An 18-foot tree is 3 times as tall as when planted. Which equation can you solve to find out the tree's height on the day it was planted?
Answer:
3 • h = 18
Step-by-step explanation:
True or False? If x>0 and a>1, then (ln x/ln a) = ln (x/a) Counter example if false.
...?
The statement "If x > 0 and a > 1, then (ln x/ln a) = ln (x/a)" is false.
This can be shown by using the properties of logarithms.
The correct relationship is given by the change of base formula, which states that for any positive x, a, and b, where a and b are not equal to 1.
The following holds:
[tex][ \frac{\ln x}{\ln a} = \log_a x ][/tex]
Therefore, the correct relationship is:
[tex][ \frac{\ln x}{\ln a} = \log_a x ][/tex]
This shows that the original statement is false.
on a certain clock the minute hand is 4 in long and the hour hand is 3 in long. How fast is the distance between the tips of the hands changing at 4 PM? ...?
The angle between the minute and hour hands of a clock at 4 PM decreases at a speed of 330 degrees per hour. However, the rate at which the distance between the tips of the hands changes depends on the specific time and must be calculated using trigonometric differentiation.
Explanation:To solve this problem, we first need to understand the rate at which an hour hand and a minute hand of a clock cover the distance. The hour hand takes 12 hours to complete a 360 degree rotation, i.e., it moves at a rate of 30 degrees per hour. The minute hand covers a 360 degree rotation in 60 minutes (or 1 hour), i.e., it moves at a rate of 360 degrees per hour.
At 4 PM, the hour hand will be at 120 degrees (4 hours * 30 degrees/hour) and the minute hand will be at the top of the clock, or at 0 degrees. Therefore, the minute and hour hands are 120 degrees apart. However, this angle decreases over time since the minute hand moves faster than the hour hand. To determine how fast this angle is decreasing, we calculate the relative angular velocity of the minute hand with respect to the hour hand, which is the difference of their velocities, 360 degrees - 30 degrees = 330 degrees per hour. This is the speed at which the angle between the two hands is changing.
Trigonometry is used to calculate the distance between the tips of the hands, however, the variation of this distance with respect to time is complex and depends on the specific time. So at any given time, the rate of change in the distance between the tips of the hands should be calculated using principles of trigonometric differentiation.
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The rate at which the distance between the tips of the hands of a clock is changing at 4 PM can be calculated using the rates at which the minute and hour hands are moving. At 4 PM, the rate is approximately -30 degrees per hour. Using the formula for the distance between two points on a circle, the rate of change of the distance can be calculated to be approximately 8*sqrt(3) inches per hour.
Explanation:To find the rate at which the distance between the tips of the hands is changing, we need to consider the speeds at which each hand is moving. The minute hand moves at a constant speed of 1 revolution per hour, or 360 degrees per hour. The hour hand moves at a speed of 1/12 revolution per hour, or 30 degrees per hour.
At 4 PM, the minute hand is pointing at the 12 and the hour hand is pointing at the 4. The angle between the minute hand and the hour hand is 120 degrees. To find the rate at which this angle is changing, we take the derivative of the angle with respect to time, which gives us -30 degrees per hour.
Since the lengths of the hands are given in inches, the rate at which the distance between the tips of the hands is changing will be in inches per hour. Using the formula for the distance between two points on a circle, which is given by 2r*sin(theta/2), where r is the radius of the circle (in this case, the length of the minute hand) and theta is the angle between the two points (in this case, the angle between the minute hand and the hour hand), we can calculate the rate of change of the distance. Plugging in the values, we have 2*4*sin(120/2) = 2*4*sin(60) = 2*4*sqrt(3)/2 = 8*sqrt(3) inches per hour.
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16.
Write the following ratio in simplest form.
8 years to 14 months
814814
4747
7474
487487
Esmeralda likes to listen to music while she works out. She had a playlist in her MP3 player that lasted 40 mintues but she accidentally deleted 25 percent of the music. Does Esmeralda have enough music on her playlist for a 30 mintues workout? Explain your answer.
Esmeralda deleted 10 minutes of music from her 40-minute playlist. With the remaining 30 minutes of music, she has enough for a 30-minute workout.
Explanation:To determine if Esmeralda has enough music on her playlist for a 30 minute workout, we need to calculate how much music she has remaining after deleting 25%.
Let's start by finding 25% of the original music duration. To do this, we multiply the original duration (40 minutes) by 0.25:
25% of 40 minutes = 40 minutes * 0.25 = 10 minutes
Therefore, Esmeralda deleted 10 minutes of music.
To find out how much music she has left, we subtract the deleted music from the original duration:
Remaining music = Original duration - Deleted music = 40 minutes - 10 minutes = 30 minutes
Since the remaining music duration is exactly 30 minutes, Esmeralda has enough music on her playlist to last for a 30-minute workout.
What are the terms in the expression 7x+4y+17x+4y+1 ?
what is 34 47+4788×63÷799-69°08 (839+578)=
Which expression represents this word phrase?
15 divided by a number then decreased by 2
(15÷n)+2
(2÷n)+15
(15÷n)−2
(2÷n)−15
Angle C has what measurement according to the protractor?
Answer:
Option A is correct.
Step-by-step explanation:
In this figure we have to find the measurement of angle C.
As it clear from the picture the angle c is an acute angle which is less than 90° angle. We always measure the angles from the given point A. Therefore this is 50° angle.
So the answer would be option A. 50°.
what one is bigger a liter of ketchup or 750 milliliter of ketchup
What percent of 88 is 72.6? ...?
72.6 is 82.5 percent of 88. To find what percent 72.6 is of 88, divide 72.6 by 88 and then multiply by 100%. This gives you 82.5%, which means 72.6 is 82.5 percent of 88.
Explanation:To find what percent 72.6 is of 88, you can use the formula:
Percentage = (Part / Whole) × 100%
In this case, the 'Part' is 72.6 and the 'Whole' is 88. Plugging these numbers into the formula:
Percentage = (72.6 / 88) × 100%
Percentage = 0.825 × 100%
Percentage = 82.5%
So, 72.6 is 82.5 percent of 88.
Find three ratios equivalent to the ratio 3 to 4
rt-2n=y solve for t
show step-by-step solution
To solve for t in the equation rt-2n=y, add 2n to both sides to get rt=y+2n, and then divide by r to find t=(y+2n)/r.
Explanation:To solve the equation rt-2n=y for t, we need to isolate t on one side of the equation. Here's a step-by-step solution:
Add 2n to both sides of the equation to get rt = y + 2n.Divide both sides of the equation by r to solve for t. This gives us t = (y + 2n) / r.Thus, the value of t in terms of y, n, and r is t = (y + 2n) / r.
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is 15/15 greater than 9/15
Yes because
15/15 equals 1 whole
While 9/15 is not equal to one
Meaning 1 whole is bigger than 9 out of 15 of something
Which equation is y = –6x2 + 3x + 2 rewritten in vertex form?
we have
[tex] y = -6x^{2} + 3x + 2 [/tex]
we know that
the vertex form of the vertical parabola equation is equal to
[tex] y=a(x-h)^{2} +k [/tex]
where
(h,k) is the vertex of the parabola
To find the equation rewritten in vertex form let's factor the equation
Factor the leading coefficient
[tex] y = -6(x^{2} - 0.5x) + 2 [/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex] y = -6(x^{2} - 0.5x+0.0625-0.0625) + 2 [/tex]
[tex] y = -6(x^{2} - 0.5x+0.0625) + 2 +0.375 [/tex]
[tex] y = -6(x^{2} - 0.5x+0.0625) + 2.375 [/tex]
Rewrite as perfect squares
[tex] y = -6(x-0.25)^{2} + 2.375 [/tex]
therefore
the answer is
[tex] y = -6(x-0.25)^{2} + 2.375 [/tex]
Clarence works at least 5 hours but not more than 7 hours. He earns $11.60 per hour. The function f(t)=11.6tf(t)=11.6t represents the amount of money he earns for working t hours.
What is the practical range of the function?
A: all multiples of 11.6 between 58 and 81.2, inclusive
B: all real numbers from 5 to 7, inclusive
C: all real numbers
D: all real numbers from 58 to 81.2, inclusive
The solution is, the practical domain is all real numbers from 5 to 7, inclusive. and the practical range is all real numbers from 58 to 81.2.
What is range ?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
Here, we have,
Clarence works more than 5 hours and less than 7 so the practical domain is all real numbers from 5 to 7, inclusive.
Function: f(t) = 11.6 t
Restrictions: 5 ≤ t ≤ 7
Domain: possible values of t: all real values between 5 and 7 inclusive
Range: possible values of f(t): from 11.6 * 5 to 11.6 *7 = from 58 to 81.2, inclusive.
Using this domain, the practical range is:
From f(5) = 11.6(5) = 58
To f(7) = 11.6(7) = 81.2
inclusive.
Answer:
the practical domain is all real numbers from 5 to 7, inclusive. and the practical range is all real numbers from 58 to 81.2
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Is this function linear or nonlinear? y=1x
The degree of the function is one. Then function y = x will be a linear function.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
If the degree of the equation is one. Then the function will be a linear function.
The function is given below.
y = 1x
y = x
The power of the variables 'x' and 'y' will be one. Then the function is a linear equation.
The degree of the function is one. Then function y = x will be a linear function.
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PLEASE I NEED THIS DONE BECAUSE IVE BEEN WORKING ON THIS ALL DAY! AND IT IS MY LAST QUESTION!
The coordinate plane below represents a city. Points A through F are schools in the city.
graph of coordinate plane. Point A is at negative 5, 5. Point B is at negative 4, negative 2. Point C is at 2, 1. Point D is at negative 2, 4. Point E is at 2, 4. Point F is at 3, negative 4.
Part A: Using the graph above, create a system of inequalities that only contain points D and E in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above. (5 points)
Part B: Explain how to verify that the points D and E are solutions to the system of inequalities created in Part A. (3 points)
Part C: Timothy can only attend a school in his designated zone. Timothy's zone is defined by y < 3x − 3. Explain how you can identify the schools that Timothy is allowed to attend. (2 points)
A triangular pyramid has ___ flat faces
at the flower shop, there are 5 times as many roses as sunflowers. if there are 252 roses and sunflowers altogether, how many roses are there? how many sunflowers are there?
Metrics are based on the british system of weights and measures. true false
Answer: it is false :)
Use the graph below for this question:
graph of parabola going through negative 1, 7 and negative 3, 9.
What is the average rate of change from x = −1 to x = −3?
5
−3
1
−1
Answer:
The correct option is 4. The average rate of change from x = −1 to x = −3 is -1.
Step-by-step explanation:
It is given that the graph of parabola going through (-1,7) and (-3,9).
It means the value of at x=-1 is 7.
[tex]f(-1)=7[/tex]
The value of at x=-3 is 9.
[tex]f(-3)=9[/tex]
The slope of a function f(x) for the interval [a,b] is
[tex]m=\frac{f(b)-f(a)}{b-a}[/tex]
We have to find the average rate of change from x = −1 to x = −3. Here a=-1 and b=-3. So the average rate of change from x = −1 to x = −3 is
[tex]m=\frac{f(-3)-f(-1)}{-3-(-1)}[/tex]
[tex]m=\frac{9-7}{-3+1}[/tex]
[tex]m=\frac{2}{-2}[/tex]
[tex]m=-1[/tex]
The average rate of change from x = −1 to x = −3 is -1. Therefore the correct option is 4.
(2r)^5, write in expanded form.
The radius of a circle is estimated to be 14 inches, with a maximum error in measurement of ±0.08 inches. Use differentials to
estimate the maximum error in calculating the area of the circle using this estimate.
The maximum error in the area of a circle with an estimated radius of 14 inches and a measurement error of "+/-0.08 inches" can be calculated using differentials as approximately 7.03 inches².
To estimate the maximum error in calculating the area of a circle with a radius of approximately 14 inches (with a measurement error of "+/-0.08 inches"), we can use differentials. The formula for the area of a circle is A =
^(2), where π is a constant (approximately 3.14159). The differential dA, which represents the change in area, is given by dA = 2πr * dr, where dr is the change in radius.
With an error in radius measurement of"+/-0.08 inches", we have dr = 0.08 inches. Therefore, the error in the area, referenced as dA, can be calculated as:
dA = 2 * π * 14 inches * 0.08 inches
This gives dA ≈ 2 * 3.14159 * 14 * 0.08 inches², which can be calculated to determine the maximum error in the area.
After performing the calculation, we find that the maximum error in the area of the circle is about 7.03 inches².
How do you number 3 and can you explain everything for detail please
One die is rolled. List the outcomes comprising the following events:
1) Event the die comes up at most 2
2) Event the die comes up 3
3) Event the die comes up even
A single six-sided die has specific outcomes for events: at most 2 consists of {1, 2}, rolling a 3 consists of {3}, and rolling an even number includes {2, 4, 6}.
When a single die is rolled, the possible outcomes for different events are as follows:
The event where the die comes up at most 2 includes the outcomes {1, 2}.
The event where the die comes up 3 includes the single outcome {3}.
The event where the die comes up even includes the outcomes {2, 4, 6}.
It is important to list all possible outcomes clearly to understand the probabilities for each event. For instance, the probability of each of these events can be calculated by counting the favorable outcomes and dividing by the total number of possible outcomes, which is 6 in the case of a single six-sided die roll.
For what numbers x, -2π ≤ x ≤ 2π, does the graph of y = csc(x) have vertical asymptotes?
For what numbers x, -2π ≤ x ≤ 2π, does the graph of y = cot(x) have vertical asymptotes? ...?
Answer:
coincides with
Step-by-step explanation:
just got it right on edg
Vertical asymptotes at x = {-2π, -π, 0, π, 2π}
Given: [tex]y=csc(x)[/tex]
To find : For what values of x , it has vertical asymptotes.
Explanation:
A given function will have vertical asymptotes when its denominator becomes equal to zero.
We know that, [tex]csc(x)=\frac{1}{sin x}[/tex]
So, [tex]Sin(x)=0[/tex] will give vertical asymptotes
x = {-2π, -π, 0, π, 2π}
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Which statement can be used to prove that a given parallelogram is a rectangle?
A.The opposite sides of the parallelogram are congruent.
B.The opposite angles of the parallelogram are congruent.
C.The diagonals of the parallelogram bisect the angles.
D.he diagonals of the parallelogram are congruent.
a country's population in 1992 was 72 million in 1998 it was 76 million estimate the population in 2012
The graph shows the influence of the temperature T on the maximum sustainable swimming speed S of Coho salmon. (b) Estimate the values of S '(5) and S '(25).
Calculating S'(5) and S'(25) involves estimating the slope of the tangent to the temperature-speed graph of Coho salmon at those temperatures. The provided data is insufficient for an exact calculation and more information or a graph is needed.
Explanation:The influence of temperature on the maximum sustainable swimming speed (S) of Coho salmon can be analyzed using calculus to find the rate of change of speed with respect to temperature, commonly represented as S'(T). To estimate the values of S'(5) and S'(25), one would typically use a graph of S versus T and look for the slope of the tangent to the curve at T=5 and T=25.
However, the given data is insubstantial for such an analysis. More context or a graph is needed to provide a specific estimate. Generally, one might use the values given for S at temperatures nearby T=5 and T=25 to calculate the approximate rates of change at these points through the use of difference quotients or other numerical methods if a graph or formula is not available.