Answer:
0.44237 units
Step-by-step explanation:
Given
[tex]v(t) = e^t*sin(e^t)[/tex]
[tex]0 \le t \le \frac{\pi}{2}[/tex]
Required
The distance traveled in this interval
We have:
[tex]v(t) = e^t*sin(e^t)[/tex]
The distance is calculated as:
[tex]d(t) = \int\limits^a_b {v(t)} \, dt[/tex]
So, we have:
[tex]d(t) = \int\limits^{\frac{\pi}{2}}_0 {e^t*sin(e^t)} \, dt[/tex]
Let:
[tex]u = e^t[/tex]
Differentiate
[tex]\frac{du}{dt} = e^t[/tex]
So:
[tex]dt = e^{-t} du[/tex]
So, we have:
[tex]d(t) = \int\limits^{\frac{\pi}{2}}_0 {e^t*sin(e^t)} \, dt[/tex]
[tex]d(t) = \int\limits^{\frac{\pi}{2}}_0 {e^t*sin(u)} \, e^{-t} du[/tex]
Rewrite as:
[tex]d(t) = \int\limits^{\frac{\pi}{2}}_0 {e^t* e^{-t}*sin(u)} \, du[/tex]
[tex]d(t) = \int\limits^{\frac{\pi}{2}}_0 {sin(u)} \, du[/tex]
Integrate:
[tex]d(t) = -\cos(u)|\limits^{\frac{\pi}{2}}_0[/tex]
Substitute [tex]u = e^t[/tex]
[tex]d(t) = -\cos(e^t)|\limits^{\frac{\pi}{2}}_0[/tex]
Split
[tex]d(t) = -\cos(e^\frac{\pi}{2}) - [-\cos(e^0)][/tex]
[tex]d(t) = -\cos(e^\frac{\pi}{2}) +\cos(e^0)[/tex]
[tex]d(t) = -0.09793 + 0.5403[/tex]
[tex]d(t) = 0.44237[/tex]
The distance traveled in this interval is: 0.44237 units
dt =
d(t) = \int\limits^2_0 {e^t*sin(e^t)} \, dt
Evaluate the expression for a = 3, b = 4, and c = 6
a^3 - b + c
Answer:
3^3 - 4+6 = 17
Step-by-step explanation:
First you would do the exponents. 3 to the power of 3 (3^3) is 27.
Then you would add 4 and 6 (4+6) which will give you 10.
Finally, you would need to subract 10 from 27 (27-10) and you would get 17.
Hope this helps! :)
Answer:
29
Step-by-step explanation:
The expression is
a^3 - b + c
You just have to plug in the numbers, then evaluate,,
(3)³ - (4) + (6)
Let's start off with the exponent, so (3)³ = 3×3×3
3×3=9
9×3=27
Now, we have 27 - (4) + (6)
We have to get rid of the parenthesis so multiply the symbol next to it, - × 4 = -4, and + × 6 = +6. Now rewrite the equation.
27 - 4 + 6
27 - 4 = 23
23 + 6 = 29
Therefore, the answer its 29.
Hope this helps,
-Ketifa
helpp
Lily bought shares for $15 each.
When she sold the shares she made
a profit of 35%.
What price did she sell the shares for?
Answer:
profit %=35%
cp=Rs15
sp=?
profit amount =?
now,
sp=35%of cp
=35 of 15
__
100
= 5.25
again,
sp =cp + profit
=15+5.5
=20.5#
Step-by-step explanation:
hope it helps
Which set of tokens represents 0?
Positive
Negative
Pls helpp!!
Answer:
C.
represent 0
hope it helps
The distance from the
Earth to the Moon is
238.900 miles. Earth's
diameter is 7,917 miles.
How many Earths
would fit
between Earth
and The Moon?
Answer:
30.1756...
Hope that this helps!
Help please (don’t judge my writing) The frequency table shows the number of Dewey Middle School students who volunteered for the Toy Drive project.
What % of the volunteers were 6th graders?
Answer:
33%
Step-by-step explanation:
(68/206) × 100 = 33%
the answer is 33%
help me with this math question gr 8 math please
Answer:
C = 112, A = 150, D = 30, B = 38
Step-by-step explanation:
I solved C first using:
30+38+c = 180 (angles along a straight line should add up to 180 since a whole circle is 360)
-
I solved A by looking across from C.
Angles on opposite sides should mirror each other but A includes 38* + C
Just by doing 112 + 38 you get 150.
-
I solved D by looking at 30*, alternative interior angles are the same so D is 30*.
-
I solved B by taking C (112) and D (30) and adding them together and subtracting from 180.
Interior angles of a triangle should all add up to 180,
112 + 30 + B = 180
From this I got that B was 38.
Alternatively you can find this out by looking at the 38 degrees, corresponding congruent angles are always the same.
I suggest reviewing this angles sheet if you're ever stuck in the future.
Answer:
C = 112, A = 150, D = 30, B = 38
Step-by-step explanation:
Members of a school sports team are raising money by selling custom water bottles at school activities. They plan to sell each bottle for $13. Each bottle costs them $6. They spend $40 for advertising. Use n to represent the number of bottles they sell. Multiply this by the money they make for each bottle, then subtract the advertising cost. Which expression represents the money that the group raises? O A. 40 - (13 - 6)n O B. (13 - 6) n - 40 O C. 13n - 6 - 40 D. 13-on-40
Answer:
B. (13 - 6)n - 40
Step-by-step explanation:
If each bottle costs them $6 and they are selling each one for $13, the amount of money they make for each bottle can be represented by (13 - 6)n
This is because this finds the profit per bottle, then multiplies it by n, which is the number of bottles they sell.
Then, since they spent $40 on advertising, subtract 40 from this.
The expression will be (13 - 6)n - 40.
The correct answer is B. (13 - 6)n - 40
The expression represents the money that the group raises is (13-6)n - 40
What is expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
According to the question
Members of a school sports team are raising money by selling custom water bottles at school activities.
Let number of bottle they sell = n
Selling price of a bottle = $13
Now ,
Selling price of n bottle = $13n
Cost price of a bottle = $6
Now ,
Cost price of n bottle = $6n
Money spent on advertising = $40
Total they spent on bottles = $6n + $40
Therefore,
Money they raise in expression = 13n - 6n - 40
= (13-6)n - 40
Hence, The expression represents the money that the group raises is (13-6)n - 40
To know more about expression here:
https://brainly.com/question/14083225
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Walter's home was originally valued at $29,275. Due to some home improvements, its value is now $56,176. How much more is Walter's home worth now?
Answer: $26901
Step-by-step explanation:
From the information given, we are informed that Walter's home was originally valued at $29,275 but that after some improvement, it is now valued at $56,176.
Therefore, the increase in the worth of Walter's home will now be the difference in the values given above. This will be:
= $56,176 - $29275
= $26901
help me with this please and thank you
Answer:
12.56
Step-by-step explanation:
d = 2r = 2(2 m) = 4 m
C = πd = 3.14 × 4 m = 12.56 m
Answer:
C=12.56 m
Step-by-step explanation:
The radius is 2 m. To find the circumference, you need d, which is the diameter.
The diameter of a circle is 2 times the radius.
d=2*2=4
Now use the formula to find the circumference
C=3.14*4=12.56
Simplificación de la raíz cuadrada de 50
Answer:[tex]5\sqrt{2}[/tex]
Step-by-step explanation:
[tex]\sqrt{50}[/tex] ==>
2x25 ==> El 25 lo puedes reducir más ==> 5x5
Como el 5 tiene dos numero que se multiplican por si mismo se convierte en uno solo y va fuera de la raiz cuadrada.
Como el 2 que multiplicaste por 25 ya no se puede reducir y no tiene par, va adentro de la raiz cuadrada.
Resultado:
[tex]5\sqrt{2}[/tex]
x2 + 4
Select all that apply
Answer:
The first three depending on what the first one says. 2 and three are definitely correct though. If the first one says x to the second power added by 4 then it is correct.
Step-by-step explanation:
Brad and sally made a total of 31 cakes for the school bake sale. Sally made 7 fewer cakes than brad. How many cakes did brad make?
Answer:
brad made 19 cakes, sally made 12
Step-by-step explanation:
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
In a circle with a 12-inch radius, find the length of a segment joining the midpoint of a 20-inch chord and the center of the circle.
x =
Answer:
X=295.6
Step-by-step explanation:
I took the test
Answer:
295.6
Step-by-step explanation:
Number 5 reason +++++++
Answer:
it's reason is : given BAD =CAD
What is the value of x in the equation below? 3x - 15 = 60
Answer:
3x=60+15
x=75/3
x=25
Thus the answer is 25
Answer:
[tex]3x - 15 = 60 \\ 3x = 60 + 15 \\ 3x = 75 \\ x = \frac{75}{3} \\ x = 25[/tex]
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
6. Nicole earned $72 in 9 hours At this rate, how
much would she earn in 12 hours?
Answer:
96
Step-by-step explanation:
Because 72/9 = 8 so every hour she earns 8$
8*12=96
The amount of money in dollars earned by Nicole in 12 hours will be $96.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
Nicole earned $72 in 9 hours. Then the amount of money in dollars earned by Nicole each hour is calculated as,
Rate = $72 / 9
Rate = $8 for each hour
At this rate, the amount of money in dollars earned by Nicole in 12 hours will be calculated as,
⇒ $8 x 12
⇒ $96
The cash in dollars acquired by Nicole in 12 hours will be $96.
More about the rate link is given below.
https://brainly.com/question/14731228
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help with this question
Answer:
angle ABD=42°
Step-by-step explanation:
join AO with dotted line
AO=OD...radii
triangle AOD is an isosceles
angle DAO=angle ODA.....base angles of isosceles
angle DAO=48°
AngleAOD=180°-(48°+48°)....angle sum of triangle
=180°-96°
=84°
Angle AOD=2×angle ABD....angle at centre twice angle circumference
2xangle ABD=84°
Angle ABD=84°÷2
=42°
what is the answer to
This?
Answer:
y=23
Step-by-step explanation:
The area of a rectangle if the length is 5 more than 4 times the width, what's the algebraic expression for this question
The area of a rectangle if the length is 5 more than 4 times the width, the algebraic expression for this is, A = (4b + 5) × b
What is the area?An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².
Given that,
The length is 5 units more than 4 times the width
Suppose,
length = l
width = b
So, according to given condition
l = 4b + 5
Now, the area for rectangle is
A = length × width
A = l × b
A = (4b + 5) × b
Hence, the algebraic expression is (4b + 5) × b
To learn more about Area check:
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helppppppppppppppppppp
Answer:
vertical opposite angles are always equal
= 143°
co-interior angles are supplementary ( 180° )
∴ x = 180 - 143 = 37
∴ x = 37°
hope this answer helps you.....
please mark as brainliest.. thank you!
I bought a 5lb bag of sugar. I used 1 2/3 for cookies and 2 3/4 for cake. How much sugar do I have left?
Answer:
7/12lb
Step-by-step explanation:
5-1 2/3-2 3/4
=5-5/3-11/4
=10/3-11/4
=40/12-33/12
=7/12lb
Answer:
[tex]\frac{7}{12}[/tex]
Step-by-step explanation:
There was an initial amount of 5 lbs.
[tex]1\frac{2}{3}+2\frac{3}{4}=4\frac{5}{12}[/tex]
4 (5/12) of the sugar was used.
[tex]5 - 4\frac{5}{12}=\boxed{\frac{7}{12}}[/tex]
(7/12) of sugar should be remaining.
Hope this helps.
A circular carnival ride has a diameter of 120 ft. Suppose you board a gondola at
the bottom of the circular ride, which is 6 ft above the ground, and rotate 240°
counterclockwise before the ride temporarily stops. How many feet above ground
are you when the ride stops?
Answer:
The height above ground when the ride stops is 96 feet
Step-by-step explanation:
The given diameter of the carnival ride, d = 120 ft.
The height of the ride above the ground, h = 6 ft.
The angle through which the ride is rotated, θ = 240° counterclockwise
Therefore, we have;
The radius of the ride, r = d/2
∴ r = 120 ft./2 = 60 ft.
We note that at 180° rotation, the ride is at the highest point, [tex]h_{max}[/tex] = 6 ft. + 120 ft. = 126 ft.
When the ride rotates a further 240° - 180° = 60° the height drops from the maximum point by y = 60 ft. × cos (60°) = 30 ft., such that the final height above ground is therefore;
h = 126 ft. - 30 ft. = 96 ft.
The height above ground when the ride stops, h = 96 ft.
. During a sale, the price of a computer is reduced by $118 from the original price $590. By what percentage is the price of the computer reduced by? a 25% b. 69% C. 20% d. 75%
Answer:
C. 20%
Step-by-step explanation:
PLEASE HELP I NEED IT TO PASS THIS CLASS
Answer:
Angle 5 = 37°
Angle 8 = 143°
Step-by-step explanation:
Angle 2 = Angle 8
Reason : Alternate exterior angles are equal.
Therefore,
Angle 8 = 143°
Angle 5 + Angle 8 = 180°
Reason : Angle 5 & 8 are in a linear pair.
Angle 5 + 143° = 180°
Angle 5 = ( 180 - 143 )°
Angle 5 = 37°
Marvin has a coupon the discount is the rental of a full-size car by $25 they decide to buy insurance for each day if the cost is $465 how much days dear well they rent the car right and solve the equation
Answer:
tht hard
Step-by-step explanation:
so i need points
Can someone pleaseeee help and if you’re correct i’ll give brainliest
Answer:
12.57
Step-by-step explanation:
Can someone please me
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The various forms of the expression use the relation ...
-5 1/4 = -5 + -1/4 = -(6 -3/4) = -6 +3/4
Of course, the minus sign in a product can be moved around according to the associative and commutative properties of multiplication.
(8)(-5 1/4)
= (8)(-5 + -1/4)
= 8(-5) +8(-1/4)
= 8(-5) -8(1/4)
= 8(-6 +3/4)
Attached is the non-equivalent expression.
please help! will give brainliest. review the graph of function h(x). what is lim x-2 h(x), if it exists
Answer:
the answer is 0 or a
What is the y-Intercept of this graph?
y
12
8
4
0
х
0
4 8 12
оо
O 2
O
4
O 8
Answer: 0
Step-by-step explanation: the graph intercepts the y axis at the vertex of this specific graph which is (0,0)
Answer:
ok
Step-by-step explanation:
[tex]38+7·(x-3)=9·(x+1)[/tex]
[tex]38 + 7x - 21 = 9x + 9[/tex]
Combine like terms.
[tex]17 + 7x = 9x + 9[/tex]
Eliminate a x.
[tex]17 = 2x + 9[/tex]
[tex]8 = 2x[/tex]
[tex]x = 4[/tex]
38 + 7x - 21 = 9x + 9
7x + 17 = 9x + 9
Subtract both sides 9
7x + 17 - 9 = 9x + 9 - 9
7x + 8 = 9x
Subtract sides 7x
7x - 7x + 8 = 9x - 7x
8 = 2x
Divide both sides by 2
8 ÷ 2 = 2x ÷ 2
x = 4
