The slope of the graph of x^3 = ln(xy) at the point (1, e) is 2e. This is found by taking the derivative of the equation to find a formula for the slope at any point, and then substitifying the given point into that formula.
Explanation:To determine the slope of a graph of the equation x3 = ln(xy) at a specific point, we need to take the derivative of the equation, which gives us the slope at any point. Given the equation x^3 = ln(xy) and the point (1, e), first we can take the derivative implicitly.
Using the chain rule and the fact that the derivative of ln(x) is 1/x, we have 3x2dx = (1/y + x/y')dx. Simplifying this gives y' = (3x2y - 1)/x, which is the derivative of the equation and represents the slope at any given point.
Substituting x = 1 and y = e into the equation of the derivative, we get y' = (3.1e - 1)/1 = 2e, so the slope at the point (1, e) is 2e.
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Graph the system of constraints and find the value of x and y that maximize the objective function.
We want to maximize C, which is C= 7x - 3y. Let's explore our intuition regarding how this will look. We know that both y and x are greater than or equal to zero, which means -3y will be a negative number (or 0) and x is a positive number (or 0). We want to get x as big as possible, given the constraints, we want y to be zero, if possible
We see that, based on the constraints, y is greater than or equal to zero,
but it has no other minimum value established. We only know that y and x add up
to 5, and that y is less than or equal to (1/5)x + 2. That means y could be
0 and still satisfy the constraints.
In order to maximize C, we want to be 5 as possible
and y to be zero:
C = 7 (5) - 3(0)
C=35
Answer: Solving Systems Using Matrices Quiz Part 1
1. c) (5,0)
2. a) 20 of type A; 20 of type B
3. d) no solution
4. a) -5
5. d) 11 -12 7 5 12 -7
6. a) (-6,8)
Factor the expression completely over the complex numbers.
x4−625
The number of males per 100 females in a country's population is called what?
A triangle has two sides of length 2 and 17. what is the smallest possible whole-number length for the third side?
A rectangular sandbox has a width of 5 feet. The sandbox is 5 times as long as it is wide. what is the perimeter of the sandbox?
Help pleaseeeeeeeeeeeeeeeeeeeeeee
Is this right? Domain and range of a function
Identify each sequence below as geometric, arithmetic, or neither.
(a) 1, 3, 5, 7, 9, 11, 13, 15
(b) 21, 16, 12, 9, 7, 6
(c) .3, .03. .003, .0003, .00003
(d) -4, -12, -36, -108, -324
Sequence (a) is an arithmetic sequence because the common difference is constant. Sequence (d) is a geometric sequence because the common ratio is constant. Sequences (b) and (c) do not follow the patterns of arithmetic or geometric sequences and are neither.
Explanation:The question asks to identify each sequence as arithmetic, geometric, or neither.
Arithmetic sequence: In an arithmetic sequence, the difference between successive terms is constant. This difference is also called the common difference. For example, the sequence (a) 1, 3, 5, 7, 9, 11, 13, 15 is an arithmetic sequence because the common difference between the terms is 2.Geometric sequence: In a geometric sequence, the ratio of any two successive terms is constant. This ratio is also called the common ratio. For example, the sequence (d) -4, -12, -36, -108, -324 is a geometric sequence because the common ratio between the terms is 3.Neither: If a sequence is not arithmetic or geometric, it is classified as neither. For example, the sequence (b) 21, 16, 12, 9, 7, 6 and (c) .3, .03, .003, .0003, .00003 do not follow the patterns of arithmetic or geometric sequences and therefore are classified as neither.Learn more about Sequence Identification here:https://brainly.com/question/30531377
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Prove: The midsegment between sides Line segment AB and Line segment BC is parallel to side Line segment AC.
When seven times a number is decreased by 66 the result is 50. what is the number?
How to find the variance of a sample with only mean standard deviation size?
Find height of triangle given hypotenuse and angle
3(x+y)=y, if (x,y) is a solution to the equation above and y cannot equal to zero what is the ratio x/y
The ratio, x/y in the equation, if y ≠ 0 is: x/y = -2/3.
What is the Solution of an Equation?Solution of an equation is the value of a variable or two variables that makes an equation true.
Given:
3(x+y)=y
We are required to find the ratio, x/y if y ≠ 0.
Thus:
3(x+y)=y
Open bracket
3x + 3y = y
Subtract 3y from both sides
3x = y - 3y
3x = -2y
Divide both sides by 3
x = -2y/3
Divide both sides by y
x/y = -2/3
Therefore, the ratio, x/y in the equation, if y ≠ 0 is: x/y = -2/3.
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How do I prove the corresponding angles theorem?
Final answer:
The corresponding angles theorem states angles in matching corners are equal when two parallel lines are intersected by a transversal. To prove this, use properties of parallel lines and transversals, and various established theorems. Euclidean postulates are employed, rather than the Pythagorean theorem or trigonometry.
Explanation:
To prove the corresponding angles theorem, one must understand that when two parallel lines are intersected by a transversal, the angles in matching corners are equal. These are called corresponding angles. For instance, suppose you have two parallel lines L1 and L2, and a transversal T that intersects them at points A and B respectively. The angle ∠PAB on line L1 would correspond to angle ∠QBA on line L2, and they would be equal.
To provide a mathematical proof, one would typically use properties of parallel lines and transversals, or other established theorems such as the alternate interior angles theorem or the exterior angle theorem. By proving all these other angles are equal due to their relationships with each other (alternate interior, consecutive interior, alternate exterior angles, etc.), one can by default establish that corresponding angles must also be equal.
Proof of this theorem often involves constructing supplementary and congruent angles and using the postulates of Euclidean geometry. The Pythagorean theorem and trigonometry need not be involved in this proof unless one is working with right triangles formed by the transversal and the parallel lines, or if dealing with more complex geometric problems.
Numbers mr. wahl is thinking of two numbers. the sum of the numbers is 27. the product of the numbers is 180. what two numbers is mr. wahl thinking of?
Mattie,Joel,and Oscar each ate 325 calories at lunch each day for 18 days.About how many calories did they eat in all
solve
5t < -15
^^^(the < sign has a line underneath along with the answers)
A. t > 3
B. t < 3
C. t > -3
D. t < -3
The function f(x)= 70x^3/4 power can be used to estimate the BMR (Basic Metabolic Rate) of mammals. In this function, x is the mass of the animal in kilograms, and f(x) is its BMR in kilocalories (kcal) per day. Note that one kcal is equal to one food calorie. The howler monkeys at a zoo are fed a diet that contains 3.35 kcal per gram. Write a function g(x) that gives the mass of food in grams that a howler monkey must eat to obtain x kilocalories of energy. Please help!
Which conjunction or disjunction is equivalent to the this inequality?
5-3 |p+4| <= -10
p + 4 ≤ 5 AND p + 4 ≥ -5
p + 4 ≤ 5 OR p + 4 ≥ -5
p + 4 ≥ 5 OR p + 4 ≤ -5
p + 4 ≥ 5 AND p + 4 ≤ -5
Why would someone choose to use a graphing calculator to solve a system of linear equations instead of graphing by hand? Explain your reasoning.
Sample Response: A graphing calculator is more accurate than graphing by hand. If the slope and/or y-intercept is a fraction or decimal, it is more difficult to accurately graph by hand. Using a calculator might also be more time efficient because it might accept a line in any form. A calculator’s window can be adjusted quickly instead of having to redraw a graph by hand when adjusting the scale.
For time efficiency and to get a more precise solution.
Why a graphing calculator is better than graphing by hand?
There are two reasons.
1) In a graphing calculator you only need to input the functions and that's all, it will graph the functions for you, so it needs a lot less time than graphing by hand.
2) When you graph by hand, there is a limit in how much of an exact solution you can get (and there may be a mistake if the line is to thick or something like that). While in a graphing calculator you can find the exact point where the graphs intersect, so you will get a more precise solution with a graphing calculator.
These are the two reasons why using a graphing calculator may be better than graphing by hand.
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Factor. 2xy+5x−12y−30
this is the anwser to your problem
(2y+5)(x-6)
5 with a negative exponent of 4 over 5 with a exponent of 3 simplified
A.) 5 with an exponent of 7
B.) 5 with a negative exponent of 1
C.) 1 over 5 (fraction)
D.) 1 over 5 with an exponent of 7
What is descriptive statistics and inferential statistics?
Descriptive statistics is a one type of statistics which involve generalization of conclusions from small selected samples.
Inferential statistic is atype of statistic which involve summarization of data in numerical form.
Michaela climbed up a mountain at an Average speed of 3 mi/h. She climbed down at an average speed of 5 mi/h. What is Michaela's average speed for the entire trip? Round to the nearest tenth
To find Michaela's average speed for the entire trip, we need to calculate the total distance traveled and the total time taken. The average speed can be calculated as (2D) / (D/3 + D/5), which is approximately 3.53 mi/h.
Explanation:To find Michaela's average speed for the entire trip, we need to calculate the total distance traveled and the total time taken.
Let's assume the distance she climbed up the mountain is D. The distance she climbed down is also D since she retraced her steps. The average speed for climbing up is 3 mi/h and the average speed for climbing down is 5 mi/h.
The total distance is 2D and the total time is D/3 + D/5. Therefore, the average speed can be calculated as (2D) / (D/3 + D/5).
Simplifying this expression gives us the average speed as 3.53 mi/h (rounded to the nearest tenth).
is the function f(x)=4-7x^5 a polynomial function? if so state its degree and leading coefficient
Answer:
Degree would be 5 and leading coefficient is -7
Step-by-step explanation:
To identify the leading look for the number with the biggest power. The degree is the power and the leading is the main number.
Yes, the function f(x) = 4 - 7x^5 is a polynomial function with a degree of 5 and a leading coefficient of -7.
Explanation:Yes, the function f(x) = 4 - 7x5 is a polynomial function.
A polynomial function is a function where the variable (x) is raised to a non-negative integer power and multiplied by coefficients. In this case, x is raised to the power of 5 which is a non-negative integer.
The degree of a polynomial function is the highest power of the variable. In this case, the degree of the function is 5.
The leading coefficient is the coefficient of the term with the highest power of the variable. In this case, the leading coefficient is -7.
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John surveyed 30 members of a country club. He found that 9 members had signed up for tennis.
What is the experimental probability that the next member surveyed will sign up for tennis?
A.
0.3
B.
0
C.
0.7
D.
1
The experimental probability that the next member surveyed will sign up for tennis is 0.3, based on the current data where 9 out of 30 members have signed up.
The question is asking for the experimental probability that the next member surveyed at the country club will sign up for tennis based on a survey of 30 members where 9 had already signed up for tennis.
To calculate the experimental probability, you divide the number of members who have signed up for tennis by the total number of members surveyed. So, the calculation would be:
Number of members who signed up for tennis: 9Total members surveyed: 30The experimental probability is then calculated as 9/30, which simplifies to 0.3. Therefore, the correct answer is:
A. 0.3
What two numbers have the product of -135 and the sum of 6?
The Statement of Theorem should be in what form?
if-then
then-if
maybe-conclusion
does not matter
Answer: If/then.
Step-by-step explanation: A theorem is a statement that has been proven on the basis of other statements, for example other theorems, which are known to be true.
We use the pattern "If A...., then B..." when we known that "A" is a statement that is true and we want to declare that since A is true, B should also be true.
20! / 16! = a 24 b 11,628 c 116,280 d A number too big to compute
20! / 16! =
20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1
divided by
16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1
equals C. 116,280
Which value is equivalent to x+4/4+x
Answer:
Step-by-step explanation:
Alright, lets get started.
Given that:
[tex]\frac{x+4}{4+x}[/tex]
Using commutative property, 4+x = x+4,
so
[tex]\frac{x+4}{x+4}[/tex]
Both numerator and denominator has same value, hence they could be cancelled.
So,
[tex]\frac{x+4}{x+4} = 1[/tex]
Hence the answer is 1 : Answer
Hope it will help :)
Answer:
c
Step-by-step explanation:
the answer is 1