Find the volume of the solid generated by revolving the region bounded by the lines and curves about the x-axis. y = x, y =1, x = 0
Answer:
The volume is: [tex]V = \frac{\pi}{3}[/tex] cubic units
Step-by-step explanation:
Volume of a solid:
The volume of a solid, given by the function f(x), over an interval between a and b, is given by:
[tex]V = \pi \int_{a}^{b} (f(x))^2 dx[/tex]
y = x, y =1, x = 0
This means that the upper function is y = 1, and the lower function is y = x. So
[tex]f(x) = (1 - x)[/tex]
The lower limit of integration is x = 0.
The upper limit is y = x when y = 1, so x = 1.
Then
[tex]V = \pi \int_{a}^{b} (f(x))^2 dx[/tex]
[tex]V = \pi \int_{0}^{1} (1-x)^2 dx[/tex]
[tex]V = \pi \int_{0}^{1} (1-2x+x^2) dx[/tex]
[tex]V = \pi (x-x^2+\frac{x^3}{3})|_{0}^{1} dx[/tex]
[tex]V = \pi(1 - (1^2) + \frac{1^3}{3})[/tex]
[tex]V = \frac{\pi}{3}[/tex]
Help me how to prove triangles inequality
it describes the relationship between the three sides of a triangle. any triangle the sum of length of two sides is always great er then the third side.
6x - 9x - 5 + 8 + 7x
Show your work.
Answer:
6x−9x−5+8+7x
=6x+−9x+−5+8+7x
Combine Like Terms:
=6x+−9x+−5+8+7x
=(6x+−9x+7x)+(−5+8)
=4x+3
Answer:
=4x+3
Step-by-step explanation:
I hope this helps
Answer:
=4x + 3
Step-by-step explanation:
Add the numbers
6
Simplify y ^2 over 6y^5.
Answer:
1/6y^3
Step-by-step explanation:
Answer:
1/6y^3
Step-by-step explanation:
cancel the common factor of y^2 and y^5
A section of a deck is shaped like a trapezoid. For this section, the length of one base is 33 feet, and the length of the other base is 42 feet. The height is 24 feet. What is the area of this section of the deck?
Answer:
I think the answer is 900
Step-by-step explanation:
Use the formula to find the area of a trapeziod (search it up the find it)
Then fill in the numbers where they belong.
What is the slope of the line that passes through the points (6, 9) and (11, 2)? *
A.7/5
B.-5/7
C.-7/5
D.5/7
PLsss I need to do this by todayy pls asap
Answer:
C
Step-by-step explanation:
what is 60% of 80 ??
Answer:
48
because I know........
Answer:
48
Step-by-step explanation:
60 divided by 100, then times 80 equals to 48
Law of Sines!
Am I on the right track?
sin34/x = sin27/11 = sinθ/θ
Answer:
x=13.5
Step-by-step explanation:
You are on the right track with sin34/x=sin27/11 (remember you don't need all three angles/sides)
[tex]\frac{sin34}{x}[/tex] = [tex]\frac{sin27}{11}[/tex]
(sin27)(x)=6.15112193818
x=6.15112193818/0.45399049974
x=13.5490102584
This 3rd and 2nd grade lvl paper dont ask why
Answer:
Across
Evapotranspiration is the sum of evaporation from plants.
Earth is surrounded by invisible gases that form a thin protective blanket that we call the atmosphere.
Water flows downhill because gravity is a form of potential energy – and the water, or anything that falls or rolls downward – flows in response to differences in potential energy (from high to low). ... Therefore, the potential energy that drives groundwater movement includes both pressure and gravity.
Precipitation: hail, rain, freezing rain, sleet and snow.
Condensation is the opposite of vaporization. Condensation occurs when a gas loses energy, slows in motion so that its cohesive force pulls the molecules close, but the molecules still have enough energy to break away from one connection only to connect with another molecule.
Down
Alternatively evaporation of the liquid should leave a solid residue. ... Dissolving is a reversible process and the solute can be recovered from a solution by evaporation though it will not always be in the exactly the same form as at the start.
Boiling. If a liquid is heated the particles are given more energy and move faster and faster expanding the liquid.
Answer: No entiendo la historia y no vengas por mí, solo quería los puntos jajaja
Step-by-step explanation:
Chase is making a cake for his daughter's birthday. The normal recipe calls for 8 ounces of butter and 16 ounces of sugar. Chase then decides to make a slightly smaller cake and only use 6 ounces of butter. How many ounces of sugar will he need in his smaller cake?
Answer:
A lot
Step-by-step explanation:
Why am I baking cakes. I SUCK.
There are 12 ounces of sugar will he need in his smaller cake.
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
The normal recipe calls for 8 ounces of butter and 16 ounces of sugar.
Let the amount of sugar will he need in his smaller cake = x
So, By definition of proportion, we get;
⇒ Amount of Butter / Amount of Sugar
⇒ 8 / 16 = 6 / x
⇒ x = 6 × 16 / 8
⇒ x = 12 ounces
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A skin-care company had 1,500 people try a new acne cream. Nine people had a mild allergic reaction. The formula is then improved and those 1,500 people try the new cream. Only 4 of them had a mild allergic reaction. What is the percent decrease in number of allergic reactions?
Answer:
The decrease in number of allergic reactions is of 0.3333%.
Step-by-step explanation:
Initial percentage:
Nine out of 1500, so the percentage is:
[tex]\frac{9*100}{1500} = \frac{900}{1500} = 0.6[/tex]
Initially: 0.6% of allergic reactions.
Final percentage:
Four out of 1500, so the percentage is:
[tex]\frac{4*100}{1500} = \frac{400}{1500} = 0.2667[/tex]
WIth the improved formula: 0.2667% of allergic reactions.
What is the percent decrease in number of allergic reactions?
0.6% - 0.2667% = 0.3333%
The decrease in number of allergic reactions is of 0.3333%.
Answer fast...Show work on both
Answer:
A) 14.3606 ft
B) 2.8112 seconds
Step-by-step explanation:
A) At maximum height which is its peak, the velocity will be zero.
Now, we are given height modeled by;
h(t) = 4.98t² - 14t + 20
v(t) = dh/dt = 9.96t - 14.
At max height which is v(t) = 0, we have;
9.96t - 14 = 0
9.96t = 14
t = 14/9.96
t = 1.4056 s
Thus, height at this time is;
h(1.4056) = 4.98(1.4056)² - 14(1.4056) + 20
h(1.4056) = 14.3606 ft
B) time of flight = 2 × time to get to peak = 2 × 1.4056 = 2.8112 seconds.
The size of a jar of coffee is increased by 1/5. The new size is later reduced by 1/5.
Is the new jar smaller, the same size or larger than the original? Explain how you worked out your answer.
Answer:
The new jar is smaller.
Step-by-step explanation:
Like what the statements says, the normal size of coffee is reduced by 1/5 and it become as the new jar which is smaller than the original.
Type of triangle the has side measures of 6cm, 7cm and 12cm. And one angle with a measure of 120 degrees
Answer:
Obtuse triangle
Step-by-step explanation:
Given
Sides: 6cm, 7cm and 12cm
Angle: 120 degree
Required
Determine the type of triangle
Because the measure of an angle of the triangle was mentioned, we have to classify the triangle by its angle.
From the question, we understand that one of the angles is greater than 90 (i.e. 120 degrees). This type of triangle are referred to as obtuse triangles.
Simplify 42/56 i am gonna need to show work so i dont fail
Answer:
42/56 = 3/4
Step-by-step explanation:
Answer:
The simplified fraction is [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Simplifying Fractions
A given fraction [tex]\frac{a}{b}[/tex] can be simplified if a and b have common factors, i.e. if they can be evenly divided by at least one equal number.
The fraction is:
[tex]\frac{42}{56}[/tex]
We'll simplify it by 2 since both numbers are even:
[tex]\frac{42}{56}=\frac{21}{28}[/tex]
The next prime common factor is 7. Dividing by 7:
[tex]\frac{42}{56}=\frac{21}{28}=\frac{3}{4}[/tex]
Thus, the simplified fraction is [tex]\frac{3}{4}[/tex]
are these correct? i hate how the teacher had me do this.but picture above.
Answer:
Yes they are correct
Step-by-step explanation:
Amelia pays $24 to rent a boat at the lake for up to six hours she constructs the inequality and number line below to represent the number of hours X she can use the boat?
solve for x. show your work.
Hello!
[tex]\large\boxed{x = 8}[/tex]
The two angles pictured are corresponding angles, so they are congruent.
Therefore:
17x - 4 = 12 + 15x
Isolate for x by subtracting 15x from both sides:
2x - 4 = 12
Add 4 to both sides:
2x = 16
Divide both sides by 2:
x = 8.
Answer:
x=8
Step-by-step explanation:
These angles are what we call corresponding angles. This simply means that they are the same. Therefore, we set 17x-4 equal to 12+15x. To isolate x, add 4 to both sides, and subtract 15x from both sides. 2x=16. x=8. To check, both angles = 132 degrees.
The legs of a right triangle are in the ratio 3:4. If the hypotenuse is 10, what is the length of the longer leg?
Answer:
8
Step-by-step explanation:
ratios of legs = 3x and 4x
Pythagorean theorum:
A^2+B^2=C^2
3x^2+4x^2=10^2
9x^2+16x^2=100
25x^2=100 --> divide by 25
x^2=4 --> x=2
length of longer leg is 4x = 4 x 2 = 8
The length of the longer leg of the triangle is 8.
What is the Pythagorean theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.
Given that, the legs of the right triangle are in the ratio of 3:4.
Therefore, let the legs of the triangles be 3x and 4x.
Since the hypotenuse of the triangle is 10, using the Pythagorean theorem it follows:
10² = (3x)² + (4x)²
100 = 9x² + 16x²
100 = 25x²
x² = 4
x = 2
Therefore, the lengths of the legs are:
3(2) = 6, and
4(2) = 8
Hence, the length of the longer leg of the triangle is 8.
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Can anyone help me pls
Answer:0.125
Step-by-step explanation:
There is only 1/8 that is whistle so convert into percent and get 0.125. Hope this helps
Answer:
0.125
Step-by-step explanation:
There are 8 possibilities.
Only 1 whistle.
1/8 = 0.125
A publisher reports that 52% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 180 found that 46% of the readers owned a laptop. Find the value of the test statistic. Round your answer to two decimal places.
Answer:
The value of the test statistic is [tex]t = -1.61[/tex]
Step-by-step explanation:
Central Limit Theorem
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Our test statistic is:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the expected mean, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
A publisher reports that 52% of their readers own a laptop.
This means that [tex]\mu = 0.52[/tex]
Sample of 180:
Means that [tex]n = 180[/tex]
By the Central Limit Theorem:
[tex]\frac{\sigma}{\sqrt{n}} = s = \sqrt{\frac{0.52*0.48}{180}} = 0.0372[/tex]
A random sample of 180 found that 46% of the readers owned a laptop.
This means that [tex]X = 0.46[/tex]
Find the value of the test statistic.
[tex]t = \frac{X - \mu}{s}[/tex]
[tex]t = \frac{0.46 - 0.52}{0.0372}[/tex]
[tex]t = -1.61[/tex]
The value of the test statistic is [tex]t = -1.61[/tex]
Is either x = 6 or x = 8 a solution to 12 + x = 20? O A. Neither is.a solution. B. X = 6 is a solution, but x = 8 is not. C. X= 8 is a solution, but x = 6 is not D. They are both solutions. SUBMIT
Answer:
C. x = 8 is a solution, but x = 6 is not
Step-by-step explanation:
12 + 6 = 18
12 + 8 = 20
20 - 12 = 8
HELPPPPP!:(
In order to ride a roller coaster, a rider must be greater than 48 inches tall. Right now, Jeff is 45 inches tall. Write an inequality that describes how many more inches Jeff must grow in order to ride the roller coaster.
Answer:
x is greater than or equal to 3 inches.
Step-by-step explanation:
The required inequality that models the situation of age to grow is given as x ≥ 3.
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Let the age to be grow be x,
According to the question,
45 + x ≥ 48
Simplifying the above expression,
x ≥ 3
Thus, the required inequality that models the situation of age to grow is given as x ≥ 3.
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Part 2: Free Response 11. The distribution of actual weights of 8-ounce chocolate bars produced by a certain machine is Normal with mean 8.1 ounces and standard deviation 0.1 ounces. Company managers do not want the weight of a chocolate bar to fall below 8 ounces, for fear that consumers will complain. (a) Find the probability that the weight of a randomly selected candy bar is less than 8 ounces.
Answer:
0.1587 = 15.87% probability that the weight of a randomly selected candy bar is less than 8 ounces.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
The distribution of actual weights of 8-ounce chocolate bars produced by a certain machine is Normal with mean 8.1 ounces and standard deviation 0.1 ounces.
This means that [tex]\mu = 8.1, \sigma = 0.1[/tex].
(a) Find the probability that the weight of a randomly selected candy bar is less than 8 ounces
This is the pvalue of Z when X = 8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{8 - 8.1}{0.1}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587
0.1587 = 15.87% probability that the weight of a randomly selected candy bar is less than 8 ounces.
ABCD is a square. If m<ACB = (11x-32)°, find the value of x.
Answer:
x = 7Step-by-step explanation:
Find the image attached
Since ABCD is a square, <ACB = 45 degrees
Given <ACB = 11x-32
Equate both
11x-32 = 45
11x = 45+32
11x = 77
x = 77/11
x = 7
Hence the value of x is 7
I need help on this plz
Answer:
None
Step-by-step explanation:
Laura is saving money to buy a game. The game cost $36, and so far she has saved three- fourths of this cost. How much money has Laura saved
Answer:
27
Step-by-step explanation:
3/4*36=27
therefore the answer is
27
the jet stream is a wind current that flows across the US from west to east. Flying with the jet stream, an airplane flew 2700 miles in 4.5 hours. Against the same wind, the return trip took 6 hours. Find the speed of the plane in stil air and the speed of the jet stream.
Answer:
The speed of the plane in still air and the speed of the jet stream are 525 miles per hour and 75 miles per hour.
Step-by-step explanation:
From Mechanical Physics, we know that absolute velocity of the airplane ([tex]v_{A}[/tex]) is equal to sum of the absolute velocity of the jet steam [tex](v_{J})[/tex] and the relative velocity of the airplane with respect to jet stream (velocity of the airplane in still air) ([tex]v_{A/J}[/tex]). Al velocities are measured in miles per hour. Let suppose that both jet stream and airplanes travels at constant velocity. Now, we construct the following system of linear equations:
Flight with the jet stream
[tex]v_{J}+v_{A/J} = \frac{2700\,mi}{4.5\,h}[/tex]
[tex]v_{J}+v_{A/J} = 600\,\frac{mi}{h}[/tex] (1)
Flight against the jet stream
[tex]v_{J} -v_{A/J} = -\frac{2700\,mi}{6\,h}[/tex]
[tex]v_{J}-v_{A/J} = -450\,\frac{mi}{h}[/tex] (2)
The solution of this system of linear equations is:
[tex]v_{J} = 75\,\frac{mi}{h}[/tex], [tex]v_{A/J} = 525\,\frac{mi}{h}[/tex]
The speed of the plane in still air and the speed of the jet stream are 525 miles per hour and 75 miles per hour.
Express in simplest radical form
Answer:
gg
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
2 x 2 =4
what is the remainder when 849,400 is divided by 216
Answer:
The remainder is 88
Step-by-step explanation:
The Remainder of a Division
We have to find the remainder when we divide 849,400 by 216.
It could be found by doing the long division, but we'll do it with a calculator.
Entering the division in the calculator we get:
849,400/216=3,932.4074...
We take the whole part of the quotient (3,932) and multiply it by the divisor:
3,932*216=849,312
The remainder is obtained by subtracting 849,400-849,312=88
The remainder is 88