The supplied statement states that the iterated integral after being converted to interpolation is 32/3.
What is the definition of an integral?In mathematics, an integral is either a number representing the region beneath a function's graph over a certain interval or just a new function, the reverse of which contains the original mechanism (indefinite integral). To complete the whole, an essential component is required. The term "essential" is almost a synonym in this context. Trigonometric functions of functional and equations are a concept in mathematics. Integral is a derivative of Middle English, Latin integer, and Medieval Latin integralis, each of which mean "making up a whole."
Therefore, the area is,
[tex]R=\left\{(x, y) \mid 0 \leq x \leq 2,0 \leq y \leq \sqrt{2 x-x^2}\right\}[/tex]
So,
[tex]y=\sqrt{2 x-x^2}[/tex]
y² = 2x - x²
x² - 2x + y² = 0
x² - 2x + 1 + y² = 1
(x-1)² + y² = 1
In other words, the area is the middle section of the disk with a radius of 1 and a center at (0,1).
Region R's polar coordinates are
x = r cos∅, y = r sin∅
So,
[tex]y=\sqrt{2 x-x^2}[/tex]
y² = 2x - x²
x² + y² = 2x
r² = 2r cos∅
r = 2 cos∅
The polar coordinates of the sphere of integration as,
[tex]R=\left\{(r, \theta) \mid 0 \leq \theta \leq \frac{\pi}{2}, 0 \leq r \leq 2 \cos \theta\right\}[/tex]
The provided integral then becomes,
[tex]\begin{aligned}& \int_0^2 \int_0^{\sqrt{2 x-x^2}} 6 \sqrt{x^2+y^2} d y d x \\= & \int_0^{\frac{\pi}{2}} \int_0^{2 \cos \theta} 6 r \cdot r d r d \theta \\= & \int_0^{\frac{\pi}{2}} \int_0^{2 \cos \theta} 6 r^2 d r d \theta \\= & \int_0^{\frac{\pi}{2}} 6\left(\frac{r^3}{3}\right)_0^{2 \cos \theta} d \theta\end{aligned}[/tex]
[tex]\begin{aligned}& =\int_0^{\frac{\pi}{2}} 2\left(8 \cos ^3 \theta-0\right) d \theta \\& =16 \int_0^{\frac{\pi}{2}} \cos ^2 \theta \cdot \cos \theta d \theta \\& =16 \int_0^{\frac{\pi}{2}}\left(1-\sin ^2 \theta\right) \cdot \cos \theta d \theta\end{aligned}[/tex]
Let u = sin∅ then du = cos ∅ d∅
If ∅ = 0 then u = 0 and if ∅ = π/2 then u = 1.
The above integral thus becomes,
[tex]\begin{aligned}& \int_0^2 \int_0^{\sqrt{2 x-x^2}} 6 \sqrt{x^2+y^2} d y d x \\= & 16 \int_0^1\left(1-u^2\right) d u \\= & 16\left(u-\frac{u^3}{3}\right)_0^1 \\= & 16\left(1-\frac{1}{3}\right)\end{aligned}[/tex]
= 32/3
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Solve the following simultaneous equations. 3* x 9-1 = 243 8×2-²-2²x+1 3% 4√2 94 + 15-
Answer: 2.55x
Step-by-step explanation:
A local hamburger shop sold a combined total of 713 hamburgers and cheeseburgers on Tuesday. There were 63 more cheeseburgers sold than hamburgers. How many hamburgers were sold on Tuesday?
Answer:
325 hamburgers were sold on Tuesday
Step-by-step explanation:
We can start solving the problem by using algebra. Let H be the number of hamburgers sold and C be the number of cheeseburgers sold. We know from the problem that:
H + C = 713 (total number of hamburgers and cheeseburgers sold)
C = H + 63 (there were 63 more cheeseburgers sold than hamburgers)
We can substitute the second equation into the first equation:
H + (H + 63) = 713
2H + 63 = 713
2H = 650
H = 325
assume you are standing on the moon where the first humans landed in the sea of tranquility. what is the length of time that you would be in sunlight? in other words, how long does daylight last on the moon? a. 24 hours b. 12 hours c. two weeks (1/2 month) d. 29.53 days (1 month) e. 27.3 days
Standing on the moon, you would be in sunlight for approximately 27.3 days.
What is length?Length is a physical measurement of distance, or the dimensions of an object. It can be measured in metres, kilometres, feet, yards, or other units of measurement. Length can also be used to describe the amount of time something takes, or the size of something, such as a book or a piece of clothing. Length is an important concept in mathematics and science, and is used to measure, compare, and quantify objects and events.
This is because the moon has no atmosphere, so it has no day and night cycles. Instead, the sun shines on the moon for an entire month, and then the moon moves into the shadow of the Earth and remains dark for the next month. The length of this daylight cycle is 27.3 days, and this is the amount of time that you would be in sunlight if standing on the moon.
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sat math scores are approximately normally distributed, with a mean of 508 and a standard deviation of 120. skye decides to take the sat exam, and scores 920. what is the probability someone scored less than her on the sat math test?
On solving the provided question, we can say that standard deviation and mean, The equivalent ACT score is using 1.545 as the z score [tex]= > X = 1.545 * 3.9 + 19.2 = 25.5[/tex]
What is standard deviation?Standard deviation is a statistic that expresses the variability or variance of a group of numbers. While a high standard deviation suggests that the values are more dispersed, a low standard deviation suggests that the values tend to be closer to the established mean. A measure of how dispersed the data are from the mean is the standard deviation (or ). When the standard deviation is low, the data tend to be grouped around the mean, and when it is large, the data are more dispersed. The average variability of the data set is measured as standard deviation. It reveals the average deviation of each score from the mean.
[tex]X = 0.675 * 198 + 1101 = 1235[/tex]
standard deviation and mean
[tex]X = 0.675 * 3.9 + 19.2 = 21.8[/tex]
scores 1407 standardized score z for 1407
[tex]z = (X-μ)/σ = (1407-1101)/198 = 1.545[/tex]
The equivalent ACT score is using 1.545 as the z score
[tex]= > X = 1.545 * 3.9 + 19.2 = 25.5[/tex]
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What is the relationship between doubling and halving?
The relationship between Doubling and halving is that in halving we simply half one of the factors and in doubling we double the other.
The Doubling and Halving is a technique that is commonly used in Multiplication of two numbers .
Let us understand the Relationship between Doubling and Halving with help of an example ;
Example : To solve 25×16, it is not that simple to directly multiply these ,
By using the Doubling and Halving method ,
we could double the number 25 to make it 50 and
then half the number 16 to make it 8.
So , the equivalent expression becomes , [tex]50\times8[/tex] ,which is much easier to solve , that is 400 .
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How do you know if an absolute value equation is all real numbers?
If the right hand side of the equation is non-negative real number, the equation will have two solution that include all real numbers.
An absolute value equation of the form |x| = k (where k is a constant) will have two solutions, one positive and one negative, that are the same distance from 0 on the number line.
To determine if the solutions of the equation include all real numbers, you can examine the value of k. If k is a non-negative real number, then the two solutions of the equation will include all real numbers, because any real number is either positive or negative and the same distance from 0 as k.
For example, if the equation is |x| = 5, the two solutions of the equation are x = 5 and x = -5, which include all real numbers.
On the other hand, if k is a negative real number or a complex number, the equation is not valid and there are no solutions.
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what is the measure of the smaller angle between the hands of a $12$-hour clock at $12:25$ pm, in degrees? express your answer as a decimal to the nearest tenth.
The measure of the smaller angle between the hands of a 12-hour clock at 12:25 pm is 137.5 degrees.
The hour hand of a 12-hour clock completes one full rotation in 12 hours while the minute hand completes one full rotation in 60 minutes. To find the measure of the angle between the hands of a 12-hour clock at 12:25 pm, we need to calculate the relative position of the hands with respect to the 12 o'clock position.
At 12:25 pm, the minute hand is pointing to the 12.25 mark on the clock which is 25 minutes after 12 o'clock and the hour hand is pointing to the 12 o'clock mark.
The minute hand moves 360 degrees every 60 minutes, so in 25 minutes, it would have moved (360/60)*25 = 75 degrees.
The hour hand moves 360 degrees every 12 hours, so in 25 minutes, it would have moved (360/12*60)*25 = (30)*25 = 750/60 = 12.5 degrees.
The angle between the hands is the absolute difference between their positions.
the angle between the hands = |75-12.5| = 62.5 degrees
However, the clock has two hands and thus we have two angles between the hands.
Therefore, the measure of the smaller angle between the hands of a 12-hour clock at 12:25 pm is 180-62.5 = 137.5 degrees.
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Select the correct answer.
which is the oldest form of money still in existence today?
a. paper money
b. metallic money
c. fiat money
d. fractionally backed paper money
The oldest type of currency still in use today, according to the claim, is metal.
What is the greatest way to define money?Money is a good that is frequently used as a basis of economic exchange. It is used to communicate values and prices and is the primary determinant of value. By effortlessly traveling from one person to another and from one country to another, money fosters commerce.
Why is it called money?Money is derived from the Latin term moneta, which means "coin," through the French term monnaie. It is thought that the Latin phrase came from a temple dedicated to Juno on Capitoline, being one Poland's seven hills. Juno was frequently linked to riches in ancient times.
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pepe is going to spin the following spinner 800800800 times. the spinner is divided into equal sections. a spinner with 5 equal sections, 4 of which are shaded and 1 of which is not shaded complete the following statement with the best prediction. the spinner will land in the shaded region... choose 1 answer: choose 1 answer: (choice a) a exactly 160160160 times (choice b) b close to 160160160 times but probably not exactly 160160160 times (choice c) c exactly 640640640 times (choice d) d close to 640640640 times but probably not exactly 640640640 times
The expected number of times out of 800 spins that the spinner will land in the shaded region for this case is 640.
How to calculate the probability of an event?Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.
Then, suppose we want to find the probability of an event E.
Then, its probability is given as:
[tex]P(E) = \frac{Number of Favourable Cases}{Number of Total Cases} = \frac{n(E)}{n(S)}[/tex]
where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
How to find that a given condition can be modeled by binomial distribution?Binomial distributions consists of n independent Bernoulli trials.
Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as:
[tex]P(X = x) = ^nC_{x} p^{x} (1-p)^{n-x}[/tex]
The expected value and variance of X are:
[tex]E(X) = np\\Var(X) = np(1-p)[/tex]
Each of the 800 spins are independent in terms of their result from each other.
Each spin ends up either in shaded region (call it success), or non-shaded region(failure).
P(success) = P(A spin landing in shaded region) = 4/5 (as there are total 5 partition of spinner possible (assuming no other outcome possible), and that there are 4 shaded regions (favorable elementary events).
If we take X = number of successes in those 800 spins, then:
[tex]X[/tex] ~ [tex]B (n=800, p = 4/5=0.8)[/tex]
The expected value of X is:
[tex]E(X) = np = 800 * 0.8 = 640[/tex]
Thus, the expected number of times out of 800 spins that the spinner will land in the shaded region for this case is 640.
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Determine which numbers in the set are natural numbers, whole numbers, integers, rational numbers, and irrational numbers, Select all that apply.{13, −15, −17/13, √7,3.63, π/4,17}
Natural Numbers: 13, 17
Whole Numbers: 13, 17
Integers: -15, 13, 17
Rational Numbers: -17/13, 3.63
Irrational Numbers: √7, π/4
First, let us understand what each type of numbers are.
Natural Numbers: All positive numbers from 1 to infinity are considered natural numbers and are therefore a component of the number system. Because they don't contain zero or negative numbers, natural numbers are also known as counting numbers. They are a subset of real numbers, which only include positive integers and exclude negative, zero, fractional, and decimal numbers.
Whole Numbers: The term "whole numbers" refers to numbers devoid of fractions, which are made up of positive integers and zero. Its symbol is "W," and its range of numbers is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,...}. The entire number zero denotes nothing or a null value.
Integers: Positive, negative, and zero are all examples of integers. The Latin word "integer" signifies "whole" or "intact." As a result, fractions and decimals are not included in integers.
Rational and Irrational Numbers: An irrational number cannot be stated using fractions, but a rational number may be expressed as the ratio of two integers with the denominator not equal to zero. Irrational numbers are non-terminating and non-recurring, whereas rational numbers have terminating decimals.
Now, in the set provided, we can classify them as follows.
Natural Numbers: 13, 17
Whole Numbers: 13, 17
Integers: -15, 13, 17
Rational Numbers: -17/13, 3.63
Irrational Numbers: √7, π/4
Thus, this is the final classification.
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2
The probability distribution of the random variable X is shown in the following table.
0
3
1 2
0.12 0.16 9 0.22
-2
P(X=x) 0.08
X
-1
P
The mean of X is 1.05.
(i) Write down two equations involving p and q and hence find the values of p and q.
(ii) Find the variance of X.
[4]
[2]
Answer:
I don't know ooo y the same time that I can come get you if you want to
Calculate the potential energy of a 50kg boulder at the ledge of a cliff 250m high (using guess method)
The potential energy of a 50kg boulder at the ledge of a cliff 250m high is 122500 J.
Potential energy is the energy carried by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.
The PE energy of a boulder 250 m from the ground is given by the formula
PE = h x m x g where h is the height above the ground, m is the mass, and g is the acceleration of gravity.
Putting the given values in the equation
PE = 250m x 50 kg x 9.8 m/s² = 122500 J
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in how many ways can we generate a 3-digit number using numbers 1,2,3,4,5 if no digit can be repeated?
There are 10 possible 3-digit numbers which can be generated using numbers 1, 2, 3, 4, and 5 without repeating any digits.
There are 5 choices for the first digit, 4 choices for the second digit, and 3 choices for the third digit. This can be expressed using the combination formula:
nCr = n! / r!(n - r)!
So, the number of possible 3-digit numbers with no digit repeated can be calculated as 5C3 = 5!/(3!*2!) = 10.
Therefore, there are 10 possible 3-digit numbers which can be generated using numbers 1, 2, 3, 4, and 5 without repeating any digits. These numbers are 123, 124, 125, 134, 135, 145, 234, 235, 245, and 345.
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which is the best measure of center for third period, and why? interquartile range, because there is 1 outlier that affects the center standard deviation, because there are no outliers that affect the center mean, because there are no outliers that affect the center median, because there is 1 outlier that affects the center
Mean, because there are no outliers that affect the center
third period: 3,2,3,1,3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2
Sorted values : 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4
The mean = ΣX / n
n = sample size, n = 15
Mean = 34 / 15 = 2.666
The median = 1/2(n+1)th term.
1/2(16)th term = 8th term.
The 8th term = 2
The best measure of centre is the mean because the values for the second period has no outliers that might have affected the centre of the distribution.
Both interquartile range and standard deviation are measures of spread and not measures of centre.
complete question
A survey was taken of students in math classes to find out how many hours per day students spend
on social media. The survey results for the first., second-, and third-period classes are as follows:
First period: 2,4,3,1,0, 2, 1, 3, 1,4,9,2,4,3,0
Second period: 3,2,3,1,3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2
Third period: 4,5, 3, 4, 2, 3, 4, 1, 8, 2, 3, 1, 0, 2, 1,3
Which is the best measure of center for second period and why? (5 points)
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Patrick is 20 years older than his son, James. In two years, Patrick will be twice as old as James. Find their present ages. Please explain what you did to get your equation and why!
Answer:
James is 18 and Patrick is 38
Step-by-step explanation:
Let p = Patrick's age
Let j= James' age
p = j + 20
p + 2 = 2(j+2) Substitute j + 20 for p
j + 20 + 2 = 2j + 4 Combine like terms.
j + 22 = 2j + 4 Subtract j from both sides
j -j + 22 = 2j - j + 4
22 = j + 4 Subtract 4 from both sides
22 - 4 = j + 4 - 4
18 = j
James is 18 years old.
Substitute 18 for j in p = j + 20
p = 18 + 20
p = 38
Patrick is 38
Help
A right triangle is drawn inside a sphere, and the hypotenuse is 16 cm. Explain how to find the volume of the sphere and show your calculations. Round the radius to the nearest hundredth and use that rounded radius to calculate the volume. Round the volume to the nearest hundredth.
Answer: The volume of a sphere can be calculated using the formula V = 4/3 * pi * r^3, where V is the volume and r is the radius of the sphere. In this case, we can use the Pythagorean theorem to find the radius of the sphere. The hypotenuse of the right triangle is 16 cm and is also the diameter of the sphere, therefore the radius of the sphere is half of the hypotenuse or 8 cm.
Now we can use this value of radius to calculate the volume of the sphere.
V = 4/3 * pi * 8^3
V = 4/3 * pi * 512
V = 2197.333 cm^3 (rounded to the nearest hundredth)
So, the volume of the sphere is 2197.333 cm^3
Step-by-step explanation:
From 2008 to 2011, worldwide sales of a popular smartphone brand can be modeled with an exponential function. In 2009, about 20.73 million of the smartphone brand were sold. - In 2008, about 11.63 million of the smartphone brand were sold. - In 2010, about 39.99 million of the smartphone brand were sold. If the sales continued to grow exponentially, about how many of the smartphone brand were sold in 2012
To determine the number of smartphones sold in 2012 with the exponential function.
What is exponential function ?
An exponential function is a mathematical function in which the variable, or the input, is in the exponent (power) of the function. It takes the form of f(x) = ab^x, where a and b are constants and x is the variable. The variable x is often time and the constant b is often greater than 1, which causes the function to grow at an increasing rate. It is often used to model growth and decay phenomena, such as population growth, radioactive decay, and others.
To estimate the number of smartphones sold in 2012, we would need to find the exponential function that models the worldwide sales of the smartphone brand from 2008 to 2011. Once we have this function, we can plug in the year 2012 as the input to estimate the number of smartphones sold in that year. However, without more information it is impossible to know the exact exponential function and the exact number of smartphones sold in 2012.
To determine the number of smartphones sold in 2012 with the exponential function.
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A consumer group is investigating two brands of popcorn, R and S. The population proportion of kernels that will pop for Brand R is 0.90. The population proportion of kernels that will pop for Brand S is 0.85. Two independent random samples were taken from the population. The following ta
As per the given distribution the consumer group claims that the difference in proportions has a mean of 0.05.
The term mean in math is defined as the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Here we have given that the consumer group is investigating two brands of popcorn, R and S.
And the population proportion of kernels that will pop for Brand R is 0.90 where as the population proportion of kernels that will pop for Brand S is 0.85.
Then the difference of the mean is calculated as,
=> 0.90 - 0.85
=> 0.05
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Solve the following pair of simultaneous equations 3^y+1=1/9 and 5^y/125^x=125
Answer:
Step-by-step explanation:
[tex]3^{y}[/tex] + 1 = 1/9
3^y = -8/9
5^y/125^x = 125
5^y/5^3x = 125
5^(y-3x) = 5^3
y-3x = 3
Your question is incorrect as 3^x can never be negative.
But, now you know y - 3x = 3, so, use this to get the values when you reconsider the correct question.
Thanks
What is 1/2 as a decimal and percent?
1/2 as a decimal is 0.5. As a percent, it is 50%. 1/2 can be written as a decimal by dividing the numerator (1) by the denominator (2).
In this case, 1 divided by 2 is 0.5. To convert this decimal to a percent, simply multiply it by 100. 0.5 multiplied by 100 is 50%, so 1/2 as a percent is 50%.
1/2 is 0.5 as a decimal and 50% as a percent.
1/2 is equal to 0.5 when written as a decimal. This means that 1 is divided by 2, resulting in 0.5. To convert this decimal to a percentage, it is necessary to multiply it by 100. When 1/2 is multiplied by 100, it comes out to be 50%, meaning that 1/2 as a percent is 50%. This shows that 1/2 is equal to 0.5 as a decimal and 50% as a percent.
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What is the length of the children shoes?
Answer:
60mm
Step-by-step explanation:
240*1/4=60mm
Answer:
40 mm
Step-by-step explanation:
Given information:
The average adult shoe is 240 mm in length.The children's shoes are smaller than the adult shoesTo find the length of the children's shoes, multiply the length of the adult shoes by the scale factor:
[tex]\begin{aligned}\implies 240 \times \dfrac{1}{6}&=\dfrac{240 \times 1}{6}\\\\&=\dfrac{240}{6}\\\\&=\dfrac{40 \times 6}{6}\\\\&=40\; \sf mm\end{aligned}[/tex]
Therefore, the length of the children's shoes is 40 mm.
the congruent sides of an isosceles triangle are each $5$ cm long, and the perimeter is $17$ cm. in centimeters, what is the length of the base?
The congruent sides of an isosceles triangle are each $5$ cm long, and the perimeter is $17$ cm. the length of the base is 7 cm.To calculate the length of the base of an isosceles triangle, we can use the formula of the perimeter.
The perimeter is the sum of all sides of a triangle, so the formula is Perimeter = Side1 + Side2 + Base. In this case, the two congruent sides are each 5 cm long, and the perimeter is 17 cm. So, if we set up an equation, we have 17 = 5 + 5 + Base. We can then solve the equation for Base by subtracting 10 from both sides.
This gives us 17 - 10 = 5 + Base, and then subtracting 5 from both sides gives us 12 = Base. Then, we can divide both sides by 12 to get 1 = Base / 12. Lastly, we can multiply both sides by 12 to get 12 = Base. Therefore, the length of the base is 7 cm.
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Write an expression that represents the height of a tree that begins at 6.7 feet and increases by 2.9 feet per year. Let t represent the number of years.
An expression that represents the height of a tree is 6.7 + 2.9.
What is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Here, we have
Given
The initial height of the tree is 6.7 feet
The increase in height per year = 2.9 feet
Thus,
The expression will be = 6.7 + 2.9t,
Here t represents the number of years.
Hence, an expression that represents the height of a tree is 6.7 + 2.9.
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Your company will generate $57,000 in annual revenue each year for the next seven years from a new information database. if the appropriate interest rate is 7.8%, what is the present value of the savings?
If a new information database generates $57,000 in yearly income for your organization over the following seven years. The funds are worth $298,795.93 in current value.
What is percent?A percentage is a fraction of a whole represented as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the share of the total by the total and multiply by 100. The term "percent" comes from the Latin per centum, which means "hundred" or "by the hundred". The symbol for "percent" came from the Italian expression per cento, which means "for a hundred".
Here,
PVA= Present value = ?
r = Interest rate = 7.8%
t = Time = 7 years
Let plug in the formula
PVA = $57,000{[1 − (1/(1+.078)^7)]/.078}
PVA = $57,000{[1 − (1/1.078^7)]/.078}
PVA = $57,000{[1 − (1/1.6917)]/.078}
PVA = $298,795.93
If your organization will make $57,000 in annum income from a new information database over the next seven years. The current value of the savings is $298,795.93.
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Find angle V using law of sines, round up 1 decimal
Using sine law, the length of t is 11.34 units
What is Law of SinesA fundamental conclusion of trigonometry that connects a triangle's sides and angles is known as the law of sines. It claims that the following relationship holds for any triangle with sides a, b, and c and opposite angles a, b, and c:
a / sin A = b / sin B = c / sin C
In other words, each of the triangle's three sides has a length that is equal to the sine of the angle opposite it. Any triangle, correct or not, can be related to another triangle in this way.
When some of the information is available, it is common to utilize the Law of Sines to find the triangle's unknown side lengths or angle measurements. In addition to the Law of Cosines, it can also be employed alone.
Using sum of angle of triangle;
V + U + T = 180
v + 100 + 36 = 180
v + 136 = 180
v = 180 - 136
v = 44°
8 / sin 44 = t / sin 100
t = 8 sin100 / sin44
t = 11.34
The value of t is 11.34 units
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What is the volume, in cubic inches, of the cylinder below?
Answer:
[tex]\boxed{\mathrm{108 \pi \;cubic\; inches}}[/tex]
3rd Choice
Step-by-step explanation:
Volume of a cylinder V is given by the equation:
[tex]V = \pi r^2h\\\\\textrm{where r = radius of the cylinder}\\\\\textrm{and, h = height of the cylinder}\\\\[/tex]
[tex]\textrm{From the diagram we see the diameter of the cylinder = 6 in }\\\\\mathrm{radius = \dfrac{diameter}{2} }\\\\\mathrm {So\; radius = \dfrac{6}{2} = 3\;in}\\\\[/tex]
[tex]\mathrm{h = 12\;in}\\\\\\\\\mathrm{V= \pi \cdot 3^2 \cdot 12}\\\\\mathrm{V = \pi \cdot 9 \cdot 12}\\\\\mathrm{V = 108 \pi}[/tex]
Answer
Volume of cylinder = [tex]\boxed{\mathrm{108 \pi \;cubic\; inches}}[/tex]
7.1703171 round to the nearest tenth
To round to the nearest tenth, we examine the digit in the hundredth's place (the second decimal place).
In this case, the number is 7. Since 7 is greater than or equal to 5, we round the digit in the tenth's place up by one.
7.1703171 rounded to the nearest tenth is 7.2.
How do you solve an infinite arithmetic sequence?
We have explained all the steps to solve an infinite arithmetic sequence.
What is an arithmetic sequence?
An arithmetic sequence is a sequence of numbers in which each term is the sum of the previous term and a constant called the common difference.
When it comes to solving an infinite arithmetic sequence, you can use the following formulas:
The n-th term of an arithmetic sequence can be represented as a+(n-1)d, where "a" is the first term, "d" is a common difference, and "n" is the position of the term in the sequence.
The sum of the first n terms of an arithmetic sequence is represented as S_n = n/2(2a + (n-1)d), where "a" is the first term, "d" is a common difference, and "n" is the number of terms.
If a sequence is infinite, the sum of all terms can be represented as S_inf = a/(1-r) where "a" is the first term and "r" is the common ratio (r=1+d)
Hence, we have explained all the steps to solve an infinite arithmetic sequence.
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Find the slope of the line that passes through the given coordinates please help asap I'll give brainliest answer
Answer:
The slope of the line is -10/11
Step-by-step explanation:
To find the slope with points you would use the formula [tex]m = \frac{y2 - y1}{x2 - x1}[/tex]
Now since the line crosses the y-axis at 17, that would be where the y-intercept is, meaning there is a point at (0, 17).
With that, we can find the slope with (11, 7) and (0, 17) in the formula above
So, [tex]m = \frac{17 - 7}{0 - 11}[/tex]
which will simplified to, [tex]m = -\frac{10}{11}[/tex]
So the slope is - 10/11
Jane is creating a stained glass windowpane that will be 5 inches by 7 inches. To make the
rectangular windowpane, Jane fuses together two triangles of colored glass. What is the
perimeter of one triangle? If necessary, round to the nearest tenth. Plsss helpppppp !
Perimeter of one triangle is 20.6 inches.
What is perimeter of triangle?
Perimeter is the length of the boundaries of a closed triangle.
if we add the 3 side lengths of a triangle then the perimeter is determined.
What is the perimeter of one triangle as stated above?
Jane wants to have a rectangular stained glasses that has length 7 inches and width 5 inch.
If she fuses together two triangles of colored glass for obtaining a rectangle, then each triangle will have 3 similar side length.
each triangle has first side length = 5 inches
second side length = 7 inches
other side length = hypotenuse of right-angled triangle
=√(5² + 7²) = √74 inches
A rectangle has four right angles and therefore, the triangles that are developed based on the rectangle must be right-angled.
perimeter of triangle = sum of three side length = (5 + 7+√74) = 20.6 inches
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