Answer:
∫[tex]6x^5(x^6-2)\,dx[/tex] = [tex]\frac{1}{2}(x^6-2)^2+C[/tex]
Step-by-step explanation:
To find:
∫[tex]6x^5(x^6-2)\,dx[/tex]
Solution:
Method of substitution:
Let [tex]x^6-2=t[/tex]
Differentiate both sides with respect to [tex]t[/tex]
[tex]6x^5\,dx=dt[/tex]
[use [tex](x^n)'=nx^{n-1}[/tex]]
So,
∫[tex]6x^5(x^6-2)\,dx[/tex] = ∫ [tex]t\,dt[/tex] = [tex]\frac{t^2}{2}+C_1[/tex] where [tex]C_1[/tex] is a variable.
(Use ∫[tex]t^n\,dt=\frac{t^{n+1} }{n+1}[/tex] )
Put [tex]t=x^6-2[/tex]
∫[tex]6x^5(x^6-2)\,dx[/tex] = [tex]\frac{1}{2}(x^6-2)^2+C_1[/tex]
Use [tex](a-b)^2=a^2+b^2-2ab[/tex]
So,
∫[tex]6x^5(x^6-2)\,dx[/tex] = [tex]\frac{1}{2}(x^6-2)^2+C_1=\frac{1}{2}(x^{12}+4-4x^6)+C_1=\frac{x^{12} }{2}-2x^6+2+C_1=\frac{x^{12} }{2}-2x^6+C[/tex]
where [tex]C=2+C_1[/tex]
Without using substitution:
∫[tex]6x^5(x^6-2)\,dx[/tex] = ∫[tex]6x^{11}-12x^5\,dx[/tex] = [tex]\frac{6x^{12} }{12}-\frac{12x^6}{6}+C=\frac{x^{12} }{2}-2x^6+C[/tex]
So, same answer is obtained in both the cases.
Jack did 3/5 of the problems on his weekend homework before Sunday. On Sunday, he solved 1/3 of what was left and the last 4 problems. How many problems were assigned for the weekend?
Answer:
15 problems were assigned for the weekend.
Step-by-step explanation:
Let x denote the number of problems assigned for the weekend.
Before Sunday, he did 3/5 of the problems, so he is left with (1-3/5)x = 2/5 x of the problems.
On Sunday, he solved 1/3 of what was left of the problems, so he is left with (1 - 1/3)(2/5 x) = (2/3) * (2/5) x = 4/15 x problems.
4/15 x equals 4 because those were the last remaining problems, so we can solve for x:
[tex]\frac{4}{15}x=4\\x = 4 \cdot \frac{15}{4} = 15[/tex]
So 15 problems were assigned for the weekend.
Michelle pays $66.85 for a costume pattern and 8 yards of fabric. The costume pattern cost $4.85 how much does each yard of fabric cost?
Answer:
I got $7.75.
Step-by-step explanation:
66.85-4.85=62
62/8=7.75.
what is the answer to 3x + 7 = 82?
Answer:
x=25
Step-by-step explanation:
Answer:
x = 25
Step-by-step explanation:
3x + 7 = 82
3x + 7 - 7 = 82 - 7
3x = 75
3x/3 = 75/3
x = 25
the quotient of k and ten
Answer:
k/10
Step-by-step explanation:
Quotient of k and 10 simplified to k/10
Explain each nature of mathematics in your own undertanding.
A science of measures-
An intellectual game-
The art of drawing conclusions-
A tool subject-
A system of logical procedures-
An intuitive method
Answer:
Each nature of mathematics in my own understanding is written below in complete detail.
Step-by-step explanation:
Now, much more than geometry and arithmetic, mathematics now is a distinct system that compromises with data, computations, and pronouncements from science; with reasoning, inference, and proof; and with mathematical principles of natural appearances, of human response, a system of logical procedures and social systems.
Which of the following functions represent exponential growth?
Which of the following functions represent exponential decay?
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Answer:
1. a, b, c - represent growth
2. b, c, d - represent decay
Step-by-step explanation:
If increasing x results in a larger value, the function represents growth. If it results in a smaller value, the function represents decay.
__
To answer these questions, you can look at the base and the exponent. When we say "exponent" here, we mean the coefficient of the exponent variable. There are four possibilities:
growth:
exponent positive, base > 1exponent negative, base < 1decay:
exponent positive, base < 1exponent negative, base > 1__
Growth questions:
1.77^x -- growth
1.5^(x/2) -- growth
0.5^(-x) -- growth (= 2^x)
e^(-t) -- decay (e ≈ 2.718)
Decay questions:
1.7^x -- growth
1.7^(-2x) -- decay
(1/3)^x -- decay (= 3^(-x))
2^(-x) -- decay
Y really help in this problem !
I will give you 40 points
Answer:
160
Step-by-step explanation:
Compound Interest
When Jack turned 21, he decided to start investing $200 a month every year for nine years. At age 30, he decided to stop investing altogether.
Blake started a little later, investing $200 a month every month starting at age 30, all the way until the ripe old age of 67.
Assuming that they were both amazing at investing and made 11% interest per year, how much money will they both have at age 67?
Answer:
Jack $1800 Blake $7400
Step-by-step explanation:
which equation shows that 9 is a factor of 72
Answer:
Step-by-step explanation:
Volunteers for a human performance study were randomly divided into two groups. The first group had their flexibility measured in the morning after a short meditation session while the second group had their flexibility measured in the afternoon with no previous meditation session. The flexibility scores of the two groups were compared. This experiment was not double-blind because:
a. some of the volunteers stretched before they went to the study location.
b. volunteers were allowed to keep their eyes open while having their flexibility measured.
c. volunteers were randomized into the two groups.
d. the volunteers knew whether they had meditated before having their flexibility measured.
Answer:
C
Have a wonderful day!
The experiment was not double-blind because volunteers were randomized into the two groups. The correct option is c.
What is a double-blind experiment?A type of clinical experiment where neither the research team nor the subjects are aware of the treatment or intervention they are receiving until the trial is complete. As a result, the study's findings are less likely to be skewed.
Because neither the participant nor the clinician is aware of who has received what treatment, double-blind studies are regarded as the most trustworthy sort of research. This is done in an effort to lessen bias and the placebo effect.
Both the researchers and the test subjects must be uninformed of who is receiving the treatment and who is receiving a placebo in a double-blind trial.
Therefore, the correct option is c. volunteers were randomized into the two groups.
To learn more about a double-blind experiment, refer to the link:
https://brainly.com/question/29829648
#SPJ5
The price of an Item has been reduced by 70%. The original price was $90. What is the price of the item now?
Answer:
The price of the item is $27.
Step-by-step explanation:
$90 is reduced by 70% means: $90 - 0.70*$90 = (1 - 0.70)*$90 = 0.30*$90 = $27. The price of the item is $27 now.
Answer: 63
Reason: My brain
The value of a baseball card can be represented by the equation Y - 3x+ 39, where x represents the number of year
that Robert has owned the card and y represents the total value, in dollars, of the card. What was the value of the card when Robert originally purchased it?
$3
$13
$36
$39
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Answer:
$39
Step-by-step explanation:
Assuming your equation is supposed to be ...
y = 3x +39
The value of y when x = 0 is 39.
The value of the card when Robert purchased it was $39.
Answer: $39
Step-by-step explanation:
How many 1/12 make a quarter?
Answer:
3
Step-by-step explanation:
3/12 = .25
.25 = a quarter
plz mark brainliest ! :)
Answer:
3
Step-by-step explanation:
Let the number of 1/12 that make a quarter be x.
x * 1/12 = 1/4
Multiply both sides by 12.
x * 1/12 * 12 = 1/4 * 12
x = 3
Answer: 3
Jennie charges $200 per passenger for a sunset sailing
tour on her catamaran, while Paul charges $250 per
passenger. We can define the amount of money each
person earns per cruise as a random variable.
Let A = the amount of money Jennie earns and let B =
the amount of money Paul earns.
What is the mean of the sum and the mean of the
difference of the amount of money that Jennie and
Paul earn on a randomly selected cruise?
MA+B= $
HA-B = $
A = 200X and B = 250Y
|--234.163
PA= $730, CA = $192.62
Mg = $962.5, o= $253.425
-232.5
272.687
1692.5
Answer:
1692.5 and -232.5
Step-by-step explanation:
The mean of the sum would be as follows:
1692.5
The difference of the amount of money earned by Jennie and Paul would be:
-232.5
Mean
Given that,
Money earned by Jennie(A) [tex]= 200X[/tex]
Money earned by Paul(B) [tex]= 250Y[/tex]
μ[tex]_{A}[/tex] = $[tex]730[/tex] & σ[tex]_{A}[/tex] = $ [tex]192.62[/tex]
μ[tex]_{B}[/tex] [tex]=[/tex] $[tex]962.5[/tex] & σ[tex]_{B}[/tex] [tex]=[/tex] $ [tex]253.425[/tex]
So,
The mean of the sum [tex]= 1692.5[/tex]
The difference of the amount of money [tex]= -232.5[/tex]
Learn more about "Mean" here:
brainly.com/question/521501
Find the slope of the line below. If necessary, use a slash (/) to indicate a
division bar.
(4,3)
(-6,-3)
m =
Answer:
3/5
Step-by-step explanation:
As we move (right) from the first point to the second, we see x (the run) increasing by 10 and y (the rise) by 6. Thus, the slope of the line shown in the diagram is
m = rise / run = 6/10 = 3/5
please help ASAP I'll make brainleist
Answer:
D. k= g -3
Step-by-step explanation:
Flip the equation
g−3=k
then Add 3 to both sides
g−3+3=k+3
Lonnie plans to join the gym. He must pay a $35 membership fee. He will
then pay $5 each month. What is the slope?
Answer:
5
Step-by-step explanation:
The slope will be the constant amount that the cost increases by each month.
In this situation, 5 is the slope, because he has to pay $5 each month.
35 is not the slope, and is instead the y intercept. This is because this is the cost at 0 months, since it is the membership fee.
So, the correct answer is 5.
what’s the slope of the line?
Answer:
4/3
Step-by-step explanation:
You use Rise over Run.
It runs 3 blocks to the left (+).
It rises 4 blocks up (+).
Answer:
is the change in y over the change in x
what is the domain of f(x)=4 by the power of 2
Answer:
f(x)=16
Step-by-step explanation:
which expression is equivalent to 38*5?
150+13
185-13
190+40
200-10
38×5 is 190
200-10 is the only thing that makes 190 therefore your answer is the last one!
hope this helped
Solve for x. Round to the nearest tenth if necessary.
Answer:
x = 19
Step-by-step explanation:
Since, both the triangles (small and large) given in the picture are similar,
Their corresponding sides will be in the same ratio.
By applying this property,
[tex]\frac{20}{36}= \frac{30}{30+(x+5)}[/tex]
[tex]\frac{5}{9}= \frac{30}{x+35}[/tex]
5(x + 35) = 9 × 30
5x + 175 = 270
5x = 270 - 175
5x = 95
x = [tex]\frac{95}{5}[/tex]
x = 19
15. Hatice Hanım, 3 çocuğuna birer
ayakkabı almıştır. Ayakkabılar için satıcıya
500 TL veren Hatice Hanım, 5 TL para
üstü almıştır. Ayakkabıların fiyatları eşit
olduğuna göre bir ayakkabının fiyatı kaç
liradır?
A) 150
B) 155
C) 160
D) 165
Answer:
D
Step-by-step explanation:
Merhaba!
500-5=495
bir ayakkabı=495/3=165
Good work ;)
Jin surveyed 300 of the students in his school about their favorite color. Students could choose between red and purple. 207 students said their favorite color was purple. What percentage of the surveyed students said their favorite color was red
Answer:
31%
Step-by-step explanation:
Tom had 3 times as many pencils than Max. Tom then gave 24 pencils to Max and they now had the same amount of pencils. How many pencils did they have altogether?
Answer:
24×3=72
Sooo the answer 72✨
I need help with this question this question is worth 25 points.
Answer:
i hope it help you :)
Step-by-step explanation:
1)x=25 ,m<KOL=m<DOA=80ْ
2)x=13 ,m<UOT=m<VOS=93ْ
3)x=8 , m<KOL=m<NOM=142ْ
4)x=20 ,m<HOG=m<EOF=46ْ
5)x=53 ,m<ROS=m<QOP=10ْ
6)x=14 , m<LOM=m<KOJ=127
the sum of the terms of a sequence 1+ 3 + 5 + 7 + 9
Answer:
if you add it all up it is 25
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
1 + 3 + 5 +7 +9
1+3 = 4
4+5 + 7 +9
4+5=9
9 + 7 +9
9+7 = 16
16 + 9 = 25
Ps: You can just search online
Solve for y. Thank you.
Answer:
[tex]y = \sqrt{ \frac{wz}{x} } [/tex]
hence c. Patrick Mahomes is right.
Factorise
x^2 - 5x - 6
Answer:
(x+1)(x-6)
thats the ans :)
PUT THE NUMBERS IN ORDER FROM LEAST TO GREATEST.
-29/5^2
(1, 2.5)
4,21
5.5
6
9
DONT SKIP ILL GIVE 40 POINTS.!!!
Answer:
boop
Step-by-step explanation:
I will give brainliest!
Answer:
B
Hope its right
Step-by-step explanation: