Answer:
[tex]\displaystyle \int\limits^{\pi/2}_ {0} \,(t^2-3t)\sin t\, dt = \pi -5[/tex]
Step-by-step explanation:
We want to evaluate the integral:
[tex]\displaystyle \int\limits^{\pi/2}_ {0} \,(t^2-3t)\sin(t)\, dt[/tex]
Since this is a product of two functions, we can use Integration by Parts. Recall that:
[tex]\displaystyle \int u\, dv = uv - \int v\, du[/tex]
Let u be t² - 3t and let dv be sin(t).
Thus:
[tex]du = 2t - 3\, dt[/tex]
And:
[tex]\displaystyle v = \int \sin t\, dt = - \cos t[/tex]
So:
[tex]\displaystyle =\left(-\cos t\right)\left(t^2-3t\right)\Bigg|_0^{\pi/2}-\int_{0}^{\pi/2} \left(-\cos t\right)\left(2t-3\right)\, dt[/tex]
Simplify:
[tex]\displaystyle = - \left(\cos t\right)(t^2-3t)\Bigg|_{0}^{\pi /2}+\int\limits^{\pi/2}_ {0} \,\cos(t)(2t-3)\, dt[/tex]
We can use IBP once more.
Let u be 2t - 3 and let dv be cos(t). Therefore:
[tex]du = 2\, dt[/tex]
And:
[tex]\displaystyle v = \int \cos t\, dt = \sin t[/tex]
So:
[tex]\displaystyle = - \left(\cos t\right)(t^2-3t)\Bigg|_0^{\pi/2}+\left(\sin(t)(2t-3)\Bigg|_0^{\pi /2}-\int\limits^{\pi/2}_0 \, 2\sin(t)dt \right)[/tex]
Evaluate:
[tex]\displaystyle =-\left(\cos t\right)(t^2-3t)+\sin(t)(2t-3)+2\cos(t)\Bigg|_0^{\pi /2}[/tex]
Evaluate the first section:
[tex]\displaystyle \begin{aligned} &= -\cos\left(\frac{\pi}{2}\right)\left(\left(\frac{\pi}{2}\right)^2-3\left(\frac{\pi}{2}\right)\right)+\sin\left(\frac{\pi}{2}\right)\left(2\left(\frac{\pi}{2}\right)-3\right)+2\cos \left(\frac{\pi}{2}\right)\right) \\ \\ &= (0) + (1)(\pi -3) + (0) \\ \\ &= \pi -3 \end{aligned}[/tex]
And the second:
[tex]\displaystyle \begin{aligned} &= -\cos(0)((0)^2-3(0))+(\sin(0))(2(0)-3)+2\cos(0 ) \\ \\&=(0)+(0)+(2) \\ \\ &= 2\end{aligned}[/tex]
Therefore:
[tex]\displaystyle \int\limits^{\pi/2}_ {0} \,(t^2-3t)\sin(t)\, dt = (\pi -3) -(2) = \pi -5[/tex]
A tortoise and a hare are competing in a 2000-meter race. The arrogant hare decides to let the tortoise have a 510-meter head start. When the start gun is fired the hare begins running at a constant speed of 8 meters per second and the tortoise begins crawling at a constant speed of 6 meters per second. -Let t represent the number of seconds that have elapsed since the start gun was fired. 1) Write an expression in terms of t that represents the hare's distance from the starting line (in meters) 2) Write an expression in terms of t that represents the tortoise's distance from the starting line (in meters) 3) Write an expression in terms of t that represents the number of meters the tortoise is ahead of the hare.
Answer:
1. 8t
2. 510 + 6t
3. 510 - 2t
Step-by-step explanation:
1. Since the hare moves at a speed of 8 metres per second, the distance it moves from the starting line is d = speed × time = 8t
2. Since the rabbit moves at a speed of 6 metres per second, and gets a head start of 510 metres, the distance it moves from the starting line is d = 510 m + speed × time = 510 + 6t
3. The distance the tortoise is ahead of the hare is thus, distance moved by rabbit - distance moved by hare in time, t.
d' = 510 + 6t - 8t
= 510 - 2t
15 POINTS FOR CORRECT PERSON!! PLEASE HELP The product (5+ i ) (5-i) is a real number, 26. What are the factors (5+i) and (5-i) called? Imaginary units Complex conjugates Imaginary numbers Or complex numbers?
Answer:
Complex numbers
Step-by-step explanation:
Given
[tex](5 + i)[/tex] and [tex](5 - i)[/tex]
Required
Determine what both factors are called
From the list of given options. option "complex numbers" answer the question correctly
This is because when numbers are written in form [tex]a + bi[/tex] where [tex]b \neq 0[/tex] and [tex]i = \sqrt{-1}[/tex]; such a number are referred to as complex number
Some other examples are:
[tex]-7 + 3i[/tex]
[tex]2 - 7i[/tex]
[tex]4 + i[/tex]
And lots more
Write the equation 9y=12x+0.2 in standard form identify A B C
Answer:
60x-45y=-1
A = 60
B = -45
C =-1
Step-by-step explanation:
[tex]9y=12x+0.2\\Re-write\:0.2\:as\:1/5-12x =-9y+\frac{1}{5} \\\\Multiply\:all \:terms \:by\:-1\\-1(-12x=-9y+1/5)\\\\12x =9y-\frac{1}{5} \\\\Multiply\: through\: by \:5\\5(12x =9y - \frac{1}{5} )\\\\60x = 45y -1\\\\60x-45y =-1[/tex]
16x^2-1=0
help algebra 2
Answer:
16x²=1
x²=1/16
x=√(1/16)
x=+- (1/4)
what five parts make up a data table
Answer:
Step-by-step explanation:
Check boxes.
Sorting (on columns)
Icons that communicate alerts.
Pagination.
Headers Row.
Find an equation of a plane through the point (3, 0, 2) which is orthogonal to the linex=?2+3t,y=2+4t,z=?1?3tin which the coefficient of x is 3.
Answer: 3x + 4y - 3z - 3 = 0
Step-by-step explanation:
with the given point (3, 0, 2), the plane is orthogonal to this line so it
has directional ratios (3, 4, -3)
therefore the given equation can be written as;
(x+2)/3 = (y-2)/4 = (z+1)/-3
so equation of the plane passing through point x1, y1 and z1 in the one point form is given as;
a(x-x1) + b(y - y1) + c(z -z1) = 0
abc represent the direction ratio
so we substitute
3(x-3) + 4(y-0) + (-3(z-2)) = 0
3x - 9 + 4y - 0 - 3z + 6 = 0
3x + 4y - 3z - 3 = 0
therefore the equation of the plane through the point is 3x + 4y - 3z - 3 = 0
drag each statement to show it true,based on the graph.
Answer:
1). Cinnamon costs $7 per one pound
2). Price per pound of the cinnamon equals $[tex]\frac{5.25}{0.75}[/tex].
Step-by-step explanation:
x-values on the graph define the weight of cinnamon and y-values define the price.
Slope of the line drawn from the origin (0, 0) and (0.75, 5.25) will determine the per lb price of the cinnamon.
Slope of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] will be,
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
If the points on the given line re (0,0) and (0.75, 5.25),
Slope = [tex]\frac{5.25-0}{0.75-0}[/tex]
= 7
Therefore, two options are the correct options.
1). Cinnamon costs $7 per one pound
2). Price per pound of the cinnamon equals $[tex]\frac{5.25}{0.75}[/tex].
ILL GIVE YOU BRAINLIST !!!
Evaluate the expression given the replacement values.
Answer:
24
Step-by-step explanation:
[tex]a^{2}[/tex]= 49 because any number squared is positive.
Since b=2,
2(-4)= -8.
Then this is 49-8-17, which equals 24.
Answer:
24
Step-by-step explanation:
Wayne flips a weighted magic trick coin 100 times. If the coin landed on heads just 19 times out of 100 , how many times is the coin expected to land on tails out of 800 flips? (Hint: the probability that the coin will land on heads is not equal to 0.5 .) A 152 B 648 C 800 D 912
Answer:
152 (Answer A)
Step-by-step explanation:
The experimental probability of obtaining a head is 19/100, or 0.19.
If the coin is flipped 800 times, the expected number of heads will thus be:
0.19(800 flips) = 152 (Answer A)
Find the domain of the function.
f(x)=9x+7
What percent of 150 is 33.5?
Answer:
22.33
Step-by-step explanation:
x%(150)=33.5
x/100 x 150=33.5
x/2 x 3=33.5
x=2/3 x 33.5
x=67/3
x=22.33
Answer:
Click at the above pic and the ans will appear.
Hope it helps :)
Alisa types 900 words in 20 minutes. What is her typing speed words per minute?
Answer:
45 words per minute!
Step-by-step explanation:
Divide 900 by 20!
Answer:
Her typing speed is 45 word per minute
Step-by-step explanation:
20x = 900
divided 20 on both sides
x = 45
A(-2, 1), B(-4,-1), and C(0, -1) and is
reflected in the line x = 2.
What is the coordinate of C'?
EVALUATE !!!! ILL GIVE YOU BRAINLIST HAVE TO GET IT RIGHT !!!!
N = 3/4 , x = 8 , y = 6 , m = 3
Answer:
12Step-by-step explanation:
[tex]nxy\div m\\\\n =3/4\\x =8\\y =6\\m=3\\\\\frac{3}{4} \times 8 \times 6 \div 3\\\\\mathrm{Divide\:the\:numbers:}\:6\div \:3=2\\=\frac{3}{4}\times \:8\times \:2\\\\\mathrm{Convert\:element\:to\:fraction}:\quad \:8=\frac{8}{1}\\=2\times \frac{3}{4}\times \frac{8}{1}\\\\\mathrm{Convert\:element\:to\:fraction}:\quad \:2=\frac{2}{1}\\=\frac{3}{4}\times \frac{8}{1}\times \frac{2}{1}\\\\Multiply\:fractions\\=\frac{3\times \:8\times \:2}{4\times \:1\times \:1}\\\\=\frac{48}{4}\\\\Simplify\\=12[/tex]
Answer:
it is 12
Step-by-step explanation:
3/4×8×6÷3=12
I HOPE this help plz mark me as brainliest
mike, dave and john worked for a total of 56 hours. Dave worked 6 more than 4 times as many hours as mike. John worked 6 less than 3 times as many hours as Mike. How long did Dave work?
Answer:
1. Dave worked for 34 hours.
2. Perimeter of the rectangle is 172 cm.
Step-by-step explanation:
1. Determination of the hours Dave worked.
Let D represent Dave.
Let M represent Mike.
Let J represent John.
Tota time worked by Dave, Mike and John is 56 hours. This can be written as:
D + M + J = 56 ..... (1)
Dave worked 6 more than 4 times as many hours as Mike. This can written as:
D = 6 + 4M .....(2)
John worked 6 less than 3 times as many hours as Mike. This can be written as:
J = 3M – 6 ........ (3)
Substituting the value of F and J into equation 1, we have:
D + M + J = 56
D = 6 + 4M
J = 3M – 6
6 + 4M + M + 3M – 6 = 56
6 – 6 + 4M + M + 3M = 56
8M = 56
Divide both side by 8
M = 56/8
M = 7
Substitute the value of M into equation (2) to obtain the value of D.
D = 6 + 4M
M = 7
D = 6 + 4(7)
D = 6 + 28
D = 34
Therefore, Dave worked for 34 hours .
2. Determination of the perimeter.
Length (L) = 64 cm
Width (W) = 22 cm
Perimeter (P) =?
P = 2(L + W)
P = 2 (64 + 22)
P = 2 (86)
P = 172 cm
Therefore, the perimeter of the rectangle is 172 cm
Find an equation of the plane.
The plane through the point (1, -1, - 1 ) and parallel to the plane 5x - y - z = 6
Answer: equation of the plane is 5x - y - z - 7 = 0
same as ( 5x - y - z = 7 )
Step-by-step explanation:
Given data;
5x - y - z = 6
therefore vector of plane is n° = ( 5, -1, -1)
so equation will be
n°(x-x₀, y-y₀, z-z₀) = 0
( 5, -1, -1) (x-x₀, y-y₀, z-z₀) = 0
5(x- (1)) -1(y - (-1)) -1(z - (-1)) = 0
5x - 5 - y - 1 - z - 1 = 0
5x - y - z - 7 = 0
Therefore equation of the plane is 5x - y - z - 7 = 0
same as ( 5x - y - z = 7 )
If John has drank three drinks per day how many will he have drank in 3 day's?
Answer:
9 drinks
Step-by-step explanation:
3+3+3=9
Or 3*3=9
Answer:
9
Step-by-step explanation:
TUV = 9x + 1 TUW = 7x-9 WUV 5x-11
Answer:
7
Step-by-step explanation:
9x + 1 = 7x - 9 + 5x - 11
9x + 1 = 12x - 20
9x + 1 - 1 = 12x - 20 - 1
9x = 12x - 21
9x - 12x = 12x - 12x -21
-3x = -21
-3x/3 = -21/-3
x = 7
Hope that helps!
Six classes of 31,28,27,32,24 and 26 students are to travel on buses that each hold 36 students. How many buses are needed?
Answer:
5 buses
Step-by-step explanation:
You add all the students up to get 168, because that's the total number of students, and divide it by 36. The buses can only carry 36 people, so you will need 4.666 buses, but you can't have 0.666 of a bus, so you will need 5 buses to fit everyone.
Veronica has been wanting to learn to ice skate for years!
When the Glacier Zone Ice Rink opened, Veronica bought 12
ice-skating lessons during their grand-opening sale. Veronica
paid $305.40 in all. How much did each lesson cost?
Answer:
25.45 per lesson
Step-by-step explanation:
divide $305.40 by 12
Inferential statistics allow you to decide whether a difference between the experimental and the control group is due to:________
a. manipulation; chance
b. manipulation; experimental error
c. sampling error; independent variable
d. independent variable; experimental error
Answer:
Option (A)
Step-by-step explanation:
There are 2 main branches of statistics. They are:
1. Descriptive Statistics
2. Inferential Statistics
Descriptive statistics describes the characteristics of observed subjects or items while Inferential statistics makes inferences, based on given or derived data.
Inferential Statistics allow you to decide whether a difference between the experimental group and control group is due to manipulation or chance.
The Experimental group is the group that an effect is tested on while the Control group is the group that is left untested or uninfluenced. Inferential statistics allow you to decide whether a difference between these 2 groups is due to
- manipulation or interference by any force (which may be the experimenter/researcher)
or
- probability which is chance.
Option a. manipulation; chance
Inferential statistics is a statistical method for estimating the characteristics of a larger population from a small but representative sample. In other words, it enables the researcher to make generalizations about a larger group based on a smaller subset of that group.
Inferential statistics allow you to decide whether a difference between the experimental and the control group is due to a. manipulation; chance
For more information:
https://brainly.com/question/20982963?referrer=searchResults
Drag the fraction that is equivalent to each repeating decimal. Each fraction may be used only once.
Answer:
Step-by-step explanation:
The easiest way to do any of these is to put the fraction into your calculator and see what comes up.
So for 32/9 you get 3.5555555555 which is the same as 3.5 with a bar over it.
7/30 is the same as .23333333333 which is the same as 0.23 with a bar over the three.
5/3 = 1.6666666 which is 1.6 with a bar over the 6
4/9 is 0.4444444 which is the same as 0.4 with a bar over the 4.
What is the quotient of 8,595 ÷ 24?
a. 334 R 3
b. 334 R 7
c. 358 R 3
d. 358 R 7
help please! and fast.
Answer:
358.125
Step-by-step explanation:
Your welcome!
4(z – 2) + 3z
Need help
Answer:
5z-8
Step-by-step explanation:
(8z-8)+3z=
5z-8
Answer:
z-8
Step-by-step explanation:
4(z -2)+3z
4z -8 +3z
-3 -3
z -8
(4 - 7m) - (-n + 2m - 1) pls helppp
Step-by-step explanation:
4 - 7m + n - 2m + 1
5 + 5m + n
i think is complicated
HURRRRYYYYYYY PLEASE Write the equation of the line that passes through the points (-8,-1) and (5,−7). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Answer:
y + 8 = 2x + 2
Step-by-step explanation:
Use the points given to find the slope. Divide the difference in y-values by the difference in x-values.
(-1) - (-7) = 6
5 - (-8) = 3
6/3 = 2
The slope is 2.
Now, pick one of the points to put in point-slope form. It doesn't matter which. You will get the right answer either way. I will use (-1, -8).
y - y₁ = m(x - x₁)
y - (-8) = 2(x - (-1))
y + 8 = 2(x + 1)
y + 8 = 2x + 2
Write each improper fraction as a mixed number in simplest form -72/27=
What is the difference between math content and math skills
Answer
B
Step-by-step explanation:
Took quiz
which of the following verifies that triangle YXZ is similar to triangle QPR?
Answer:
AA postulate
Step-by-step explanation:
Because both the angle are identical?
What the of x is in 3x+5=12
Answer: 2.333
Step-by-step explanation:
Subtract 5 from both sides of equation
Divide each side of equation by 3