Answer:
The Place Value of '4' will be 400 if we keep it in the Hundreds place
The Face Value of '4' will remain the same
1-3x less than or equal to -2x< 3x+5
Answer:
x∈ [1; +∞)
Step-by-step explanation:
First write down the whole inequality:
1 - 3x ≤ -2 ﹤ 3x + 5
Then it can be seen that there are two separate inequalities here, so we have a system of inequalities:
{1 - 3x ≤ -2,
{3x + 5 ﹥ -2;
we express x from both inequalities:
From the first one:
-3x ≤ -2 - 1
-3x ≤ -3 / : (-3)
x ≥ 1
From the second one:
3x ﹥ -2 - 5
3x ﹥ -7 / : 3
[tex]x﹥ - \frac{7}{3} [/tex]
[tex]x﹥ - 2 \frac{1}{3} [/tex]
So, now that we have expressed x from both inequalities, we can write down the general range of x values for them (as you can see in the picture, the answer is the common values of x for both inequalities, both red and green colors):
x∈ [1; +∞)
Help please ! I’ll mark brainliest <333
Answer:
A) 6; B) 29∘; C) 29∘; D) 151∘
Step-by-step explanation:
A) Since ∠3 = ∠5 (opposite angles), we can make an equation:
5x - 1 = 3x + 11
5x - 3x = 11 + 1
2x = 12 / : 2
x = 6
B) ∠3 = 5x - 1 (x = 6)
∠3 = 5 × 6 - 1 = 29∘
C) ∠3 = ∠1 = 29∘ (cross angles)
D) ∠2 = 180∘ - ∠1 = 180∘ - 29∘ = 151∘
Find the value of the discriminant for the quadratic:
x²- 7 + 6 = 0
Value of the discriminant?
How many zeros?
What type?
(a) The discriminant is positive (25)
(b) The quadratic equation has two zeros.
(c) The type of the zeros is real and distinct.
What is the discriminant of the quadratic equation?The given quadratic equation is: x² - 7x + 6 = 0
To find the discriminant, we use the formula:
Discriminant = b² - 4ac
Here, a = 1, b = -7, and c = 6.
So, the discriminant is:
b² - 4ac = (-7)² - 4(1)(6) = 49 - 24 = 25
Therefore, the discriminant is 25.
To determine the number of zeros, we use the discriminant as follows:
If the discriminant is positive (greater than zero), then the quadratic equation has two real and distinct roots.If the discriminant is zero, then the quadratic equation has one real and repeated root.If the discriminant is negative (less than zero), then the quadratic equation has two complex conjugate roots.Here, the discriminant is positive (25), so the quadratic equation has two real and distinct roots.
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Consider a scenario in which Romeo responds positively to Juliet's feelings, and Juliet responds equally to her own feelings, but responds negatively to Romeo's feelings. The corresponding system is: R = 1 j = -R+J (a) Use the (A,T) chart to classify the behavior of the system. (b) Calculate the eigenvalues and eigenvectors of the system. Sketch the behavior of the system in the phase plane. (c) Sketch in particular the solution curb that starts at R(0) = 1, J0) = 1. (d) Predict what will happen to the couple in the long term, if starting at this initial point.
The solution curve represents a spiral that converges towards the origin.
(a) To classify the behavior of the system, we can use the (A,T) chart. Here, A is the sum of the elements in each row of the system matrix and T is the sum of the absolute values of the off-diagonal elements.
The system matrix for this scenario is:
[ 0 1 ]
[-1 1 ]
So, A = 1 for both rows, and T = 1 (absolute value of the off-diagonal element).
Using the (A,T) chart, we can see that the system is a focus.
(b) To find the eigenvalues and eigenvectors of the system, we need to solve the characteristic equation:
| 0-lambda 1 | |u| |0|
| -1 1-lambda| [tex]\times[/tex] |v| = |0|
Expanding the determinant, we get:[tex]\lambda^2[/tex] -[tex]\lambda[/tex] + 1 = 0
Solving for lambda using the quadratic formula, we get:[tex]\lambda[/tex] = (1 +/- sqrt(3)i) / 2
So, the eigenvalues are complex conjugates with a real part of 1/2. The eigenvectors can be found by solving the system of linear equations:(0 - lambda)u + v = 0
(-1)u + (1 - lambda)v = 0
For lambda = (1 + sqrt(3)i) / 2, we get:u = [1, -1 + sqrt(3)i]
For lambda = (1 - sqrt(3)i) / 2, we get:u = [1, -1 - sqrt(3)i]
(c) To sketch the solution curve that starts at R(0) = 1, J(0) = 1, we can use the eigenvectors and eigenvalues. The general solution for the system can be written as:[x(t), y(t)] = [tex]c_1 \times u_1 \times e^(l \ambda1 \times t) + c2 \times u2 \times e^(\lambda2 \times t)[/tex]
where c1 and c2 are constants determined by the initial conditions, u1 and u2 are the eigenvectors, and lambda1 and lambda2 are the eigenvalues.
Plugging in the values, we get:
[tex][x(t), y(t)] = c_1 \times [1, -1 +\ sqrt(3)i] \times e^{((1 + \sqrt(3)i)t} / 2) + c_2\times [1, -1 - \sqrt(3)i] \times e^{((1 - \sqrt(3)i)t} / 2)[/tex]
Using the initial condition R(0) = 1, J(0) = 1, we get:
[tex]c_1 + c_2 = 1[/tex]
(-1 + sqrt(3)i)c1 + (-1 - sqrt(3)i)c2 = 1
Solving for [tex]c_1[/tex] and [tex]c_2[/tex], we get:
[tex]c_1[/tex] = (1 + sqrt(3)i) / (2[tex]\times[/tex] sqrt(3)i)
[tex]c_2[/tex]= (1 - sqrt(3)i) / (2 [tex]\times[/tex] sqrt(3)i)
Plugging in these values, we get:
[x(t), y(t)] = [1, 0] [tex]\times[/tex] e^((1 + sqrt(3)i)t / 2) + [0, 1] [tex]\times[/tex] e^((1 - sqrt(3)i)t / 2)
This solution curve represents a spiral that converges towards the origin.
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A manufacturer of graphing calculators has determined that 11,000 calculators per week will be sold at a price of $98. At a price of $93, it is estimated that 13,150 calculators would be sold.
(a) Determine a linear function that will predict the number of calculators y that would be sold at a given price x.
(b) Use this model to predict the number of calculators that would be sold each week at a price of $73.
a: ______ b:______
Answer:
(a) To determine the linear function that predicts the number of calculators sold at a given price, we need to find the equation of the line that passes through the points (98, 11,000) and (93, 13,150).First, we can find the slope of the line using the formula:slope = (change in y) / (change in x)slope = (13,150 - 11,000) / (93 - 98)slope = -430 per 1 dollar decrease in price(Note that we can interpret the negative slope as an inverse relationship between price and quantity demanded. As price decreases, the quantity demanded increases.)Next, we can use the point-slope form of a line to find the equation of the line:y - y1 = m(x - x1)where y1 = 11,000, x1 = 98, and m = -430.y - 11,000 = -430(x - 98)Simplifying and solving for y, we get:y = -430x + 51,340Therefore, the linear function that predicts the number of calculators sold at a given price is:y = -430x + 51,340(b) To predict the number of calculators that would be sold each week at a price of $73, we can substitute x = 73 into the linear function we found in part (a):y = -430(73) + 51,340y = 18,140Therefore, we predict that 18,140 calculators would be sold each week at a price of $73.
A carton of milk is supposed to contain 16 fluid ounces but it only contain 15 fluid ounces. What is the percent error?
Answer:
Step-by-step explanation:
error = 16 - 15 = 1 fluid ounce
percent error [tex]=\frac{1}{16} \times 100=\frac{100}{16}=6.25 \%[/tex]
The length of a classroom is 7 meters. How many centimeters long is the classroom?
Answer:
700 cm
Step-by-step explanation:
Mutiply the value by 100.
what is the area of an equilateral triangle whose side length is 8 cm? leave your answer in simplest radical form.
The area of the equilateral triangle with a side length of 8 cm is 16√(3) cm².
To find the altitude of an equilateral triangle with a side length of 8 cm, we can use the Pythagorean theorem.
The Pythagorean theorem is states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In these triangles, the side opposite the 60-degree angle is half the length of the hypotenuse, which is 8 cm. Using the Pythagorean theorem, we can find that the length of the altitude is:
Altitude = √(8² - (4²)) = √(48) = 4√(3)
Now that we know the altitude, we can plug it into the formula for the area of a triangle:
Area = (base x height) / 2 = (8 x 4√(3)) / 2 = 16√(3) cm²
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PLEASE HELP ME WITH THESE QUESTIONS. WILL MARK BRAINLIEST IF ANSWERED CORRECTLY. I RLLY NEED HELP ASAP. NEW QUESTIONS 1-4
Therefore , the solution of the given problem of angles comes out to be lim x→2 g(x) = lim x→2 [(x² - 4)/(x - 2)] = 4.
What does an angle mean?Both the largest and the tiniest walls of a skew are determined by an intersection of the lines that connect that make up its ends. A junction could possibly bring two routes together. Another result of two objects interacting is an angle. They most closely resemble dihedral shapes. Two line beams can be arranged in a variety of ways between their extremities to form a two-dimensional curve.
Here,
The abbreviated formula for f(x) = (4x³ - 3x² - 10x - 3)/(x³ - x² - 6x) is as follows:
f(x) = (4x³ - 3x² - 10x - 3)/(x³ - x² - 6x)
f(x) = [(4x³ - 12x) + (9x² - 3)] / (x(x² - x - 6))
f(x) = [4x(x² - 3) + 3(3x² - 1)] / [x(x - 3)(x + 2)]
f(x) = [4x/(x-3)] + [3/(x+2)] - [3x/(x²-x-6)]
Consequently, the abbreviated form is:
f(x) = [4x/(x-3)] + [3/(x+2)] - [3x/(x²-x-6)]
Direct substitution can be used to find the limit of the equation g(x) = (x2 - 4)/(x - 2) as x approaches 2, which results in the undetermined form 0/0. In order to take the derivative of the numerator and denominator with regard to x, we can apply L'Hopital's rule as follows:
g(x) = (x² - 4)/(x - 2)
g'(x) = [(2x) * (x - 2) - (x² - 4) * 1] / (x - 2)²
g'(2) = 4
As x gets closer to 2, the maximum of g(x) is as follows:
lim x→2 g(x) = lim x→2 [(x² - 4)/(x - 2)] = 4
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the waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 6 minutes. find the probability that a randomly selected passenger has a waiting time greater than 4.25 minutes.
The probability of a person being randomly choosing having waiting time greater than 4.25 is 0.2917 or 29.17%.
To answer this question we need to know about-
Probability is the measure of the likelihood of an event to happen. The probability value ranges between 0 and 1.
When the probability value is 0, it means that the event is impossible to happen.
When the probability value is 1, it means that the event is certain to happen.
Uniform distribution is when the values of a probability distribution are spread uniformly across the interval, it is called a Uniform distribution
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 6 minutes.
The probability that a randomly selected passenger has a waiting time greater than 4.25 minutes is found as follows:
Let X = Waiting time of a randomly selected passenger P(X > 4.25) = ?
Now we have to use the uniform distribution formula to find the probability:
P(C< X >D)=C-D/B-A
where C = lower value of the selected interval
D= upper value of the selected interval
B= highest value of the selected interval
A= lowest value of the selected interval
putting above values in the formula -
P(X > 4.25) = 6 - 4.25/6-0= 0.2917
Hence the probability that a randomly selected passenger has a waiting time greater than 4.25 minutes is 0.2917.
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nelly has 250 discs. this is 14 less than 8 times the number of discs valerie has.
In winter, the price of apples suddenly went up by $0. 75 per pound. Sam bought 3 pounds of apples at the new price for a total of of $5. 88. Write an equation to determine the original price per pound
The equation to determine the original price per pound is 3(x + 0.75) = 5.88, where x is original price per pound. so, the original price is $1.21.
Let x be the original price per pound of apples.
When the price increased, the new price became x + 0.75.
Sam bought 3 pounds of apples at the new price for a total of $5.88. This can be expressed as:
3(x + 0.75) = 5.88
Expanding the left side of the equation, we get:
3x + 2.25 = 5.88
Subtracting 2.25 from both sides, we get:
3x = 3.63
Dividing by 3, we get:
x = 1.21
Therefore, the original price per pound of apples was $1.21.
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This time, make a simple coaster that "bumps" the axis at x = 500. remember to make sure that the track rises before it falls! y = ax(x – 1000 )
The coaster starts at a height of 250, then drops down to 0 at x=500, and then rises back up to a height of 250. The bump is located at x=500 and is the highest point on the coaster.
y = -0.0005(x-500)² + 250
The coaster starts at the highest point (y=250) when x=0 and then drops down to x=500 by following the equation y=ax(x-1000). To create the bump, we need to make the coaster rise before it falls, so we use a quadratic equation that has a vertex at x=500 and y=250 (the initial height).
The equation y = -0.0005(x-500)² + 250 is a downward-facing quadratic equation with a maximum value of y=250 at x=500. This means that as the coaster approaches x=500, it starts to rise, and then falls down again. The coefficient -0.0005 controls the steepness of the coaster's drop and the height of the bump.
Here's a graph of the coaster:
^
260| *
| *
| *
| *
| *
height | *
| *
| *
0 +--------------->
0 500 1000 x-axis
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Find the area of the rectangle below:
What is the area?
Step-by-step explanation:
Find length b by using the Pythagorean theorem for right triangles
17^2 = 8^2 + b^2
b = 15
the area = L x W = 15 X 8 = 120 cm^2
Answer:
120
Step-by-step explanation:
Find out B- 17 squared- 8 squared ( square root) = 15
b = 15
8 X 15 = 120
we used the method of pythagoros - a squared + b squared = c squared
Have a nice day !
A fish-tank has a length of 25 centimeters, a width of 10 centimeters, and a depth of 8 centimeters.
Find the volume of the fish tank.
Step-by-step explanation:
L X W X D = volume = 25 X 10 X 8 = 2000 cm^3
Answer:
2,000 cubic units are the volume of the fish tank
Step-by-step explanation:
The formula of volume is length x width x height
So to find the volume just multiply 25 x 10 x 8
To get the volume of the fish tank which is 2,000 cubic units
10. Triangle GHI is circumscribed about circle K with GH = 20 units, HI = 14 units, and IG= 12 units. Find the length of each segment whose endpoints are G and the points of tangency on GH and GI.
Answer:
c
Step-by-step explanation:
8²+6²=c²
64+36=c²
100=c²
√100 = √c²
10=c
The segment GT1 is part of the radius of circle K, so it has a length of 10 units and segment GT2 is also part of the radius of circle K, so it has a length of 10 units as well.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given that Triangle GHI is circumscribed about circle K with GH = 20 units, HI = 14 units, and IG= 12 units.
We have to find the length of each segment whose endpoints are G and the points of tangency on GH and GI.
Let's call the points of tangency on GH and GI T1 and T2 respectively.
The segment GT1 is part of the radius of circle K, so it has a length of 10 units.
The segment GT2 is also part of the radius of circle K, so it has a length of 10 units as well.
8²+6²=c²
64+36=c²
100=c²
√100 = √c²
10=c
Hence, the segment GT1 is part of the radius of circle K, so it has a length of 10 units and segment GT2 is also part of the radius of circle K, so it has a length of 10 units as well.
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midpoint of -34 and -37
Answer:
Step-by-step explanation:
35.5
Show all work to receive credit.
1. A pyramid has a height of 18 in. and a base with area 256 in2. What is the volume of the pyramid?
Answer:
1536 in^3.
Step-by-step explanation:
Volume = 1/3 * area of base * height
= 1/3 * 256 * 18
= 1536 in^3.
QUESTION 2 2.1 Determine the following products: 2.1.1 x(x-1) 2.1.2 (-3)(x² + 3x + 9)
The products of 2.1.1 x(x-1) 2.1.2 (-3)(x² + 3x + 9) is -3x² - 9x - 27
How to find the products: 2.1.1 x(x-1) 2.1.2 (-3)(x² + 3x + 9)2.1.1 x(x-1) can be simplified using the distributive property of multiplication:
x(x-1) = xx - x1 = x^2 - x
2.1.1 x(x-1):
Expanding the expression x(x-1) using the distributive property:
x(x-1) = x^2 - x
Therefore, the product of 2.1.1 is:
x(x-1) = x^2 - x
2.1.2 (-3)(x² + 3x + 9):
Expanding the expression (-3)(x² + 3x + 9) using the distributive property:
(-3)(x² + 3x + 9) = -3x² - 9x - 27
Therefore, the product of 2.1.2 is:
(-3)(x² + 3x + 9) = -3x² - 9x - 27
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Garrets mortage payment was orignially 3,130 per month. Now, after refinanceing his home loan, Garregs mortage payment s 30% that it used to be. How much is Garretts monthly payment now.
After re-financeing his home loan, Garrets mortage payment is 30 percent less that it used to be the value of Garretts monthly payment now is 2191.
A hypothec loan, also known as a mortgage loan, is a type of loan that is commonly used by real estate purchasers to secure funds for the purchase of property, or by property owners seeking to obtain funds for any purpose, while simultaneously placing a lien on the property being mortgaged. In essence, a mortgage can be described as a situation where a borrower provides collateral in exchange for a loan.
we need to find how much is Garretts monthly payment now:
therefore first we need to find 30% of 3130 that is,
30 x 3130/100 = 939
now we need to subtract this value from the originally mortgage amount
therefore, 3130 - 939 = 2191
therefore, the value of Garretts monthly payment now is 2191.
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If the t-statistic for a variable is 2.54, is the variable statistically significant? No Yes
Yes, the variable is statistically significant if the t-statistic is 2.54.
How to determine the statistical significance?Follow these steps:
1. Identify the degrees of freedom (df) for your sample. The df is typically calculated as the sample size minus 1 (n-1).
2. Choose a significance level (α), commonly used values are 0.05 or 0.01.
3. Consult a t-distribution table using the chosen α and degrees of freedom to find the critical t-value.
4. Compare the t-statistic (2.54) to the critical t-value.
If the t-statistic (2.54) is greater than the critical t-value, the variable is statistically significant at the chosen significance level.
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in an experiment, once the independent and dependent variables are determined, we have a choice to make about the other variables. if we hold everything else constant, we are reducing what kinds of variables? a. intervening b. confounding c. random d. control
The correct option - d. control. After identifying the variables that are independent and dependent in an experiment, we can decide what to do with the remaining variables. We are diminishing "control" if we keep everything else constant.
Explain about the control variables?Something kept constant or constrained in a research study is referred to as a control variable. Although not being relevant to the study's goals, this variable is controlled since it could have an impact on the results.
Variables can be controlled either directly by maintaining their value throughout a study (for example, by maintaining a constant room temperature in such an experiment) or indirectly by using techniques like randomization as well as statistical control . Research biases including omitted variable bias can be avoided by including control variables in your analysis.Thus, after identifying the variables that are independent and dependent in an experiment, we can decide what to do with the remaining variables. We are diminishing "control" if we keep everything else constant.
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A rectangular pool 24 feet long, 8 feet wide, and 4 feet deep is filled with water. Water is leaking from the pool at the rate of 0. 40 cubic foot per minute. At this rate how many hours will it take for the water level to drop 2 feet?
It will take 32 hours for the water level to drop 2 feet.The rate of leaking is 0.40 cubic feet per minute.
To calculate how many hours it will take for the water level to drop 2 feet, we can use the following formula:Time (in hours) = Volume of water (in cubic feet) ÷ Rate of leaking (in cubic feet per minute)In this case, the volume of water is equal to the volume of the pool, which can be calculated using the formula V = l × w × h, where l is the length of the pool, w is the width of the pool, and h is the height of the pool. In this case, l = 24, w = 8, and h = 4, so the volume of the pool is V = (24)(8)(4) = 768 cubic feet.The rate of leaking is 0.40 cubic feet per minute.Therefore, the time (in hours) it will take for the water level to drop 2 feet is equal toTime (in hours) = 768 cubic feet ÷ 0.40 cubic feet per minute Time (in hours) = 1920 minutes Time (in hours) = 32 hoursTherefore, it will take 32 hours for the water level to drop 2 feet.
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Graph the given function to determine the zeros and the locations of the x-intercepts. f(x)=3x2−21x+18
The x-intercepts of the function are x₁ = 1, x₂ = 6.
What is a quadratic equation?Any equation of the form [tex]\rm ax\²+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
To find the zeros, we need to solve the equation f(x) = 0. We can use the quadratic formula for this, which is given by:
x = (-b ± √(b² - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation ax² + bx + c.
[tex]x = (-(-21) \pm \sqrt{((-21)^2 - 4(3)(18))) / 2(3)}\\\\x = (21 \pm\sqrt{(441 - 216)) / 6}\\\\x = (21 \pm\sqrt{(225)) / 6}\\\\x_1 = 1 \ \rm and \ x_2 = 6[/tex]
Therefore, the zeros of the function f(x) are x₁ = 1 and x₂ = 6.
To find the x-intercepts, we need to plot the graph of the function and look for the points where the graph intersects the x-axis. We can start by plotting a few points to get a rough idea of the shape of the graph:
When x = 0, f(x) = 1
When x = 1, f(x) = 0
When x = 2, f(x) = 0
When x = 3, f(x) = 0
When x = 4, f(x) = 6
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HELP 25 points
For Number 3 fill in the blanks of the process.
(9 points total: 0.5 points for each blank!)
(3x3)(8x + 1)
= (24x^2)(8x) + (3x+3)(1)-8x+ (8x) - 3(192x^)
= (192x^)x² + 3x - (3x-2)x - 3
= (192x^)x² - (192x^)x - 3
3.
Answer:
(3x^3)(8x + 1)
= (3x^3)(8x) + (3x^3)(1)
= 24x^4 + 3x^3
= 3x^3(8x + 1) + 24x^2 - 24x^2 + 3x^3
= 3x^3(8x + 1) - 24x^2 + 3x^3
= 24x^4 - 24x^2 + 3x^3
= 3x^3 + (-24x^2 + 24x^4)
Step-by-step explanation:
5/18 + 2/12
A) 1/2
B) 4/9
C) 8/18
D)7/30
Answer:
B. 4/9
Step-by-step explanation:
We can simplify the given expression by finding a common denominator for 18 and 12. The least common multiple of 18 and 12 is 36.
Multiplying the first fraction 5/18 by 2/2 (which equals 1) to get a denominator of 36:
5/18 = 5/18 x 2/2 = 10/36
Multiplying the second fraction 2/12 by 3/3 (which equals 1) to get a denominator of 36:
2/12 = 2/12 x 3/3 = 6/36
Now we can add the two fractions with the same denominator:
10/36 + 6/36 = 16/36
We can simplify this fraction by dividing the numerator and denominator by their greatest common factor, which is 4:
16/36 = 4/9
Therefore, the solution is B) 4/9.
Answer:
the answer for the question is b) 4/9
Julian has 10 apples and he gives 2 apples to his friends about how many apples he has left.
PLEASE HELP!!!
1.) Circle A has been transformed to Circle B. What is the translation rule for these circles?
A.) (x-2),(y+3)
B.) (x+2),(y+3)
C.) (x-1),(y+4)
D.) (x+4),(y+3)
*Please Show All Work***
2.) Circle A has been transformed to Circle B. What is the scale factor of Circle A to Circle B?
The translation of circle A to circle B is achieved using the translation rule
B.) (x + 2),(y + 3)The scale factor of Circle A to Circle B is 2
What is translation in geometry?In geometry, translation refers to a transformation that moves an object in a straight line without changing its size, shape, or orientation.
This movement is done by sliding the object along a line, which is called the axis of the translation.
The scale factor is solved by comparing the diameter
Circle A has diameter of 2 units
Circle B has diameter of 4 units
let the scale factor be k
diameter of circle A * k = diameter of circle B
2 * k = 4
k = 4 / 2
k = 2
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please help me
A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after n days:
f(n) = 12(1.03)n
Part A: When the scientist concluded his study, the height of the plant was approximately 16.13 cm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(n) represent? (2 points)
Part C: What is the average rate of change of the function f(n) from n = 3 to n = 10, and what does it represent? (4 points)
(10 points)
The required answers are Part A: Domain: {n | n is a positive integer}, Part B: 12, Part C: 0.98 cm/day.
How to deal exponential function?Part A:
To plot the growth function f(n), we need to consider a reasonable domain that includes all relevant values of n. Since we are dealing with the growth of a plant, the domain should only include positive integers, as it does not make sense to talk about fractional or negative days. Therefore, a reasonable domain to plot the growth function would be:
Domain: {n | n is a positive integer}
Part B:
The y-intercept of the graph of the function f(n) is the value of f(0), which can be found by substituting n = 0 into the equation:
[tex]$f(0) = 12(1.03)^0 = 12(1) = 12[/tex]
Therefore, the y-intercept of the graph represents the initial height of the plant, which is 12 cm.
Part C:
The average rate of change of the function f(n) from n = 3 to n = 10 can be found using the formula:
Average rate of change = (f(10) - f(3))/(10 - 3)
We can evaluate f(10) and f(3) using the given equation:
f(10) = 12(1.03)^10 ≈ 18.27
f(3) = 12(1.03)^3 ≈ 13.41
Substituting these values into the formula, we get:
[tex]$Average rate change=\frac{(f(10) - f(3))}{10-3} \approx0.98[/tex]
Therefore, the average rate of change of the function f(n) from n = 3 to n = 10 is approximately 0.98 cm/day. This represents the average daily growth rate of the plant during this period.
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Find an equation following defining the following function and state the domain of the function.
The value of the addition of the two composite function is (x - 6) + √(x + 7).
What are functions?A function in mathematics is a relationship between a set of possible outputs (the range) and a set of inputs (the domain), with the assets that each input is connected to exactly one output. By carrying out operations like addition, subtraction, multiplication, division, and composition with other functions, functions can be changed. By summing the results of the two functions f(x) and g(x), we may add them. In a similar manner, we may combine two functions, f(x) and g(x), by inserting the output of g(x) into f(x).
Given that f(x) = x - 6 and g(x) = √(x + 7).
The composite function (f + g)(x) is given as:
(f + g)(x) = f(x) + g(x)
= (x - 6) + √(x + 7)
Hence, the value of the addition of the two composite function is (x - 6) + √(x + 7).
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