Answer:
The answer is c. 30 cm, 40 cm, 50 cm. This set of measures could not be the side lengths of a right triangle, as it does not satisfy the Pythagorean theorem. The Pythagorean theorem states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the square of the hypotenuse (50 cm) is not equal to the sum of the squares of the other two sides (30 cm and 40 cm).
Step-by-step explanation:
below is the graph of y=1/x^2. Transform to make it the graph of y=1/(x-2)^2 +3
Answer:
The transformation to make the graph of y=1/x^2 into y=1/(x-2)^2 +3 involves shifting the graph horizontally by 2 units to the right, and vertically by 3 units up.
The transformation can be achieved by applying the following changes to the original equation:
Substitute x with (x-2) in the denominator of the fraction: 1/(x-2)^2
Add 3 to the fraction: 1/(x-2)^2 +3
This will give us the new equation y=1/(x-2)^2 +3, and the graph of this equation will be a parabola shifted 2 units to the right and 3 units up from the original graph of y=1/x^2.
For each positive integer n, consider the pair (3^n −1, 5^n −1). For n = 1, this is the pair (2, 4) and for n = 2, it is (8, 24). Can you find a value for n such that both numbers in the pair (3^n − 1, 5^n − 1) are divisible by d = 7? Can you find more than one such n? Do you think there are finitely or infinitely many n such that 3n − 1 and 5n − 1 are both divisible by d = 7? Why? Explain your reasoning as carefully as you can.
Now, what if we replace d = 7 with d = 11? Or with d = 13? What if we take d = 77
or d = 1001? Describe any patterns you think are interesting
There is no value of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by 7.
For d=7, we can see that:
3² - 1 = 8 is divisible by 7, but 5² - 1 = 24 is not divisible by 7.
For larger values of d such as 11, 13, 77, and 1001, we can use a similar approach to see if there are any values of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by d. However, finding an exact value of n for larger values of d may be difficult without using more advanced mathematical methods.
In general, the number of values of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by a given integer d will depend on the properties of the numbers 3, 5, and d. For example, if d is a prime number that is not a divisor of either 3 or 5, it is likely that there are only a few values of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by d.
However, if d is a composite number or a divisor of either 3 or 5, there may be more values of n such that both 3ⁿ⁻¹ and 5ⁿ⁻¹ are divisible by d. Whether there are finitely or infinitely many such n will depend on the specific values of 3, 5, and d.
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Three large cones hang from the ceiling in an office building in front of a bank of windows. The height of each cone is 12 feet and the circumference of the base of each cone is 8π feet. The base and 50% of the lateral surface of each cone is painted red, and the rest of each cone is painted black.
What is the total surface area painted black? Use π≈3.14.
Enter your answer, rounded to the nearest tenth, in the box.
The total surface area painted black is 12.6 sq. feet.
Solving for the total surface area painted black we have:The surface area of a cone with height h and circumference of the base c can be calculated using the formula:
A = πr^2 + πrs,
where,
r = the radius of the base
s = the slant height.
We can find the radius of the base by dividing the circumference by 2π:
r = c / (2π)
= 8π / (2π)
r = 4.
The slant height can be found using the Pythagorean theorem:
s = √(r² + h²)
= √(4² + 12²)
= √(16 + 144)
= √(160)
s = 12.7279
So the surface area of each cone is:
A = πr² + πrs
= π * 4² + π * 4 * 12.7279
= 3.14 * 4² + 3.14 * 12.7279
= 50.265...
The base and 50% of the lateral surface are painted red, which is a total of 50% + 100% / 2 = 75% of the surface area.
So the total surface area painted black is:
(100% - 75%) * A
= 25% * A
= 25% * 50.265
= 12.566
Rounding to the nearest tenth, the total surface area painted black is 12.6 sq. feet.
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Put the function P= 35(1.3)^t in the form P0ekt When written in this form, you have:
K=
P0=
Writing the function P = 35(1.3)^t in the form P(0)e^{kt}, the value of k = log(1.3) and P(0) = 35.
The function is P = 35(1.3)^t
At t = 0, P = 35, so P(0) = 35
P = 35e^{kt} .................Equation 1
P = 35(1.3)^t .................Equation 2
Now dividing the equation, we get
P/P = 35e^{kt}/35(1.3)^t
1 = e^{kt}/(1.3)^t
Multiply by (1.3)^t on both side, we get
1.3^t = e^{kt}
Now taking log of both side, we get
log [1.3^t] = log[e^{kt}]
Using the formula log[m^n] = n logm
t log(1.3)= kt loge
t log(1.3)= kt
Divide by t on both side, we get
k = log(1.3)
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An angle measures 8.4° more than the measure of its supplementary angle. What is the measure of each angle?
The measure of each angle are 94.2° and 85.8°.
How to detemine the measure of each angleLet's call the measure of the first angle x.
Since the angle is supplementary to another angle, their measures add up to 180°.
So, the measure of the second angle is 180° - x.
Also, the first angle measures 8.4° more than the second angle, so:
x = (180° - x) + 8.4°
Solving for x:
2x = 188.4°
x = 94.2°
So the first angle measures 94.2° and the second angle measures 180° - 94.2° = 85.8°.
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brewer, a graduate student, would like to determine how often college students are going to local restaurants to eat lunch instead of eating on campus. which method should be used to gather data? case study
For performing this analysis Brewer can use a method such as a survey for gathering the data.
Brewer would like to determine how often college students are going to local restaurants to eat lunch instead of eating on campus. He will require a large amount of data to determine this.
This data that he requires can be gathered using the method of survey, and a conclusion can be drawn from the data with the help of statistical analysis and probability analysis.
Surveys can be conducted by email or in an online survey form and can include both open-ended and closed-ended questions to gather both quantitative and qualitative data on the subject.
In this case, the survey can also be conducted by using orthodox methods of gathering data, such as observing people who are going to eat at local restaurants and on campus, although this is not the most ideal method.
Surveys allow the researcher to reach a large number of participants and gather data efficiently and effectively.
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The best way for her to find this data reliably is by using survey's
She can go around campus and survey the other students, and eventually get enough data to find an answer to her question (I also took the test and this answer was right)
have a good day :)
While on a beach, your friend discovers a different genie. This genie also offers two purses to choose from and he gives you the following graph to show how the money in each purse will grow. The set of triangular marks that lie on a line represent values in Purse A, and the set of square marks that make a curve represent those in Purse B.
The genie is still deciding how many days he will let the money in the purses grow. Help your friend plan a strategy for picking the purse with the most money while the genie thinks.
Strategy should be, choosing purse A if number of days is less than 10,if it is more than 10 , he should choose purse B.
If there are 10 days, he can choose any of the purse.
What is an inequality?Inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.
Given,
Genie provides friend two purses,
Purse A and Purse B
Graph of Growth in amount to number of days is given.
By the graph,
Intersection point is on 10th day
Till 10th day Amount of purse A is grows more than amount of purse B.
After 10th day amount of purse B starts growing more than amount of purse A
Let no. of days be x
If x < 10, he should choose purse A.
If x > 10 he should choose purse B.
If x = 10, he can choose any purse.
Hence, Friend should choose purse A if number of days is less than 10.
Friend should choose purse B if number of days is greater than 10.
If number of days is 10, he can choose any of the purse.
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Write the equation of AB in slope intercept form. Then check whether c lies on ab by substituting the coordinates of point c into the equation
The equation does not hold true, indicating that point C does not lie on line AB.
The equation of line AB can be written in slope intercept form as y = mx + b. The slope of line AB can be found using the equation m = (y2-y1)/(x2-x1). Substituting the coordinates of points A and B into the equation, we get m = (2-4)/(-5-2) = -2/7. The slope-intercept form of this equation is y = -2/7x + b. We can find the value of b by substituting the coordinates of point A into the equation. We get b = 4 + 2/7 = 19/7.
Therefore, the equation of AB in slope-intercept form is y = -2/7x + 19/7. To check whether point C lies on line AB, we must substitute the coordinates of point C into the equation. We get y = -2/7(-1)+19/7 = -2/7 + 19/7 = 17/7. Since the y-coordinate of point C is 8, the equation does not hold true, indicating that point C does not lie on line AB.
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Please help very urgent! A fair maiden can sew the border of a tapestry in six hours. Her sister works twice as fast. If they are working together, how long will it take them to finish the border?
Let's call the time it takes the fair maiden to sew the border of the tapestry "t". So, her sister can sew the border in t/2 hours.
Working together, they can sew the border in t + t/2 = 1.5t hours.
Since we know the fair maiden can sew the border in 6 hours, we can substitute this into the equation to find t:
6 + 6/2 = 1.5t
Simplifying the right side of the equation:
6 + 3 = 1.5t
9 = 1.5t
Dividing both sides of the equation by 1.5:
t = 6
So the fair maiden can sew the border in 6 hours and her sister can sew the border in 6/2 = 3 hours.
Working together, it would take them 6 + 3 = 9 hours to sew the border of the tapestry.
find the two values that x can have if 3x² + 14 = 89
Answer:
x = 5, -5
Step-by-step explanation:
3x² + 14 = 89
3[tex]x^{2}[/tex] = 75
[tex]x^{2}[/tex] = 25
x = 5 or -5
WEATHER A same-day forecast of the temperature tends to be within 2.25°F of the actual temperature. The
forecast for a particular day is 16°F.
Let x be the actual temperature. Find the range of possible temperatures for the day when the forecast is 16°F.
If WEATHER A same-day forecast of the temperature tends to be within 2.25°F of the actual temperature. The range of possible temperatures for the day when the forecast is 16°F is: 13.75°F to 18.25°F.
How to find range of possible temperatures?Let x be the actual temperature.
Find the range of possible temperatures for the day when the forecast is 16°F.
The range of possible temperatures for the day is:
Range = 16°F - 2.25°F
Range = 13.75°F
Range = 16°F + 2.25°F
Range = 18.25°F
The range is from 13.75°F to 18.25°F.
Therefore the actual temperature can be anywhere from 13.75°F to 18.25°F.
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someone please help me find the inverse function of g(x)=(x+10)^2
The inverse function of the function g(x) will be y = √(x) - 10.
What is the inverse function?Let the function f is given as
y = m(x + a) + c
Then the inverse function of the function f will be given by swapping x with y and y with x.
The function is given below.
g(x) = (x + 10)²
Replace x with y and g(x) with x, then we have
x = (y + 10)²
(y + 10)² = x
y + 10 = √x
y = √(x) - 10
The inverse function of the function g(x) will be y = √(x) - 10.
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a square has a perimeter of ( 20x + 32) inches, whats the length of one side
Answer:
5x + 8
Step-by-step explanation:
(20x + 32) / 4
5x + 8
Find the rate of change for the situation: Ron completed 3 math assignments in one hour and Duke completed 6 assignments in two hours
The rate of change is 3.0, or three assignments are completed every hour when timed in hours.
How is the rate of change per hour determined?The formula R = D/T, or rate of change equals the distance travelled divided by the time required to do so, can be used to approach rate of change problems in general.Divide the y-value change by the x-value change to determine the average rate of change. Identifying changes in quantifiable parameters like average speed or average velocity calls for the knowledge of the average rate of change.The pace of change of the condition is determined by the slope, which is calculated using the slope formula.m = (6 - 3) miles / (2 - 1) hour = 3 miles / 1h
The rate of change is 3.0, or three assignments are completed every hour when timed in hours.
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A manufacturing process generates cans of frozen concentrated orange juice.
The collection of all cans the process has or could have generated is defined as
the ____.
(A) representative sample (B) population
(C) researcher’s sample (D)conceptual sample
As per the concept of hypothesis the collection of all cans the process has or could have generated is defined as the population
In statistics, a hypothesis is an assumption made about a population of data, usually with the goal of testing it.
The term "population" refers to the collection of all possible items of data or objects, while a "sample" is a smaller subset of the population that is used to draw conclusions about the population.
In the case of the manufacturing process for cans of frozen concentrated orange juice, the "population" would be the collection of all cans that the process has or could have generated.
This is because the goal is to make conclusions about the entire population, rather than just a portion of it.
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13 = 2m + 5
ThANK U
M=
m = 4
13=2m+5
-5 -5 subtract 5 from both side
8=2m
8/2=2m/2 divide both side by 2
4=m
How do you start solving trigonometric identities like this?
sin(x-y)/csc (x+y) = sin^2x-sin^2y
The lesson I'm taking explains this one, but I don't understand it. Here are the steps in the example:
The function sin(x-y)/cosec(x+y)=sin²x-sin²y
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
We have to prove that sin(x-y)/cosec(x+y)=sin²x-sin²y
Using the identity cosecx=1/sinx
We get sin(x-y)/cosec(x+y)=sin(x-y)sin(x+y)
We know sin(x+y)=sinxcosy+cosxsiny
sin(x-y)=sinxcosy-cosxsiny
Now sin(x-y)sin(x+y)=(sinxcosy-cosxsiny)(sinxcosy+cosxsiny)
=sin²xcos²y-cos²xsin²y
=sin²x(1-sin²y)-(1-sin²x)sin²y
=sin²x-sin²xsin²y-sin²y+sin²xsin²y
=sin²x-sin²y
Hence, we proved that sin(x-y)/cosec(x+y)=sin²x-sin²y
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Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9
By completing squares, we will see that the solutions of the given quadratic equation are:
x = -3 ± √(21/2)
How to solve the quadratic equation?
Here we know that Inga is solving the quadratic equation below:
2x² + 12x - 3 = 0
The steps that she can do is try to complete squares, first we can take the 2 as a common factor to get:
2(x² + 6x) - 3 = 0
Now we can add 18 in both sides, then we will get:
2(x² + 6x) - 3 + 18 = 18
We can put that 18 inside the first term:
2(x² + 6x + 9) - 3 = 18
And now we can complete squares, because:
x² + 6x + 9 = x² + 2*3*x + 3² = (x + 3)²
Replacing that we will get:
2(x + 3)² - 3 = 18
2(x + 3)²= 18 + 3 = 21
2(x + 3)² = 21
(x + 3)² = 21/2
x = -3 ± √(21/2)
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the value of \frac{\sqrt{12}}{\sqrt{10}}\cdot \frac{\sqrt{5}}{\sqrt{6}} is closest to the whole number .
The value of [tex]\frac{\sqrt{12}}{\sqrt{10}}\cdot \frac{\sqrt{5}}{\sqrt{6}}[/tex] is closest to the whole number 1.
What is multiplication?
Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
An expression,
[tex]\frac{\sqrt{12}}{\sqrt{10}}\cdot \frac{\sqrt{5}}{\sqrt{6}}[/tex].
Simplifying,
{(√2 × √6) / (√2 × √5)} × √5/ √6
= 1.
Therefore, the value is 1.
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determine whether the set s spans r3. if the set does not span r3, then give a geometric description of the subspace that it does span. s = {(6, 7, 1), (−3, 4, 7), (1, −3, 4)}
The set S = {(6, 7, 1), (−3, 4, 7), (1, −3, 4)} spans R³
For (x, y, z) ∈ R³, we can find scalars a, b, c for which the equation
(x, y, z) = a(6, 7, 1) + b (−3, 4, 7) + c (1, −3, 4) is true.
We can write above equation (x, y, z) = a(6, 7, 1) + b (−3, 4, 7) + c (1, −3, 4) as system of equations,
6a - 3b + c = x
7a + 4b - 3c = y
a + 7b + 4c = z
Above system of equations in matrix form as,
[tex]\begin{bmatrix}6 & -3 & 1 \\7 & 4 & -3 \\1 & 7 & 4\end{bmatrix}\begin{bmatrix}a\\b \\c\end{bmatrix}=\begin{bmatrix}x \\y \\z\end{bmatrix}[/tex]
The determinant of coefficient matrix is,
[tex]\left|\begin{matrix}6 & -3 & 1 \\7 & 4 & -3 \\1 & 7 & 4\end{matrix}\right|=360[/tex]
Since the determinant of the coefficient matrix is not zero (it equals 360), the coefficient matrix is invertible.
This means, the system of equations must have solution.
Therefore, S = {(6, 7, 1), (−3, 4, 7), (1, −3, 4)} spans R³
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What is 1/3 as a fraction?
Answer:
0.333333...
Step-by-step explanation:
look this almost imposble but there is few ways that can give you an examples
divide 1 by 3 to divide fisrt put a 0 than dot becuze you can't devid it normaly naw give the 1 a 0 so it is ten so dived so 0.3 naw do it again so it endless but not infinty ok so thanks it is 0.3333333. sometimes pick ansear like this 0.3... or 0.3 white a line on top iv it
The fraction 1/3 is comparable to one third. As a result, it is a third of a sum.
What is fraction?In general, any number of equal pieces is represented by a fraction, which is a portion of the entire. A fraction, such as one-half, eight-fifths, or three-quarters, indicates the number of parts of a particular size when it is used in daily speech. Part of a whole is a fraction. The quantity is written as a quotient in mathematics, where the numerator and denominator are divided. Each is an integer in a simple fraction. Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other. An equal division of a whole number into smaller parts is called a fraction.To learn more about fraction, refer to:
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the factored representation of the polynomial 5s2 5s−30 is: (s- )(s- ) note: all edit boxes should be filled with integer numbers.
The polynomial 5s2 + 5s - 30 can be factored as (s + 6)(s - 5). This is done by finding two numbers whose product is -30 and whose sum is 5. They are -6 and 5.
The factored representation of the polynomial 5s2 + 5s - 30 can be found by factoring. First, we need to find two numbers whose product is -30 and whose sum is 5. This can be done by trial and error or by using the Fundamental Theorem of Algebra. When these two numbers are found, the polynomial can be factored as (s + 6)(s - 5). To factor the polynomial, we can use the factor theorem. This states that if a and b are factors of a polynomial, then (x-a) and (x-b) are factors of the polynomial. In our case, a=6 and b=-5. So, the polynomial can be written as (s + 6)(s - 5). We can then use the distributive property to expand the polynomial and verify that it is the same as the original polynomial.
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what is the order from least to greatest with these numbers 0.000167, 0.0000097, 0.0000000045
Answer:
0.0000000045, 0.0000097 and 0.000167 isthe acending order
how many page faults occur for fifo algorithm for the following reference string with four-page frames? 1, 2, 3, 4, 5, 3, 4, 1, 6, 7, 8, 7, 8, 9, 7, 8, 9, 5, 4, 5, 4, 2
As per the FIFO algorithm, there have been a total of 13 page faults.
The FIFO algorithm is a page replacement strategy used in operating systems to manage the allocation of memory frames to pages.
For the given reference string of
=> 1, 2, 3, 4, 5, 3, 4, 1, 6, 7, 8, 7, 8, 9, 7, 8, 9, 5, 4, 5, 4, 2
with four-page frames, we can see that there will be multiple page faults. Initially, all four frames are empty, so there will be four page faults as the first four pages are brought into memory.
Then, when page 5 is needed, the oldest page in memory, page 1, is replaced leading to another page fault.
As the reference string continues, there are several page faults that occur as pages are replaced
By the end of the reference string, there have been a total of 13 page faults.
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PLEASE HELP SOLVE THIS QUESTION
The slope of this line is m = 1.
An equation of this line is y = x.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Based on the information provided, we can logically deduce the following data points on the line:
Points on x-axis = (0, 1).Points on y-axis = (0, 1).Substituting the given data points into the slope formula, we have the following;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (1 - 0)/(1 - 0)
Slope (m) = 1/1
Slope (m) = 1
At data point (1, 1), an equation of this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y represents the data points.Substituting the parameters, we have:
y - 1 = 1(x - 1)
y = x - 1 + 1
y = x
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A baketball tournament tarted at 12:15pm and ended at 4:00pm did the tournament lat more than 4 hour? i put 3:45 min. Am i right
No, you're incorrect. The tournament lasted from 12:15pm to 4:00pm, which is a duration of 3 hours and 45 minutes. So, the tournament lasted less than 4 hours.
To calculate the duration, you subtract the start time from the end time:
4:00pm - 12:15pm = 3 hours and 45 minutes
Therefore, the tournament lasted for 3 hours and 45 minutes, which is less than 4 hours.
Here's a step-by-step breakdown of the calculation:
Start by calculating the number of whole hours between the start and end time.
4:00pm - 12:15pm = 3 hours
Next, calculate the number of remaining minutes.
4:00pm - 12:15pm = 45 minutes
So the total duration of the tournament was 3 hours and 45 minutes, which is less than 4 hours.
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What is the approximate density of a nucleus?
On average, an atom's nucleus has a density of 2.31017 kg/m³.
Why is density of nucleus so high?According to nuclear density, the ratio of mass to volume inside an atom's nucleus determines its density. The nuclear density is highly high because the atomic nucleus makes up the majority of an atom's mass despite being relatively small in relation to the rest of the atom.
On average, an atom's nucleus has a density of 2.31017 kg/m³. Nuclear density is what causes this. It is the same for all nuclei since it is independent of the mass or size of the nucleus.
The nucleus is particularly dense because to its high mass and small size. A penny's worth of material would weigh more than 30 million tons if it had the same density as an atom's nucleus.
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Unit 6 Final Test
Would appreciate some help as soon as its available (Has 3 parts) (ASAP)
1. The population of a town was 88 in 2016. The population quadruples every year.
(a) Use the exponential growth model to write an equation that estimates the population t years after 2016.
(b) Estimate the population of the town in 2023. Show your work.
Answer:
2. Convert the following into a single log statement from the many log statements to 1.
7 Log x + 2log y – log 23 – 3 log z
NOTE: You must show this in at least two steps.
1st line should be to convert the 2 the 3 and the 7 only.
2nd line can be the final answer.
Answer:
3. A savings account is started with an initial deposit of $500. The account earns 7% interest compounded annually.
(a) Write an equation to represent the amount of money in the account as a function of time in years.
(b) Find the amount of time it takes for the account balance to reach 1 million. Show your work.
Note: 1 million is a 1 with 6 zeros. Note2: you must use log functions to solve.
Answer:
The population of the city in 2023 is 1.6 * 10^6.
What is the exponential function?The exponential function is a mathematical function that describes the growth of a quantity as a power of another quantity.
In mathematics, the exponential function is used to model a wide range of phenomena including exponential decay, compounding interest, and population growth.
Using the exponential growth model;
P = Poe^rt
P = population at time t
Po = Initial population
r = Population growth rate
t = time
4Po = Poe^rt
If t = 1
4Po/Po = e^r
4 = e^r
r = ln4
r = 1.4
The population in 2023 is;
P = 88e^1.4 * 7
P = 1.6 * 10^6
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Find the ymmetric equation of the line that pae through the point P(−2,1,0)
and i parallel to the vector v⃗ =⟨0,2,−3⟩
x + 2 = -2y + 2
y - 1 = 2z + 2
z - 3 = 3x + 6
This is the symmetric equation of the line that passes through the point P and is parallel to the vector .
What is symmetric equation?
A line that passes through the point P and is parallel to the vector v can be represented by the parametric equation:
x = -2 + 0t
y = 1 + 2t
z = 0 - 3t
where t is a scalar parameter. To find the symmetric equation of this line, we need to convert the parametric equation to a normal form. We'll start by finding a point on the line other than P, then use those two points to find the direction vector of the line. Let's use t = 1, then the line passes through the point Q(-2 + 01, 1 + 21, 0 - 3*1) = (-2, 3, -3). The direction vector of the line is found by subtracting the position vectors of P and Q:
d = Q - P = (-2 - (-2), 3 - 1, -3 - 0) = (0, 2, -3) = v
So, the direction vector and the vector v are equal, which means the line is parallel to v. Now we have two points on the line, P and Q, which we can use to find the symmetric equation of the line:
(x + 2)/0 = (y - 1)/2 = (z + 3)/(-3) = t
x + 2 = -2t
y - 1 = 2t
z + 3 = 3t
Rearranging the above equations, we get:
x = -2 - 2t
y = 2t + 1
z = 3t - 3
Since t is a scalar parameter, it can be eliminated from the equations to obtain the symmetric equation of the line:
x + 2 = -2y + 2
y - 1 = 2z + 2
z - 3 = 3x + 6
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x + 2 = -2y + 2
y - 1 = 2z + 2
z - 3 = 3x + 6
This is the symmetric equation of the line that passes through point P and is parallel to the vector.
What is the symmetric equation?
A line that passes through the point P and is parallel to the vector v can be represented by the parametric equation:
x = -2 + 0t
y = 1 + 2t
z = 0 - 3t
where t is a scalar parameter. To find the symmetric equation of this line, we need to convert the parametric equation to a normal form. We'll start by finding a point on the line other than P, then use those two points to find the direction vector of the line. Let's use t = 1, then the line passes through the point Q(-2 + 01, 1 + 21, 0 - 3*1) = (-2, 3, -3). The direction vector of the line is found by subtracting the position vectors of P and Q:
d = Q - P = (-2 - (-2), 3 - 1, -3 - 0) = (0, 2, -3) = v
So, the direction vector and the vector v are equal, which means the line is parallel to v. Now we have two points on the line, P and Q, which we can use to find the symmetric equation of the line:
(x + 2)/0 = (y - 1)/2 = (z + 3)/(-3) = t
x + 2 = -2t
y - 1 = 2t
z + 3 = 3t
Rearranging the above equations, we get:
x = -2 - 2t
y = 2t + 1
z = 3t - 3
Since t is a scalar parameter, it can be eliminated from the equations to obtain the symmetric equation of the line:
x + 2 = -2y + 2
y - 1 = 2z + 2
z - 3 = 3x + 6
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Find the value of x for which // m.
105°
(3x - 18)
m
The value of x is 3.
What are Parallel lines?parallel lines are coplanar infinite straight lines that do not intersect at any point.
The lines l and m are the parallel lines.
3x-18+105=180
3x+87=180
Subtract 87 on both sides
3x=180-87
3x=93
Divide both sides by 3
x=31
Hence, the value of x is 3.
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