + 1.078 × 10⁻⁵
= 10.00 × 10⁻⁵
= 10⁻⁴
Thus, the required expression that can be simplified without the conversion of terms is 9.32 × 10 ⁻⁵ + 1.078 × 10⁻⁵. Option A is correct.
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Answer:
9.32 × 10 ⁻⁵ + 1.078 × 10⁻⁵
Step-by-step explanation:
X is the midpoint of UV. Y is the midpoint of UW. If mZUYX= 46, find mZW.
mZW=
U
Y
W
Answer:
46°
Step-by-step explanation:
As m<UYX and m<W is corresponding angle because X is the midpoint of UV and Y is the midpoint of UW, therefore
m<W = 46°
I hope my answer helps you.
Answer:
m<W = 46 degrees
Step-by-step explanation:
UX = UV/2 ==> This is because X is the mid-point of UV, dividing UV by 2
to make UX
UY = UW/2 ==> Y is the mid-point of UW, dividing UW by 2 to make UY
XY = VW/2 ==> Since X is the midpoint of UV and Y is the midpoint of UW,
segment XY is exactly in the middle of point U and
segment VW, so segment XY is half of segment VW.
Since all sides of the small triangle(ΔUXY) are exactly half of all sides in the big triangle(ΔUVW), The corresponding angles in each triangle are equal to each other:
Hence, m<UYX = m<UWV
m<UWV ==> m<W = 46 degrees ==> since m<UYX=46, m<W = 46 as well
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10:35 AM Sat Dec 10
Homework 6.2
:
ด
1.) Mr. Keith is paid semimonthly. His annual salary is $64,733. What is his semimonthly
salary rounded to the nearest cent?
3%
Sa
Mr. Keith's semimonthly salary is $16183.25.
What is rounded to the nearest cent?
If the number is five or higher and is to the right of the full cents, increase the cents by one. The cents should remain the same if the number is four or less.
For instance: $143.864. Consider the last digit, 4, since it is less than 5 and the cents should remain the same. Rounding up from $143.864 to $143.86.
Given that the annual salary of Mr. Keith is $64,733.
Semiannual means 4 times in yearly.
Thus divide whole salary by 4 to get semimonthly salary.
Therefore the semimonthly income is $64,733/4 = $16183.25 (rounded to the nearest cent)
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HELP IM IN K12 PLEASE HELP
Step-by-step explanation:
p = a + 3
Three more a than p
Determine the number and type of solutions for the equation x^2+8x+15=0
Two different irrational-number solutions
One repeated irrational-number solution
One repeated rational-number solution
Two different rational-number solutions
Two imaginary-number solutions
Answer:
Step-by-step explanation:
disc=8²-4×1×15=64-60=4=2²>0
it is a perfect square and >0
so it has one repeated rational number solution.
As part of a study on the selection of grand juries in Alameda county, an educational level of grand jurors was compared with the county distribution:
Educational Level County # of Jurors
Elementary 28.4% 1
Seconday 48.5% 10
Some College 11.9% 16
College Degree 11.2% 35
Total 100% 62
Could a simple random sample of 62 people from the county show a distribution of educational level so different from the county-wide one? Chose one option and explain.
1) this is absolutley possible
2)this is possible, but fantastically unlikely
3)this is possible but unlikely-the chance is around 10% or so
4)this is nearly certain
This is possible but fantastically unlikely. A simple random sample of 62 people from the county would be unlikely to produce a distribution of educational levels so different from the county-wide one. The chances of this happening are extremely small.
A simple random sample is a sample drawn from a population in such a way that each member of the population has an equal chance of being selected. In this case, the population is the county, and the sample is the group of 62 grand jurors. When a simple random sample is drawn, it is possible for the sample to be different from the population in various ways.
For example, the sample may have a different distribution of educational levels than the population. However, the larger the sample size is, the more likely it is that the sample will be representative of the population. In this case, the sample size of 62 is relatively small, so it is possible that the sample will be different from the population in terms of educational level. However, the chance of this happening is not very high, since the sample size is not very large.
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The cross-country team had a fundraiser selling wreaths for $25 each. They made $15 for each wreath they sold. If they sold 114 wreaths, (a) how much money did they pay to make each wreath, (b) how much money did they collect, and (c) how much money did they make? If they made $180, (d) how many wreaths did they sell?
Answer:
(a) They paid $25-$15=$<<25-15=10>>10 to make each wreath.
(b) They collected $15114=$<<15114=1710>>1710.
(c) They made $1710-$10114=$<<1710-10114=180>>180.
(d) They sold $180/$15=<<180/15=12>>12 wreaths.
Step-by-step explanation:
Sure, here is a breakdown of the solution:
(a) The cross-country team paid $10 to make each wreath because they sold the wreaths for $25 and made $15 for each wreath they sold, so the cost to make each wreath was $25-$15=$10.
(b) They collected $1710 because they sold 114 wreaths and made $15 for each wreath they sold, so they collected a total of $15*114=$1710.
(c) They made $180 because they collected $1710 and it cost them $10 to make each wreath, and they sold 114 wreaths, so the total cost of making all the wreaths was $10*114=$1140. They made $180 because they collected $1710 and it cost them $1140 to make all the wreaths, so their profit was $1710-$1140=$180.
(d) They sold 12 wreaths because they made $180 and it cost them $15 to make each wreath, so they sold $180/$15=12 wreaths.
A rectangular solar panel is 84 cm by 35 cm. By adding the same amount to each dimension, the area is doubled. How
much is added?
Answer:
21
Step-by-step explanation:
84x35=2940
2940x2=5880
84+21=105
35+21=56
105*56=5880
I want to know some example of a continuous function which is continuous at exactly one point. We know that f(x)=1x is continuous everywhere except at x=0. But i think this in reverse manner but i dont get any example. So please help me out!
Examples of a continuous function that is continuous at exactly one point are x=0,1,2,3,4.
In mathematics, a continuous function is one where a continuous variation of the argument results in a continuous variation of the function's value (i.e., a change without a leap). This indicates that there aren't any discontinuities or sudden changes in value. More specifically, a function is continuous if it is possible to guarantee that its value will not vary significantly even with arbitrarily tiny changes to its parameter.
We know that the modulus function,
f(x)=∣x∣ is continuous but not differentiable at x=0.
So,
f(x)=∣x∣+∣x−1∣+∣x−2∣+∣x−3∣+∣x−4∣ is continuous but not differentiable at x=0,1,2,3,4.
Hence, this is the answer.
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Triangle TVW is dilated according to the rule
(x,y)(three-fourths x, three-fourths y) to create the image triangle T'V'W', which is not shown.
On a coordinate plane, triangle T V W has points (negative 4, 8), (0, 4), and (4, 4).
What are the coordinates of the endpoints of the segment T'V'?
T'(-3, 6) and V'(0, 3)
T'(-3, 6) and V'(0, 1)
T'(-1, 2) and V'(0, 3)
T'(-1, 2) and V'(0, 1)
The coordinates of the endpoints of the segment T'V' are equal to: A. T'(-3, 6) and V'(0, 3).
What is dilation?In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.
Next, we would have to dilate the coordinates of triangle TVW by using the following transformation rule with a scale factor of 3/4: (x, y) → (3x/4, 3y/4)
For coordinate T, we have;
Coordinate T = (-4, 8) → (3/4(-4), 3/4(8)) = Coordinate T' = (-3, 6).
For coordinate V, we have;
Coordinate V = (0, 4) → (3/4(0), 3/4(4)) = Coordinate V' = (0, 3).
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Answer:
A. T'(-3, 6) and V'(0, 3)
Step-by-step explanation:
Graph: y ≤ -2
Is (-2,-7) a solution? yes or no
Is ( 2,-1) a solution? yes or no
Answer:
(-2,-7) , yes
(2,-1) , no
Step-by-step explanation:
the question says y is less than or equal to -2 . In the first order pair (-2,-7) , x= -2 & y = -7 in the number line -2 comes first than -7 it means -2 is grater than -7 so the answer is yes but in the second order pair (2,-1) the value of x is 2 and the value of y is = -1 thus -1 is grater than -2 however the question says y should be less or equal but not greater than -2 so the answer is yes for the first order pair and no for the second one
Find the area of the parallelogram with vertices P(1, 0, 2), Q(3, 3, 3), R(7, 5, 8), and S(5 , 2, 7).
The area of parallelogram with the vertices is √269 when vertices are P(1, 0, 2), Q(3, 3, 3), R(7, 5, 8), and S(5 , 2, 7).
Given that,
The vertices are P(1, 0, 2), Q(3, 3, 3), R(7, 5, 8), and S(5 , 2, 7).
We have to find the area of parallelogram with the vertices.
We know that,
PQ=Q-P=(3,3,3) -(1,0,2)=(2,3,1)
PR=R-P=(7,5,8) -(1,0,2)=(6,5,6)
Find area using cross product as
Area= |PQ x PR|
=|i (3(6)-1(5)) - j (2(6)-1(6)) + k (2(5)-3(6)) |
= |i (18 - 5) - j (12 -6) + k (10 -18) |
= |{13; 6; -8}|
=√(13²+6²+(-8)²)
=√269
Therefore, the area of parallelogram with the vertices is √269 when vertices are P(1, 0, 2), Q(3, 3, 3), R(7, 5, 8), and S(5 , 2, 7).
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A population of squirrels lives in a forest with a carrying capacity of 1800 Assume logistic growth with growth constant k = 0.8 yr-1 . (a) Find a formula for the squirrel population P(t) , assuming an initial population of 450 squirrels_ P(t) 1800/(1+3e^(-0.8t)) (b) How long will it take for the squirrel population to double? doubling time ~ 83 years
By applying formulas of logistic growth we can find the answers as part (a) P(t) = 1800 / (1+3e^(-0.8t)) and part(b) 1.37 years
What is logistic growth?In a logistic growth the growth rate decreases with the passage of time until the growth reaches the maximum capacity at infinite time.
What is formula for logistic growth?The formula is f(t) = L / (1+ ye^(-kt))
where L is the maximum value, k is the growth rate, y is a constant and t is time.
Part(a)
In this case, L = 1800, k = 0.8 yr-1
f(t) = 1800 / (1 + ye^(-0.8)t)
at t = 0 , f = 450,
450 = 1800/ (1+y)
solving this gives, y = 3
Thus the final answer is f(t) = 1800/ (1+ 3e^(-0.8t))
Part(b)
we need to find the time when f(t) = 900
900 = 1800/(1+3e^(-0.8t))
t = 1.37 years
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