The volume of the solid generated by revolving the region about the y-axis is approximately 0.200 cubic units.
To use the shell method to find the volume of the solid generated by revolving the region bounded by the curves [tex]$y=1$[/tex], [tex]$y=\frac{1}{2\pi e^{x^2/7}}$[/tex], [tex]$x=0$[/tex], and [tex]$x=1$[/tex] about the y-axis, we need to integrate along the x-axis.
The basic idea of the shell method is to take a vertical strip of width [tex]$dx$[/tex]and height [tex]$f(x)$[/tex] and revolve it about the y-axis to generate a thin shell of thickness [tex]$dx$[/tex] and radius x.
The volume of the solid is then given by the integral:
[tex]$$V = \int_{x=0}^{x=1} 2\pi x f(x) dx $$[/tex]
where [tex]$f(x)$[/tex] is the height of the shell at the position [tex]$x$[/tex]. In this case,
[tex]$f(x) =[/tex] [tex]1 - \frac{1}{2\pi e^{x^2/7}}$.[/tex]
So, we have:
[tex]$$V = \int_{x=0}^{x=1} 2\pi x \left(1 - \frac{1}{2\pi e^{x^2/7}}\right) dx $$[/tex]
Now, we can evaluate this integral using integration by substitution.
Let [tex]$u=x^2/7$[/tex], so [tex]$du/dx = 2x/7$[/tex] and [tex]$x,dx = 7/2,du$[/tex]. The integral becomes:
[tex]$$V = \int_{u=0}^{u=1/7} \frac{2\pi}{7} e^{-u} (7/2) du = \pi\int_{0}^{1/7} e^{-u} du$$[/tex]
Evaluating this integral gives:
[tex]$$V = \pi\left[-e^{-u}\right]_{0}^{1/7} = \pi\left(1 - e^{-1/7}\right) \approx \boxed{0.200}$$[/tex]
Therefore, the volume of the solid generated by revolving the region about the y-axis is approximately 0.200 cubic units.
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Need help!! with this question please
The statement true for A, C and E is the second statement r → p ∨ q.
What is Truth Table?.Truth table is a table which describes the truth value of a complex statement regarding to the truth value of single statements.
Given is a truth table.
Consider r → p ∨ q, for the statements A, C and E.
For A, p is true and q is true, then p ∨ q is true. So r is true.
For C, p is true and q is false, then p ∨ q is true. So r is true.
For E, p is false and q is true, then p ∨ q is true. So r is true.
Hence the correct statement is r → p ∨ q.
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what is 2/3 times 2/7?
Answer:
2/3 x 2/3 as a fraction is 4/9.
Step-by-step explanation:
We are performing simple fractional multiplication to get the answer, i.e., 2 x 2 = 4. The numerator of the fraction is multiplied with the numerator of the other, i.e., 3 x 3 = 9.
Answer:
4/21
Step-by-step explanation:
Just line them up side by side, then multiply 2×2 and 3×7. Hope this helps
Finding the Volume of a Solid In Exercises 23 and 24, use the disk method or the shell method to find the volumes of the solids generated by revolving the region bounded by the graphs of the equations about the given lines. 23. y = x, y = 0, x= 3 (a) the x-axis (b) the y-axis (c) the line x = 3 (d) the line x = 6 24. y = x, y = 2, X (a) the x-axis (b) the line y = 2 (c) the y-axis (d) the line x = -1
(a) Revolving about the x-axis, the volume of the solid is 3Pi
(b) Revolving about the y-axis, the volume of the solid is 18 Pi
(c) Revolving about the line x=3, the volume of the solid is 0
(d) Revolving about the line x=6, the volume of the solid will be 32/3 Pi
The region bounded by y=x, y=0, and x=3 is a triangle in the first quadrant.
To find the volume of the solid generated by revolving this region about an axis, we can use the disk or washer method.
(a) Revolving about the x-axis:
Each cross-section of the solid perpendicular to the x-axis is a disk with radius x and thickness dx.
The volume of each disk is [tex]\pi x^2 dx[/tex].
The limits of integration are 0 and 3, the x-coordinates of the intersection points of the two curves.
Hence, the volume of the solid is
[tex]V &= \int_0^3 \pi x^2 dx\\\\\&= \left[\frac{\pi}{3}x^3\right]_0^3\\\\\&= \frac{9\pi}{3}\\\\\&= 3\pi.[/tex]
(b) Revolving about the y-axis:
Each cross-section of the solid perpendicular to the y-axis is a washer with outer radius 3 and inner radius x, and thickness dx.
The volume of each washer is [tex]\pi(3^2-x^2)dx.[/tex]
The limits of integration are 0 and 3.
Hence, the volume of the solid is
[tex]V &= \int_0^3 \pi(3^2-x^2)dx\\\\\&= \left[\pi(9x-\frac{x^3}{3})\right]_0^3\\\\\&= \pi(27-\frac{27}{3})\\\\\&= 18\pi.[/tex]
(c) Revolving about the line x=3:
Each cross-section of the solid perpendicular to the line x=3 is a washer with outer radius 3-x and inner radius 3-x-|x|, and thickness dx.
The volume of each washer is[tex]\pi((3-x)^2-(3-x-|x|)^2)dx[/tex].
The limits of integration are -3 and 3.
Hence, the volume of the solid is
[tex]V &= \int_{-3}^3 \pi((3-x)^2-(3-x-|x|)^2)dx\\\\\&= \left[8\pi\int_0^3 (3-x-|x|)dx\right]\\\\\&= 8\pi\int_0^3 (3-2x)dx\\\\\&= 8\pi\left[3x-x^2\right]_0^3\\\\\&= 8\pi(9-9)\\\\\&= 0.\\\\[/tex]
(d) Revolving about the line x=6:
Each cross-section of the solid perpendicular to the line x=6 is a washer with outer radius |3-x| and inner radius |x-6|, and thickness dx.
The volume of each washer is[tex]\pi(|3-x|^2-|x-6|^2)dx.[/tex]
The limits of integration are 0 and 3.
Hence, the volume of the solid is
[tex]V &= \int_0^3 \pi(|3-x|^2-|x-6|^2)dx\\\\\&= \left[\frac{32\pi}{3}\right]\\\\\&= \frac{32}{3}\pi.[/tex]
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This should be easy: Marcus bought 5 crates of apples. Each crate held 2.9 pounds of apples. How many pounds of apples did Marcus buy in all?
Answer:
14.5
Step-by-step explanation:
2.9(5)=14.5
Answer:
14.5p
here,
lets start off by looking at the full scale problem. We already know that each crate can hold 2.9 apples at a time. We also know that we have 5 crates in total.
hence,
we would multiply [tex]5(2.9)=14.5[/tex] or [tex]5x2.9=14.5[/tex]
find x in the png below
Answer:
The x-intercept is 27/8, or 3.375.
Step-by-step explanation:
0 = -8/3x + 9
-8/3x = -9
-9 * -3/8 = 27/8
x = 27/8
A single-factor ANOVA study consists ofr=6treatments with sample sizesni≡10. a. Assuming that pairwise comparisons of the treatment means are to be made with a 90 percent family confidence coefficient, find theT,S, andBmultiples for the following numbers of pairwise comparisons in the family:g=2,5,15. What generalization is suggested by your results? b. Assuming that contrasts of the treatment means are to be estimated with a 90 percent family confidence coefficient, find theSandBmultiples for the following numbers of contrasts in the family:g=2,5,15. What generalization is suggested by your results?
The generalization suggested by these results is that as the number of contrasts increases, the multiples decrease.
a. For each of the g numbers of pairwise comparisons in the family (2, 5, and 15), the T, S, and B multiples can be calculated using the following formulas:
[tex]T = t α/2 (g-1)S = t α/2 (g-1) √2/(n-1)B = t α/2 (g-1) √(2/n)[/tex]
Where tα/2 is the t-value associated with the given family confidence coefficient (in this case, 90%) and g is the number of pairwise comparisons.
For g=2, the T, S, and B multiples are 3.078, 2.179, and 2.500 respectively. For g=5, the multiples are 2.571, 1.711, and 2.001 respectively. For g=15, the multiples are 2.228, 1.429, and 1.641 respectively.
The generalization suggested by these results is that as the number of pairwise comparisons increases, the multiples decrease.
b. For each of the g numbers of contrasts in the family (2, 5, and 15), the S and B multiples can be calculated using the following formulas:
[tex]S = t α/2 (g-1) √2/nB = t α/2 (g-1) √(2/n)[/tex]
Where tα/2 is the t-value associated with the given family confidence coefficient (in this case, 90%) and g is the number of contrasts.
For g=2, the S and B multiples are 2.179 and 2.500 respectively. For g=5, the multiples are 1.711 and 2.001 respectively. For g=15, the multiples are 1.429 and 1.641 respectively.
The generalization suggested by these results is that as the number of pairwise comparisons or contrasts increases, the multiples decrease.
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What is the equation for the line of reflection?
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The solution is, the line of reflection is y = 1.
What is line of reflection?When reflecting a figure in a line or in a point, the image is congruent to the preimage. A reflection maps every point of a figure to an image across a fixed line. The fixed line is called the line of reflection.
here, we have,
The given figure shows two triangles reflected horizontally.}
We can find the line reflection because it would be an horizontal line half way. Remember that horizontal lines have the form y = k, where k = 1 in this case,
Hence, the line of reflection is y = 1.
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Four girls (Barbara, Donna, Cindy, and Nicole) ran in a relay race as a team. Each girl ran one part of the race. The team's total time was 11 & 3/5 minutes. What was Cindy's time? (IM GIVING 40 POINTS!!!!)
Barbaras time: 3 & 3/10
Donna's time:2 & 4/5
Cindy's time: Find out
Nicole's time: 2 & 1/10
Answer:
Step-by-step explanation:
The expression for the team time is:
[tex]11\frac{3}{5} =3\frac{3}{10} +2\frac{4}{5} +2\frac{1}{10} +X\\[/tex]
Where X= Cindy's Time
Isolating X from the equation:
[tex]X=11\frac{3}{5}-(3\frac{3}{10} +2\frac{4}{5}+2\frac{1}{10})\\\\ X=11\frac{3}{5}-(8\frac{1}{5})\\ \\ X=3\frac{2}{5}[/tex]
Cindy's time was [tex]3\frac{2}{5}[/tex] minutes.
You will need a pencil and paper.
Shalonda is deciding what to wear. She has three pairs of jeans and wants to wear either a blue shirt or a red shirt. How many different combinations are possible?
5 combinations
6 combinations
7 combinations
8 combinations
Answer:
6 combinations
Step-by-step explanation:
3 pairs of Jeans & 2 shirts
3 x 2 = 6
6 combinations
Janna wants to make s'mores at a backyard campfire. The table below shows the parts of marshmallows to graham crackers to make s'mores. S'mores Marshmallows Graham Crackers 4 8 12 13 At this rate, how many marshmallows and graham crackers will Janna use to make 13 s'mores? Janna will use 17 marshmallows and 21 graham crackers to make 13 s'mores. Janna will use 26 marshmallows and 39 graham crackers to make 13 s'mores. Janna will use 16 marshmallows and 24 graham crackers to make 13 s'mores. Janna will use 39 marshmallows and 26 graham crackers to make 13 s'mores.
The number of marshmallows and graham crackers will Janna use to make 13 s'mores is 26 and 36, the correct option is 36.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that;
S'mores Marshmallows Graham Crackers 4 8 12 13
Now,
8/4 = 2 Marshmallows for each S'mores,
12/4 = 3 Graham Crackers for each S'mores.
For, 13 S'mores,
2*13=26
3*13=39
Therefore, by algebra the answer will be 26 and 39.
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How do I solve? I don’t understand L hospital rule. Are there other methods
a) The result of the limit as x tends to +7/4 as required is; -∞.
b). The result of the limit as x tends to -7/4 as required is; -21/8.
What is the value of the limit as x tends to ±7/4?Since the limit expression which is to be evaluated is; (-21x / 7 -4x).
a). Therefore, when x tends to; +7/4; we have;
= (-21 • 7/4) / ( 7 - (4• 7/4) )
= (-147/4 ) / 0
= -∞
b) When x tends to; -7/4 ; we have that;
= (-21 • -7/4) / ( 7 - (4 • -7/4) )
= ( -147/4 ) / 14
= -21 / 8.
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which expression represents “10 less than the product of a and b”
1. (a+ b) 10
2. ab-10
3. 10- ab
4 a (b-10)
Answer:
2
Step-by-step explanation:
ab - 10. this means 10 is less than the product of a and b
How do I answer this?
What is k = ?
What is X = ?
How do I slove?
The value of the scale factor of dilation (k) is 5/3 and the value of x is 21
How to determine the value of kThe variable k is the scale factor of dilation of the triangles
This is calculated as
k = Image triangle/Pre-image triangle
Substitute the known values in the above equation, so, we have the following representation
k = 15/9
So, we have
k = 5/3
How to determine the value of xThis is calculated as
x * 5/3 = 35
So, we have
x = 3 * 35/5
Evaluate
x = 21
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simplify √8/18
answers:
a. -1/3
b. 2/3
c. 3/2
d. 2
Answer:
b. 2/3
Step-by-step explanation:
8 = 4 x 2
√8 = √4 x √2
√4 = 2
√8 = 2 x √2 = 2√2
18 = 9 x 2
√18 = √9 x √2
√9 = 3
√18 = 3 x √2 =3√2
√(8/18) = 2√2 / 3√2 = 2/3
Please Help!
Find The Point-Slope And Slope Intercept of the following image.
The equation that represents the relationship between the number of miles to tread thickness will be y = - 0.12x + 9.
What is the equation of a line passing through two points?Let the equation of the line pass through (x₁, y₁) and (x₂, y₂). Then the equation of the line is given as,
[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]
Let 'x' be the number of miles and 'y' be the tread thickness. Then the two points are (15, 7.2) and (35, 4.8). Then the equation is given as,
(y - 7.2) = [(7.2 - 4.8) / (15 - 35)] (x - 15)
y - 7.2 = -0.12(x - 15)
y - 7.2 = - 0.12x + 1.8
y = - 0.12x + 9
The equation that represents the relationship between the number of miles to tread thickness will be y = - 0.12x + 9.
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Wendy will have new carpet installed on her rectangular bedroom floor. The floor is 15 feet in length and 12 feet in width. The carpet costs $27.50 per square yard, and installation costs $4.15 per square yard. Which statement about the total cost of the carpet and installation is true?
a. The total cost is $379.80 since $31.65×12 = $379.80.
b. The total cost is $633.00 since $31.65×20 = $633.00.
c. The total cost is $474.75 since $31.65×15 = $474.75.
d. The total cost is $4,950.00 since $27.50×180 = $4,950.00
The statement that is true about the total cost of the carpet and installation is: The total cost of the carpet and installation is $633.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
To determine the total cost of the carpet and installation, we first need to calculate the area of Wendy's bedroom floor, which is:
Area = Length x Width
Area = 15 ft x 12 ft
Area = 180 square feet
We can then convert the area to square yards by dividing by 9:
Area in square yards = 180 sq ft / 9
Area in square yards = 20 sq yd
The cost of the carpet is $27.50 per square yard, so the cost of the carpet alone is:
Carpet cost = 20 sq yd x $27.50/sq yd
Carpet cost = $550
The installation cost is $4.15 per square yard, so the cost of the installation alone is:
Installation cost = 20 sq yd x $4.15/sq yd
Installation cost = $83
To find the total cost, we need to add the cost of the carpet and the installation
Total cost = Carpet cost + Installation cost
Total cost = $550 + $83
Total cost = $633
Therefore, the statement that is true about the total cost of the carpet and installation is: The total cost of the carpet and installation is $633.
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prove that if if events a and b are independent, then they are also independent conditioned onevent c.
If events A and B are independent, then they remain independent when conditioned on event C.
To prove that if events A and B are independent, then they are also independent conditioned on event C, we can use the definition of conditional probability.
Recall that two events A and B are independent if and only if P(A and B) = P(A) * P(B). And the conditional probability of A given B can be calculated as P(A | B) = P(A and B) / P(B).
It follows that P(A and B) = P(A) * P(B) if occurrences A and B are independent. Substituting this into the expression for conditional probability, we get:
[tex]P(A | B) = P(A) * P(B) / P(B) = P(A)[/tex]
Similarly, we can prove that P(B | A) = P(B). This means that the probability of A and B given event C are equal to the probabilities of A and B, respectively, given that A and B are independent. Hence, events A and B are also independent conditioned on event C
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Triangle A'B'C' with coordinates of
A'(9,-2), B'(-5, 0), and C'(-2,-4) is the image of
triangle ABC after a translation of (x + 4, y - 6). What
could be possible coordinates for the original vertices
of triangle ABC?
Answer:
Step-by-step explanation:
translation: (x+4, y-6)
original image
A(5,4) A'(9,-2)
B(-9,6) B'(-5,0)
C(-6,2) C'(-2,-4)
How do you find the parametric equation of a line segment joining two points?
The parametric equation of a line segment joining two points (x1, y1) and (x2, y2) is given by [tex]x = x1 + t(x2 - x1) and y = y1 + t(y2 - y1)[/tex].
The parametric equation of a line segment joining two points (x1, y1) and (x2, y2) is given by [tex]x = x1 + t(x2 - x1) and y = y1 + t(y2 - y1)[/tex]. Here, t is a real variable and its value lies between 0 and 1. This is because when t = 0, the equation gives the coordinates of the first point (x1, y1) and when t = 1, the equation gives the coordinates of the second point (x2, y2). For example, if the two points are (3, 4) and (7, 8), then the parametric equation of the line segment joining them can be obtained as [tex]x = 3 + t(7 - 3) = 3 + 4t and y = 4 + t(8 - 4) = 4 + 4t[/tex]. This equation can be used to easily find the coordinates of any point on the line segment joining the two points.
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Referring to the Fig. in Question #23, find the cosine of angle S. Reduce the answer to the lowest terms.
The cosine of the angle S is 4/5
How to deterine the cosine of the angle SFrom the question, we have the following parameters that can be used in our computation:
The triangle
On the triangle and with the use of law of cosines, we have
cos(S) = Adjacent/Hypotenuse
This means that
cos(S) = 8/10
Simplify
cos(S) = 4/5
Hence, the solution is 4/5
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ByIf If the mass of 100 cm³ of a certain metal is 254 g, draw a graph connecting mass with volume up to 100 cm³. Read off: a the mass of 37 cm³ and 64 cm³ of the metal b the volume which has a mass of 100 g and 208 g.
The mass and volume of two metals is 93.98g, 165.56g and 39.37cm3,81.89cm3.
How are density, volume and mass of a substance related?Suppose that a finite amount of substance is there having its properties as:
mass of substance = m kg
density of substance = d kg/m³
volume of that substance = v m³
Then, they are related as:
[tex]d = \dfrac{m}{v}[/tex]
Given that;
Mass of 100cm3 of metal = 254g
Mass of b volume with 37cm3 and 64cm3 is 100g and 208g.
Now,
m=pv
254=p*100
p=2.54g/cm3
m=2.54v
Part A;
V1 =37cm3
V2=64cm3
m1= 2.54 x 37= 93.98g
m2= 2.54 x 64= 165.56g
Part B:
V1=m1/2.54 = 100/2.54 = 39.37cm3
V2=208/2.54 = 81.89cm3
Therefore, the volumes will be 39.37cm3 and 81.89cm3
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S A black bear was tracked across Central Florida logging approximately 120 miles in 30 days.
For 24 miles of M34’s journey, he was tracked walking along the Kissimmee River.
How many days was he traveling along the Kissimmee River?
Answer: 6 days
120 miles divided into 30 days is 4 miles per day.
24 miles divided by 4 miles is 6 , which means the bear spent 6 days walking along Kissimmee River.
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A Ferris wheel is 24 meters in diameter and is boarded from a platform that is 1 meter above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 16 minutes. The function h (t) gives a person's height in meters above the ground t minutes after the wheel begins to turn.
a. Find the amplitude, midline, and period of h (t).
b. Assume that a person has just boarded the Ferris wheel from the platform and that the Ferris wheel starts spinning at time t=0. Find a furmula for the height function h(t).
c. If the Ferris whell continues to turn, how high off the ground is a person after 52 minutes?
a. The amplitude is 12m, the midline is 13m, and the period of h (t) is 16 minutes.
How to solve these?a. The amplitude of the height function h(t) is 12 meters (24 meters diameter / 2).
The midline of the height function is 12 meters (24 meters diameter / 2) + 1 meter (height of the platform).
The period of the height function is the time it takes for the Ferris wheel to complete one full cycle, which is 16 minutes.
b. The height function h(t) can be modeled as a sinusoidal function, where h(t) = 12 cos (2πt/16) + 13.
The cosine function models the cyclical change in height as the Ferris wheel turns.
The 2π in the argument of the cosine function represents the full revolution of the Ferris wheel, and the 16 in the argument of the cosine function represents the time it takes for the Ferris wheel to complete one revolution.
The 13 at the end of the equation is the midline of the height function, which represents the average height of the person above the ground.
c. To find the height of a person after 52 minutes, we substitute t = 52 into the height function h(t) = 12 cos (2πt/16) + 13:
h(52) = 12 cos (2π x 52/16) + 13
h(52) = 12 cos (13π) + 13
h(52) = 12(-1) + 13
h(52) = 1 meter
So, a person would be 1 meter above the ground after 52 minutes.
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: A major corporation is building a 4325 acre complex of homes, offices, stores, schools, and churches in the rural community of Glen Cove. As a result of this development, the planners have estimated that Glen Clove's population (in thousands) t yr from now will be given by the following function.P(t) = 35t^2 + 125t + 200/t^2 + 4t + 40(a) What is the current population of Glen Cove? (b) What will be the population in the long run?
The current population of Glen Cove is 5,000 people and in the long-run, the population of Glen Cove will approach 35,000 people.
Corporation:A corporation may be a corporate entity whose shareholders elect a board of directors to supervise its operations. the dissimilarity between the business and an organization is that an organization may be a sort of business that's suitable for smaller businesses and organizations, whereas a corporation may be a kind of business that's appropriate for larger enterprises and entities.
The population in Glen Clove's population that is t years from now will be
P(t) = [tex]\frac{35t^2 + 125t + 200}{t^2 + 4t + 40}[/tex]
The current population can be calculated by substituting t = 0 in P(t).
So,
P(0) = [tex]\frac{35(0)^2 + 125(0) + 200}{(0)^2 + 4(0) + 40}[/tex]
P(0) = 5
Thus, the current population of Glen Clove is 5 thousand.
(b)For the long run, t tends to infinity. So, evaluate the infinite limit for the given function as follows:
[tex]\lim_{t \to \infty} P(t)= \lim_{t \to \infty}P(t)\frac{35t^2 + 125t + 200}{t^2 + 4t + 40}[/tex]
=[tex]\lim_{t \to \infty}\frac{t^2(35+\frac{125}{t} +\frac{200}{t} )}{t^2(1+\frac{4}{t} +\frac{40}{t^2} )}[/tex]
= [tex]\lim_{t \to \infty}\frac{(35+\frac{125}{t} +\frac{200}{t} )}{1+(\frac{4}{t} +\frac{40}{t^2} )}[/tex]
Now, solve further by putting the limits as follows:
As t approaches infinity, the terms in the numerator approach 0, while the terms in the denominator approach 1, so the limit of P(t) as t approaches infinity is:
lim t -> infinity P(t) = 35 / 1 = 35
So, in the long-run, the population of Glen Cove will approach 35,000 people.
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Need help PLSSS THANK YOU
Using the figure the true trigonometry statements are
A. (sin A)² + (cos A)² = 1
C. 1/(cos A)² - (tan A)² = 1
D. (sin A)² + (cos A)² + (tan A)² = 1/(cos A)²
How to show the statements are trueA. (sin A)² + (cos A)² = 1 this is a fundamental trigonometry identity
say angle A = 30
(sin 30)² + (cos 30)² = 1
C. 1/(cos A)² - (tan A)² = 1
1/(cos A)²= 1 + (tan A)²
1/(cos A)²= 1 + (sin A)² / (cos A)²
1/(cos A)²= ((cos A)² + (sin A)²) / (cos A)²
and (cos A)² + (sin A)² = 1, hence
1/(cos A)²= 1/(cos A)² this is true
D. (sin A)² + (cos A)² + (tan A)² = 1/(cos A)²
recall (sin A)² + (cos A)² = 1
1 + (tan A)² = 1/(cos A)² same as line 2 in C hence this is true
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“Simplify the following using the properties of exponents”
A). (3x^-3y^5)^4
B). 5x^0
Answer:
[tex]A)81x^{-12}y^{20}\\\\B)5\\\\C) x^\frac{2}{3}[/tex]
Step-by-step explanation:
[tex]A) (3x^{-3}y^5)^4=(3)^4 \,\cdot\, (x^{-3})^4\,\cdot\,(y^5)^4=81x^{-12}y^{20}\\\\B) 5x^0=5(1)=5\\\\C) \frac{x^{\frac{5}{6} }}{x^{\frac{1}{6} }} =x^{\frac{5}{6} -\frac{1}{6} }=x^{\frac{5-1}{6} }=x^{\frac{4}{6} }=x^\frac{2}{3}[/tex]
Given that an investment into a college fund is represented by A=12,000e^(0.023*12) , match each value to the correct description of the value in the context of the question. 12,000 The amount of money in the account at the end of the time given. e
The initial amount of money invested into the college fund 0.023
The interest rate.
The interest is compounded continuously.
The amount of years the money is invested.
As per compound interest, the account balance at the end of 12 years is approximately $17,217.
Compound interest is an important concept in finance and investing, and it plays a critical role in understanding how your money can grow over time. When you invest money, your initial investment earns interest, and over time, that interest can also earn interest, resulting in exponential growth.
In the context of this question, the investment into a college fund is represented by the equation
=> [tex]A = 12,000e^{0.023*12}[/tex]
where A is the amount of money in the account at the end of the time given. Let's break down the different components of this equation and see how they relate to compound interest.
First, we have the initial investment, which is not explicitly given in the equation, but we can infer that it is 12,000. This is the amount of money that is initially invested into the college fund.
Next, we have the interest rate, which is 0.023.
Finally, we have the amount of time that the money is invested, which is 12 years in this case. The longer the money is invested, the more time there is for compound interest to work its magic and grow the account balance.
Putting all of these components together, we can use the equation
=> [tex]A = 12,000e^{0.023*12}[/tex]
to calculate the amount of money in the college fund at the end of 12 years.
By plugging in the values for the initial investment, interest rate, and time, we can see that the account balance at the end of 12 years is approximately $17,217.
This represents the power of compound interest and how it can turn a modest initial investment into a substantial sum over time.
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there are 234 students in 9 different classrooms. what is the ratio of students to classrooms bro?
The ratio of students to classrooms is 26:1
What is ratio?A ratio is defined as the comparison of two or more numbers indicating their sizes in relation to each other.
It shows how many times one number contains another.
For example, if there are 20 oranges and 15 lemons in a bowl of fruit, then the ratio of oranges to lemons is 20 to 15.
From the information given, we have that;
234 students in 9 different classrooms
The ratio of students to classrooms would be;
= 234: 9
Find the least common factor
= 26: 1
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Describe the values needed to create a box plot
A box plot is a special type of diagram that shows the quartiles in a box and the line extending from the lowest to the highest value.
What is Box plot?
Box plots, also known as box-and-whisker plots or box-whisker plots, provide a clear pictorial representation of the distribution of the data. They also demonstrate how remote the extreme numbers are from the majority of the data. Five values are used to create a box plot: the minimum value, the first quartile, the median, the third quartile, and the maximum value. These numbers are used to gauge how closely other data points adhere to them. Use a horizontal or vertical number line along with a rectangular box to create a box plot. The axis' ends are identified by the smallest and greatest data values. The first quartile designates one end of the box, while the third quartile designates the opposite end.
The box plot distribution will demonstrate how skewed, tightly packed, and symmetrical the data are.
In the box and whisker plot:
The box's upper and lower quartiles serve as its ends, allowing it to cross the interquartile range. The vertical line inside the box denotes the median, and the two lines outside the box serve as its whiskers, extending to the highest and lowest observations.
Hence, A box plot is a special type of diagram that shows the quartiles in a box and the line extending from the lowest to the highest value.
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6. The scatter plot shows the average heights of children ages 2-12 in a
certain country. Which line is the best model of the data?
Average Height (inches)
60
50
40
30
20
0
ty
0
f
Average Heights
in Country X
4
S
8
12
Age (years)
m
16
N
X
Answer:
do you have an image of the question?