A particle is moving with the given data. Find the position of the particle.
a(t) = [tex]t^{2}[/tex] − 4t + 5, s(0) = 0, s(1) = 20
How do I find s(t)=?
Recall that
[tex]\dfrac{dv(t)}{dt} = a(t) \Rightarrow dv(t) = a(t)dt[/tex]
Integrating this expression, we get
[tex]\displaystyle v(t) = \int a(t)dt = \int(t^2 - 4t + 5)dt[/tex]
[tex]\:\:\:\:\:\:\:= \frac{1}{3}t^3 - 2t^2 + 5t + C_1[/tex]
Also, recall that
[tex]\dfrac{ds(t)}{dt} = v(t)[/tex] or
[tex]\displaystyle s(t) = \int v(t)dt = \int (\frac{1}{3}t^3 - 2t^2 + 5t + C_1)dt[/tex]
[tex]\:\:\:\:\:\:\:= \frac{1}{12}t^4 - \frac{2}{3}t^3 + \frac{5}{2}t^2 + C_1t + C_2[/tex]
Next step is to find [tex]C_1\:\text{and}\:C_2[/tex]. We know that at t = 0, s = 0, which gives us [tex]C_2 = 0[/tex]. At t = 1, s = 20, which gives us
[tex]s(1) = \frac{1}{12}(1)^4 - \frac{2}{3}(1)^3 + \frac{5}{2}(1)^2 + C_1(1)[/tex]
[tex]= \frac{1}{12} - \frac{2}{3} + \frac{5}{2} + C_1 = \frac{23}{12} + C_1 = 20[/tex]
or
[tex]C_1 = \dfrac{217}{12}[/tex]
Therefore, s(t) can be written as
[tex]s(t) = \frac{1}{12}t^4 - \frac{2}{3}t^3 + \frac{5}{2}t^2 + \frac{217}{12}t[/tex]
Student A, lives in Phoenix, Arizona and submits an assignment for math class. The teacher notices the student IP address is 75.167.171.149. Has this student committed one of the forms of plagiarism? Check all that apply.
Group of answer choices
Yes, this student is using an academic broker.
Yes, this student copied directly from an online site.
No, this students IP address matched her location.
No, the teacher does not have proof plagiarism.
Answer:
Yes, this student copied directly from an online site.
Step-by-step explanation:
According to whatismyip.live, this IP address is from Chandler, Arizona not Phoenix.
Use the ratio of a 45-45-90triangle to solve for the variables. Make sure to simplify radicals. Leave your answers as radicals in simplest form.
Answer:
Step-by-step explanation:
in this specific case the two legs are congruent:
b = 18
For the Pythagorean theorem
a = √ 2 * 18^2 = 18√2
What are the degree and leading coefficient of the polynomial?
- 3v² - 2v^3+ 6-8v
9514 1404 393
Answer:
degree: 3leading coefficient: -2Step-by-step explanation:
The highest degree term is -2v^3. Its degree is 3, so the degree of the polynomial is 3. Its coefficient is -2, so the leading coefficient is -2.
How many proportional relationships are shown in the coordinate plane below?
Answer:
The answer is B) There is one proportional relationship
Step-by-step explanation:
The green line (the one at the top) does not go through the origin. This is not a proportional relationship.
Problem: It does not go through 0,0
----------------------------------------------------------------------------------------------------------------
The blue line (the one in the middle) is a straight line through the origin. This is a proportional relationship.
Reason: It goes through 0,0
----------------------------------------------------------------------------------------------------------------
The purple line (the one at the bottom) does not go through the origin. This is not a proportional relationship.
Problem: It does not go through 0,0
----------------------------------------------------------------------------------------------------------------
Conclusion: Since the green and purple lines are not proportional but the blue line is, this means only 1 line is proportional.
Note:
I know my answer is very late but I wanted to help anyone who needs it for future reference.
The polygons in each pair are similar. Find the missing side length.
Let missing side be x
If both polygons are similar
[tex]\\ \sf\longmapsto \dfrac{3}{4}=\dfrac{18}{x}[/tex]
[tex]\\ \sf\longmapsto 3x=4(18)[/tex]
[tex]\\ \sf\longmapsto 3x=72[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{72}{3}[/tex]
[tex]\\ \sf\longmapsto x=24[/tex]
If you deposit $500 dollars “Each Month!” Into an account paying 3% interest, compounded monthly, how much would be in said account after 4 years.
Please show proper work and give a good explanation in regards as to how you got your answer
Answer:
26029.26
Step-by-step explanation:
Assuming we are investing the 500 at the end of the period and starting with 500 in the account
[ P(1+r/n)^(nt) ]+PMT × {[(1 + r/n)^(nt) - 1] / (r/n)}
PMT = the monthly payment
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the time in years
[ 500(1 + .03/12)^(4*12) ]+500 × {[(1 + .03/12)^(4*12) - 1] / .03/12)}
[ 500(1 + .0025)^(48) ]+500 × {[(1 + .0025)^(48) - 1] / .0025)}
563.66 +25465.60
A 230 pound man, a 140 pound woman, a 750 pound crate of equipment, an 80 pound bag of concrete. What percent of the total weight was concrete?
What percent of the total weight was human?
?
What is the equation of a parabola whose focus is (-4, -1)
and whose directrix is
y = -5?
x²
y = + x – 1
8
o
y = -
x²
--X+1
8
y?
x =
+ у - 1
8
y2
X = -
8 Y+1
Answer:
1st option,
y = x²/8 + x - 1
Answered by GAUTHMATH
[tex]\sqrt{4+\sqrt{4+\sqrt{4+...+\sqrt{4}[/tex]
Answer:
y=0.5+sqrt(17)
Step-by-step explanation:
Let y=sqrt{4+sqrt{4+...+sqrt(4)}
y=sqrt(4+y). (Since it's an infinite series)
y^2=4+y, y=0.5-sqrt(17) or 0.5+sqrt(17). We will omit the negative since root values are positive.
33. The population of Canada, y (in millions), can be approximated by the relation y=
0.146x + 31, where x represents the number of years since 2000.
a. Approximate the population of Canada in the year 2006.
b. In what year did the population of Canada reach approximately 32,752,000?
Answer:x=6573/500,x=13(73/500
Step-by-step explanation:
It will takes 12 years to reach approximately 32,752,000.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
y = 0.146x + 31
where x represents the number of years since 2000.
a) The population of Canada in the year 2006
x= 6
y= 0.146 x 6 + 31
y = 31.876
b) The population of Canada reach approximately 32,752,000 in
y = 32.752
0.146x + 31= 32.752
0.146x = 1.752
x= 1.752/0.146
x= 12
Hence, it will takes 12 years to reach approximately 32,752,000.
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I do not understand this and could use help it needs the work shown
Answer:
a = 9
Step-by-step explanation:
The given trinomial is :
[tex]x^2-6x+\_\_\__[/tex]
let the blank is a.
So, we need to find the value of a so that it results in a perfect square trinomial.
We know that, [tex](m-n)^2=m^2-2mn+n^2[/tex]
So,
[tex]x^2-6x+a=x^2-2(1)(3)+3^2\\=(x-3)^2[/tex]
So, the value of a is 9. If a is 9, then only it would be a perfect square trinomial.
Find "n" if the Standard Error of Mis 4 and the population standard deviation is 16.
Given:
Standard error = 4
Population standard deviation = 16
To find:
The value of n.
Solution:
The formula of standard error is:
[tex]SE=\dfrac{\sigma}{\sqrt{n}}[/tex]
Where, SE is standard error , [tex]\sigma[/tex] is population standard deviation and n is the total number of elements.
Substituting [tex]SE=4,\sigma=16[/tex] in the above formula, we get
[tex]4=\dfrac{16}{\sqrt{n}}[/tex]
[tex]\sqrt{n}=\dfrac{16}{4}[/tex]
[tex]\sqrt{n}=4[/tex]
Taking square on both sides, we get
[tex]n=4^2[/tex]
[tex]n=16[/tex]
Therefore, the value of n is 16.
A simple random sample of 27 filtered 100-mm cigarettes is obtained from a normally distributed population, and the tar content of each cigarette is measured. The sample has a standard deviation of 0.20 mg. Use a 0.05 significance level to test the claim that the tar content of filtered 100-mm cigarettes has a standard deviation different from 0.30 mg, which is the standard deviation for unfiltered king-size cigarettes. Complete parts (a) through (d) below. a. What are the null and alternative hypotheses?
Answer:
The null hypothesis is [tex]H_0: \sigma = 0.3[/tex]
The alternative hypothesis is [tex]H_1: \sigma \neq 0.3[/tex]
Step-by-step explanation:
Test if the tar content of filtered 100-mm cigarettes has a standard deviation different from 0.30 mg.
At the null hypothesis, we test if the standard deviation is of 0.3, that is:
[tex]H_0: \sigma = 0.3[/tex]
At the alternative hypothesis, we test if the standard deviation is different of 0.3, that is:
[tex]H_1: \sigma \neq 0.3[/tex]
What is the surface area of the cube below?
9 9 9
A. 508 units2
B. 405 units2
C. 486 units
D. 729 units2
Answer:
The formula of the surface area of a cube is 6 x s²
→ s = 9
→ s² = 9²
→ s² = 81
→ 6 x 81 = 486
So, the surface area of the cube is 486 units².
The surface area of a cube is 486 units².
What is Surface Area?The area is the space occupied by a two-dimensional flat surface. It is expressed in square units. The surface area of a three-dimensional object is the area occupied by its outer surface.
We have to find Surface Area of Cube.
Edge length of cube = 9 unit
So, Surface area of Cube
= 6 x s²
= 6 x 9²
= 6 x 81
= 486 units².
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Given that f(x) = 2x + 9, find the value that makes f(x) = 27.
Answer:
9
Step-by-step explanation:
f(x) = 2x+9
f(x) = 27
so, you get:
2x+9=27
2x=18
x=9
Megan and Suzanne each have a plant. They track the growth of their plants for four weeks.
Whose plant grew at a faster rate, and what was the rate?
Suzanne’s at 2 inches per week
Suzanne’s at 1.5 inches per week
Megan’s at 3 inches per week
Megan’s at 2.5 inches per week
Megan’s plant grew at a faster rate, Growing at a rate of 3 inches per week.
What is the slope?The y-rate axis of change with respect to the x-axis is known as the slope.
y = mx + b, where slope = m and y-intercept = b, is the slope-intercept form equation of a line.
We are aware that a slope's graph or rate of change will be steeper the higher its absolute value.
Given, Megan and Suzanne each have a plant. They track the growth of their plants for four weeks.
From the given options, Megan's plant which is growing at a rate of 3 inches per week has a faster growth rate.
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State if the scenario involves a permutation or a combination. Then find the number of possibilities.
The student body of 290 students wants to elect a president and vice president.
Permutation/Combination:
Answer:
Answer:
Permutation. ; 83810 ways
Step-by-step explanation:
Permutation and combination methods refers to mathematical solution to finding the number of ways of making selection for a group of objects.
Usually, selection process whereby the order of selection does not matter are being treated using permutation, while those which takes the order of selection into cognizance are calculated using combination.
Here, selecting 2 members (president and vice president) from 290 ; since order of arrangement does not matter, we use permutation ;
Recall :
nPr = n! ÷ (n - r)!
Hence,
290P2 = 290! ÷ (290 - 2)!
290P2 = 290! ÷ 288!
290P2 = (290 * 289) = 83810 ways
Find f(-2) if f(x) =x^4 +2x^2-1
Answer:
Plug -2 in for x of f(x)
--> -2^4 + 2(-2)^2 - 1
---> 23
f(-2) = 23
What is the name of this prism?
A. trapezoidal prism
B. pentagonal prism
C. sphere
D. hexagonal prism
To mix weed killer with water correctly, it is necessary to mix 18 teaspoons of weed killer with 3 gallons of water. How many gallons of water are needed to mix with the entire box if it contains 24 teaspoons of weed killer
*20 points*
A rancher’s herd of 250 sheep grazes over a 40-acre pasture. He would like to find out how many sheep are grazing on each acre of the pasture at any given time, so he has some images of the pasture taken by the state department of agriculture’s aerial photography division. Here are three samples of the images.
Sample 1: 4
Sample 2: 1
Sample 3: 9
How do the sample statistics compare to the population mean and standard deviation?
There will be about 6.25 sheep on each acre.
250/40 = 6.25
What is the polynomial function of lowest degree with rational real coefficients, and roots -3 and square root of 6?
9514 1404 393
Answer:
f(x) = x³ +3x² -6x -18
Step-by-step explanation:
In order for there to be a root of √6, there must be a factor of (x-√6). In order for there to be rational coefficients, there needs to be another factor of (x+√6) in the minimal polynomial. Then the minimal polynomial with the required roots is ...
f(x) = (x +3)(x -√6)(x +√6) = (x +3)(x² -6)
f(x) = x³ +3x² -6x -18
I NEED HELP ON MATH PLS
Answer:
5/2 or 2½ or 2.5
Step-by-step explanation:
20/8 = 2.5
10/4 = 2.5
If my savings of $x grows 10 percent each year, how much will i have in 2 years?
Answer:
20 percent
Step-by-step explanation:
Each year is 10 percent so 10x2 or 10+10 will equal 20
please help me with geometry
Answer:
How to improve my geometry?
Part 1 of 3: Getting the Grade
Attend every class. Class is a time to learn new things and solidify the information that you may have learned in the previous class.
Draw diagrams. Geometry is the math of shapes and angles. ...
Form a study group. ...
Know how to use a protractor. ...
Do all of the assigned homework. ...
Teach the material. ...
Do lots of practice problems. ...
Seek extra help. ...
Step-by-step explanation:
Question 1 of 10
The value of 9 is not-3 because
Answer:
It's a negative.
Step-by-step explanation:
The value of a positive number is still a positive number.
c) The exponential model A = 513.5e0.009t describes the population, A, of a
country in millions, t years after 2005. Use the model to determine when the
population of the country will be 602 million.
Answer:
zotfnKhxitfupoydkfslfndckv
Round number to nearest tenth
Answer:
a= 13.5
c=18.7
B= 46
Step-by-step explanation:
What type of line is PQ?
A. altitude
B. angle bisector
C. side bisector
D. median
The line PQ of the triangle is an altitude. The correct option is A.
What is the altitude of the triangle?
A line segment passing through a triangle's vertex and running perpendicular to the line containing the base is the triangle's height in geometry.
The extended base of the altitude is the name given to this line that contains the opposing side. The foot of the altitude is the point at where, the extended base and the height converge.
In the given triangle the line segment PQ is passing through a triangle's vertex and running perpendicular to the line containing the base is the triangle's height in geometry.
Therefore, the line PQ of the triangle is an altitude. The correct option is A.
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