(a) State the Mean Value Theorem. (b) Prove that
[In x - In y l > I x - y I if 0 < x < y <1. (c) Prove that
[In x - In y l >1/2 I x - y I if 2 < x < y
Answers
(a) The Mean Value Theorem states the existence of a point where a function's derivative equals its average rate of change. (b) Proved [ln(x) - ln(y)] > |x - y| for 0 < x < y < 1. (c) Proved [ln(x) - ln(y)] > 1/2|x - y| for 2 < x < y.
(a) The Mean Value Theorem states that if f(x) is a differentiable function on the interval [a, b], then there exists a point c in (a, b) where the derivative of f(x), denoted as f'(c), is equal to the average rate of change of f(x) over [a, b], which is (f(b) - f(a))/(b - a).
(b) To prove the inequality [ln(x) - ln(y)] > |x - y| for 0 < x < y < 1, we apply the Mean Value Theorem to the function f(t) = ln(t) on the interval [x, y]. By evaluating f'(c) = (ln(y) - ln(x))/(y - x) for some c in (x, y), we can simplify the expression and conclude that [ln(x) - ln(y)] > |x - y|.
(c) To prove the inequality [ln(x) - ln(y)] > 1/2|x - y| for 2 < x < y, we again apply the Mean Value Theorem to the function f(t) = ln(t) on the interval [x, y]. By evaluating f'(c) = (ln(y) - ln(x))/(y - x) for some c in (x, y), we simplify the expression and show that [ln(x) - ln(y)] > 1/2|x - y|.
By utilizing the Mean Value Theorem in both cases, we establish the desired inequalities for the given intervals.
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Related Questions
Which of the following pairs of numbers contains like fractions?
A.32 and 2/3
B.5/6 and 10/12
c. 6/7 and 157
D.312 and 4/4
Answers
Answer:
B.5/6 and 10/12
Step-by-step explanation:
The given values are;
\(\frac{5}{6}\) and \(\frac{10}{12}\)
\(\frac{10}{12}\) ,
reducing to the smallest term by dividing by 2;
is \(\frac{5}{6}\)
So;
\(\frac{5}{6}\) and \(\frac{10}{12}\) are both like fractions.
what do I get if I divide 1 by 5/13
Answers
5/13 or 0.385
Step-by-step explanation:
so evething by 1 is the same number
so 1×5/13 is = to 5/13 or 0.385
Complete the table of values below: x -3 -2 -1 0 1 2 3 How the graph relates to y=2x y=2x Answer Answer Answer Answer Answer Answer Answer Not applicable y=-2x Answer Answer Answer Answer Answer Answer Answer multiplied by Answer y=(3)(2x)
Answers
Answer:
The values of x are:
x : -3, -2, -1, 0, 1, 2, 3
Let's solve each by putting each value of x into each equation:
a \(y = 2^x\)
> x = -3
=> y = 2^(-3) = 1/8
> x = -2
=> y = 2^(-2) = 1/4
> x = -1
=> y = 2^(-1) = 1/2
> x = 0
=> y = 2^0 = 1
> x = 1
=> y = 2^1 = 2
> x = 2
=> y = 2^2 = 4
> x = 3
=> y = 2^3 = 8
b. \(y = -2^x\)
> x = -3
=> y = -2^(-3) = -1/8
> x = -2
=> y = -2^(-2) = -1/4
> x = -1
=> y = -2^(-1) = -1/2
> x = 0
=> y = -2^0 = -1
> x = 1
=> y = -2^1 = -2
> x = 2
=> y = -2^2 = -4
> x = 3
=> y = -2^3 = -8
c. \(y = (3)(2^x)\)
> x = -3
=> y = 3 * 2^(-3) = 3 * 1/8 = 3/8
> x = -2
=> y = 3 * 2^(-2) = 3 * 1/4 = 3/4
> x = -1
=> y = 3 * 2^(-1) = 3 * 1/2 = 3/2
> x = 0
=> y = 3 * 2^0 = 3 * 1 = 3
> x = 1
=> y = 3 * 2^1 = 3 * 2 = 6
> x = 2
=> y = 3 * 2^2 = 3 * 4 = 12
> x = 3
=> y = 3 * 2^3 = 3 * 8 = 24
Input these values into the table.
Answer:
a y = 2^x
> x = -3
=> y = 2^(-3) = 1/8
> x = -2
=> y = 2^(-2) = 1/4
> x = -1
=> y = 2^(-1) = 1/2
> x = 0
=> y = 2^0 = 1
> x = 1
=> y = 2^1 = 2
> x = 2
=> y = 2^2 = 4
> x = 3
=> y = 2^3 = 8
b. y = -2^x
> x = -3
=> y = -2^(-3) = -1/8
> x = -2
=> y = -2^(-2) = -1/4
> x = -1
=> y = -2^(-1) = -1/2
> x = 0
=> y = -2^0 = -1
> x = 1
=> y = -2^1 = -2
> x = 2
=> y = -2^2 = -4
> x = 3
=> y = -2^3 = -8
c. y = (3)(2^x)
> x = -3
=> y = 3 * 2^(-3) = 3 * 1/8 = 3/8
> x = -2
=> y = 3 * 2^(-2) = 3 * 1/4 = 3/4
> x = -1
=> y = 3 * 2^(-1) = 3 * 1/2 = 3/2
> x = 0
=> y = 3 * 2^0 = 3 * 1 = 3
> x = 1
=> y = 3 * 2^1 = 3 * 2 = 6
> x = 2
=> y = 3 * 2^2 = 3 * 4 = 12
> x = 3
=> y = 3 * 2^3 = 3 * 8 = 24
Step-by-step explanation:
HELP PLEASE TO CONFUING FOR ME
Answers
Answer:wow this is hard
Step-by-step explanation:
The output of a system is . The final value theorem cannot be used:
Answers
The final value theorem cannot be used for the given system output Y(s) = 1 / (s³ + 4s²) because the system is unstable. The correct option is A.
The final value theorem is used to find the steady-state value of a system's output y(t) as t approaches infinity, given the Laplace transform of the output Y(s). The final value theorem states that the steady-state value of y(t) is equal to the limit of s * Y(s) as s approaches 0.
For the final value theorem to be applicable, the system must be stable, meaning that all the poles of the system's transfer function must have negative real parts. In an unstable system, at least one of the poles has a positive real part.
In this case, the system has the transfer function Y(s) = 1 / (s³ + 4s²), which has poles at s = 0 and s = -2. The pole at s = 0 has a zero real part, indicating that the system is unstable.
Therefore, the correct answer is A. The final value theorem cannot be used because the system is unstable.
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Complete question:
The output of a system is Y(s)= 1/ s³+4s². The final value theorem cannot be used:
A. because the system is unstable
B. because there are poles
C. because there are two
D. because there are zeros system is at the imaginary axis poles at the origin at the imaginary axis unstable
2x^6/20x^7
pls help me i have a test today and i don’t know how to solve it
Answers
Answer:
\(\frac{1}{10x}\)
Step-by-step explanation:
\(\frac{2x^{6} }{20x^{7} } = \frac{x^{6} }{10x^{7} } \\\\=\frac{1}{10x}\)
How much principal must be deposited in a 5 year simple interest account that pays 4,75% interest to earn $500 in interest
Answers
Answer: $2105.26
Step-by-step explanation:
Concept:
The formula to find simple interest is I=Prt
Given:
t=5 year
r=4.75%
I=$500
Solve:
I=Prt
500=P(4.75%)(5)
100=P(4.75%)
P=$2105.26Find equations of the normal plane and osculating plane of the curve at the given point. x = 5 sin(3t), y = t, z = 5 cos(3t): (0, π,-5) find equation of the normal plane and osculating plane of the curve at the given point.x= 5 sin(3t), y= t, z= 5 cos(3t); (0, phi, -5) normal plane =osculating plane=
Answers
The equation of the osculating plane is 24x + 12√10(y-π) - 3z - 6π√10 = 0.
Given curve, x=5sin(3t), y=t, z=5cos(3t); (0, π,-5).
To find the normal plane equation, the unit normal vector of the curve at the point must first be found. The unit tangent and unit binormal vectors are both derived from the unit tangent vector.
To calculate the tangent vector, the following steps are taken:
Equation of the curve is given as,
x=5sin(3t),
y=t,
z=5cos(3t).
Differentiating above equation with respect to t, we get;
dx/dt = 15 cos(3t)
dy/dt = 1
dz/dt = -15 sin(3t)
The unit tangent vector T is given by,
T = 1/√(dx/dt² + dy/dt² + dz/dt²) (dx/dt i + dy/dt j + dz/dt k)
Substituting the given values, we get
T = (3√10/10) i + (1/√10) j - (3/√10) k
Since we have to find the normal vector, we will differentiate the unit tangent vector,T, to get the unit normal vector N.
Let's differentiate T to obtain N:
dn/dt = 1/√(dx/dt² + dy/dt² + dz/dt²) [d²x/dt² i + d²y/dt² j + d²z/dt² k] + {(-1/2)(2t)(2t')/√(dx/dt² + dy/dt² + dz/dt²)³} [dx/dt i + dy/dt j + dz/dt k]
On substituting, we get,
N = (-9/√10) i + (3√10/10) j + (9/√10) k
Therefore, the normal plane equation is given by,(-9/√10)(x) + (3√10/10)(y-π) + (9/√10)(z+5) = 0.
To find the osculating plane equation, the coordinates of the point of tangency (P) and the principal normal vector, N, are required.
The equation of the osculating plane is then written as follows:
xT + yN = c,
where c is a constant value that is calculated by substituting the coordinates of P into the equation.Let us calculate the value of P and N,
To find the value of P, we substitute t=π in the given curve,
Thus,
x(π) = 5sin(3π) = 0,y(π) = π,z(π) = 5cos(3π) = -5
Therefore, the point of tangency P is (0, π, -5).
From the above derivation, we know that the unit normal vector N is(-9/√10) i + (3√10/10) j + (9/√10) k
Therefore, the unit principal normal vector is given by,
B = T x N= [(3√10/10) i + (1/√10) j - (3/√10) k] x [- (9/√10) i + (3√10/10) j + (9/√10) k]
= [(3√10/10) (9/√10) + (3/√10) (3/√10)] i + [(9/√10) (1/√10) - (3√10/10) (- 3/√10)] j + [(1/√10) (- 3/√10) - (3√10/10) (3√10/10)] k
= (24/√10) i + (12√10/10) j - (3/√10) k
The osculating plane equation is given by,
xT + yB = c
Now substituting x=0, y=π and z=-5 in above equation, we get
c = π(12√10/10) = (6π√10/5)
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To rent a car from The Car Rental Place Juan must pay $20 plus an additional $1.50 per mile that he drives. If Juan has a total of $350 to spend on renting a car, how many miles can he afford to drive it?
Answers
Answer:
220 miles
Step-by-step explanation:
$350 - $20 = $330
$330 ÷ $1.50 = 220.
Here's the formula:
$350 = $20 + $1.50x
Graph the inequality y < 1 - 3x
Answers
Answer:
13
Step-by-step explanation:
in a pitch black room you have a drawer with 27 black socks, 18 grey socks, and 9 navy socks. how many socks do you take out to ensure you get a pair that is not navy?
Answers
There is a 5/6 probability that you will remove pairs of socks to make sure you obtain a pair that is not navy.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.
Statistics is the study of events that follow a probability distribution.
So, we know that:
27 black socks.
18 grey socks.
9 navy socks.
Probability formula: P(E) = Favouravle events/Total events
Now, insert values in the formula as follows:
P(E) = Favouravle events/Total events
P(E) = 27+18/27+18+9
P(E) = 45/54
P(E) = 15/18
P(E) = 5/6
Therefore, there is a 5/6 probability that you will remove pairs of socks to make sure you obtain a pair that is not navy.
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Correct question:
in a pitch-black room, you have a drawer with 27 black socks, 18 grey socks, and 9 navy socks. What is the probability that you take out pairs of socks to ensure you get a pair that is not navy?
what fraction of 2 1/2 is 4/5?
Answers
Answer: The fraction of 2 1/2 that is 4/5 is: \(=\frac{8}{25}\)
A fraction usually comprise of a part which not a whole number but a ratio of two numbers.
The first thing to do is to change the mixed fraction 2 1/2 to an improper fraction.
i.e.
\(2\frac{1}{2} \\\) → \(\frac{5}{2}\)
\(= \frac{5}{2}\\\)
Step-by-step explanation:
So we will want to divide \(\frac{5}{2}\) from \(\frac{4}{5}\) in order to determine what fraction of \(2\frac{1}{2} \\\\\) is \(\frac{4}{5}\)
Mathematically, we have:
\(=\frac{4}{5}\) ÷ \(\frac{5}{2}\)
\(=\frac{4}{5}\) × \(\frac{2}{5}\)
\(=\frac{8}{25}\)
Therefore, we can conclude that the fraction of 2 1/2 that is 4/5 is \(=\frac{8}{25}\)
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Please give me branliest and Good rating thank you.
DUE TODAY PLEASE HELP WELL WRITTEN ANSWERS ONLY!!!!
Answers
Answer:
\(r = \sqrt{ {(6 - 2)}^{2} + {(1 - ( - 3))}^{2} } \)
\(r = \sqrt{ {4}^{2} + {4}^{2} } = \sqrt{16 + 16} = \sqrt{32} \)
So the equation of the circle is
\( {(x - 2)}^{2} + {(y + 3)}^{2} = 32\)
A telephone pole is secured with a cable as shown. The cable makes an angle of 80° with the ground and is secured 7 m from the bottom of the pole. A second cable is attached from the top of the pole and secured to the ground three times as far from the pole as the first cable and on the same side. Find the angle the second cable makes with the ground, rounded to the nearest degree. 80° 7 m
Answers
The angle the second cable makes with the ground is 68° (rounded to the nearest degree).
Given that:A telephone pole is secured with a cable as shown. The cable makes an angle of 80° with the ground and is secured 7 m from the bottom of the pole. A second cable is attached from the top of the pole and secured to the ground three times as far from the pole as the first cable and on the same side.The required:Find the angle the second cable makes with the ground, rounded to the nearest degree.Step-by-step explanation:Let AB be the telephone pole and P be the point at which the first cable is attached to the pole such that PB = 7m and angle APB = 80°Let QC be the second cable and Q be the point at which the second cable is attached to the ground, such that CQ = 3PB = 3 × 7 = 21mWe need to find the angle QCB (let this angle be x)AC = AB + BC = AB + CQAB = AC - BC = 21 sec 80° - 21 tan 80° = 197.239 - 9.3646 = 187.8745mNow in right ΔABCtan 80° = BC/ABBC = AB tan 80° = 187.8745 tan 80° = 46.1883mIn right ΔQCBtan x = BC/CQBC = CQ tan x = 21 tan x = 46.1883/21x = tan -1 (46.1883/21) = 68.2959°≈ 68°Hence, the angle the second cable makes with the ground is 68° (rounded to the nearest degree).
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find the inverse matrix or type none use decimals [3 2
4 1]
Answers
Answer:
none
Step-by-step explanation:
accellus
The inverse matrix or type none of the given matrix is given as \(\rm A^{-1} = \dfrac{1}{-5}\begin{bmatrix}3& 4\\2 & 1 \\\end{bmatrix}\\\).
What is the matrix?A matrix is a specific arrangement of items, particularly numbers. A matrix is a row-and-column mathematical structure. The a_{ij} element in a matrix, such as M, refers to the i-th row and j-th column element.
The matrix is given below.
\(A = \begin{bmatrix}3& 2\\4 & 1 \\\end{bmatrix}\)
Then the transpose of a will be
\(\rm adj \ A = \begin{bmatrix}a_{11} & a_{21} \\a_{12} & a_{22} \\\end{bmatrix}\\\\\rm adj \ A = \begin{bmatrix}3& 4\\2 & 1 \\\end{bmatrix}\)
Then the value of matrix A will be
\(\rm \left| A \right|= \begin{vmatrix}3& 2\\4 & 1\end{vmatrix}\\\\\left| A \right|= 3*1 - 4*2\\\\|A| = -5\)
Then the inverse matrix is defined as
A⁻¹ = Adj A / |A|
Then we have
\(\rm A^{-1} = \dfrac{\begin{bmatrix}3& 4\\2 & 1 \\\end{bmatrix}}{-5}\\\\\\A^{-1} = \dfrac{1}{-5}\begin{bmatrix}3& 4\\2 & 1 \\\end{bmatrix}\\\)
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PLEASE HELP ME PLS U WOULD BE A LIFE SAVER AND ILL GIVE U BRAINLY PLS
In a game of chance, players spin a pointer on the spinner with eight equal-sized sections.
The sample space is 1,1,2,3,3,4,5,5
What are the probabilities of each outcome in the sample space? ( write each answer in fraction form)
Answers
Answer:
See belowStep-by-step explanation:
The are 8 total outcomes and 5 possible numbers:
Probability = favorable outcomes / total outcomes
P(1) = 2/8 = 1/4P(2) = 1/8P(3) = 2/8 = 1/4P(4) = 1/8P(5) = 2/8 = 1/4A rectangular gate is made using 6 straight pieces of steel.
5 m
12 m
The weight of the steel is 2.5 kg per metre.
+
Work out the total weight of the steel gate.
Pythagoras' Theorem - A Simple Approach View One Minute Version
Overview
11.
معاص
Answers
Answer:
Total weight is 150 kg
Step-by-step explanation:
Firstly, we need the weight of the diagonal
To get this, we shall use the Pythagoras’ theorem which states that the square of the hypotenuse equals the sum of the squares of the two other sides
The diagonals stand for the hypotenuse
Thus, we have that;
d^2 = 5^2 + 12^2
d^2 = 25 + 144
d^2 = 169
d^2 = 13^2
d = 13
The 6 sides technically includes the whole rectangle sides, then the two diagonals
The total length here is;
2(5 + 12 + 13) = 60 meters
Steel weight is 2.5 kg per meter
Weight of 60 m will be ;
60 * 2.5 = 150 kg
T/F regardless of whether a distribution of scores that is symmetrically shaped has one mode or two modes, the mean value tends to be similar to the median value.
Answers
True
In a symmetrically shaped distribution of scores, regardless of whether it has one mode or two modes, the mean value tends to be similar to the median value.
When a distribution is symmetric, it means that the data is evenly distributed around the central point, resulting in a bell-shaped curve. In such cases, the mean, median, and mode are typically close to each other.
The mean is the arithmetic average of all the scores in a distribution, while the median represents the middle value when the scores are arranged in ascending or descending order. In a symmetric distribution, the mean and median are located at the exact center of the distribution.
If the distribution has only one mode, it means that there is one prominent peak or high point in the data. In this case, the mean and median will coincide with the mode and will be similar.
If the distribution has two modes, it means that there are two prominent peaks in the data, but they are symmetrical around the center. Even though there are multiple modes, the mean and median will still be similar and tend to be located between the two modes.
In summary, in symmetrically shaped distributions, regardless of the presence of one or two modes, the mean and median values are expected to be close to each other.
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3. Jose began the day with eight Magikarps. After spending the day at the lake, he ended up with sixteen Magikarps.
Answers
We can find the percentage of increase in the number of Magikarps that Jose captured in the lake by taking the initial number of them and subtracting it from the number that he had by the end of the day, like this:
16 - 8 = 8
Now, we just have to divide 8 by 16 and then multiply by 100, like this:
\(\frac{8}{16}\times100=50\)Then, his number of Magikarps increased a 50%
Researchers try to gain insight into the characteristics of a ______ population by examining a of the population. Select one:
a. Description
b. Model
c. Replica
d. Sample
Answers
Researchers try to gain insight into the characteristics of a sample population by examining a sample of the population.
A sample is a subset of individuals or units taken from a larger population. Researchers use sampling methods to select a representative group of individuals from the population they are interested in studying. By studying the sample, researchers can make inferences and draw conclusions about the characteristics, behaviors, or trends that may exist within the entire population.
The goal of sampling is to obtain a sample that accurately represents the population in terms of its relevant characteristics. Researchers carefully select their samples to ensure that they are representative and minimize bias. This allows them to generalize the findings from the sample to the larger population with a certain level of confidence.
By examining a sample, researchers can collect data, analyze patterns, and draw conclusions about the population as a whole. This approach is more feasible and practical than attempting to study the entire population, especially when the population is large or geographically dispersed.
Therefore, researchers use samples to gain insight into the characteristics of a population, making option d. "Sample" the correct answer.
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A motorbike is for sale at $13000. Finance is available at $3000 deposit and monthly
repayments of $520 for 4 years. What is the interest paid?
Answers
520 x 12 months x 4 years = 24960
24960 + 3000 deposit = 27,960 total paid.
27,960 - 13,000 = 14,960 total interest paid
what is the probability that a randomly chosen return shows an adjusted gross income of $50,000 or more?
Answers
The probability that a randomly chosen return shows an adjusted gross income of $50,000 or more is 33.2%.
For mutually exclusive events, use the following addition rule:
P(A or B) = P(A) +P(B)
The corresponding probabilities is :
P( income > $50000) = P( >50)
= P(50 - 90) +P( 100 - 499) +P( ≥ 500)
= 0.215 + 0.100 +0.006
= 0.321
Therefore, the probability of a random selection returning is
P( income > 50000) = 0.321
Now ,
P( income ≥ 50000 and ≥ 100000 ) = P( > 100000)
= 0.100 + 0.006
= 0.106
The Probability Condition is:
P(A/B) = P(A and B) / P(B)
Therefore,
P( ≥ $100000 / $ $50000)
= P( ≥ $100000 and $ $50000)/ P( ≥ $50000)
= 0.106/ 0.321
≈ 0.3302
= 33.2%
Therefore, the conditional probability of earning at least $50000 and more is 33.2%
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how much nitrogen and phosphorus should be included in the fertilizer for a farmer to get the highest yield? two levels of n (hi and low) are crossed with two levels of p (hi and low) giving four combinations of fertilizer to be studied: hh, hl, lh and ll. the experimenters had 12 acres available for the study and three acres were assigned at random to each of the combinations. assume the data are four independent srss, one from each of the four populations of planting densities, and that the distribution of the yields is normal. the data follow. treatment combination (np) yield (bushels per acre) n mean stdev hh 150.1, 113.0, 118.4 3 127.17 20.04 hl 166.9, 120.7, 135.2 3 140.93 23.63 lh 165.3, 130.1, 139.6 3 145.00 18.21 ll 134.7, 138.4, 156.1 3 143.07 11.44 answer the following questions: 1. the farmers are interested in whether there is any difference between the low-low combination (it is the cheapest) and the average of the remaining three levels. what hypotheses do they want to test? 2. what contrast would be used to test this hypothesis? 3. what contrast would be used to compare the high- to low-nitrogen content fertilizers? 4. what about for the high- to low-phosphorus content fertilizers? 5. what contrast compares the ll combination to the hh combination? 6. for each of the contrasts above, list the contrast coefficients.
Answers
The contrast coefficients would be as follows:
µll - (µhh + µhl + µlh) / 3: -1, -1, -1, 3µhl - µll: 1, -1, 0, 0µlh - µhl: 0, 1, -1, 0µll - µhh: -1, 0, 0, 1The farmers are interested in whether there is any difference between the low-low combination (it is the cheapest) and the average of the remaining three levels. The hypotheses they want to test are:
H0: µll - (µhh + µhl + µlh) / 3 = 0HA: µll - (µhh + µhl + µlh) / 3 ≠ 0
To test this hypothesis, the following contrast would be used:
µll - (µhh + µhl + µlh) / 3To compare the high- to low-nitrogen content fertilizers, the following contrast would be used:
µhl - µllTo compare the high- to low-phosphorus content fertilizers, the following contrast would be used:
µlh - µhlTo compare the ll combination to the hh combination, the following contrast would be used:
µll - µhhFor each of the contrasts above, the contrast coefficients would be as follows:
µll - (µhh + µhl + µlh) / 3: -1, -1, -1, 3µhl - µll: 1, -1, 0, 0µlh - µhl: 0, 1, -1, 0µll - µhh: -1, 0, 0, 1Learn more about coefficients
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9000 dollars is placed in an account with annual interest rate of 7.75 how much will be in the account in 18 year nearest cent
Answers
Answer:
9139.50
Step-by-step explanation:
since it didn't mention any withdraws from the account or any charges, its just a matter of multiplying 7.75 by 18 and adding it to the original balance.
Answer:
9139.50
Step-by-step explanation:
A farmer planted 32 rows of sweet peppers. Each row had 16 sweet pepper plants. How many plants does he have ALTOGETHER
Answers
Answer:
512
Step-by-step explanation:
32*16=512
Answer:
I would think 512
Step-by-step explanation:
He has 32 rows of 16 plants. That would be 16 times the amount of rows he has. So I would think 16 x 32=512
The volume of this prism is 2465cm3. the area of the cross-section is 85cm2. work out x .
Answers
The value of x is 29 cm.
To find the value of x, we can use the formula for the volume of a prism, which is V = A * h, where V is the volume, A is the area of the cross-section, and h is the height. In this case, we are given that the volume is 2465 cm^3 and the area of the cross-section is 85 cm^2. We need to solve for the height, h.
Using the formula, we have 2465 = 85 * h. To solve for h, we divide both sides of the equation by 85, giving us h = 2465 / 85 = 29 cm.
Therefore, the value of x is 29 cm.
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He creates paths through the garden along line segment a b, line segment x y, and line segment z y. Which correctly compares the lengths of the paths?the path along line segment x y is longer than the path along line segment z y, and the path along line segment z y is longer than the path along line segment a b. The path along line segment a b is longer than the path along line segment z y, and the path along line segment z y is longer than the path along line segment x y. The path along line segment z y is longer than the path along line segment x y, and the path along line segment x y is longer than the path along line segment a b. The path along line segment z y is longer than the path along line segment a b, and the path along line segment a b is longer than the path along line segment x y.
Answers
The journey along Line segment X Y is longer than the path along Line segment Z Y, and the path along Line segment Z Y is longer than the path along Line segment A B, hence Option-A is the correct answer.
Given that,
He makes paths that follow Line segments A and B, X and Y, and Z and Y through the garden.
We have to find which accurately compares the pathways' lengths.
We know that,
The length of the third side in a triangle is proportional to the angle Ф if the lengths of the two sides that make up the angle Ф are fixed.
XY > YZ because XY's opposing angle (79°) is greater than YZ's (65°).
As before, YZ > AB because the opposing angle of YZ (65°) is greater than that of AB (36°).
Since both sides of the angle are the same length (8 feet),
As a result, assertion A. is accurate. (Answer)
Therefore, The journey along Line segment X Y is longer than the path along Line segment Z Y, and the path along Line segment Z Y is longer than the path along Line segment A B, hence Option-A is the correct answer.
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Answer:
It's A
Step-by-step explanation:
I got 100 on the quiz
Determine whether the sequence is increasing, decreasing, or not monotonic. an 3n(-2)? A. increasing B. decreasing C. not monotonic
Answers
Answer:
The sequence is defined by the formula an = 3n(-2), where n is a positive integer. To determine if the sequence is increasing, decreasing, or not monotonic, we need to look at the difference between successive terms.
Let's calculate the first few terms of the sequence:
a1 = 3(1)(-2) = -6
a2 = 3(2)(-2) = -12
a3 = 3(3)(-2) = -18
The difference between successive terms is:
a2 - a1 = -12 - (-6) = -6
a3 - a2 = -18 - (-12) = -6
Since the difference between successive terms is always the same (-6), the sequence is decreasing, and the answer is B. decreasing.
mp = 480 discount = 12 % find the sp
Answers
Step-by-step explanation:
hope it is helpful to you
Answer:
422.4
Step-by-step explanation:
MP=480
Discount%=12%
SP=?
We know that,
SP=MP-Discount%of MP
=480-12%×480
=480-57.6
=422.4
please help w part b! right picture this time
Answers
Answer:
View the image below
Step-by-step explanation:
