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Related Questions
Integration of ∫(cos3x+3sinx)dx integration
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Answer:
[tex] I = \dfrac{1}{3}sin(3x) - 3cos(x) + C[/tex]
Step-by-step explanation:
We need to integrate the given expression. Let I be the answer .
[tex]\implies\displaystyle\sf I = \int (cos(3x) + 3sin(x) )dx \\\\\implies\displaystyle I = \int cos(3x) + \int sin(x)\ dx [/tex]
Let u = 3x , then du = 3dx . Henceforth 1/3 du = dx .Rewrite using du and u .[tex]\implies\displaystyle\sf I = \int cos\ u \dfrac{1}{3}du + \int 3sin \ x \ dx \\\\\implies\displaystyle \sf I = \int \dfrac{cos\ u}{3} du + \int 3sin\ x \ dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3}\int \dfrac{cos(u)}{3} + \int 3sin(x) dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3} sin(u) + C +\int 3sin(x) dx \\\\\implies\displaystyle \sf I = \dfrac{1}{3}sin(u) + C + 3\int sin(x) \ dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3}sin(u) + C + 3(-cos(x)+C) \\\\\implies \underset{\blue{\sf Required\ Answer }}{\underbrace{\boxed{\boxed{\displaystyle\red{\sf I = \dfrac{1}{3}sin(3x) - 3cos(x) + C }}}}}[/tex]
Answer:
[tex]\displaystyle \large{\frac{\sin 3x}{3} - 3\cos x + C}[/tex]
Step-by-step explanation:
We are given the indefinite integral:—
[tex]\displaystyle \large{\int (\cos 3x + 3\sin x) \ dx}[/tex]
Important Formulas
[tex]\displaystyle \large{\int f(ax+b) \ dx = \frac{1}{a} F(ax+b) + C}\\\displaystyle \large{\int \cos(ax) \ dx = \frac{1}{a} \sin (ax) + C \ \ \tt{(a \ \ is \ \ a \ \ constant.)}}\\\displaystyle \large{\int \sin x \ dx = - \cos x + C}\\\displaystyle \large{\int [f(x) \pm g(x)] \ dx = \int f(x) \ dx \pm \int g(x) \ dx}\\\displaystyle \large{\int kf(x) \ dx = k \int f(x) \ dx \ \ (\tt{k \ \ is \ \ a \ \ constant.})}[/tex]
Therefore, from the integral, apply the properties above:—
[tex]\displaystyle \large{\int (\cos 3x + 3\sin x) \ dx = \int \cos 3x \ dx + \int 3 \sin x \ dx}\\\displaystyle \large{\int (\cos 3x + 3\sin x) \ dx = \int \cos 3x \ dx + 3 \int \sin x \ dx}\\\displaystyle \large{\int (\cos 3x + 3\sin x) \ dx = \frac{1}{3} \sin 3x + 3\cdot -\cos x + C}\\\displaystyle \large{\int (\cos 3x + 3\sin x) \ dx = \frac{\sin 3x}{3} - 3\cos x + C}[/tex]
Hence, the solution is:—
[tex]\displaystyle \large \boxed{\frac{\sin 3x}{3} - 3\cos x + C}[/tex]
In basketball each basket scored from inside the 3 point line is worth 2 points. Each basket scored from outside the 3 point line is worth 3 points. Part B
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WITHIN THE NEXT 5 MIN I WILL GIVE U BRAINIEST
50 POINTS
1. Harold is at the bottom of the
Grand Canyon but he forgot his
phone at the top of the trail. We
decide to help him and lower his
phone to him. After the first
second, it is 16 feet closer to him,
after three seconds, it is 80 feet
closer to him. If the Grand
Canyon is 6000 feet deep, how
long will it take for the phone to
reach Harold?
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Opps, wrong answer
Deleted
A bakery makes a $5 profit for each cake it sells. It makes
a $6 profit for each pie it sells. The expression 5c+6p
represents the profit for selling c cakes and p pies. How
much profit is made if the bakery sells 10 cakes and 7 pies?
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Answer:
$92
Step-by-step explanation:
Find the profit by plugging in 10 as c and 7 as p into the expression:
5c + 6p
5(10) + 6(7)
50 + 42
= 92
So, the bakery will make $92
simplify: The question in photo
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Answer:
Step-by-step explanation:
A freshly isolatedsample of 90Y was found to have an activity of 8.9 x 105 disintegrations per minute at 1:00pm on December 3, 2003. At 2:15pm on Dec, 17, 2003, its activity was redetermined and found to be 2.6 x 104 disintegrations per minute. Calculate the half-life of 90Y.
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Answer:
3960 minutes
Step-by-step explanation:
From;
0.693/t1/2 = 2.303/t log No/N
t1/2 = half life of 90Y
No = initial activity of 90Y = 8.9 x 10^5 disintegrations per minute
N= activity of 90Y after time t = 2.6 x 10^4 disintegrations per minute
t = time taken
Since the time elapsed is 20,235 minutes, we substitute into the formula above.
0.693/t1/2 = 2.303/20235 log 8.9 x 10^5/2.6 x 10^4
0.693/t1/2 = 1.75 * 10^-4
t1/2 = 0.693/ 1.75 * 10^-4
t1/2 = 3960 minutes
A number is equal to half the sum of the same number and ten. Set up and equation and find that number.
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9514 1404 393
Answer:
n = n/2 + 1020Step-by-step explanation:
Let n represent the number. Then half the number is n/2. We are told that ...
n = n/2 +10 . . . . the number equals half the number plus 10
n/2 = 10 . . . . . . .subtract n/2
n = 20 . . . . . . . . multiply by 2
The number is 20.
please help me someone
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Base = 5 * 12 = 60 in^2
Height = 4 in
Perimeter is the sum of all straight
Perimeter = 20 + 16 + 48
Perimeter = 84 in
Perimeter of base = 12 * 2 + 5 * 2 = 34
Asap plzz,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
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so based on the given information, we can create an equation 150+25m=500
we can now solve for m
subtract 150
25m=350
divide by 25
m=350/25
m=350/25 which is option A
Find the probability that a randomly selected dog owner
spent $100 or more on health care and the dog was a
mixed breed. (Type your answer in SIMPLIEST form)
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4x+(3x+2)=3x(4+2)................................
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Can anyone help? ................
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there is a 90 and a 26 which equals 116
a line equals 180 degrees
you have to subtract 116 from 180
x=64
answer:
x = 64
step-by-step explanation:
in order to solve this, we have to add up all the angles given and subtract from 360° in order to find xwe subtract from 360° because a circle adds up to 360°since there is a square shown as an angle, it is 90°so we know that, 180 + 26 + x + 90 = 360°
now, we solve for x180 + 26 + x + 90 = 360°
296 + x = 360
x = 64°
A marketing research firm would like to survey undergraduate and graduate college students about whether or not they take out student loans for their education. There are different cost implications for the region of the country where the college is located and the type of degree. The survey cost table is provided below:
Student type
Region undergraduate graduate
East $10 $15
Central $12 $18
West $15 $21
The requirements for the survey are as follows:
The survey must have at least 1500 students.
At least 400 graduate students.
At least 100 graduate students should be from the West
No more than 500 undergraduate students should be from the East
At least 75 graduate students should be from the Central region
At least 300 students should be from the West
The marketing research firm would like to minimize the cost of the survey while meeting the requirements. Let X1 = # of undergraduate students from the East region, X2 = # of graduate students from the East region, X3 = # of undergraduate students from the Central region, X4 = # of graduate students from the Central region, X5 = # of undergraduate students from the West region, and X6 = # of graduate students from the West region.
Required:
Clearly state the problem (objective function, constraints)
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Answer:
Objective Minimize 10x1 +15x2 + 12x3+18x4+15x5+ 21x6
The central total cost $ 17586 due to the number of central undergraduate students 1458 is very high.
The total minimum cost would $ 17586 +$260+ $300= $ 18146
Step-by-step explanation:
Let
X1 = # of undergraduate students from the East region,
X2 = # of graduate students from the East region,
X3 = # of undergraduate students from the Central region,
X4 = # of graduate students from the Central region,
X5 = # of undergraduate students from the West region, and
X6 = # of graduate students from the West region.
Then the cost functions are
y1= 10x1 +15x2
y2= 12x3+18x4
y3= 15x5+ 21x6
According to the given conditions
The constraints are
x1 +x2 + x3+x4+ x5+ x6 ≥ 1500------- A
15X2 +18X4+21X6 ≥ 400---------B
21X6 ≥ 100
X6 ≥ 100/21
X6 ≥ 4.76
Taking
X6= 5
10X1 ≤ 500
X1 ≤ 500/10
X1≤ 5
18X4 ≥ 75
X4 ≥ 75/18
X4 ≥ 4.167
Taking
X4= 5
Putting the values
15X5+ 21X6 ≥ 300
15X5+ 21(5) ≥ 300
15X5+ 105 ≥ 300
15X5 ≥ 300-105
15X5 ≥ 195
X5 ≥ 195/15
X5 ≥ 13
Putting value of X6 and X4 in B
15X2 +18X4+21X6 ≥ 400
15X2 +18(5)+21(5) ≥ 400
15X2 +195 ≥ 400
15X2 ≥ 400-195
15X2 ≥ 205
X2 ≥ 205/15
X2 ≥ 13.67
Taking X2= 14
Now putting the values in the cost equations to check whether the conditions are satisfied.
y1= 10x1 +15x2
y1= 10 (5) + 15(14)= 50 + 210= $ 260
y3= 15x5+ 21x6
y3= 15 (13) + 21(5)
y3= 195+105= $ 300
x1 +x2 + x3+x4+ x5+ x6 ≥ 1500
5+14+x3+5+13+5≥ 1500
x3≥ 1500-42
x3≥ 1458
y2= 12x3+18x4
y2= 12 (1458) + 18 (5)
y2= 17496 +90
y2= $ 17586
The cost can be minimized if the number of students from
Undergraduate Graduate
East Region X1≤ 5 X2 ≥ 13.67
Central X3≥ 1458 X4 ≥ 4.167
West X5 ≥ 13 X6 ≥ 4.76
This will result in the required number of students that is 1500
Constraints:
East Undergraduate must not be greater than 5
East Graduate must not be less than 13
Central Undergraduate must be greater than 1458
Central Graduate must be greater than 4
West Undergraduate must be greater than 13
West Graduate must be greater than 4
The central total cost $ 17586 due to the number of central undergraduate students 1458 is very high.
The east region has a least cost of $260 and west region has a cost of $300.
The total minimum cost would $ 17586 +$260+ $300= $ 18146
PLEASE HELP ILL GIVE BRAINLIEST AND A THANKS
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Answer:
[tex]forth \: line \: - 5x - 3x + 3 = 6 \\ - 8x + 3 = 6 \\ - 8x = 3 \\ x = \frac{3}{ - 8} [/tex]
Find the surface area of the square pyramid.
S=
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HELP ASAP!!!!!!
Colin saved $30 in July, $21.50 in August, and $50 in September. He spent $18 on video games and $26.83 on books. How much money does Colin have left?
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= $56.67
the store is selling lemons at 0.53 each. each lemon yields about 2 tablespoons of juice. how much will it cost to buy enough lemons to make three 9inch lemon pies, each requiring half a cup of lemon juice?
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Answer:
$6.36
Step-by-step explanation:
3 pies require 3/2 cups of lemon juice
16 tablespoons = 1 cup
need 24 tablespoons of lemon juice
need 12 lemons at $0.53 each
total cost = 12 x 0.53 = $6.36
i need some help if you could
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Step-by-step explanation:
35A) arc AC = 360-(100+110+80)=
360-290 = 70°
35B) L D = ½× 70 = 35°
35C) L AEC = ½(100+70)=½×170= 85°
35D) L P = ½(100-70) = ½×30 = 15°
Of the sundaes recently sold at Ice Cream Haven, 4 had nuts and 20 did not. Considering this
data, how many of the next 84 sundaes sold would you expect to have nuts?
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(1/6)*84= 14 had nuts
20/24= 5/6
(5/6)* 84 = 70 no nuts
The expectation of having nuts in the 84 sundaes if 4 had nuts and 20 did not is 14.
What is division?It is a fundamental operation in mathematics where you divide a number into smaller parts.
Given:
The sundaes had nuts = 4,
Total sundaes = 24,
So from this the possibility of having nuts in sundae = 4/24 = 1 / 6,
Hence, in 84 sundaes the possibility of having nuts is = 1 / 6 × 84 = 14,
Therefore, the expectation of having nuts in the 84 sundaes is 14.
To know more about division:
https://brainly.com/question/27566440
#SPJ2
Find the volume of the cylinder. Find the volume of a cylinder with the same radius and double
the height.
The volume of the cylinder is __ in.³.
The volume of a cylinder with the same radius and double the height is __ in.³.
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about 78.54
V=π·5^2·1 = 78.54
Answer:
Find the volume of the cylinder.
[tex]\star \: \: \purple{Volume_{(cylinder)} = \pi {r}^{2} h}[/tex]
[tex]\star \: \: \purple{Volume_{(cylinder)} = 3.14 \times ( {5)}^{2} \times 1 }[/tex]
[tex]\star \: \: \purple{Volume_{(cylinder)} =3.14 \times 25 \times 1 }[/tex]
[tex]\star \: \: \purple{Volume_{(cylinder)} =78.50 \: in {}^{3} }[/tex]
Find the volume of a cylinder with the same radius and double the height.
[tex]\star \: \: \purple{Volume_{(cylinder)} = \pi {r}^{2} h}[/tex]
[tex]\star \: \: \purple{Volume_{(cylinder)} = 3.14 \times {(5)}^{2} \times 2}[/tex]
[tex]\star \: \: \purple{Volume_{(cylinder)} = 3.14 \times 25 \times 2}[/tex]
[tex]\star \: \: \purple{Volume_{(cylinder)} = 157 \: in {}^{3} }[/tex]
Find the perimeter of a
hexagon with each side
measuring 184 ft.?
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Answer:
P = 1104
a - Side
Step-by-step explanation:
P = 1104
a - Side
Answer:
P=1140
Step-by-step explanation:
P=1140 BANANA SORRY THE ANSWER I DONT HAVE IT BUT HAVE A GOOD DAY
If the standard deviation of the data values in a sample is 13, what is the
variance of the data values?
A. 169
B. 225
C. 289
D. 361
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Answer:
A. 169 is the correct answer
A ski resort claims that there is a 75% chance of snow on any given day in January and that snowfall happens independently from one day to the next. A family plans a four-day trip to this ski resort in January. Let X represent the number of days it snows while the family is there. What are the mean and standard deviation of X?
Option Choices:
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Answer:
Its D
Step-by-step explanation:
Using the binomial distribution, it is found that the mean and the standard deviation of X are given as follows:
[tex]\mu_X = 3, \sigma_X = 0.87[/tex]
What is the binomial probability distribution?The expected value of the binomial distribution is:
[tex]\mu_X = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sigma_X = \sqrt{np(1-p)}[/tex]
In this problem, the proportion and the sample size are given as follows:
p = 0.75.n = 4.Hence, the mean and the standard deviation are given by:
[tex]\mu_X = np = 4(0.75) = 3[/tex]
[tex]\sigma_X = \sqrt{np(1-p)} = \sqrt{4(0.75)(0.25)} = 0.87[/tex]
More can be learned about the binomial distribution at https://brainly.com/question/24863377
#SPJ2
Find the volume of this solid figure. Use π = 3.14.
WITH SOLUTION PLEASE AND NO LINKS!
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Step-by-step explanation:
you can get simply V= ABh πr^2 h π3.14^2 x 17.9 then you get the answer Ihope I can help you
what is the lenght of rectangle whose area is 240cm
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Answer:
16
Step-by-step explanation:
I don't know how to explain but it is 16
Answer:
Since the Width (W) of the rectangle is not given, the answer would be Length (L) = 240/W
Step-by-step explanation:
A = L*W
240 = L*W
240/W = L
Eight members of a school marching band are auditioning for 3 drum major
positions. How many ways can students be chosen to be drum major?
*
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Answer:
Step-by-step explanation:
Which equation shows 3/4 x+1/2y=1/8 converted to slope intercept form?
A. Y=3/2x-1/4
B.Y=-3/8x+1/16
C. Y=3/8x-1/16
D.Y=-3/2x+1/4
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Answer:
D
Step-by-step explanation:
Please i need help over here
Two dice are tossed simultaneously, what is the probability that?
1. sum oc the out come is more than 7?
2. the sum of the square of individual outcome is less than 20?
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Answer:
5 / 12
11 / 36
Step-by-step explanation:
The sample space for 2 dice = 6² = 36
Number of outcomes where sum is less than 7 = 15
Probability = required outcome / Total possible outcomes
P(obtaining a sum less Than 7) = 15 / 36 = 5/12
Number of outcomes where Sum of individual outcome is less than 20 = 11
P(sum of individual outcome less than 20) = 11/ 36
A 10 foot ladder is leaning against a building. It forms a 30 degree angle with the ground. How far away from the building is the foot of the ladder? Round your answer to the nearest hundredth. 5 feet, 5.77 feet, 8.66 feet, or 20 feet
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x = 8.66 ft
Step-by-step explanation:
cos 30 = adj/hyp = x/10
---> x = (10 ft)cos30
= 8.66 ft
2. If an older television with an aspect ratio of 4:3 has a screen area of 1550 square inches, but the image displayed has an aspect ratio of 16:9, how much area does the image actually occupy? First determine what percent of the screen does the image occupy?
a. 825.5 sq. in.
b. 1162.5 sq. in.
c. 1181.5 sq. in.
d. 1375.5 sq.in.
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If not let me know