Answer:
1,45 cubic units
Step-by-step explanation:
The method of cylindrical shells demands that the volume of the solid is given by:
[tex]V=2\pi\int_a^b xf(x)dx[/tex] (1)
In this case you have that f(x) is:
[tex]f(x)=cos(\frac{\pi}{2}x)[/tex]
a = 0
b = 1
First, you solve the integral, by parts:
[tex]\int xf(x)dx=\int xcos(\frac{\pi}{2}x)dx=x(\frac{2}{\pi})sin(\frac{\pi}{2}x)-\int (\frac{2}{\pi})sin(\frac{\pi}{2}x)dx\\\\=(\frac{2}{\pi})xsin(\frac{\pi}{2}x)+(\frac{2}{\pi})^2cos(\frac{\pi}{2}x)+C[/tex]
Next, you calculate the volume of the solid, by replacing the solution to the integral in the equation (1):
[tex]V=2\pi[(\frac{2}{\pi})xsin(\frac{\pi}{2}x)+(\frac{2}{\pi})^2cos(\frac{\pi}{2}x)]_0^1\\\\V=2\pi[(\frac{2}{\pi})-(\frac{2}{\pi})^2]=1,45u^3[/tex]
hence, the volume of the solid generated is 1,45 cubic units
make b the subject of the formula a = sqrt(b+6)
Answer:
a = √(b+ 6)
a² = b + 6 (Square both sides)
b = a² - 6 (subtract 6 from both sides)
Answer:
b = a^2 - 6
Step-by-step explanation:
a = sqrt(b+6)
Find the square of both sides
a^2 = (b+6). Open brackets
a^2 = b+6
Subtract 6 from both sides
a^2 - 6 = b + 6 -6
b = a^2 - 6
Given that RT ≅ WX, which statement must be true?
Answer:RT is congruent to WX
Step-by-step explanation:
Answer: RT
Step-by-step explanation:
PLs help me find the surface area of the box thxsssss
Answer:
290 in^2
Step-by-step explanation:
front side x 2 = 176
top + bottom = 48
sides x 2 = 66
Sum = 290
Answer:
Total surface area S_tot = 290 in² thus c. is your answer
Step-by-step explanation:
length l = 8 in
width w = 3 in
height h = 11 in
diagonal d = 13.9283883 in
total surface area S_tot = 290 in²
lateral surface area S_lat = 242 in²
top surface area S_top = 24 in²
bottom surface area S_bot = 24 in²
volume V = 264 in³
Formula and Agenda:
Formulas for a rectangular prism:
Volume of Rectangular Prism:
V = lwh
Surface Area of Rectangular Prism:
S = 2(lw + lh + wh)
l = length
w = width
h = height
d = diagonal
S_tot = total surface area
S_lat = lateral surface area
S_top = top surface area
S_bot = bottom surface area
V = volume
What's the chance of NOT rolling a seven using a pair of dice.
Answer:
5/6
Step-by-step explanation:
total possible = 36
Favorable = 6
1 6
6 1
2 4
4 2
3 4
4 3
Part/whole
6/36
= 1/6
NOT = 5/6
Try to form a triangle by dragging points a and d, is it possible to form a triangle with side lengths 1, 5, and 3 units
Answer:
It is not possible.
Step-by-step explanation:
The triangle inequality theorem states that any 2 sides of a triangle must be greater than or equal to the other side. If you add 3 and 1, you get 4, and that is less than 5, so the triangle cannot exist.
Answer:
1. No
2. Yes
3. No
4. Yes
5. Yes
Step-by-step explanation:
These are the answers for edge 2021
Simplify the expression (3 - 4i)(1 + 5i) - (2 - i). Show your work please! I have the answer: 21 + `12i but I need to show my work, thank you!
Answer:
21+12i i hope this will help you
Step-by-step explanation:
(3-4i)(1+5i)-(2-i)
=[3(1+5i)-4i(1+5i)]-(2-i)
=[3+15i-4i-20i²]-(2-i)
=(3+11i-20i²)-(2-i)
opening brackeys
=3+11i-20i²-2+i
=3+11i+1i-20i²-2
as we know that i²=-1
=3-20(-1)-2+12i
=3+20-2+12i
=21+12i
The expression (3 - 4i)(1 + 5i) - (2 - i) is simplified as 21 + 12i
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the expression be A = (3 - 4i)(1 + 5i) - (2 - i)
Now , we know i² = -1
And , on simplifying the expression , we get
A = (3 - 4i)(1 + 5i) - (2 - i)
A = 3 + 15i - 4i - 20i² - 2 + i
A = -20i² + ( 3 - 2 ) + ( 15i - 4i + i )
A = -20 ( -1 ) + 1 + ( 11i + i )
A = 20 + 1 + 12i
A = 21 + 12i
Hence , the value of the expression (3 - 4i)(1 + 5i) - (2 - i) is ( 21 + 12i )
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a rectangular sheet of paper dimentions 44 cm x 18 cm is rolled along its length and cylinder is formed . find voloume of cylinder so formed
Answer:
1134cm³
Step-by-step explanation:
rolled along the length means the length becomes the height of the cylinder.
length of rectangle = height of cylinder= 44 cm
breadth of rectangle = circumference of top and bottom circles = 18 cm
to find radius = 2πr = 18
2 * 22/7 *r = 18
22/7r = 18/2
22/7r = 9
r = 9*7/22
r= 63/22
Volume of cylinder formula = πr²h
= 22/7 * 63/22 * 63/22 *44
= 63 * 18
= 1134 cm³
(We cannot take it as a hollow cylinder because a rectangular sheet can only have one radius)
Hope this helps you!
PLEASE HELP. Will give brainliest to whomever answers first.
Answer:
2π/3 I believe !
Step-by-step explanation:
Using the order of operations, what is the last calculation that should be done to evaluate 4(8 − 6)52 − 6 ÷ (−3)?
4(8 − 6)52 − 6 ÷ (−3)
4(2)52 − 6 ÷ (−3)
4(2)(25) − 6 ÷ (−3)
200 − 6 ÷ (−3)
200 − (−2)
Answer & Step-by-step explanation:
4(8 - 6)52 - 6 ÷ (-3)
First, subtract 6 from 8
4(2)52 - 6 ÷ (-3)
4(2)(52) - 6 ÷ (-3)
Multiply 2 by 52
416 - 6 ÷ (-3)
Divide -6 by -3.
416 + 2
Add 2 to 416
418
So, your evaluated answer would be 418.
Answer:
its 200+2
So addition is the last calculation to be done.
Step-by-step explanation:
ASAP PLS! WILL MARK BRAINLYEST AND 6TH GRADE MATH
Answer:
The correct answer is B!
Step-by-step explanation:
Answer:
its b
Step-by-step explanation:
URGENT
What is the value of y?
A.72°
B.36°
C.54°
D.108°
Answer:
72 + 2y = 180
2y = 108
y = 108/2
y = 54
C. 54
Answer:
C
Step-by-step explanation:
Sum of three angles of triangle = 180
72 + y + y = 180 {add like terms}
72 +2y = 180 {Subtract 72 from both sides}
2y = 180 - 72
2y = 108 {divide both sides by 2}
y = 108 / 2
y = 54°
Sierra is driving to visit her family. She wants to drive at least 500 miles today. She has already driven 248 miles and will keep driving at a constant speed of 62 miles per hour. What number of hours can Sierra drive to meet her goal of at least 500 miles? 500 ≤ 248 + 62x Both need different answers please
Answer:
4.06451 hours
note this answer is not rounded as you did not indicate round to what decimal values.
Step-by-step explanation:
Solving using equation
500 ≤ 248 + 62x
500-248 ≤ 62x
252 ≤ 62x
252/62 ≤ x
4.06451 ≤ x
Another way to solve
500-248= 252
she needs to travel 252 miles
speed = 62mph
note: speed = distance/time
therefore time= distance/speed
time = 252/62 = 4.06451
Number of hours Sierra needs to travel to meet her goal is 4.065 hours.
What is Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
Sierra wants to drive at least 500 miles today.
She has already driven 248 miles.
Remaining distance is driving at a constant speed of 62 miles per hour.
Let the time needed for the remaining distance to complete is x.
Speed = Distance / Time
Distance = Speed × Time
Distance = 62x
Total distance covered = 248 + 62x
This must be at least 500.
248 + 62x ≥ 500
62x ≥ 500 - 248
62x ≥ 252
x ≥ 252 / 62
x ≥ 4.065
Hence Sierra has to drive at least 4.065 hours to meet her goal.
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Ryan went to the store to buy some walnuts. The price per pound of the walnuts is $4.50 per pound and he has a coupon for $2.75 off the final amount. With the coupon, how much would Ryan have to pay to buy 5 pounds of walnuts? Also, write an expression for the cost to buy pp pounds of walnuts, assuming at least one pound is purchased.
Answer:
19.75.
Expression: 4.50pp - 2.75
(pp is the variable, pretend)
There are 60 minutes in a hour the total number of minutes is a function of the number of hours as shown in the table does this situation represent a linear or non linear function and why?
Answer:
It represents a linear function because there is a constant rate of change.
Step-by-step explanation:
As an hour passes, the minutes increase at a constant time of 60. A constant increase indicates a linear function.
help please and thank you
What is the y intercept of the function f(x)= -2/9x + 1/3?
Answer:
1/3
Step-by-step explanation:
plug in 0 for x
0 * anything = 0 (cancels out the -2/9) and you're left with 1/3
wegnerkolmp2741o plz help me only wegnerkolmp2741o
Answer:
1. Triangular prism
5 faces6 vertices9 edges2. Trapezoidal prism
6 faces8 vertices12 edges3. Pentagonal prism
7 faces10 vertices15 edges4. Hexagonal prism
8 faces12 vertices18 edgesurgent please help me!!!!
Answer:
D. both lines
Step-by-step explanation:
I am 100% sure! Please give brainiest!!!
The following ratios form a proportion.
5\18 = 10/90
True False
Answer:
this is false because 5/18 is equivalent to 10/36
Can someone pls help me solve this problem! I really need help ASAP! Plz help plz help!
Answer:
R=6
Step-by-step explanation:
T+R+A=100
T=88 A=6 R=?
88+R+6=100
Move known numbers to other side
R=6
Quadrilaterals ABCD and PQRS shown below are two similar figures.
Find the values of x and y.
Answer:
x = 12, y = 16
Step-by-step explanation:
Since the figures are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{AD}{PS}[/tex] = [tex]\frac{DC}{SR}[/tex] , substitute values
[tex]\frac{20}{2x+6}[/tex] = [tex]\frac{18}{27}[/tex] ( cross- multiply )
18(2x + 6) = 540 ( divide both sides by 18 )
2x + 6 = 30 ( subtract 6 from both sides )
2x = 24 ( divide both sides by 2 )
x = 12
-------------------------------------------
and
[tex]\frac{AB}{PQ}[/tex] = [tex]\frac{DC}{SR}[/tex] , substitute values
[tex]\frac{y}{24}[/tex] = [tex]\frac{18}{27}[/tex] ( cross- multiply )
27y = 432 ( divide both sides by 27 )
y = 16
Angel wants to distribute a certain amount of money among his children. IF you split $10 each, you have $35 left, and if you split $15 each, you still have $5 left. Indicates the amount of money distributed.
Answer:
95
Step-by-step explanation:
Let x be the number of children
10x+35 = money
15x+5 = money
Set the equations equal
10x+35 = 15x+5
Subtract 10x from each side
35 = 5x+5
Subtract 5 from each side
30 =5x
Divide by 5
30/5 =5x/5
6 =x
There are 6 children
10x+35 = money
10(6) +35
60+35
95
The amount of money is 95
Neon green is a paint color that contains the colors yellow and green in the ratio 3:5 by volume. How many ml of each color is in 100ml of neon green paint? Show your thinking
The length of a rectangle is 20 units more than its width. The area of the rectangle is x4−100.
Which expression represents the width of the rectangle?
1. x2−10 because the area expression can be rewritten as (x2−10)(x2+10) which equals (x2−10)((x2−10)+20).
2. x2+10 because the area expression can be rewritten as (x2+10)(x2−10) which equals (x2+10)((x2+10)−20).
3. x2−30 because the area expression can be rewritten as (x2+10)(x2−10) which equals (x2+10)((x2−30)+20).
4. x2+30 because the area expression can be rewritten as (x2−10)(x2+10) which equals (x2−10)((x2+30)−20).
Answer:
[tex]1. x^2-10[/tex] because the area expression can be rewritten as [tex](x^2-10)(x^2+10)[/tex]which equals [tex](x^2-10)((x^2-10)+20).[/tex]
Step-by-step explanation:
Area of the rectangle [tex]=(x^4-100)[/tex]
[tex]x^4-100=(x^2)^2-10^2\\$Applying difference of two squares: a^2-b^2=(a-b)(a+b)\\(x^2)^2-10^2=(x^2-10)(x^2+10)[/tex]
Since the length of a rectangle is 20 units more than its width.
[tex]Width: x^2-10\\Length=x^2+10=x^2-10+20[/tex]
The correct option is therefore 1.
Answer:
x2−10 because the area expression can be rewritten as (x2−10)(x2+10) which equals (x2−10)((x2−10)+20).Step-by-step explanation:
The area of the rectangle is [tex]x^{4} -100[/tex], which can be factored as [tex](x^{2} +10)(x^{2} -10)[/tex], because it's the difference of two perfect squares.
But, we know that [tex]l=20+w[/tex], where [tex]l[/tex] is the length and [tex]w[/tex] is the width.
Additionally, [tex]l=x^{2} -10+20[/tex] and [tex]w=x^{2} -10[/tex], which means [tex]l=x^{2} +10[/tex].
Therefore, the right answer is A.
A Car travels 42 km
On 7 litres of petrol. How long will it travel
on 12 litres of petrol.
Answer:
The answer is 72
Step-by-step explanation:
You'll do 42 divided by 7 times 2
42/7x2
Hope it helps.
A car travels 72 km on 12 liters of petrol.
What is Division method?
Division method is used to distributing a group of things into equal parts.
Given that;
A Car travels 42 km on 7 liters of petrol.
Now,
Since, On 7 liters of petrol a car travel 42 km
Hence, On 1 liter of petrol distance cover by a car = 42 ÷ 7
= 6 km
So, On 12 liters of petrol distance cover by a car = 6 × 12
= 72 km
Thus, A car travels 72 km on 12 liters of petrol.
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Use the equation e^x+e^-x/e^x-e^-x=t tosolve for x
Answer:
Solve the rational equation by combining expressions and isolating the variable
x = ln ( t − √ t ^2 + 4 )/2x = ln ( t +√ t ^2 + 4 )/2Answer:
Step-by-step explanation:
I assume that the equation is
[tex]e^x+\frac{e^{-x}}{e^x} -e^{-x}=t \\[/tex]
[tex]e^x+\frac{1}{e^{2x}}-\frac{1}{e^x} = t[/tex]
[tex]e^{3x}+1-e^x=e^{2x}t[/tex]
[tex]e^{3x}-te^{2x}-e^x=-1[/tex]
Let u = e^x
[tex]u^3-tu^2-u=-1[/tex]
[tex]u(u^2-tu-1) = -1[/tex]
if u=1, then [tex]u^2-tu-1 =-1 \longleftrightarrow u^2-tu=0[/tex]
then u = 0 (reject) or u = t
So far, we have u = 1 and u = t
if u =1, e^x =1 , then x = 0
if u = t, then e^x = t or x = lnt
Can someone please help me.
Answer:
96
Step-by-step explanation:
Because math
What is angle m 2 ? What is angle m 1?
Answer:
Angle measure two is equal to 75º and Angle measure one is equal to 105º
Step-by-step explanation:
I know this because angle one is alternate exterior angle with angle 7 and angle seven forms a staight line with angle 75 so to find angle 7 you have to do 180-75 and that would equal 105.
for angle two it is interior angles with angle 75 so this means that are congruent angles which means they both have the same measure
Answer: <2 is 75 degrees & <1 is 105 degrees
Step-by-step explanation:
The radius of a circle is 12 in. What is the circle's diameter?
Answer:
24 in
Step-by-step explanation:
The diameter of a circle is twice its radius which is 12 * 2 = 24.
Answer:
The diameter is 24 inches
Step-by-step explanation:
The radius of a circle is 1/2 of the circles diameter
r = d/2
d = 2r
d = 2*12
d = 24
The diameter is 24 inches
a food scientist wants to know if increasing the amount of lemon juice in a hummus recipe by 10% will increase the shelf life of the product, so he prepares 100 Badges of the recipe - 50 following the old recipe and 50 with extra lemon juice –and?checks each batch once per day to see how long it stays fresh. What type of data source is this?
Answer:
b. Experiment
Step-by-step explanation:
Setting up conditions so that you can examine the outcome is called an "experiment."
Answer:
[tex]\fbox{\begin{minipage}{10em}Option B-Experiment\end{minipage}}[/tex]
Step-by-step explanation:
As described, the food scientist performs the research based on the actual data, without using a computer or any simulation devices.
=> The data source is not generated from a computer simulation.
=> Option A-Simulation is incorrect.
The food scientist intentionally prepares the research by conducting an experiment, in which 100 badges are used, 50 badges following the old recipe and 50 badges with extra lemon juice.
=> This is not a subjective process, but a purposely attempting to observe the amount of lemon juice in a specific manner.
=> This is not a survey.
=> Option C-Survey is incorrect.
=> Option B-Experiment is correct.
Hope this helps!
:)
i need help one more time !!
Answer:t=8
Step-by-step explanation:
solve for t by simplifying both sides of the equation,then isolating the variable
Answer:
[tex]t = 8[/tex]
Step-by-step explanation:
→You need to get "t," by itself, and to do this, you must multiply both sides by the reciprocal of [tex]\frac{1}{4}[/tex], which is 4. You are multiplying because you can't divide by a fraction.
[tex]\frac{1}{4} t=2[/tex]
[tex]4*\frac{1}{4} t=2*4[/tex]
[tex]t = 8[/tex]