Answer:
It is 72
Step-by-step explanation:
Hope it helps
Answer:
72
Step-by-step explanation:
It was very easy question.
The base of a solid is the region in the first quadrant between the graph of y=x2 and the x -axis for 0≤x≤1 . For the solid, each cross section perpendicular to the x -axis is a semicircle. What is the volume of the solid?
Answer:
The volume of the solid is π/40 cubic units.
Step-by-step explanation:
Please refer to the graph below.
Recall that the area of a semi-circle is given by:
[tex]\displaystyle A=\frac{1}{2}\pi r^2[/tex]
The volume of the solid will be the integral from x = 0 to x = 1 of area A. Since the diameter is given by y, then the radius is y/2. Hence, the volume of the solid is:
[tex]\displaystyle V=\int_0^1\frac{1}{2}\pi \left(\frac{y}{2}\right)^2\, dx[/tex]
Substitute:
[tex]\displaystyle V=\frac{1}{2}\pi\int_0^1\left(\frac{x^2}{2}\right)^2\, dx[/tex]
Simplify:
[tex]\displaystyle V=\frac{1}{2}\pi \int_0^1\frac{x^4}{4}\, dx[/tex]
Integrate:
[tex]\displaystyle V=\frac{1}{2}\pi \left[\frac{x^5}{20}\Big|_0^1\right][/tex]
Evaluate:
[tex]\displaystyle V=\frac{\pi}{40}\left((1)^5-\left(0\right)^5\right)=\frac{\pi}{40}\text{ units}^3[/tex]
The volume of the solid is π/40 cubic units.
Volume of a solid is the measure of the 3 dimensional space it occupies. The volume of the considered solid is obtained as [tex]\dfrac{\pi}{40} \: \rm unit^3[/tex]
How to find the volume of a three dimensional region bounded by curves?For that, we can try to find infinitesimally small 3-d region's volume, and then integrate that region over the dimensions available to get the total volume of the specified region.
We can also use the fact that continuous curves are almost linear and non-changing in infinitely zoomed region.
The given solid has base bounded by x-axis, [tex]y=x^2[/tex] and 0≤x≤1
Its three dimensional region is along the z axis, for each x, there is a semicircle perpendicular with radius being 'y'.
If we take [tex]dx[/tex]x-axis, then the curve [tex]y=x^2[/tex]cylinder(split from height because of semicircle)) with diameter y, and height [tex]dx[/tex]volume is : [tex]V_{dx} = \dfrac{1}{2} \times \pi (\dfrac{y}{2})^2 \times dx = \dfrac{\pi (x^2)^2}{8}dx = \dfrac{\pi x^4}{8} dx[/tex]
Integrating this for 0≤x≤1, we will get the volume of the three dimensional region needed as:
[tex]V = \int_0^4V_{dx} = \int_0^1 \dfrac{\pi x^4}{8} dx = \dfrac{\pi}{8} [\dfrac{x^5}{5}]^1_0 = \dfrac{\pi 1^4}{40} = \dfrac{\pi}{40}[/tex] (in cubic units).
Thus, the volume of the considered solid is obtained as [tex]\dfrac{\pi}{40} \: \rm unit^3[/tex]
Learn more about volume of three dimensional region here:
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The variables x and y vary inversely, and x = 12 when y = 6. Use the inverse variation formula, k = xy, to
find y when x = 3.
Answer:
D=24
Step-by-step explanation:
y inversely as x
x=k/y
By cross multiplication
k=xy
k=12*6
k=72
finding y
72=3y
y=24
The value of y given the inverse proportional relationship between the variables is b24.
What is the inverse proportion?When two variables vary inversely, as one of the variable increases, the other variable decreases.
The equation that represents inverse proportion : x = k / y
where b = constant of proportionality
k = xy
k = 12 x 6 = 72
y = k / x
72 / 3 = 24
To learn more about inverse proportion, please check: https://brainly.com/question/27233899
If n12=1536
then n=
Hellllllllllllllppppp
Answer:
this should help you understand...
Step-by-step explanation:
what is the length of the hypotenuse of the triangle when x=7?
Answer:
c=57.8
Step-by-step explanation:
6*7+4=46
5*7=35
c= 46^2+35^2=57.80138
Brie needs cups of flour for her recipe. Which amount is enough for Brie's recipe?
Answer:
2[tex]\frac{1}{2}[/tex] cups
Step-by-step explanation:
Hi there,
When dealing with these types of problems, it is highly recommended to set the same denominators for the fractions you are dealing with. In this problem, we can see that 2[tex]\frac{1}{2}[/tex] is equivalent to [tex]\frac{5}{2}[/tex]; making this the correct answer choice.
Hope this explanation helps.
Cheers.
If 2^2x = 2^3, what is the value of x?
Answer:
x = 2
Step-by-step explanation:
evaluate y-x when y= -9 and x = -5
Answer:
-5
Step-by-step explanation:
a) 2x – 7x +3y if x= 3, y= -4
b) y + 3xy if x= 7, y= 5
c) 5x3 + 2y2 if x= 2, y =3
What is the area of the circle with the radius of 5? Round to the nearest tenth.
Answer:
Step-by-step explanation:
area of circle=π(5)²=25 π≈25×3.14≈78.5
Answer:
A≈78.54
Step-by-step explanation:
A=πr2=π·52≈78.53982
Also i left this out but the radius of the circle is 5.
Chill im only a 7th grade nerd studying in Real Estate and Finances
Also hopes this helps ;0
Escribe en forma de potencia y encuentra el valor
a) 2⁴ . 2² =
b) (-5)⁸/(-5)³=
c) ((-9)² )3³
Answer:
a) =2^(4+2)
=2^6
=64
b) =(-5)^(8-3)
=(-5)^5
= - 3125
c) =(81)(27)
=2187
Suppose you have a right triangle with congruent legs and a hypotenuse that measure (12√5)/5. What is the length of the smaller leg? Round to the nearest hundredth
Answer:
5.4 is the length
Step-by-step explanation:
5.333 - (12√5)/5 - round to nearest hundreth (5.4)
length total 5.4
Thanks and Rate my Answer Please!
The length of the smaller leg is 3.8 unit.
What is Pythagoras theorem?Pythagoras theorem states that "the sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c)" i.e.
[tex]c^{2} = a^{2} + b^{2}[/tex]
Let the length of the leg be b and a.
According to the given question.
We have a rigth triangle which have congruent legs.
And hypotenuse, c = [tex]\frac{12\sqrt{5} }{5}[/tex]
Since, the legs are congruent.
Therefore,
a = b
Now, according to the Pythagoras theorem.
[tex]c^{2} = a^{2} + b^{2}[/tex]
[tex]\implies c^{2} = a^{2} + a^{2}[/tex]
[tex]\implies c^{2} = 2a^{2}[/tex]
[tex]\implies (\frac{12\sqrt{5} }{5} )^{2} = 2a^{2}[/tex]
[tex]\implies \frac{144\times 5}{25} = 2a^{2}[/tex]
[tex]\implies \frac{144}{5} = 2a^{2}[/tex]
[tex]\implies \frac{72}{5} = a^{2}[/tex]
[tex]\implies a = \sqrt{\frac{74}{5} }[/tex]
[tex]\implies a = \sqrt{14.8}[/tex]
[tex]\implies a = 3.84[/tex]
[tex]\implies a = 3.8[/tex] unit
Hence, the length of the smaller leg is 3.8 unit.
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A carnival game involves drawing a card from a deck of 40 cards, replacing it, shuffling the deck, and drawing another
card. Thirty of the cards are blank and ten are labeled 8 tokens. Your prize is the sum of the cards you draw. What is the
expected payoff for this game?
4 tokens
2 tokens
8 tokens
O tokens
Answer:
4 tokens.
Step-by-step explanation:
The expected value of a given event is calculated as:
EV = (x₁*p₁ + x₂*p2 + ... + xₙ*pₙ)
Where xₙ is the n-th outcome, and pₙ is its probability.
In this case, our experiment is:
You draw two times.
We have 30 cards with no prize
We have 10 cards with a prize.
A total of 40 cards.
As we draw two times (and the first time we draw a card we put it back in the deck) we can consider the events as independent, so we can find the expected value per draw.
Now we can define:
x₁ = drawing a blank card = 0 tokens
The probability will be equal to the quotient between the number of blank cards and the total number of cards
p₁ = 30/40 = 3/4
x₂ = drawing a prized card = 8 tokens.
The probability will be equal to the quotient between the number of prized cards and the total number of cards:
p₂ = 10/40 = 1/4
Then the expected value per draw is:
EV = ( (3/4)*0 tokens + (1/4)* 8 tokens) = 2 tokens.
And we have two draws, then the expected value of two draws is two times the expected value per draw, this means that the expected value in our case is:
expected value = 2*(2 tokens) = 4 tokens.
The correct option is the first one, counting from the top.
simplify:(-5/8x3/7x4/-15)+(4/7x-21/8)
Answer:
4x/7 - 143/56
Step-by-step explanation:
In a sample of 800 people, 420 are in favor of a proposed scoring system. A golf course wants to implement an electronic scoring system where shots are counted by satellites to reduce human error and to show real-time scores at the clubhouse. Is there enough evidence to conclude that the majority of the golfing community is a proponent of the new system at an alpha level of .05. Determine the number of tails for this problem, the critical value and the test statistic.
Answer:
We accept H₀ with 95 % of Confidence Interval we have enough evidence to conclude that the majority of members agree with the new system
Step-by-step explanation:
Sample size 800
Sample x₁ = 420 ( number of people in favor of a proposed scoring system), then
p₁ = 420/800 p₁ = 0,525 p₁ = 52,5 % then
q₁ = 1 - p₁ q₁ = 1 - 0,525 q₁ = 0,475
Sample size enought to use the approximation of the binomial didtribution to normal distribution
If significance level is 0,05 α = 0,05
and from z-table we look for z(c) ( z critical value)
z (c) = 1,64
Hypothesis Test:
Null Hypothesis H₀ p₁ = 0,5
Alternative Hypothesis Hₐ p₁ > 0,5
Alternative hypothesis tells us about a one tail-test to the right
To calculate
z(s) = ( p₁ - 0,5) / √ (p₁*q₁) / n
z(s) = 0,025 / √ 0,525*0,475/800
z(s) = 0,025 / √0,000311
z(s) = 0,025/0,01765
z(s) = 1,416
Comparing z(c) and z(s)
z(s) < z(c) 1,416 < 1,64
z(s) is in the acceptance region we accep H₀.
jackson spent 8.55 for 3 bags of chips.how many bags of chips can he got for $30
Answer:
10
Step-by-step explanation:
Find the slope and y-intercept from the following graph of a linear equation.
The amount of water that fits in a fish tank represents the _______________ of the fish tank.
Answer:
Volume
Step-by-step explanation:
The amount of water that fits in a fish tank represents the Volume of the fish tank.
When you pour water, it occupies the space and the weight of the tank increases. So, it represent the volume
A. Without using pencil and paper to actually find the products, how will the product of 3 x 10.6 compare to the product of 2.7 x 10.6? Explain your answer.
B. How will the product of 2.7 X 10.6 compare to the product of 3 X 10.6? Explain your answer.
how do i answer these i forgot all this-
Answer:
Step-by-step explanation:
in A , because we are multiplying a number by the same number in each case, 10.6 we know, that the 3 as compared to the 2.7 , will make a bigger number 3*10.6 is greater than 2.7 * 10.6 , it's just a quick way to make sure our answer is good
in B, as above, we know that 2.7*10.6 will be less than 3*10.6 see?
how do you do stuff like 20 x 0.4?? i forgot
Answer: the answer is 8.0
Step-by-step explanation: what i do is 20*4 which is 80 and i just add the decimals back in hoped this helped :))
What is m<1? Help please
Answer:
139
Step-by-step explanation:
Inside angles of a triangle = 180 degrees
61 + 78 = 139
180 - 139 = 41
unknown interior angle = 41 degrees
So m<1 = 139
(Or just add the two interior angles together)
If a gold ring has a sale price of $21, what was the original price?
There was a sale that was 30% off.
Answer:
27.30
Step-by-step explanation:
What is the greatest common factor of 10x^2 and 15x ?
Answer:
5
Step-by-step explanation:
because 5 is used for both numbers and that's why
Answer:
5x
Step-by-step explanation:
Both 10 and 15 have a HCF of 5
And both values have x in common
At a peace summit, seven Hatfield and nine McCoy family
members sit down for a meeting. If the Sheriff orders two
randomly selected participants to shake hands at the end of
the meeting, what is the probability that the two are from
different families?
Answer:
0.525 = 52.5% probability that the two are from different families.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this problem, the order in which the two participants are selected is not important, so we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Desired outcomes:
1 from the Harfield family(from a set of 7).
1 from the McCoy family(from a set of 9). So
[tex]D = C_{7,1}*C_{9,1} = \frac{7!}{1!6!}*\frac{9!}{1!8!} = 7*9 = 63[/tex]
Total outcomes:
2 from a set of 16. So
[tex]T = C_{16,2} = \frac{16!}{2!14!} = 120[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{63}{120} = 0.525[/tex]
0.525 = 52.5% probability that the two are from different families.
A hang glider dropped his cell phone from a height of 450 feet. How many seconds did it take for the cell phone to reach the ground?
Answer:
t = 9.58 s
Step-by-step explanation:
Given that,
The height from where the cell phone is dropped, h = 450 feet
We need to find the time for the cell phone to reach the ground. Let the time be t. Using second equation of kinematics to find it.
[tex]h=ut+\dfrac{1}{2}at^2[/tex]
u is initial velocity, u = 0
a = g
So,
[tex]h=\dfrac{1}{2}at^2\\\\t=\sqrt{\dfrac{2h}{g}} \\\\t=\sqrt{\dfrac{2\times 450}{9.8}} \\\\t=9.58\ s[/tex]
So, it will take 9.58 seconds to reach the ground.
A cube with a surface area of 54 square centimeters is shown.
Twelve cubes like the one shown are combined to create a larger cube. What is the volume, in cubic centimeters of the new cube?
Answer:
54 cm
Step-by-step explanation:
they are the same i think
Need help ASAP now plz now z now now now
In the image below, the length of the arc defined by the sector is
Answer:
10pi feet
Step-by-step explanation:
The formula for arc length (degrees) is: 2pi x radius x angle/360
2pi x 30 x 60/360
60pi x 1/6
10pi
is 2+2=4 or is it 2+2=22
Answer:
[tex]2+2=4[/tex] obviously...
Pls mark brainliest!Answer:
well it depends
Step-by-step explanation:
if you wanna be hallarius then 22 but the real mathmatics is 4
PLS GIVE BRAINLIEST
pls help me i suck at math and i really need this done.
Answer:
1.x²+x-2
=x²+2x-x-2
=x(x+2)-1(x+2)
=(x+2)(x-1)
2.
(x²+x-2)/(x-1)
={x²+2x-x-2}/(x-1)
={x(x+2)-1(x+2)}/(x-1)
={(x+2)(x-1)}/(x-1)
=(x+2) true
Easy problem just look at the photo
Answer:
55
Step-by-step explanation:
a triangle adds up to 180°
25+30+x= 180
55+x=180
x=180-55
x=125
x and y is a straight line so it adds up to 180°
x=125 y=?
x+y=180
125+y=180
y=180-125
y=55°
y= 55°