Answers
Answer:
The function that passes through (0, 0) is [tex]f(x) = \frac{1}{6}\cdot e^{2\cdot x^{3}} - \frac{1}{6}[/tex].
Step-by-step explanation:
Firstly, we integrate the function by algebraic substitution:
[tex]\int {x^{2}\cdot e^{2\cdot x^{3}}} \, dx[/tex] (1)
If [tex]u = 2\cdot x^{3}[/tex] and [tex]du = 6\cdot x^{2} dx[/tex], then:
[tex]\int {e^{2\cdot x^{3}}\cdot x^{2}} \, dx[/tex]
[tex]\frac{1}{6}\int {e^{u}} \, du[/tex]
[tex]f(u) = \frac{1}{6}\cdot e^{u} + C[/tex]
[tex]f(x) = \frac{1}{6}\cdot e^{2\cdot x^{3}} + C[/tex]
Where [tex]C[/tex] is the integration constant.
If [tex]x = 0[/tex] and [tex]f(0) = 0[/tex], then the integration constant is:
[tex]\frac{1}{6}\cdot e^{2\cdot 0^{3}} + C= 0[/tex]
[tex]C = -\frac{1}{6}[/tex]
Hence, the function that passes through (0, 0) is [tex]f(x) = \frac{1}{6}\cdot e^{2\cdot x^{3}} - \frac{1}{6}[/tex].
Related Questions
find the LCM of ;
(1+4x+4x2-16x) and (1+2x-8x3-16x4)
Answers
Answer:
16x4−4x2+4x−116x4−4x2+4x−1
=16x4−(4x2−4x+1)=16x4−(4x2−4x+1)
=(4x2)2−(2x−1)2∵a2−2ab+b2=(a−b)2=(4x2)2−(2x−1)2∵a2−2ab+b2=(a−b)2
=(4x2−2x+1)(4x2+2x−1)∵a2−b2=(a−b)(a+b
Step-by-step explanation:
what is the correct answer to my question ?
Answers
Answer:
13/17
Step-by-step explanation:
Can I get the answer for those
Answers
Answer:
1) 5.64
2) 17.321
1) [tex]\frac{21}{28}[/tex]
2) [tex]\frac{16}{34}[/tex]
3) [tex]\frac{28}{35}[/tex]
4) [tex]\frac{32}{24}[/tex]
Step-by-step explanation:
SOH - CAH - TOA
Sin = [tex]\frac{O}{H}[/tex] Cos = [tex]\frac{A}{H}[/tex] Tan = [tex]\frac{O}{A}[/tex]
O = opposite, A = adjacent, H = hypotenuse
First two, use Pythagorean Theorem
If you want to calculate the angle on the last 4, use inverse of function and put in the ratio.
For example :
1) Tan Z = [tex]\frac{21}{28}[/tex]
[tex]Tan^{-1}[/tex] ( [tex]\frac{21}{28}[/tex])
Z = 36.9°
Martina made$391for17hours of work. At the same rate, how many hours would she have to work to make$253? a 11 hours b 9 hours c 22 hours d 33 hours
Answers
Answer:
11 hours is right answer i hope it will help you
A person is standing close to the edge on a 56 foot building and throws the ball vertically upward. The quadratic function h(t)=-16^2+104t+56 models the balls height above the ground,h(t),in feet, T seconds after it was thrown
what is the maximum height of ball.=
How many seconds did it take to hit the ground=
Please help!
Answers
Answer:
Part 1)
225 feet.
Part 2)
7 seconds.
Step-by-step explanation:
The height h(t) of the ball above the ground after t seconds is modeled by the function:
[tex]h(t)=-16t^2+104t+56[/tex]
Part 1)
We want to determine the maximum height of the ball.
Notice that the function is a quadratic with a negative leading coefficient, so its maximum will be at its vertex point.
The vertex of a parabola is given by:
[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = -16, b = 104, and c = 56.
Find the x- (or rather t-) coordinate of the vertex. So:
[tex]\displaystyle t=-\frac{(104)}{2(-16)}=\frac{104}{32}=\frac{13}{4}=3.25\text{ seconds}[/tex]
In other words, the ball reaches its maximum height after 3.25 seconds.
To find the maximum height, substitute this value back into the function. Hence:
[tex]\displaystyle h(3.25)=-16(3.25)^2+104(3.25)+56=225\text{ feet}[/tex]
The maximum height of the ball is 225 feet in the air.
Part 2)
We want to find the amount of time it took for the ball to hit the ground.
When the ball hit the ground, its height above the ground is zero. Therefore, we can set h(t) to 0 and solve for t:
[tex]0=-16t^2+104t+56[/tex]
We can simplify a bit. Divide both sides by -8:
[tex]0=2t^2-13t-7[/tex]
We can factor. Find two numbers that multiply to 2(-7) = -14 and add to -13.
-14 and 1 works! Therefore, split the second term into -14 and 1:
[tex]\displaystyle 0=2t^2-14t+t-7[/tex]
Factor out a 2t from the first two terms and group the last two terms:
[tex]0=2t(t-7)+(t-7)[/tex]
Factor by grouping:
[tex]0=(2t+1)(t-7)[/tex]
Zero Product Property:
[tex]2t+1=0\text{ or } t-7=0[/tex]
Solve for each case:
[tex]\displaystyle t=-0.5\text{ or } t=7[/tex]
Since time cannot be negative, we can ignore the first case.
Therefore, it takes seven seconds for the ball to hit the ground.
A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 50% of this population prefers the color green. If 14 buyers are randomly selected, what is the probability that exactly 12 buyers would prefer green
Answers
Answer:
The probability that exactly 12 buyers would prefer green
=0.00555
Step-by-step explanation:
We are given that
p=50%=50/100=0.50
n=14
We have to find the probability that exactly 12 buyers would prefer green.
q=1-p
q=1-0.50=0.50
Using binomial distribution formula
[tex]P(X=x)=nC_r p^r q^{n-r}[/tex]
[tex]P(x=12)=14C_{12}(0.50)^{12}(0.50)^{14-12}[/tex]
[tex]P(x=12)=14C_{12}(0.50)^{12}(0.50)^2[/tex]
[tex]P(x=12)=14C_{12}(0.50)^{14}[/tex]
[tex]P(x=12)=\frac{14!}{12!2!}(0.50)^{14}[/tex]
[tex]P(x=12)=\frac{14\times 13\times 12!}{12!2\times 1}(0.50)^{14}[/tex]
[tex]P(x=12)=91\cdot (0.50)^{14}[/tex]
[tex]P(x=12)=0.00555[/tex]
Hence, the probability that exactly 12 buyers would prefer green
=0.00555
Find the values of the sine, cosine, and tangent for ZA C A 36ft B
24ft
Answers
Find the values of the sine, cosine, and tangent for ∠A
a. sin A = [tex]\frac{\sqrt{13} }{2}[/tex], cos A = [tex]\frac{\sqrt{13} }{3}[/tex], tan A = [tex]\frac{2 }{3}[/tex]
b. sin A = [tex]3\frac{\sqrt{13} }{13}[/tex], cos A = [tex]2\frac{\sqrt{13} }{13}[/tex], tan A = [tex]\frac{3}{2}[/tex]
c. sin A = [tex]\frac{\sqrt{13} }{3}[/tex], cos A = [tex]\frac{\sqrt{13} }{2}[/tex], tan A = [tex]\frac{3}{2}[/tex]
d. sin A = [tex]2\frac{\sqrt{13} }{13}[/tex], cos A = [tex]3\frac{\sqrt{13} }{13}[/tex], tan A = [tex]\frac{2 }{3}[/tex]
Answer:d. sin A = [tex]2\frac{\sqrt{13} }{13}[/tex], cos A = [tex]3\frac{\sqrt{13} }{13}[/tex], tan A = [tex]\frac{2 }{3}[/tex]
Step-by-step explanation:The triangle for the question has been attached to this response.
As shown in the triangle;
AC = 36ft
BC = 24ft
ACB = 90°
To calculate the values of the sine, cosine, and tangent of ∠A;
i. First calculate the value of the missing side AB.
Using Pythagoras' theorem;
⇒ (AB)² = (AC)² + (BC)²
Substitute the values of AC and BC
⇒ (AB)² = (36)² + (24)²
Solve for AB
⇒ (AB)² = 1296 + 576
⇒ (AB)² = 1872
⇒ AB = [tex]\sqrt{1872}[/tex]
⇒ AB = [tex]12\sqrt{13}[/tex] ft
From the values of the sides, it can be noted that the side AB is the hypotenuse of the triangle since that is the longest side with a value of [tex]12\sqrt{13}[/tex] ft (43.27ft).
ii. Calculate the sine of ∠A (i.e sin A)
The sine of an angle (Ф) in a triangle is given by the ratio of the opposite side to that angle to the hypotenuse side of the triangle. i.e
sin Ф = [tex]\frac{opposite}{hypotenuse}[/tex] -------------(i)
In this case,
Ф = A
opposite = 24ft (This is the opposite side to angle A)
hypotenuse = [tex]12\sqrt{13}[/tex] ft (This is the longest side of the triangle)
Substitute these values into equation (i) as follows;
sin A = [tex]\frac{24}{12\sqrt{13} }[/tex]
sin A = [tex]\frac{2}{\sqrt{13}}[/tex]
Rationalize the result by multiplying both the numerator and denominator by [tex]\sqrt{13}[/tex]
sin A = [tex]\frac{2}{\sqrt{13}} * \frac{\sqrt{13} }{\sqrt{13} }[/tex]
sin A = [tex]\frac{2\sqrt{13} }{13}[/tex]
iii. Calculate the cosine of ∠A (i.e cos A)
The cosine of an angle (Ф) in a triangle is given by the ratio of the adjacent side to that angle to the hypotenuse side of the triangle. i.e
cos Ф = [tex]\frac{adjacent}{hypotenuse}[/tex] -------------(ii)
In this case,
Ф = A
adjacent = 36ft (This is the adjecent side to angle A)
hypotenuse = [tex]12\sqrt{13}[/tex] ft (This is the longest side of the triangle)
Substitute these values into equation (ii) as follows;
cos A = [tex]\frac{36}{12\sqrt{13} }[/tex]
cos A = [tex]\frac{3}{\sqrt{13}}[/tex]
Rationalize the result by multiplying both the numerator and denominator by [tex]\sqrt{13}[/tex]
cos A = [tex]\frac{3}{\sqrt{13}} * \frac{\sqrt{13} }{\sqrt{13} }[/tex]
cos A = [tex]\frac{3\sqrt{13} }{13}[/tex]
iii. Calculate the tangent of ∠A (i.e tan A)
The cosine of an angle (Ф) in a triangle is given by the ratio of the opposite side to that angle to the adjacent side of the triangle. i.e
tan Ф = [tex]\frac{opposite}{adjacent}[/tex] -------------(iii)
In this case,
Ф = A
opposite = 24 ft (This is the opposite side to angle A)
adjacent = 36 ft (This is the adjacent side to angle A)
Substitute these values into equation (iii) as follows;
tan A = [tex]\frac{24}{36}[/tex]
tan A = [tex]\frac{2}{3}[/tex]
.Solve : 3 / 8 (x-5) = 11 -7x
Answers
Answer:
1.74 or [tex]\frac{103}{59}[/tex]
Step-by-step explanation:
3(x-5) = 8 (11-7x)
3x-15=88-56x
59x=103
x = 1.74
What is 5.071 in words?
Answers
Answer:
Step-by-step explanation:
The number 5.071 written in english words is "five and seventy-one thousandths
I am Your Crush boy you have never seen a boy like me if you will see me you will fall in my love. come zom Id- 6622308635 pas- 6UC3yE
Answers
Answer:
I don't know the answer to ur question. LOL
Answer:
stop being desperate
nobody is gonna fall in love with some desperate weirdo
If the angles (4x + 4)° and (6x – 4)° are the supplementary angles, find the value of x.
Answers
Answer:
18
Step-by-step explanation:
Supplementary angles means sum of angles is 180.
4x + 4 + 6x - 4 = 180
4x + 6x + 4 - 4 = 180
10x = 180
x = 180 / 10
x = 18
Answer:
x=18 degree
Step-by-step explanation:
If they are supplementary angles, then their sum = 180 degree
4x+4 + 6x-4 =180
4x+6x + 4-4 = 180
10x = 180
x=180/10
x=18
One number is 2/3 of another number. The sum of the two numbers is 40. Find
the two numbers.
Answers
Answer:
5353454
Step-by-step explanation:
Answer: 16 and 24
Step-by-step explanation:
2x+3x= 40
5x = 40
x=8
that means 2x8 equal 16 and 3x8 equals 24 which leads us to the answer
30 POINTS
Help on Part B pleaseeee
Answers
In verse of B.g(x)=[tex]\frac{x+5}{4}[/tex] is:
4x-5
Answer:
Solution given:
B.g(x)=[tex]\frac{x+5}{4}[/tex]
let
g(x)=y
y=[tex]\frac{x+5}{4}[/tex]
Interchanging role of x and y
we get:
x=[tex]\frac{y+5}{4}[/tex]
doing crisscrossed multiplication
4x=y+5
y=4x-5
So
g-¹(x)=4x-5
Given that,
→ g(x) = x+5/4
Then g(x)=y,
→ y = x+5/4
Now we can interchange role of x and y,
→ x = y+5/4
Then use the cross multiplication,
→ 4x = y+5
→ y = 4x-5
Hence, g-¹(x) = 4x-5 is the solution.
if i need 90 square feet of tile and each piece of tile covers 0.34 square feet, how much do i need in pieces
Answers
Answer:
265
Step-by-step explanation:
9514 1404 393
Answer:
265
Step-by-step explanation:
Let t represent the number of tiles needed. Then the area covered by those t tiles will be ...
area = t·0.34 ft²
We want that area to be 90 ft², so we can solve this equation for t:
90 ft² = t·(0.34 ft²)
90 ft²/(0.34 ft²) = t ≈ 264.71
About 265 tiles are needed to cover 90 ft².
The data set shows the number of players on each softball team in a tournament:
9
12
8
7
7
21
11
9
8
7
10
7
10
11
Which of the following statements is true based on the data set?
There is one outlier that indicates an unusually large number of players on that team.
There are two outliers that indicate an unusually large number of players on those two teams.
There is one outlier that indicates an unusually small number of players on that team.
There are two outliers that indicate an unusually small number of players on those two teams.
Answers
A student ran out of time on a multiple choice exam and randomly guessed the answers for two problems. Each problem had 5 answer choices - a, b, c, d, e- and only one correct answer. What is the probability that she answered neither of the problems correctly? Do not round your answer. (If necessary, consult a list of formulas.)
Answers
Answer:
there is a 64% chance that the student got both problems wrong
a 32% chance that they got only 1 correct
and a 4% chance that they got both correct
Step-by-step explanation:
There are 25 total possible combinations of answers, with 8 possible combinations where the student would get 1 answer right, and 1 combination where the student would get both answers correct.
[tex]25-9=16[/tex]
[tex]\frac{16}{25} =\frac{x}{100}[/tex]
[tex]\frac{64}{100}[/tex]
[tex]64[/tex]%
[tex]\frac{8}{25} =\frac{y}{100}[/tex]
[tex]\frac{32}{100}[/tex]
[tex]32[/tex]%
[tex]\frac{1}{25} =\frac{z}{100}[/tex]
[tex]\frac{4}{100}[/tex]
[tex]4[/tex]%
Which is a stretch of an exponential decay function?
f(x) =4/5(5/4)
f(x) = 4/5(4/5)
f(x) =5/4(4/5)
fx) = 5/4(5/4)
Answers
Answer:
f(x) = 4/5(5/4)Step-by-step explanation:
correct me if I am wrong
We have 9 pens, of which 5 are green ink, 3 are red ink, and 1 is black. If we put the pens in a line, how many arrangements are possible
Answers
Answer:
504 arrangements are possible
Step-by-step explanation:
Arrangements of n elements:
The number of arrangements of n elements is given by:
[tex]A_{n} = n![/tex]
Arrangements of n elements, divided into groups:
The number of arrangements of n elements, divided into groups of [tex]n_1, n_2,...,n_n[/tex] elements is given by:
[tex]A_{n}^{n_1,n_2,...,n_n} = \frac{n!}{n_1!n_2!...n_n!}[/tex]
In this case:
9 pens, into groups of 5, 3 and 1. So
[tex]A_{9}^{5,3,1} = \frac{9!}{5!3!1!} = 504[/tex]
504 arrangements are possible
1. Write 3.3.3.3.3 as a power.
Answers
Answer:
3^5
Step-by-step explanation:
On the iPad it looks like that but the five is on the top right smaller
Answer:
3⁵
every 3 has it own power that is 1 however that .3 confused us
Write a polynomial f(x) that satisfies the given conditions. Polynomial of lowest degree with zeros of -2 (multiplicity 3), 3 (multiplicity 1), and with f(0) = 120.
Answers
Answer:
Step-by-step explanation:
Polynomial f(x) has the following conditions: zeros of -2 (multiplicity 3), 3 (multiplicity 1), and with f(0) = 120.
The first part zeros of -2 means (x+2) and multiplicity 3 means (x+2)^3.
The second part zeros of 3 means (x-3) and multiplicity 1 means (x-3).
The third part f(0) = 120 means substituting x=0 into (x+2)^3*(x-3)*k =120
(0+2)^3*(0-3)*k = 120
-24k = 120
k = -5
Combining all three conditions, f(x)
= -5(x+2)^3*(x-3)
= -5(x^3 + 3*2*x^2 + 3*2*2*x + 2^3)(x-3)
= -5(x^4 + 6x^3 + 12x^2 + 8x - 3x^3 - 18x^2 - 36x - 24)
= -5(x^4 + 3x^3 - 6x^2 - 28x -24)
= -5x^4 - 15x^3 + 30x^2 + 140x + 120
which is the correct answer?
Answers
Answer:
11/12
Step-by-step explanation:
1/4 + 2/3
= 3/12 + 8/12
= 11/12
2) There are 40 boys and 60 girls in a class of students. What is the ratio of girls to students
Answers
Answer:
60:100, 6/10, 3/5, 6 to 10, etc.
Step-by-step explanation:
You take the number of girls over total students which is boys + girls. Since there's 40 boys and 60 girls, it's 60 girls to 100 students which can be written in several ways.
Answer:
60:100 / 3:5
Step-by-step explanation:
You first add the total number of students which is (40boys + 60girls) which gives us 100 students.
Then arrange the ratio of girls to students as per the question that is 60:100, reduce it to its lowest term that is dividing the ratio by 20, and finally got 3:5
The last dividend paid by Wilden Corporation was $1.55. The dividend growth rate is expected to be constant at 1.5% for 2 years, after which dividends are expected to grow at a rate of 6.0% forever. The firm's required return (rs) is 12.0%. What is the best estimate of the current stock price?
Answers
Answer:
Net present value= $25.17
Step-by-step explanation:
We are told that The last dividend paid was $1.55 and that the dividend growth rate is constant at 1.5% for 2 years.
Thus;
1) After 1st year;
1.55 × (1 + 0.015) = 1.57325 Div1
After 2nd year;
1.57325 × (1 + 0.015) = 1.59685 Div2
After that 2 years it grows at 6% Constant rate forever;
1.59685 × (1 + 0.06) = 1.69266 Div3
Let's now use the dividend formula which grows in perpetuity at a rate of "g" since required return is 12%:
Thus;
V = 1.69266/(0.12 - 0.06) = 28.211
Thus; Div2 = 28.211 + 1.59685 ≈ 29.80785
Now, using the financial calculator of the Cash Flow function, we have:
Div0 = 0
Div1 = 1.57325
Div2 = 29.80785
i% = 12
Net present value = (1.57325/(1 + 0.12)) + ((1.59685 + 28.211)/(1 + 0.12)²)
Net present value= $25.17
What is the volume of the triangular prism shown below?
10
A. 100 cu. units
B. 200 cu. units
C. 400 cu. units
D. 300 cu. units
Answers
Answer:
B. 200 cu. units
Step-by-step explanation:
Volume of the triangular prism = ½*b*h*l
Where,
b = 8 units
h = 5 units
l = 10 units
Plug in the values
Volume of the prism = ½*8*5*10
= 4*5*10
= 200 cu. units
Find the domain and range of the relation.
Answers
the answer is in the picture above
Is AFGH ~ AJKL? If so, identify the similarity postulate or theorem that
applies.
G
K
10
6
30°
30°
Н
A. Similar - SAS
B. Cannot be determined
C. Similar - SSS
D. Similar - AA
Answers
Answer: B. Cannot be determined
Explanation:
We can't use SAS since we don't have two pairs of proportional sides. We only know one pair of sides. This also rules out SSS as well since we'd need 3 pairs of proportional sides.
We can't use AA because we don't have two pairs of congruent angles.
Currently, we simply don't have enough information to determine if the triangles are similar or not.
match the description in column a to its corresponding word in column b.
help me plsssss
Answers
Answer:
1-a
2-h
3-g
4-d
5-c
6-j
7-f
8-k
9-b
10-i
numbers are column A and alphabets are column B!
What is the domain of D(t) as it applies in this situation?
Answers
Answer:
t could be all real numbers.
Step-by-step explanation:
The function D(t) is given by:
[tex]D(t)=-1.5t+12[/tex]
The domain is all the posible x-values for which the function is defined.
In our case, t could be all real numbers.
The answer is the first option.
I hope it helps you!
(3a+2b-4c)+(3a+2b-4c)
Answers
6
+
4
−
8
Step-by-step explanation:
Please mark me as brain list and please like my answer and rate also
Answer:
hope this will help you more
HELP
BELP
Identify the range of the function shown in the graph
Answers
Answer:
Range = -1 ≤ y ≤ 2
Step-by-step explanation:
The function's range is the y-values the function can have as its output. -1 is the minimum y-value and 2 is the maximum y-value.