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].
To solve the system of linear equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 by using the linear combination method, Henry decided that he should first multiply the first equation by –3 and then add the two equations together to eliminate the x-terms. When he did so, he also eliminated the y-terms and got the equation 0 = 0, so he thought that the system of equations must have an infinite number of solutions. To check his answer, he graphed the equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 with his graphing calculator, but he could only see one line. Why is this?
i have a time limit someone answer fast plsss (taking this down at 4:20 pm)
Answer:
The lines are:
3x - 2y = 4and
9x - 6y = 12Since after multiplying by -3 the equations sum to 0, the equations are same.
Same equations produce overlapping lines, hence you can see one line only.
Divide second equation by 3
3x-2y=4LInes are same so you can see only one line
If x+1/x = 12, find the value of x^2+1/x^2
[tex]\boxed{\sf (a+b)^2=a^2+b^2+2ab}[/tex]
Now
[tex]\\ \sf\longmapsto x+\dfrac{1}{x}=12[/tex]
[tex]\\ \sf\longmapsto \left(x+\dfrac{1}{x}\right)^2=12^2[/tex]
[tex]\\ \sf\longmapsto x^2+2\times x\times \dfrac{1}{x}+\left(\dfrac{1}{x}\right)^2=144[/tex]
[tex]\\ \sf\longmapsto x^2+\dfrac{1}{x^2}+2=144[/tex]
[tex]\\ \sf\longmapsto x^2+\dfrac{1}{x^2}=144-2=142[/tex]
Answer:
122
Step-by-step explanation:
x+1/x = 12
x + 1 = 12x
x = 1/11
(1/11)² + 1 / (1/11)² = 1/121 +1 /1/121 = 122
Which graph represents x < 15?
Answer:
B
Step-by-step explanation:
x<15
There is an open circle at 15 and the line goes to the left
All 20 children at a party were given one cookie, and then some were given an additional cookie. If a total of
32 cookies were given out, how many children received an additional cookie?
8
O 10
О о о
O 12
o 14
Answer:
If there were 20 children at a party, and each were given one cookie, then a total of 20 cookies were given out.
However, this is not the case, as 32 cookies were given out. So, we can see that 32 - 20 children, or 12 children, received one additional cookie.
Let me know if this helps!
A reacher deposited Rs 66000 in his/her saving account for as many years as the rate of interest per annum .If he/ she received Rs 10560 as interest at the end of saving period find the time duration and rate of interest.
Help me pls
I need the answer as quickly as possible
Answer:
Time and rate is 4 years and 4% respectively.
Step-by-step explanation:
P = Rs 66000
so
T = R
I = 10560
so
I = PTR/100
Rs 10560 = (66000*T^2)/100
or, Rs 1056000 = 66000*T^2
or. 1056000/66000 = T^2
or, 16 = T^2
OR, T =√16
so T = 4
Then
T = R
so, R = 4
how would i find the area of the blue region and the perimeter of the outer window frame
Answer:
The diameter is 6. The radius is 3. For the half of the orange circle.
The area of the half of the small orange circle is = pi*r*r = pi*3*3.
The diameter is 24. The radius is 12.
The area of the half of the light orange circle and the other colors is = pi*r*r = pi*12*12
The area of dark orange, light blue, purple and green figures = pi*12*12 – pi*3*3 = 135*pi
To get the area of the blue figure we need to divide 135*pi into ¼ and you will get the area of the blue figure.
The area of the blue figure =( ¼ )*135*pi *(1/2) = ¼ *1/2 = 1/8
The area of the blue figure is = 135pi / 8
B) outside perimeter of the window frame = 28 +pi*14 = 71.98
Hope this helps you :)
what should be added to 7777 to get 4999
Find f(2) given f(x) = -3x^3 + x^2 – 3
Answer:
D
Step-by-step explanation:
f(x) = -3x^3 + x^2 – 3 f(2) means that wherever you see a x, put in a 2.
f(2)= -3(2)^3 + (2)^2 - 3
f(2) = -3*8 + 4 - 3
f(2) = - 24 + 1
f(2) = - 23
[tex]\\ \sf \longmapsto f(2)[/tex]
[tex]\\ \sf \longmapsto -3(2)^3+(2)^2-3[/tex]
[tex]\\ \sf \longmapsto -3(8)+4-3[/tex]
[tex]\\ \sf \longmapsto -24+1[/tex]
[tex]\\ \sf \longmapsto -23[/tex]
If Ahmad’s balance is $85, what will the minimum payment be?
The median for the given set of six ordered data values is 29.5
9 12 25_ 41 50
What is the missing value?
Answer:
34
Step-by-step explanation:
let the missing value is x
(25+x) /2 = 29.5
25+x = 29.5(2)
25+x = 59
x = 59-25
x = 34
Hi I need help could someone please help me
Answer:
it's hypotenuse
Step-by-step explanation:
The vertical motion of a mass attached to a spring is described by the given initial-value problem. 4x " + x' + x = 0, x(0) = 8, x'(0) = 4
Determine the maximum vertical displacement of the mass. (Round your answer to three decimal places.)
Answer:
m = 4
k = 25.56
b = 20
The differential equation for damping motion is:
where,
Substitute the values in the differential equation and consider x" = r², x' =r and solve:
Therefore, solution is given by:
at t = 0, x = 1
at t = 0
x' =0
Step-by-step explanation:
Order: NS 1,500 ml over 15 h. After 6 hours 1,200 ml remain in the bag. The facility policy indicates that flow rate adjustments may not exceed 25% of the original rate. Recalculate the flow rate so that the infusion will finish on time, and decide if the adjustment is within the guidelines.
Answer:
ask ya fadaaaaaaaaàaaa
Step-by-step explanation:
guvdhcjnhcxh
Complete the function table
need help with math plz thanks
Answer:
0
Step-by-step explanation:
[tex]f(x)=2x-4\\f(2)=2(2)-4\\f(2)=4-4\\f(2)=0[/tex]
Answer:
0
Step-by-step explanation:
If f(x) = 2x - 4
Then f(2) = 2(2) -4
f(2) = 4 - 4
= 0
The median of a triangle divides it into two________.
The median of a triangle divides it into two equal triangles of equal areas.
Must click thanks and mark brainliest
Question
Express all real numbers less than -2 or greater than or equal to 3 in interval notation.
Real numbers can be expressed using the following interval,
[tex]\mathbb{R}=(-\infty,\infty)[/tex]
Of course infinities are not just normal infinities but thats out of the scope of this question.
Real numbers less than two can be expressed with,
[tex](-\infty,\infty)\cap(-\infty,-2)=\boxed{(-\infty,-2)}[/tex]
The [tex]\cap[/tex] is called intersection ie. where are both intervals valid. First we took real numbers then we intersected them with real numbers valued less than -2 and we got real numbers which are less than -2.
Similarly we can perform with "greater than or equal to 3" real numbers,
[tex](-\infty,\infty)\cap[3,\infty)=\boxed{[3,\infty)}[/tex]
So we have one interval stretching from negative infinity to (but not including) -2, and another interval stretching from including 3 to positive infinity.
If we want numbers in both intervals we can express this two ways,
First way is to use [tex]\cup[/tex] union operator to denote we want numbers from two intervals,
[tex]\boxed{(-\infty,2)\cup[3,\infty)}[/tex]
The second way is to specify which numbers we do not want, we do not want -2 and everything up to but not including 3, which is expressed with the following interval
[tex][-2,3)[/tex]
Now we just take out the not wanted interval from real numbers and we will remain with all wanted numbers,
[tex]\boxed{(-\infty,\infty)-[-2,3)}[/tex]
Hope this helps.
Lấy ngẫu nhiên 25 lọ thuốc Vitamin tổng hợp do một máy tự động đóng chai ta thu được s'2 =0,012(l2).Máyđượcgọilàđạtchuẩnnếuđộphântántheoquyđịnhlà2 =0,005(l2). Với mức ý nghĩa 0,05 hãy kiểm định máy đóng chai có đạt chuẩn không? Biết lượng thuốc trong chai là biến ngẫu nhiên có phân phối chuẩn.
Answer:
I really can't read this
Step-by-step explanation:
Can someone help me find the answer?
Answer:
a. x = 3/a
Step-by-step explanation:
Add all like terms on left hand side of the equation:
5 ax + 3 ax => 8 ax
Bring like term 4ax on left hand side
8ax - 4ax
=> 4ax
Therefore we get 4ax = 12
ax = 12/4
ax = 3
x = 3/a
solve for x. please help !
Answer:
-2
Step-by-step explanation:
3x + 8x - 3 = -25
Move the -3 over to the other side. This will make the -3 into positive 3
3x + 8x = -25 + 3
Now add like terms
11x = -22
Divide both sides by 11 to get x by itself
x = -2
Answer:
x= -2
Step-by-step explanation:
First you combine the like terms 3x and 8x which then gives you 11x
then you'll have 11x-3=-25
add 3 to both sides and you have 11x=-22
divide the 11 on both sides
then you'll have x=-2
Find the median of the following number 40,30,32,39,34,35,35,37
Terms given
40,35,32,39,34,35,35,37No of terms=8
We know
[tex]\boxed{\sf Mean=\dfrac{Sum\;of\:terms}{No\;of\:terms}}[/tex]
[tex]\\ \sf\longmapsto Mean=\dfrac{40+35+32+39+34+35+35+37}{8}[/tex]
[tex]\\ \sf\longmapsto Mean=\dfrac{270}{8}[/tex]
[tex]\\ \sf\longmapsto Mean=35[/tex]
Final Answer:
35
Step-by-step explanation:
-median is the middle number in the data set-
arrange the data set from least to greatest:
40, 30, 32, 39, 34, 35, 35, 37 ⇒ 30, 32, 34, 35, 35, 37, 39, 40
we start from the lowest number and the highest number and work your way to the middle:
30, 32, 34, 35, 35, 37, 39, 40
notice that there is no middle number:
30, 32, 34, 35, ?, 35, 37, 39, 40
so what we do is add both 35's and then divide it by 2
35 + 35 = 70 ÷ 2 = 35
median: 35
A ___________ gives theoretical probabilities of each possible event in an experiment.
A. probability outcome
B. sample space
C. random event
D. probability distribution
A probability outcome gives theoretical probabilities of each possible event in an experiment so option (A) will be correct.
What is probability?The probability of an event occurring is defined by probability.
Do not take underestimate probability it has several uses in daily life whether forecasts and like that.
Theoretical probability is the probability that shows by the probability formula while experimental probability is an actual probability that can obtain by experiments.
There are various situations in our daily lives where we might need to make predictions about how things will turn out.
Probability outcome which comes out by mathematical formula is always theoretical probability while actual experiment gives us experimental probability hence probability outcome will be the correct answer.
For more information about the probability
brainly.com/question/11234923,
#SPJ2
log13 X + log13 (12x-1)=1
Solve for x by simplifying both sides of the equation, then isolating the variable.
x ≈ 0.13893498
How many 1.5 ft
pieces of pipe can you cut from a 12ft pipe
Answer:
8 pieces.
Step-by-step explanation:
12 / 1.5
= 24 / 3
= 8.
Need help is this right or what is the right answer
Answer:
A
Step-by-step explanation:
the answer is A and not C. equation in form of y=mx+b
so start off by (0,2) and you can see the graph go by 1 x and 1 y.
C=n+2
Answer:
A
Step-by-step explanation:
its starting point is 2 up to +2 and it goes up at out by 1 so n also ik this was already answered but i want the brainly points
I need help please can not figure out this problem
How many 2cm×2cm cubes can be packed in a box 1m long,20cm wide and 4cm deep.
Answer:
1000
Step-by-step explanation:
I guess, something went wrong with the text up there.
I assume it should say 2cm×2cm×2cm cubes. right ? because a cube has 3 dimensions, not just 2.
otherwise an infinitely large number of "just squares" would fit into the box ...
so, the box is
1m×20cm×4cm = 100cm×20cm×4cm = 8000 cm³
a single cube would be
2cm×2cm×2cm = 8 cm³
therefore,
8000 / 8 = 1000 cubes can be packed into that box, since the dimensions of the box in relation to the dimensions of the cubes do not force to have some empty left over space. the box can be packed tightly.
Which of the following algebraic steps will solve the equation 5p= -35 and what is the solution
Answer:
p=-7
Step-by-step explanation:
5p=-35
Divide both sides by 5
5p/5 =-35/5
therefore p=-7
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{5p= -35}\\\\\underline{\huge\text{DIVIDE 5 BOTH SIDES}}\\\\\mathsf{\dfrac{5p}{5p}= \dfrac{-35}{5}}\\\\\large\text{CANCEL out: }\dfrac{5}{5}\large\text{ because that gives you 1}\\\large\text{KEEP: }\dfrac{-35}{5}\large\text{ because that gives you the value of p.}\\\\\large\textsf{p = }\mathsf{\dfrac{-35}{5}}\\\\\mathsf{-35\div5= p}\\\\\large\text{Simplify above and you have your result to the p-value.}\\\\\boxed{\boxed{\huge\text{Therefore your answer is: \textsf{p = -7}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Find y on this triangle
Answer:
5√3 / 2
Step-by-step explanation:
tan 30 = ( 5 / 2 ) / y
1 / √3 = 5 / 2y
2y = 5√3
y = 5√3 / 2
What is the value of b? -11b + 7 =40 (also there is another question in the bottom of the picture. If you can answer it please do)
Problem 1
The idea here is to follow PEMDAS in reverse to undo what is happening to the variable b, so we can isolate it.
-11b + 7 = 40
-11b = 40-7
-11b = 33
b = 33/(-11)
b = -3
To check this value, plug it back into the original equation. You should get 40 on each side to help confirm the answer.
Answer: b = -3=====================================================
Problem 2
There are two ways we can solve. One method is to use the hint your teacher gave you. So we'll distribute first and then follow the same idea as problem 1
9(p-4) = -18
9p-36 = -18
9p = -18+36
9p = 18
p = 18/9
p = 2
Another method you can use is to follow these steps
9(p-4) = -18
p-4 = -18/9
p-4 = -2
p = -2+4
p = 2
Either way, we get the same result. To check the answer, replace every p with 2 in the original equation. You should get -18 on the left side after simplifying.
Answer: p = 2