Answer:
-12 < x < 18
Step-by-step explanation:
x-3 < 15
x < 18
and
-x + 3 < 15
-x < 12
x > -12
Given the curve [tex]\displaystyle \large{y=e^{-x}\sin x \ \ (x\geq 0)[/tex] let the area enclosed by the curve and the x-axis (above the x-axis) be S0, S1, S2, ... , Sn, ... in order from y-axis. Find [tex]\displaystyle \large{ \lim_{n \to \infty} \sum_{k=0}^{n} S_k}[/tex]
The given curve crosses the x-axis whenever x is a multiple of π, and it lies above the x-axis between consecutive even and odd multiples of π. So the regions with area S₀, S₁, S₂, ... are the sets
[tex]R_0 = \left\{(x, y) : 0 \le x \le \pi \text{ and } 0 \le y \le e^{-x}\sin(x)\right\}[/tex]
[tex]R_1 = \left\{(x, y) : 2\pi \le x \le 3\pi \text{ and } 0 \le y \le e^{-x}\sin(x)\right\}[/tex]
[tex]R_2 = \left\{(x, y) : 4\pi \le x \le 5\pi \text{ and } 0 \le y \le e^{-x}\sin(x)\right\}[/tex]
and so on, with
[tex]R_k = \left\{(x, y) : 2k\pi \le x \le (2k+1)\pi \text{ and } 0 \le y \le e^{-x}\sin(x)\right\}[/tex]
for natural number k.
The areas themselves are then given by the integral
[tex]S_k = \displaystyle \int_{2k\pi}^{(2k+1)\pi} \int_0^{e^{-x}\sin(x)} dy \, dx = \int_{2k\pi}^{(2k+1)\pi} e^{-x}\sin(x) \, dx[/tex]
Integrate by parts twice. Take
[tex]u = e^{-x} \implies du = -e^{-x} \, dx[/tex]
[tex]dv = \sin(x) \, dx \implies v = -\cos(x)[/tex]
so that
[tex]\displaystyle \int e^{-x}\sin(x) \, dx = -e^{-x}\cos(x) - \int e^{-x}\cos(x) \, dx[/tex]
then
[tex]u = e^{-x} \implies du = -e^{-x} \, dx[/tex]
[tex]dv = \cos(x) \, dx \implies v = \sin(x)[/tex]
so that
[tex]\displaystyle \int e^{-x}\cos(x) \, dx = e^{-x}\sin(x) + \int e^{-x}\sin(x) \, dx[/tex]
Overall, we find
[tex]\displaystyle \int e^{-x}\sin(x) \, dx = -e^{-x}\cos(x) - e^{-x}\sin(x) - \int e^{-x}\sin(x) \, dx[/tex]
or
[tex]\displaystyle \int e^{-x}\sin(x) \, dx = -\frac12 e^{-x} (\cos(x)+\sin(x)) + C[/tex]
Using the antiderivative and the fundamental theorem of calculus, we compute the k-th area to be
[tex]\displaystyle S_k = -\frac12 e^{-(2k+1)\pi} (\cos((2k+1)\pi)+\sin((2k+1)\pi)) + \frac12 e^{-2k\pi} (\cos(2k\pi)+\sin(2k\pi))[/tex]
[tex]\displaystyle S_k = \frac12 e^{-2k\pi} \cos(2k\pi) \left(e^{-\pi} + 1\right)[/tex]
[tex]\displaystyle S_k = \frac{e^{-\pi}+1}2 e^{-2k\pi}[/tex]
Since [tex]\left|e^{-2\pi}\right|<1[/tex], the sum we want is a convergent geometric sum. As n goes to ∞, we have
[tex]\displaystyle \lim_{n\to\infty} \sum_{k=0}^n S_k = \frac{e^{-\pi}+1}2 \cdot \frac1{1 - e^{-2\pi}} = \boxed{\frac{e^\pi+1}{4\sinh(\pi)}}[/tex]
Find the output for f(x) = -3 |2x - 9| + 4.
When x = -5
SHOW EVERY STEP!
Hey there!
f(x) = -3|2x - 9| + 4
y = -3|2x - 9| + 4
y = -3|2(-5) - 9| + 4
y = -3|-10 - 9| + 4
y = -3|19| + 4
y = -57 + 4
y = -53
Therefore, your answer should be: f(x) = -53
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Can someone plz help me?
Answer:
A. 5(y+3) = 5(3+y)
Step-by-step explanation:
You might need: 3 Calculator
2
Find the area of the shape.
Either enter an exact answer in terms of t or use 3.14 for it and enter your answer as a decimal.
units?
Answer:
90/360 x 3.14 x [tex]2^{2}[/tex]. (put into calculator)
Step-by-step explanation:
This is a sector of a circle we can see that there is a right angle (90 degrees) so we can say there is 90/360 of a circle.
The formula for the area of a circle is pi times radius squared.
We can use this but also need to use 90/360.
We can say the area of the shape is 90/360 x 3.14 x [tex]2^{2}[/tex].
RS is the perpendicular bisector of TU. Find x and y
Answer:
x = 1
y = 30°
Step-by-step explanation:
is RS is ⊥ to TU then TS = US so we can use this equation to find 'x':
20x-3 = 5x+12
15x = 15
x = 1
we also know that RS intersecting with TU creates a 90° angle
if 3y = 90 then y = 30
5. What linear function defines the following Arithmetic Sequence?
-4, -1, 2, 5, 8,...
an = 4 - 3(n-1)
an = -4 -3(n-1)
an = 4 + 3(n - 1)
an = -4 + 3(n - 1)
Answer
A
Step-by-step explanation:
The linear function defines the arithmetic sequence is an = -4 + 3(n - 1). The correct option is D.
What is an arithmetic progression?
The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The given series is -4, -1, 2, 5, 8. The common difference of the series is calculated as,
d = -1 - ( -4 )
d = -1 + 4
d = 3
The equation will be written as,
an = a₁ + d(n - 1)
an = -4 + 3(n - 1)
Therefore, the linear function that defines the arithmetic sequence is an = -4 + 3(n - 1). The correct option is D.
To know more about arithmetic progression follow
https://brainly.com/question/6561461
#SPJ2
At the gym, Hillary swims every 6 days and runs every 4 days. If she did both activities today, in how many days will she do both activities again on the same day?"
Answer:
we know that
Hillary
swims every 6 days---> Multiples of 6---> 6-12-18-24-30-36-42-48-54
runs every 4 days-----> Multiples of 4----> 4-8-12-16-20-24-28-32-36-40-44-48
cycles every 16 days---> Multiples of 16---> 16-32-48-64
therefore
In 48 days she will do all three on the same day.
the answer is
48 days
Step-by-step explanation:
The length of a retangle garden is 4 yards more than its width The area of the garden is 60 square yards Find the with of the garden
Answer pls in standard form too
Answer:
a)
Slope form y=2x+3
Standard form 2x-y=-3
b)
Slope y=3/5x-6
Standard 3x-5y=30
c)
slope y=-3/2x+9
standard 3x+2y=18
d)
slope y=-3x+0
standard = 3x+y=0
Step-by-step explanation:
a)
Slope form y=2x+3
Standard form 2x-y=-3
b)
Slope y=3/5x-6
Standard 3x-5y=30
c)
slope y=-3/2x+9
standard 3x+2y=18
d)
slope y=-3x+0
standard = 3x+y=0
Ali uses 1.5 cups of flour to bake a dozen cupcakes. at this rate,how many cups of flour will she need to bake 30 cupcakes?
A.3.75c
B.3c
C.2.4c
D.2.75c
Answer:
A
Step-by-step explanation:
1.5 c flour = 12 cupcake
0.75 c flour = 6 cupcake
1.5 + 1.5 + 0.75 = 3.75 c flour
if 3/15 is equivalent to 45/n. find n
Answer:
n = 225
Step-by-step explanation:
Multiply 15 by 15
I’ll give 100 points
Answer:
2055 is the answer.
Step-by-step explanation:
If x represents the number of minutes and y represents the hiker elevation in feet.
y = 8.19x + 663
y = 8.19(170) + 663
y = 1392.3 + 663
y = 2055.3
Hope it helps:)
Answer:
:)
Step-by-step explanation:
Pls answer these two questions
Answer:8 and 22
Step-by-step explanatio
Lillian read 43 pages in 1 1/3 hours. At what rate, in pages per hour, did she read?
Answer:
hi
Step-by-step explanation:
Answer:
She reads one page in 1.40
Is 6 a factor of the number 56 yes or no?
Answer:
No it is not a factor of 56
Answer:
No
Step-by-step explanation:
6,12,18,24,30,36,42,48,54,60
Write 2^40 as a power with the following base
a) 2^2
b)2^5
c)2^8
d)2^10
Answer:
2^2×20
Step-by-step explanation:
2^2×20
because 2×20=40
so, 2^2×20=2^40
The Following are the representation of [tex]2^{40[/tex] as a power in different bases
a) [tex]2^{ 2 * 20}[/tex]
b) [tex]2^{ 5 * 8}[/tex]
c) [tex]2^{ 8 * 5}[/tex]
d) [tex]2^{ 10 * 2}[/tex]
What are Exponents and power?Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion.
For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base.
Given:
[tex]2^{40[/tex] as a power
so, writing the above in given bases
a) 2²
= [tex]2^{ 2 * 20}[/tex]
= [tex]2^{40[/tex]
b)[tex]2^5[/tex]
= [tex]2^{ 5 * 8}[/tex]
= [tex]2^{40[/tex]
c) [tex]2^8[/tex]
= [tex]2^{ 8 * 5}[/tex]
= [tex]2^{40[/tex]
d) [tex]2^{10[/tex]
= [tex]2^{ 10 * 2}[/tex]
= [tex]2^{40[/tex]
Learn more about exponents and power here:
https://brainly.com/question/15722035
#SPJ2
I need to know how to get the roots for example what is the root of 2 root 5
Answer:
Square roots are when you multiply the same number by itself like for example, the square root of 5 is 25, because 5*5=25
Step-by-step explanation:
The value of the root of 2√5 is approximately 2.116.
Here, we have,
To find the root of a number, you can use the concept of radicals.
The "root" refers to the inverse operation of raising a number to a power. For example, the square root (√) is the most common root, and it represents finding a number that, when squared, gives the original number.
To find the root of a number, such as the square root (√), you can use the following notation:
√(2 * √(5))
In this case, we have the square root of (2 times the square root of 5).
To simplify this expression further, we can break it down step by step:
Step 1: Simplify the square root of 5:
√(5) = 2.236 (approximately)
Step 2: Substitute the simplified value back into the original expression:
√(2 * 2.236)
Step 3: Simplify the expression:
√(4.472) = 2.116 (approximately)
Therefore, the root of 2√5 is approximately 2.116.
To learn more on square root click:
brainly.com/question/29286039
#SPJ4
help me pls... ....
Step-by-step explanation:
A1
1 yard = 3 feet
1 foot = 12 inches
therefore,
100 yards = 100×3×12 inches = 3600 inches
A2
again, 1 yard = 3 feet
8 ft = 8/3 = 2.67 yards = 2 2/3 yards
A3
1 gallon = 8 pints
A4
1 liter = 1000 milliliters (remember, "mili" means 1/1000).
therefore,
2.2 liters = 2.2×1000 = 2200 milliliters
A5
again, 1 liter = 1000 milliliters
therefore
1 milliliter = 1/1000 liter
670 milliliters = 670 × 1/1000 liter = 670/1000 liter =
= 0.67 liter
B1
1 kg (kilogram) = 1000 grams ("kilo" means 1000).
we have 3 layers.
each layer weighs (cake plus icing)
1/2 kg + 100 g = 500 g + 100 g = 600 g
3 layers then weigh
3×600 g = 1800 g
the additional candle weighs 250 g.
so, the total is
1800 g + 250 g = 2050 g = 2.05 kg
B2
area is 110 m².
1 m = 100 cm ("centi" means 1/100).
and 1 m² is then 100×100 = 10000 cm².
so, the area in cm² is
110 × 10000 = 1,100,000 cm²
the top area of one brick = 10 × 20 = 200 cm²
so, we need
1,100,000 / 200 = 11,000 / 2 = 5500 bricks
Please find the area...
f(x)=−2x^2+2x−20
Find f(−8)
Answer: -164
Step-by-step explanation:
Answer:-164
Step-by-step explanation:
−2(−8)
2
+2(−8)−20
Plug into each x-value
−
2
(
64
)
+
2
(
−
8
)
−
20
−2(64)+2(−8)−20
Square first
−
128
−
16
−
20
−128−16−20
Multiply
f
(
−
8
)
=
−
164
f(−8)=−164
what is 3x + 4y = 10
6x - 4y = 8
Answer:
x=2
y=1
Step-by-step explanation:
9x+0=18
so it's x=2
6=4y=10
so y=1
Find the residual values, and use the graphing calculator tool to make a residual plot. A 4-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled given with entries negative 2. 7, negative 0. 9, 1. 1, 3. 2, 5. 4. The third column is labeled predicted with entries negative 2. 84, negative 0. 81, 1. 22, 3. 25, 5. 28. The fourth column is labeled residual value with all entries blank. Does the residual plot show that the line of best fit is appropriate for the data? No, the points are in a curved pattern. No, the points are evenly distributed about the x-axis. Yes, the points are in a linear pattern. Yes, the points have no pattern.
The residual of a regression is the difference between the actual value and the predicted value
The true statement about the residual plot is (c) Yes, the points are in a linear pattern
The entries are given as:
x Given Predicted Residual
1 -2.7 -2.84
2 -0.9 -0.81
3 1.1 1.22
4 3.2 3.25
5 5.4 5.28
The residual of a line of best fit is calculated using:
[tex]Residual = Actual - Predicted[/tex]
Using the entry headings, the formula would be:
[tex]Residual = Given - Predicted[/tex]
So, the residuals of the 5 entries are:
[tex]Residual_1 = -2.7 - -2.84 =0.14[/tex]
[tex]Residual_2 = -0.9 - -0.81 =-0.09[/tex]
[tex]Residual_3 = 1.1 - 1.22 =-0.12[/tex]
[tex]Residual_4 = 3.2 - 3.25 =-0.05[/tex]
[tex]Residual_4 = 5.4 - 5.28 =0.12[/tex]
So, the entries become:
x Given Predicted Residual
1 -2.7 -2.84 0.14
2 -0.9 -0.81 -0.09
3 1.1 1.22 -0.12
4 3.2 3.25 -0.05
5 5.4 5.28 0.12
See attachment for the residual plot.
From the plot, we can see that the points are in a linear pattern.
Hence, the true statement about the residual plot is (c)
Read more about residuals at:
https://brainly.com/question/4333650
The difference between a number and 16 is 49.
ANYBODY KNOW THE ANSWER?~
Hey there!
GUIDE
• The word “sum” means add
• The word “difference” means subtract
• The word “product” means multiply
• The word “quotient” means divide
• The word “is” means equal to
• The “unknown number” is a variable that is not known. So people usually label it as a variable until they figure out what the unknown value is.
Now that we have that information out the way we can solve for your given question.
“The [DIFFERENCE] between [a number] & 16 [is] 49
Lets break it down
• DIFFERENCE (between) = subtract☑️
• A NUMBER = UNKNOWN (so we will label it is as “n”]☑️
• 16 will stay the same because NOTHING was done to it!
• IS = is equal to☑️
We have the key terms out of the way so now we met our answer
ANSWER:
“n - 16 = 49”
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
A construction team is going to Guatemala to help a missionary build a church building. The construction team will be there for 24 days, which is 50% more days than they need to complete construction. How many days will they need to complete the church building
Answer:
72
Step-by-step explanation:
50% means ½ of the usual days,
if 50% = 24 days
then the usual day is 48 days
so, 48+24= 72
The total number of gallons of water in a tank, w, after t minutes is given in this table and the plot.
What is an equation showing the relationship between w and t?
Enter your answer by filling in the box to complete the equation.
w =
The equation showing the relationship between w and t is [tex]w = 4t[/tex]
From the table, we have the following points:
(0,0) and (1,4)
Start by calculating the slope (m)
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{4 -0}{1 -0}[/tex]
Simplify the numerator and the denominator
[tex]m = \frac{4}{1}[/tex]
Divide 4 by 1
[tex]m = 4[/tex]
The equation is then calculated as:
[tex]w = m(t - t_1) + w_1[/tex]
This gives
[tex]w = 4(t - 0) + 0[/tex]
Simplify
[tex]w = 4t[/tex]
Hence, the equation is [tex]w = 4t[/tex]
Read more about linear equations at:
https://brainly.com/question/14323743
A motorcycle can travel 60 miles per gallon. Approximately how many gallons of fuel will the motorcycle need to travel 40 km? [1 mile = 1. 6 km] 0. 04 0. 08 0. 20 0. 42.
The motorcycle needs to travel 40 km, 0.42 gallons of fuel.
Given that,
A motorcycle can travel 60 miles per gallon.
We have to find,
How many gallons of fuel will the motorcycle need to travel 40 km?
According to the question,
The motorcycle travel 60 miles per gallon,
The motorcycle travels 40 km,
To convert it into kilometers 60 miles per gallon.
[tex]\rm 1 \ mile = 1.6\ k.m.\\\\60 \ miles \times 1.6 \ k.m. = 96 \ k.m.[/tex]
Therefore,
The gallons of fuel will the motorcycle need to travel 40 km is,
[tex]= \dfrac{96}{40}\\\\= 0.42[/tex]
Hence, The motorcycle needs to travel 40 km, 0.42 gallons of fuel.
For more details refer to the link given below.
https://brainly.com/question/13108874
need help
a rectangular garden is 50m long and 45 m broad A path 2m wide is. running inside the garden . Calculate the cost of gravelling the path at rs 40 per square meter.....
Answer:
Rs. 14560
Hope you could get an idea from here.
Doubt clarification - use comment section.
In rectangle ABCD
L=50mB=45m[tex]\\ \sf{:}\longrightarrow Area=LB[/tex]
[tex]\\ \sf{:}\longrightarrow Area=50(45)[/tex]
[tex]\\ \sf{:}\longrightarrow Area=2250m^2[/tex]
In rectangle PQRS
L=50-2=48mB=45-2=43m[tex]\\ \sf{:}\longrightarrow Area=LB[/tex]
[tex]\\ \sf{:}\longrightarrow Area=48(43)[/tex]
[tex]\\ \sf{:}\longrightarrow Area=2064m^2[/tex]
Now
[tex]\\ \sf{:}\longrightarrow Area_{(Path)}=Area_{(ABCD)}-Area_{(PQRS)}[/tex]
[tex]\\ \sf{:}\longrightarrow Area_{(Path)}=2250-2064=186m^2[/tex]
Cost:-
[tex]\\ \sf{:}\longrightarrow 186(40)[/tex]
[tex]\\ \sf{:}\longrightarrow Rs 7440[/tex]
Joseph removes 5/8 gallon of white paint from a can.
Then he adds 5/8 gallon of blue paint to the can.
Write and evaluate an addition expression to find
the overall increase or decrease in the amount of
paint in the can.
Create the expression from the data:
The gallon of paint begins as a whole: 8/8
Then he removes 5/8 gallons of paint from the can: - 5/8
Then he adds 5/8 of a different colored paint to the can: + 5/8
Now combine:
8 / 8 - 5 / 8 + 5 / 8 = 8/8
The paint can is full, then he removes an amount from the can. He then pours more paint into the can that is equal to the amount he originally removed. Therefore, the paint can remained full.
What is the value of the expression Negative 225 divided b (negative 15)?
What is the value of the expression 30 divided by (negative 6)?
Answer:
-15-5Step-by-step explanation:
What is the value of the expression Negative 225 divided b (negative 15)?
What is the value of the expression 30 divided by (negative 6)?
I answer for what I understand
-225 : 15 = - 15
30 : (- 6 ) = -5
A pipe is leaking at the rate of 16 fluid ounces per minute. Use unit analysis to find out how many gallons the pipe is leaking per hour.
Answer:
The answer is 7.5 gallons per hour.
Step-by-step explanation:
16 fluid ounces multiplied by 60 minutes equals 960 fluid ounces
16 * 60 = 960
960 fluid ounces divided by 128 fluid ounces (which is 1 gallon) equals 7.5 gallons.
960 / 128 + 7.5
So the answer is 7.5 gallons per hour.
Hope this helps! :)
