Answer:
700
Step-by-step explanation:
Answer:
700
Step-by-step explanation:
7 hundred in standard form is 700.
Evaluate:
[tex] \int \limits^{2}_{1} { \sin }^{3} x. \cos(2x) dx[/tex]
hello, anyone can help me if you don't mind, I am getting confused.
Thanks, I really appreciate
Recall some identities:
sin²(x) + cos²(x) = 1
cos(2x) = cos²(x) - sin²(x)
and from the first identity, you can establish that
cos(2x) = 2 cos²(x) - 1
So, rewrite the integrand as much as possible in terms of cos(x) :
[tex]\sin^3(x) \cos(2x) = \sin(x) \sin^2(x) (\cos^2(x)-\sin^2(x)) \\\\ \sin^3(x) \cos(2x) = \sin(x) (1-\cos^2(x)) (2\cos^2(x) - 1)[/tex]
Then in the integral, substitute u = cos(x) and du = -sin(x) dx. With some rewriting, you end up with
[tex]\displaystyle \int_1^2 \sin^3(x) \cos(2x) \,\mathrm dx = -\int_{x=1}^{x=2} (1-\cos^2(x))(2\cos^2(x)-1) (-\sin(x)\,\mathrm dx) \\\\ = -\int_{u=\cos(1)}^{u=\cos(2)} (1-u^2)(2u^2-1)\,\mathrm du \\\\ = \int_{\cos(1)}^{\cos(2)} (1-3u^2+2u^4) \,\mathrm du \\\\ = \left(u-u^3+\frac25u^5\right)\bigg|_{\cos(1)}^{\cos(2)} \\\\ = \left(\cos(2)-\cos^3(2)+\frac25\cos^5(2)\right) - \left(\cos(1)-\cos^3(1)+\frac25\cos^5(1)\right) \\\\ = \boxed{\cos(2) - \cos^3(2) + \frac 25 \cos^5(2) - \cos(1) + \cos^3(1) - \frac25 \cos^5(1)}[/tex]
What is the value of (x – 3) if – 5(3x – 9) = -15?
The value of the required expression (x- 3 ) using the given equation -5(3x - 9) = -15 is equal to 1.
Let's solve for the value of "x" in the given equation:
-5(3x - 9) = -15
First, distribute the -5 on the left side of the equation:
-15x + 45 = -15
Now, subtract 45 from both sides to isolate the term with "x":
-15x = -60
Divide both sides by -15 to solve for "x":
x = 4
Now that we have the value of "x," we can find the value of (x - 3):
x - 3
= 4 - 3
= 1
Therefore, the value of (x - 3) is 1.
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divide 8 1/2 by the positive difference 4 4/5 and 7 7/10
[tex]\\ \sf\longmapsto 8\dfrac{1}{2}\div \left(4\dfrac{4}{5}-7\dfrac{7}{10}\right)[/tex]
[tex]\\ \sf\longmapsto \dfrac{17}{2}\div \left(\dfrac{24}{5}-\dfrac{77}{10}\right)[/tex]
[tex]\\ \sf\longmapsto \dfrac{17}{2}\div\left(\dfrac{48-77}{10}\right)[/tex]
[tex]\\ \sf\longmapsto \dfrac{17}{2}\div \left(\dfrac{29}{10}\right)[/tex]
[tex]\\ \sf\longmapsto \dfrac{17}{2}\times \dfrac{10}{29}[/tex]
[tex]\\ \sf\longmapsto \dfrac{17(10)}{2(29)}[/tex]
[tex]\\ \sf\longmapsto \dfrac{170}{58}[/tex]
[tex]\\ \sf\longmapsto \dfrac{85}{29}[/tex]
[tex]\\ \sf\longmapsto 2\dfrac{27}{29}[/tex]
Answer:
2 27/29Step-by-step explanation:
The positive difference is the result of subtraction of the smaller number from the greater number.
The positive difference of 4 4/5 and 7 7/10 is:
7 7/10 - 4 4/5 = 77/10 - 48/10 = 29/10Now division:
8 1/2 : 29/10 = 17/2 * 10/29 = 85/29 = 2 27/2918. If geeta saves 40% of his monthly income and she spends Rs. 15000 every month, find her monthly income
Answer:
Her monthly income is Rs. 21000
Step-by-step explanation:
15000 x ( 1 + 40 % )
= 15000 x 140 %
= 21000
Find the volume of the cylinder.
Either enter an exact answer in terms of it or use 3.14 for T.
Answer:
188 units cubed
Step-by-step explanation:
0.189 divided by 1.75=
Explain your answer
Answer:
0.189x1000=189
1.75x1000=1750
189÷1750 = 0.108
The winning team's score in 5 high school basketball games was recorded. If the sample mean is 62.3 points and the sample standard deviation is 11.0 points, find the
98% confidence interval of the true mean.
A) 57.4 < µ < 67.2 B) 50.8 < µ < 73.8
C) 25.4 < µ < 99.2 D) 43.9 < µ < 80.7
Answer:
This is 3.747*11/sqrt(5)=18.4
the interval is (49.9,86.7), the SE added to and subtracted from the mean.
It is B
Thank You
HELP PLEASE I WOULD REALLY APPRECIATE IT - Ken can run m miles
at a pace of 6.30
minutes per mile. He
ran slower for 10
minutes to warm up.
Write an equation
that represents the
total time, t, Ken
spent running.
Answer:
keep can run millions at 30 friends all for 10 minutes for what purpose for running running of the steelers versus the dynasties of running of the
work ou the value of 19+7÷2-5
helllppp pls
Answer:
17 1/2
Step-by-step explanation:
19+7÷2-5
Solve using PEMDAS
Divide first
19 + 7/2 -5
Then add and subtract from left to right
Getting a common denominator
38/2 + 7/2 - 10/2
45/2 - 10/2
35/2
17 1/2
Volumeofasphere = ar A Walmart employee has decided that they would like to completely fill the
ball bin in the toy section with one type of ball.
The ball he decided to use had a radius of 16 cm. The ball bin is 210 centimeters tall and the opening at the
top is 150 centimeters by 150 centimeters. How many balls should fit inside the bin?
Number of balls should fit inside the bin are 216 balls.
Given:
Radius of spherical ball = 16 cm
Height of cylinder = 210 cm
Diameter of opening = 150 cm
Find:
Number of balls should fit inside the bin
Computation:
Volume of sphere = [tex][\frac{4}{3}] [\pi ][r^3][/tex]
Volume of sphere ball = [tex][\frac{4}{3}] [\pi ][16^3][/tex]
Volume of sphere ball = 17164.19 cm³
Radius of cylinder = Diameter of opening / 2
Radius of cylinder = 150 / 2
Radius of cylinder = 75 cm
Volume of cylinder = [tex][\pi ][r^2][h][/tex]
Volume of cylinder = [tex][\pi ][75^2][210][/tex]
Volume of cylinder = 3,712,500 cm³
Number of balls should fit inside the bin = Volume of cylinder / Volume of sphere ball
Number of balls should fit inside the bin = 3,712,500 / 17,164.19
Number of balls should fit inside the bin = 216.293
Number of balls should fit inside the bin = 216 balls (Approx.)
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Multiply.
(b - 7)(2b +9)
(b - 7)(2b +9)=(Simplify your answer.)
Answer:
[tex]2 {b}^{2} - 5b - 63[/tex]
Step-by-step explanation:
[tex](b - 7) \times (2b + 9)[/tex]
[tex]b \times 2b + 9b - 7 \times 2b - 7 \times 9[/tex]
[tex]2 {b}^{2} + 9b - 14b - 63[/tex]
[tex]2 {b}^{2} - 5b - 63[/tex]
b^3-21/5b+9 when b = 3
Answer:
-21b + 180 / 5
Step-by-step explanation:
Hey there!
b^3 - 21/5b + 9
= 3^3 - 21/5(3) + 9
= 27 - 63/5 + 9
= 72/5 + 9
= 117/5
Answer: 117/5
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
The subtotal amounts of a telephone bill are as follows. Find the grand amount if the service charge is 10% and VAT is 13%. (a) Rs 5000 (b) Rs 6000 (c) Rs 3000
Answer:
............................. ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,____________Step-by-step explanation:
I don't know
A total of 574 tickets were sold for the school play. They were either adult tickets or student tickets. There were 74 more student tickets sold than adult tickets. How many adult tickets were sold?
Answer:
411 #
Step-by-step explanation:
solution :
Let x = the number of adult tickets sold
Let x + 61 = the number of student tickets sold
x + x + 61 = 761
2x = 700
x = 350
x + 61 = 411
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6 less than 8 times a number (x) is equal to 14
Answer:
8x-6=14
Step-by-step explanation:
Whenever you see less next to a number, you know it's gonna be -6. If it said 6 minus 8x though, then you would do 6-8x etc. Hope this helped.
What is the volume of the following rectangular prism?
Answer:
[tex]volume \: of \: rectangular \: prism = base \: area \: \times height \\ \\ = length \times width \times height[/tex]
is 9.407 a natrual number?
Answer:
Sorry about that, I did not see the decimal. As liamly said, it is positive but is not a natural number because of the decimal.
Step-by-step explanation:
help me do this plz brainiest to whoever right
Answer:
3.16 miles
Step-by-step explanation:
Hi there!
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] where two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
We're given that the campsite is located at (1,7) and the checkpoint station is located at (4,6). We must calculate the distance between them. Plug these points into the formula:
[tex]d=\sqrt{(x_2-1)^2+(y_2-7)^2}\\d=\sqrt{(4-1)^2+(6-7)^2}\\d=\sqrt{(3)^2+(-1)^2}\\d=\sqrt{9+1}\\d=\sqrt{10}\\d\approx3.16[/tex]
Therefore, the distance between the campsite and the checkpoint is 3.16 miles when rounded to the nearest hundredth.
I hope this helps!
The sixth grade teachers bought food for a reward party. They purchased 64 bags of chips and 80 bottles of water . What is the largest number of students that can be invited to the party so they each get the same amount of chips and water?
Answer:
64
Step-by-step explanation:
Since each student must get the same amount of chips and water, the ratio of the number of chips to water received by each student is 1:1.
Hence, a maximum of 64 students can be invited to the party, as the bags of chips is lower than that of the number of bottles of water, and we take it as a 64.
2x + 3y = 6
The equation x + 2y = 16 is in standard form.
What is the slope of the line?
3y = -2x + 6
X-2
6
3
-1
y y=-3x +
y= - +
O
-0.5
+2
O
0.5
9514 1404 393
Answer:
(c) -0.5
Step-by-step explanation:
Starting from standard form ...
ax +by = c
and solving for y, we get the slope-intercept form ...
y = (-a/b)x +c/b
The coefficient of x is the slope: -a/b.
For your equation x+2y=16, the slope is -1/2 = -0.5.
What is the following difference?
230 192ab -5 V81365
solve the equation 6 = 5 x -2
Answer:
8/5 = x
Step-by-step explanation:
6 = 5x - 2
~Add 2 to both sides
8 = 5x
~Divide 5 to both sides
8/5 = x
Best of Luck!
PLEASE ANSWER QUICK 70 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Identify the property that justifies each step asked about in the answer area below.
Line 1: (9+x)x
Line 2: x(9+x)
Line 3: x(x+9)
Line 1 to Line 2:______________
Line 2 to Line 3:_______________
Answer:
The answer above me is correct!
Step-by-step explanation:
Give them BRAINLIEST! have a good day<3 :)
4x-2=18x+5
Show ur work
Step-by-step explanation:
[tex]4x - 2 = 18x + 5[/tex]
Collect like terms and simplify
[tex] - 2 - 5 = 18x - 4x \\ - 7 = 14x[/tex]
Divide both sides of the equation by 14
[tex] \frac{ - 7}{14} = \frac{14x}{14} \\ - \frac{1}{2} = x[/tex]
Answer:
x = -1/2
Step-by-step explanation:
4x-2=18x+5
-2-5=18x-4x
-7=14x
-7/14=14/14x
-1/2=x
evaluate the expression when x=3
Answer:
3. 15
6. 4
Step-by-step explanation:
Put 3 instead of x
3. 5x
= 5 × 3
= 15
6. 12 ÷ x
= 12 ÷ 3
= 4
Answer:
When X is 3 it will be
5(3)=15
Then for the second one it will be 12/3
The answer is 4
Hope I helped
Alguien me ayuda con esto?
Answer:
x=10
Step-by-step explanation:
10 a 8 son dos, entonces 14 ax es 4
Answer:
La explicación sería:
//////////////////////////
=> 9 * 2 + 4/2 = 20
=> 18 +2 =20
=> 20 =20
//////////////////////////
=> 5*2 + 8/2 = 14
=> 10 +4 =14
=> 14 =14
//////////////////////////
=> 3*2 + 10/2 = x
=> 6 + 5 = x
=> 11 = x
someone to help me complete this and explain how to do it, please
42x2 y4 − 41xyz3
Answer:
use cymath
Step-by-step explanation:
(08.01, 08.02, 08.03 HC)
Create a factorable polynomial with a GCF of 2. Rewrite that polynomial in two other equivalent forms. Explain how each form was created. (10 points)
Answer:
See the image for solution
Hope it helps
Have a great day
Approximately 54% of mathematics students do their homework on time. In a class of 250 students, what is the mean, variance, and standard deviation if we assume normality and use the normal distribution as an approximation of the binomial distribution
Answer:
135
Step-by-step explanation:
250 x 54%=135
y + (2/25) = 11/15
What’s y
Answer:
[tex]\frac{49}{75}[/tex]
Step-by-step explanation:
y= [tex]\frac{11}{15}[/tex]-[tex]\frac{2}{25}[/tex]
y= [tex]\frac{49}{75}[/tex]
Answer:
49/75
Step-by-step explanation:
y + 2/25 = 11/15
now, we could do it like the other answer and do fraction arithmetic, or we try and multiply everything out to eliminate the fractions :
15y + 30/25 = 11
375y + 30 = 275
375y = 245
y = 245/375 = 49/75
the same result, of course, but a slightly different way to get there.