Consider the equation below.
f(x) = x8 ln x
(a) Find the interval on which f is increasing. (Enter your answer using interval notation.)
Find the interval on which f is decreasing. (Enter your answer using interval notation.)
(b) Find the local minimum value of f.
(c) Find the inflection point.
(x, y) =
Find the interval on which f is concave up. (Enter your answer using interval notation.)
Find the interval on which f is concave down. (Enter your answer using interval notation.)
Answers
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(a) The interval for which the equation:f(x) = x8 ln x is increasing is (0, e-1/8].
(b) The interval for which the equation:f(x) = x8 ln x is decreasing on the interval [e-1/8, ∞).
ln order to find the interval on which f is increasing, we need to find the derivative of f(x) with respect to x and check its sign. If the derivative is positive, then the function is increasing on that interval. If the derivative is negative, then the function is decreasing on that interval. If the derivative is zero, then we have a critical point that could be a maximum or minimum.
To find the derivative of f(x), we can use the product rule and the chain rule of differentiation:f′(x) = (x8)' ln x + x8 (ln x)'= 8x7 ln x + x8 (1/x)= x7 (8 ln x + 1)The derivative is positive if 8 ln x + 1 > 0, which is equivalent to ln x > -1/8.
Therefore, the function is increasing on the interval (0, e-1/8] and decreasing on the interval [e-1/8, ∞).Answer: The interval on which f is increasing is (0, e-1/8].
( c ) The local minimum value of f(x) = x^8 ln(x) occurs at x = e^(-8) with a value of f(x) = -8e^(-64)
(d) The critical points are x = 0 and x = e^(-8)
To find the local minimum value of f(x) = x^8 ln(x), we will follow these steps:
1. Find the derivative of f(x) with respect to x.
2. Set the derivative equal to zero and solve for x. 3. Determine if the critical points are local minimum values.
4. Evaluate f(x) at the local minimum point.
Step 1: Find the derivative of f(x). Using the product rule, f'(x) = (x^8)' * ln(x) + x^8 * (ln(x))'. f'(x) = 8x^7 * ln(x) + x^8 * (1/x).
Step 2: Set the derivative equal to zero and solve for x. 0 = 8x^7 * ln(x) + x^7 * x. 0 = x^7(8ln(x) + x). The critical points are x = 0 and x = e^(-8).
Step 3: Determine if the critical points are local minimum values. Since f(x) = x^8 ln(x) is only defined for x > 0, we only consider x = e^(-8).
Step 4: Evaluate f(x) at the local minimum point. f(e^(-8)) = (e^(-8))^8 * ln(e^(-8)). f(e^(-8)) = e^(-64) * (-8).
Therefore, the local minimum value of f(x) = x^8 ln(x) occurs at x = e^(-8) with a value of f(x) = -8e^(-64)
(e) The interval for which f(x) = x^8 * ln(x) is concave up is (0, +∞)
(f) The interval for which f(x) = x^8 * ln(x) is concave down is (0, e^(-15/56)).
To find the interval on which f(x) = x^8 * ln(x) is concave up, we need to first find the second derivative and then determine the intervals where the second derivative is positive.
Step 1: Find the first derivative of f(x) using the product rule: f'(x) = (x^8)' * ln(x) + x^8 * (ln(x))' f'(x) = 8x^7 * ln(x) + x^8 * (1/x)
Step 2: Simplify the first derivative: f'(x) = 8x^7 * ln(x) + x^7 Step 3: Find the second derivative of f(x) using the product rule and the chain rule: f''(x) = (8x^7 * ln(x) + x^7)' f''(x) = (8x^7 * ln(x))' + (x^7)' f''(x) = [8x^7 * (1/x)] + 7x^6
Step 4: Simplify the second derivative: f''(x) = 8x^6 + 7x^6 Step 5: Combine like terms: f''(x) = 15x^6
Step 6: Determine the interval where f''(x) is positive: 15x^6 > 0 Since x^6 is always positive for x ≠ 0, and the coefficient 15 is also positive, the second derivative is positive for all x ≠ 0. Thus, the interval on which f(x) = x^8 * ln(x) is concave up is (0, +∞).
To find the interval on which f(x) = x^8 ln(x) is concave down, we need to find the second derivative of the function and determine where it is negative.
Step 1: Find the first derivative, f'(x), using the product rule. f'(x) = (x^8)'(ln(x)) + (x^8)(ln(x))' f'(x) = 8x^7 ln(x) + x^8(1/x) f'(x) = 8x^7 ln(x) + x^7
Step 2: Find the second derivative, f''(x), again using the product rule. f''(x) = (8x^7 ln(x))' + (x^7)' f''(x) = 56x^6 ln(x) + 8x^6 + 7x^6 f''(x) = 56x^6 ln(x) + 15x^6
Step 3: Determine where the second derivative is negative. We need to find when 56x^6 ln(x) + 15x^6 < 0. First, notice that x^6 is always non-negative. Therefore, we can factor it out: x^6 (56 ln(x) + 15) < 0 Since x^6 is non-negative, the inequality will be true when the expression in parentheses is negative: 56 ln(x) + 15 < 0 Now, solve for x: 56 ln(x) < -15 ln(x) < -15/56 x < e^(-15/56)
Step 4: Write the answer using interval notation. The interval on which f(x) = x^8 ln(x) is concave down is (0, e^(-15/56)).
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If Lin runs 16 laps at the same rate, how long does it take her?
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which table shows a proportional relationship between x and y
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Answer:D
Step-by-step explanation:in other 3 option there is no proportion ...
Answer:
the answer is D
Step-by-step explanation:
For a sledding trip you randomly select one of your four hats- red, blue with stripes, purple, or black. Write a ratio that compare the number of red hats to the number of total hats.
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Candy previously sold for $1. 60 per pound is now offered for 48 cents in a 6 ounce package. What is the ratio of former price to present price?
Answers
proportion of old cost to new cost = Subsequently the proportion of old to the new cost = 5:3
note: 16 ounces= one pound
6 ounces = ?
∴6 ounces = pounds
48 pennies = pounds
duplicating the two sides by
108 pennies = 1 pound in the new cost
= $1.08 in the new cost
proportion of old cost to new cost =
Subsequently the proportion of old to the new cost = 5:3
Current prices are those demonstrated at a given second in time, and said to be in costensible value. Constant prices are in genuine value, for example revised at changes in costs comparable to a gauge or reference datum.
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write the equation in standard form for the circle that has a diameter with endpoints (1,17) and (1,-1)
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The equation in standard form for the circle with diameter endpoints (1,17) and (1,-1) is (x - 1)^2 + (y - 8)^2 = 81.
To write the equation of a circle in standard form, we need to use the formula: (x - h)^2 + (y - k)^2 = r^2 Where (h,k) is the center of the circle and r is the radius.
We can use the midpoint formula to find the center of the circle, which is the midpoint of the diameter: Midpoint = ((x1 + x2)/2 , (y1 + y2)/2) Substituting the given endpoints, we get: Midpoint = ((1 + 1)/2 , (17 + (-1))/2) = (1, 8) So the center of the circle is (1,8).
Now we need to find the radius, which is half the length of the diameter: Length of diameter = sqrt((1-1)^2 + (17-(-1))^2) = sqrt(18^2) = 18 Radius = 18/2 = 9 Substituting the center and radius in the standard form equation, we get: (x - 1)^2 + (y - 8)^2 = 9^2 Simplifying, we get: (x - 1)^2 + (y - 8)^2 = 81
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in the analysis of a two-way factorial design, how many main effects are tested?
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In a two-way factorial design analysis, there are two main effects tested.
A two-way factorial design involves the simultaneous manipulation of two independent variables, each with multiple levels, to study their individual and combined effects on a dependent variable. The main effects in such a design represent the effects of each independent variable independently, ignoring the influence of the other variable.
When conducting a two-way factorial design analysis, there are two main effects tested, corresponding to each independent variable. The main effect of one variable is the difference in the means across its levels, averaged over all levels of the other variable. Similarly, the main effect of the other variable is the difference in the means across its levels, averaged over all levels of the first variable.
Testing the main effects allows researchers to determine the individual impact of each independent variable on the dependent variable, providing insights into their overall influence. By analyzing the main effects, researchers can assess the significance and directionality of the effects, aiding in the interpretation of the experimental results and understanding the relationship between the independent and dependent variables in the factorial design.
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Asap! I’ll mark you brainlest
What does How many kilometers did Jon run?
Add
Subtract
Divide
Multiply
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Question 6 of 18
Solve px + 17 = 12 for x.
A. x=p-5
B. x = -5-p
O C. x=
29
p
O D. X--500
Answers
Answer:
x = - \(\frac{5}{p}\)
Step-by-step explanation:
px + 17 = 12 ( subtract 17 from both sides )
px = - 5 ( isolate x by dividing both sides by p )
x = \(\frac{-5}{p}\) = - \(\frac{5}{p}\)
PLEASE PLEASE HELP!!! WILL GIVE BRAINLIEST
Answers
Answer:
a. this b>9 B. the first one C. the second one
Step-by-step explanation:
D is the first one
U(x
1
,x
2
)=x
1
α
x
2
1−α
,0<α<1
x
1
p
1
+x
2
p
2
=w
where x
1
and x
2
are consumption goods, p
1
and p
2
are the prices of those consumption goods respectively, α is a parameter, and w is the consumer's wealth. (i) [4 points] Find the partial derivative of U(x
1
,x
2
) with respect to x
1
and x
2
.
Answers
The partial derivative of the utility function \(U(x_1, x_2)\) with respect to \(x_1\) is \(a * x_1^{(a-1)} * x_2^{(1-a)}\), and the partial derivative with respect to \(x_2\) is \((1-a) * x_1^a * x_2^{(-a)}.\)
The utility function \(U(x_1, x_2)\) represents a consumer's satisfaction or preference for two consumption goods, \(x_1\) and \(x_2\). The partial derivatives provide insights into how the utility function changes as we vary the quantities of the goods.
To calculate the partial derivative with respect to \(x_1\), we differentiate the utility function with respect to \(x_1\) while treating \(x_2\) as a constant. The result is \(a * x_1^{(a-1)} * x_2^{(1-a)}\). This derivative captures the impact of changes in \(x_1\) on the overall utility, taking into account the relative importance of \(x_1\)(determined by the parameter a) and the quantity of \(x_2\).
Similarly, to find the partial derivative with respect to \(x_2\), we differentiate the utility function with respect to \(x_2\) while treating \(x_1\)as a constant. The resulting derivative is \((1-a) * x_1^a * x_2^{(-a)}.\). This derivative shows how changes in \(x_2\) affect the overall utility, considering the relative weight of \(x_2\) (given by 1-a) and the quantity of \(x_1\).
In summary, the partial derivatives provide information about the sensitivity of the utility function to changes in the quantities of the consumption goods, allowing us to understand the consumer's preferences and decision-making.
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(a) From a random sample of 200 families who have TV sets in Şile, 114 are watching Gülümse Kaderine TV series. Find the 96 confidence interval for the fractin of families who watch Gülümse Kaderine in Şile. (b) What can we understand with 96% confidence about the possible size of our error if we estimate the fraction families who watch Gülümse Kaderine to be 0.57 in Şile?
Answers
The 96 confidence interval for the fraction of families is (49.8%, 64.2%)
We are 96% confident that 49.8% to 64.2% of families watch Gülümse Kaderine in Şile
Finding the 96 confidence interval for the fraction of familiesFrom the question, we have the following parameters that can be used in our computation:
Sample size, n = 200
Familes,, x = 114
z-score at 96% confidence, z = 2.05
So, we have the proportion of families to be
p = 114/200
p = 0.57
Next, we calculate the margin of error using
E = z * √[(p * (1 - p) / n]
So, we have
E = 2.05 * √[(0.57 * (1 - 0.57) / 200]
Evaluate
E = 0.072
The confidence interval is then calculated as
CI = p ± E
So, we have
CI = 0.57 ± 0.072
Evaluate
CI = (49.8%, 64.2%)
What we understand about the confidence intervalIn (a), we have
CI = (49.8%, 64.2%)
This means that we are 96% confident that 49.8% to 64.2% of families watch Gülümse Kaderine in Şile
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the weights of students in a junior college are normally distributed with a mean of 100 lbs. and a standard deviation of 18 lbs. What is the probability that a student drawn at random will weigh less than 150 lbs
Answers
Answer: 0.9973 .
Step-by-step explanation:
Given: Weights of students in a junior college follows normal distribution with a mean = 100 lbs and a standard deviation =18 lbs.
Let X denotes the random variable that represents the weights of students .
Then, the probability that a student drawn at random will weigh less than 150 lbs will be :
\(P(X<150)=P(\dfrac{X_\mu}{\sigma}<\dfrac{150-100}{18})\\\\=P(Z<2.78 )\ \ \ \ [Z=\dfrac{X_\mu}{\sigma}]\\\\ =0.9973\ \ \ [\text{By p-value table for z}]\)
Hence, the e=required probability is 0.9973 .
Please look at photo for question, thank you so much <3
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When two triangles are similar the corresponding sides are always in the same ratio.
If triangle MNP is similar to traingle XYZ, the lengths of MNP needs to be in the same ratio with the corresponding sides of triangle XYZ
\(\frac{MN}{XY}=\frac{NP}{YZ}=\frac{MP}{XZ}\)\(\frac{MN}{6}=\frac{MP}{7}=\frac{NP}{9}\)Prove each of the given options lengths to find the one that makes the equation above be true:
Pair corresponding sides ordering its lengths from least XY to greatest YZ
First option:
\(\begin{gathered} \frac{12}{6}=\frac{14}{7}=\frac{20}{9} \\ 2=2=2.22 \end{gathered}\)As the ratios are not the same that cannot be the lengths of MNP
Second option:
\(\begin{gathered} \frac{30}{6}=\frac{35}{7}=\frac{45}{9} \\ 5=5=5 \\ \end{gathered}\)As the ratios are the same that can be the lengths of MNP
Third option:
\(\begin{gathered} \frac{13}{6}=\frac{14}{7}=\frac{16}{9} \\ 2.16=2=1.77 \end{gathered}\)As the ratios are not the same that cannot be the lengths of MNP
Fourth option:
\(\begin{gathered} \frac{3}{6}=\frac{4}{7}=\frac{5}{9} \\ 0.5=0.57=0.55 \end{gathered}\)As the ratios are not the same that cannot be the lengths of MNP
Then, the lengths of MNP could be: 30cm,35cm,45cmWhat is 15/45 in it's lowest term? Can someone help me please?
Answers
Answer:
Answer is 1/3
Step-by-step explanation:
If you divide the numerator and denominator by five you get 3/9
3/9 can be reduced if you divide the numerator and denominator by 3, then your answer is 1/3 (since 3 goes into 3 once, and 3 goes into 9 three times.)
The three-dimensional figure below is a cylinder with a hole in the shape of a rectangular prism going through the center of it. The radius is 10 yards. Find the volume of the solid in cubic yards, rounded to the nearest ten.
Answers
Answer: 1,510
Step-by-step explanation: using the formula
(pie•r2•height) - (width•length•height)
I plugged in the numbers to get
(Pie•10(2)•5) - (4•3•5)
This gives you
1,570 - 60
= 1,510
Prove this identify : 2 cos^2 (45°-A ) = 1 +sin 2 A
Answers
pls help me 10 points
Answers
Answer:
A
Step-by-step explanation:
Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)
Answer:
A
Step-by-step explanation:
A graph that shows a proportional relationship has the line go through the origin and the only graph that does is A.
Best of Luck!
Suppose we observe the following rates: 1R1 = .08, 1R2 = .12, and E(2r1) = 14. If the liquidity premium theory of the term structure of interest rates holds, what is the liquidity premium for year 2? Hint: Ry[(1+R)+E(277)+4)...Q+E(x7)+Lx)} N-1 O 6.15% O 2.15% O 14.00% O 8.45% O 12.45%
Answers
If the liquidity premium theory of the term structure of interest rates holds, 0.498% is the liquidity premium for year 2.
What is liquid premium theory?Any additional compensation that is necessary to attract investment in assets that cannot be quickly and effectively converted into cash at fair market value is known as a liquidity premium. Because it is more difficult to sell than a short-term bond, a long-term bond, for instance, will have a higher interest rate. According to the principle of the liquidity premium, bond investors favour short-dated assets that are highly liquid and have a short sales cycle over those that are longer-dated. According to another tenet of the theory, fluctuations in interest rates provide investors with compensation for greater pricing and default risks.
Given that,
1 + 1R₂= {(1 + 1R₁)(1 + E(2r₁) + L₂)}1/2
or, 1.12 = (1.8)(1.14 + L₂)1/2
or, (1.12)2/1.18 = 1.14 + L₂
or, 1.898 = 1.14 + L₂
or, L₂ = 0.498%
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5. Over what interval is the following graph DECREASING? *
Answers
Answer:
(3, 13)
Step-by-step explanation:
The curve decreases from x = 3 to x = 13.
Answer: (3, 13)
Can I have help on this?
Answers
Answer:
—4.5 and 0
Step-by-step explanation:
when x=—4.5 and x=0 y is included in the domain.
Express the fraction 1/15^7 using a negative exponent
Answers
Answer:
I think its 15^-7
Step-by-step explanation:
you can forget about the one and just look at the 15 and 7 which you get 15^-7
The fraction (1/15)⁷ can be written as 15⁻⁷ after using the properties of the integer exponent.
What is an integer exponent?In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
It is given that:
The number expression is:
= (1/15)⁷
As we know, from the definition of the integer exponent; integer exponents are exponents that should be integers. It may be a positive or negative number.
After using the properties of the integer exponent:
= (15⁻¹)⁷
= 15⁻⁷
Thus, the fraction (1/15)⁷ can be written as 15⁻⁷ after using the properties of the integer exponent.
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Find the sum of the interior angles of a polygon with 20 sides
Answers
Answer:
3240°
Step-by-step explanation:
The sum of the interior angles of a polygon is found by (n-2)(180) where n is the number of sides so (20-2)(180) = (18)(180) = 3240°
Which of the following is a like radical to 3x√5?
O x(³√5)
O √5y
O 3 (³√5x)
O y √√5
Answers
3x√5 and 3(³√5x) are like radicals because they both have the same radicand (the number or expression inside the radical symbol) of 5 and the same index (the number that indicates the root being taken) of 3. The only difference is the coefficient (the number multiplying the radical) of 3 in front of the radical symbol, which is a factor that does not affect the radical itself.
x(³√5) and y √√5 are not like radicals to 3x√5 because they have different radicands.
√5y is not a like radical to 3x√5 because it has a different index.
How many ways can you roll a single die and get a 2, followed by a 2?
Answers
there is only one way to roll a single die and get a 2, followed by a 2.
What are likely outcomes?
Likely outcomes are the outcomes that have a high probability of occurring in a given situation. In probability theory, the likelihood of an outcome is often expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
Assuming that the die is fair and has six equally likely outcomes, the probability of rolling a 2 on a single roll is 1/6. The probability of rolling two 2's in a row is the product of the probabilities of rolling a 2 on each roll, which is (1/6) x (1/6) = 1/36.
To find the number of ways to roll a single die and get a 2, followed by a 2, we can consider the possible sequences of rolls. Since we need two 2's in a row, the only possible sequence that satisfies this condition is rolling a 2 followed by another 2. Therefore, there is only one way to roll a single die and get a 2, followed by a 2.
In summary, there is only one way to roll a single die and get a 2, followed by a 2, and the probability of this event is 1/36.
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At the beginning of the first day of the experiment the mass of the substance was 1300 grams and mass was decreasing by 14% per day. Determine the mass of the radioactive sample at the beginning of the 11th day of the experiment.
Answers
The mass of the radioactive sample at the beginning of the 11th day of the experiment is approximately 286 grams.
How to find the mass?Since the mass is decreasing by 14% per day, we can find the mass at the beginning of each day by multiplying the previous day's mass by 0.86 (which is 100% - 14%).
At the beginning of the first day, the mass was 1300 grams.
At the beginning of the second day, the mass is:
1300 grams x 0.86 = 1118 grams (rounded to the nearest gram)
At the beginning of the third day, the mass is:
1118 grams x 0.86 = 962 grams (rounded to the nearest gram)
We can continue this pattern to find the mass at the beginning of the 11th day:
Mass at the beginning of the fourth day: 962 grams x 0.86 = 828 grams
Mass at the beginning of the fifth day: 828 grams x 0.86 = 711 grams
Mass at the beginning of the sixth day: 711 grams x 0.86 = 612 grams
Mass at the beginning of the seventh day: 612 grams x 0.86 = 526 grams
Mass at the beginning of the eighth day: 526 grams x 0.86 = 452 grams
Mass at the beginning of the ninth day: 452 grams x 0.86 = 388 grams
Mass at the beginning of the tenth day: 388 grams x 0.86 = 333 grams
Mass at the beginning of the eleventh day: 333 grams x 0.86 = 286 grams (rounded to the nearest gram)
Therefore, the mass of the radioactive sample at the beginning of the 11th day of the experiment is approximately 286 grams.
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HELP ME I NEED HELP HELP ME
Answers
By special right triangles, all missing side lengths are listed below:
Case 16
a = b = 12, c = 4√3, d = 24
Case 17a
a = d = 36, b = 36√2, c = 27, d = 36
How to solve geometric systems by special right triangles
In this question we find the two geometric systems formed by special right triangles, there are two kinds of right triangles (30° - 60° - 90°, 45° - 45° - 90°). We need to determine all missing side lengths. The following relationships are used:
30° - 60° - 90°:
The length of the short leg is 1 / 2 times of the length of the hypotenuse. The length of the long leg is √3 / 2 times of the length of the hypotenuse. The length of the long leg is √3 times of the length of the short leg.45° - 45° - 90°:
The length of the hypotenuse is √2 times of any leg.Now we proceed to determine all missing lengths for each case:
Case 16
a = b = 12
c = 12 / √3 = 4√3
d = 24
Case 17a
a = 18√3 / (√3 / 2) = 36
b = 36√2
c = 18√3 · (√3 / 2)
c = 27
d = 36
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plz im not lying this work is really hard so can yall plz help me
Answers
Answer:
5,740 more minutes i hope this helps
Step-by-step explanation:
I can give extra points, I just really need help. pls show work
Answers
1/2 converted into 8ths is 4/8ths, 4/8ths + 3/8ths its 7/8ths then adding the whole number miles (2+1) is 3 this equaling 3 7/8ths
Answer:
8.. answer 31/8 = 3 7/8
9 ... answer : 189/15 = 12 9/12
10 answer : 43/12 = 3 7/12
Hope this will helpful for you and plz mark me as brainlist plzzzz
True or false? the interval [1,2] contains exactly two numbers - the numbers 1 and 2.
Answers
The answer is "false". The interval [1, 2] contains all the real numbers between 1 and 2 including the endpoints.
How to write and represent an interval?An interval notation is used for representing the continuous set of real values. This is the shortest way of writing inequalities.
Intervals are represented within the brackets such as square brackets or open brackets(parenthesis).
If the interval is within a square bracket, then the end values are included in the set of values.If the interval is within parenthesis, then the end values are not included in the set of values.The square brackets represent the inequalities - 'greater than or equal or 'less than or equalThe parenthesis represents the inequalities - 'greater than' or 'less thanFinding true or false:The given interval is [1, 2]
The given statement is - 'the interval [1, 2] contains exactly two numbers - the numbers 1 and 2'
The given statement is 'false'.
This is beacuse, an interval consists set of all the real values in between the two values given.
So, according to the definition, there are not only the end values but also many real values in between them.
Thus, the answer is "false". The interval [1, 2] consists of all the real values between 1 and 2 including 1 and 2.
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how many total pounds of tnt are required to create an abatis that has 72 trees with an average diameter of 30 inches?
Answers
It would take approximately 176,369 pounds of TNT to destroy an abatis made of 72 trees with an average diameter of 30 inches, assuming an average height of 20 feet.
The formula for the volume of a cylinder is V = πr^2h. In this case, we can use the average radius of 15 inches and the average height of 240 inches to estimate the total volume of all 72 trees:
Total volume of all 72 trees = 72 x V
Total volume of all 72 trees = 72 x 169,646
Total volume of all 72 trees ≈ 12,214,832 cubic inches
In this equation, we need to know the density of wood and the REF of TNT. The density of wood can vary depending on the species, but we can use an average value of 0.5 grams per cubic centimeter (g/cm^3). The REF of TNT is 1, by definition. The factor of 0.8 in the equation accounts for losses due to fragmentation and other factors.
Converting the units of volume and density to match, we get:
Total volume of all 72 trees ≈ 200,000,000 cubic centimeters
Density of wood = 0.5 g/cm³
Plugging these values into the equation, we get:
Amount of TNT required = (Total volume of all 72 trees x Density of wood x 0.8) / REF
Amount of TNT required = (200,000,000 x 0.5 x 0.8) / 1
Amount of TNT required = 80,000,000 grams
To convert grams to pounds, we divide by 453.592, which is the number of grams in a pound:
Amount of TNT required = 80,000,000 / 453.592
Amount of TNT required ≈ 176,369 pounds
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