The area bounded by the functions y = x and y =[tex]x^2[/tex] within the domain -2 < x < 2 is 1/6 square units.
To sketch the graphs of the functions y = x and y = x^2 within the domain -2 < x < 2, we can plot a few points and connect them to form the curves.
For y = x.
When x = -2, y = -2.
When x = -1, y = -1.
When x = 0, y = 0.
When x = 1, y = 1.
When x = 2, y = 2.
Connecting these points, we get a straight line passing through the origin and extending to -2 and 2 on the x-axis.
For y = [tex]x^2[/tex]:
When x = -2, y = 4.
When x = -1, y = 1.
When x = 0, y = 0.
When x = 1, y = 1.
When x = 2, y = 4.
Connecting these points, we get a symmetrical U-shaped curve opening upward.
Now, to find the area bounded by the two functions, we need to determine the points of intersection between the two curves.
Setting y = x and y =[tex]x^2[/tex] equal to each other, we have:
x = [tex]x^2[/tex].
Simplifying this equation, we get:
x^2 - x = 0.
Factoring out an x, we have:
x(x - 1) = 0.
So, x = 0 or x = 1.The points of intersection are (0, 0) and (1, 1).
To find the area between the curves, we need to integrate the difference between the two functions over the interval [0, 1]. Since the curve y = x is above y = x^2 in this interval, the integral becomes:
∫[0, 1] (x - [tex]x^2[/tex]) dx.
Evaluating this integral gives us the area bounded by the curves.
∫[0, 1] (x -[tex]x^2[/tex]) dx = [[tex]x^2[/tex]/2 - x^3/3] evaluated from 0 to 1.
Plugging in the upper and lower limits, we get:
[1/2 - 1/3] - [0] = 1/6.
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Which of the following statement(s) is (are) true?
I. The set of all second-degree polynomials with the standard operations is a vector space. II. The set of all first-degree polynomial functions 'mx' with the standard operations is a vector space. III. The set of second quadrant vectors with the standard operations is a vector space A) 1 B) II and III C) II and III D) 11
The correct statement is: ii. The set of all first-degree polynomial functions 'mx' with the standard operations is a vector space. Option D
How to determine the true statementsWe have from the information given that;
I. The set of all second-degree polynomials with the standard operations is a vector space
II. The set of all first-degree polynomial functions 'mx' with the standard operations is a vector space
III. The set of second quadrant vectors with the standard operations is a vector space
Then , we should know that;
First degree polynomials has a vector spaceSecond degree polynomials has no vector spaceThe second quadrant vectors has both negative x-coordinates and positive y-coordinates.Learn more about polynomials at: https://brainly.com/question/4142886
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Please help! Read the question carefully! Show full solutions (no calculus) and ALL CALCULATIONS THAT LED TO THE FINAL ANSWER!
Answer:
a) x ≈ -0.5958
b) x ≈ 1.1403
c) no solutions
Step-by-step explanation:
You want to solve various exponential equations:
9^(3x-2) = 5^(7x -1)2(3^(2x)) -5(3^x) = 73^x +1 +56(3^-x) = 0StrategyThe first of these can be solve using logarithms to transform it to a linear equation. The other two can be solve by the substitution z=3^x. They each then become ordinary quadratic equations in z.
a) 9^(3x-2) = 5^(7x -1)Taking logs, we have ...
(3x -2)log(9) = (7x -1)log(5)
x(3log(9) -7log(5)) = -log(5) +2log(9)
x = log(81/5)/log(729/78125) ≈ -1.2095/-2.0301
x ≈ -0.5958
b) 2(3^(2x)) -5(3^x) = 7Using the substitution described above, this is ...
2z² -5z = 7
z² -(5/2)z = 7/2 . . . . . divide by 2
z² -(5/2)z +25/16 = (7/2) +(25/16) . . . . . . complete the square
(z -5/4)² = 81/16
z = 5/4 +9/4 . . . . . . z cannot be negative
x = log(3.5)/log(3)
x ≈ 1.1403
c) 3^x +1 +56(3^-x) = 0z +1 +56/z = 0 . . . . . using z = 3^x
z² +z +56 = 0 . . . . . multiply by z
Descartes' rule of signs tells you this has no positive real solutions for z, so the original equation has no solutions. (The graph in the third attachment has no x-intercepts.)
__
Additional comment
In general, equations consisting of a combination of polynomial and exponential expressions (as in (b) and (c)) cannot be solved algebraically. If the exponential expressions are related in a way that allows substitution (as here), then there may be algebraic methods that will work.
We like to write the equations in the form f(x) = 0, so a graphing calculator's display of the function zeros is a display of solutions to the equation. This is what we have done in the first three attachments.
Using the log expressions we developed, you can find the values of x to as many decimal places as your calculator provides. More significant digits are shown in the fourth attachment.
<95141404393>
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer: 0.6156 or in fraction form, 62%
Step-by-step explanation: To find the probability that at least one of the two people does not go on vacation, we subtract the probability that both of them go on vacation from 1. The probability that both go on vacation is 0.62 * 0.62 = 0.3844.
Therefore, the probability that one or both of them does not go on vacation is 0.6156, or about 62%.
Answer: 0.2356 and 0.1444
Step-by-step explanation:
62% of Americans go on Vacation
So out of 100 Americans, 62 go on vacation
The chance of one of them NOT going on vacation is 100-62 or 38%, however, the other person has to go on vacation, so it's 38%*62% or 0.2356, approx 40%*60% or 0.24
The chance of both of them do not go on vacation is 38%*38%, or 0.1444 or approx 40%*40% or 0.16 (very rough calculating)
For which value of x is this equation true?10 + x ÷ 3 = 12
Answer:
Hi
please mark brainliest ❣️
Thanks
Step-by-step explanation:
10 + x / 3 = 12
Cross multiply
10 + x = 12× 3
10 + x = 36
Collect like terms
x= 36 - 10
x = 26
Two cards are drawn from a deck of 52 playing cards. The first card is NOT replaced into the deck before the 2nd card is drawn What is the probability of drawing a King and then another King?
a. 2/169
b. 3/676
c. 1/169
d. 1/221
The probability of drawing a King and then another King is 1/221. Hence, the correct option is d. 1/221.
How to find the probability of drawing a King and then another KingNumber of favorable outcomes: There are 4 Kings in a deck of 52 playing cards. After drawing the first King, there will be 3 Kings remaining in the deck.
Number of possible outcomes: After drawing the first card, there will be 51 cards left in the deck. For the second card, any one of the remaining 51 cards can be drawn.
Thus, the probability can be calculated as follows:
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
= (4/52) * (3/51)
= 12/2652
= 1/221
Therefore, the probability of drawing a King and then another King is 1/221. Hence, the correct option is d. 1/221.
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A certain radioactive substance decays by 2.9% each year. Find the half-life of the substance, to 2 decimal places.
How many in years?
Answer:
23.90 years
Step-by-step explanation:
To find the half-life of a radioactive substance, we can use the formula:
[tex]\boxed{\begin{minipage}{10 cm}\underline{Half-life formula}\\\\$ t_{1/2} =\dfrac{\ln 2}{k}$\\\\where:\\\\ \phantom{ww}$\bullet$ $t_{1/2}$ is the half-life. \\ \phantom{ww}$\bullet$ $k$ is the decay constant (percentage decay rate per year)\\ \end{minipage}}[/tex]
In this case, the decay constant is 2.9% or 0.029 (expressed as a decimal). Therefore, substitute k = 0.029 into the formula:
[tex]t_{1/2} =\dfrac{\ln 2}{0.029}[/tex]
[tex]t_{1/2} =23.9016269...[/tex]
[tex]t_{1/2} =23.90\; \sf years\; (2\;d.p.)[/tex]
Therefore, the half-life of the radioactive substance, rounded to 2 decimal places, is approximately 23.90 years.
the following are the Scores of 20 students in a Diagostic exam: 34, 36, 66, 74, 76, 78, 84, 85, 99, 103, 121, 123, 123, 125, 130, 133, 137, 140, 145, 156, n=20 Find P43, Q3, AND D8
From the students diagnostic exam, the 43rd Percentile, 3rd Quartile and 8 Decile are 84.5, 138.5 and 140 respectively.
Understanding Percentile, Quartile and DecileWe first need to sort the scores in ascending order:
34, 36, 66, 74, 76, 78, 84, 85, 99, 103, 121, 123, 123, 125, 130, 133, 137, 140, 145, 156
P43 represents the 43rd percentile, which is the score below which 43% of the scores fall. To find P43, we need to calculate the index of the score that corresponds to the 43rd percentile:
P43 = (43/100) * (n + 1)
P43 = (43/100) * (20 + 1)
P43 = 8.44
Since P43 is not an integer, we can take the average of the scores at the indices 8 and 9 (since the index starts from 1):
P43 = (84 + 85) / 2
P43 = 84.5
Therefore, P43 is 84.5.
The third quartile, Q3, represents the score below which 75% of the scores fall. To find Q3, we calculate the index of the score that corresponds to the 75th percentile:
Q3 = (75/100) * (n + 1)
Q3 = (75/100) * (20 + 1)
Q3 = 15.75
Since Q3 is not an integer, we can take the average of the scores at the indices 15 and 16:
Q3 = (137 + 140) / 2
Q3 = 138.5
Therefore, Q3 is 138.5.
D8 represents the score below which 80% of the scores fall. To find D8, we calculate the index of the score that corresponds to the 80th percentile:
D8 = (80/100) * (n + 1)
D8 = (80/100) * (20 + 1)
D8 = 16.8
Since D8 is not an integer, we can round up to the nearest whole number and consider the score at the 17th index:
D8 = 140
Therefore, D8 is 140.
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1
Determine the amplitude and the period of f(x) = sin 2x.
The amplitude is
2π
212
1
2
Choose...
ㅠ
and the period is 1
22
2
Choose...
The amplitude of the function is 1/2, and the period of the function is π.
We know that,
The general form of a sine function is,
⇒ f(x) = A sin(Bx + C) + D,
where:
A is the amplitude
B is the angular frequency or 2π divided by the period
C is the horizontal shift
D is the vertical shift
Now, We have;
The function is,
⇒ f (x) = 1/2 sin 2x
Hence, By Comparing this to the function f(x) = 1/2 sin 2x, we can see that:
A = 1/2, which means that the amplitude of the function is 1/2.
B = 2, which means that the angular frequency is 2,
Or equivalently, the period of the function is 2π/2 = π.
Therefore, the amplitude of the function is 1/2, and the period of the function is π.
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What is the volume of the cylinder? A about 2414.7 cm³ Babout 6281.6 cm³ about 9076.3 cm³ 3 O about 36,305.0 cm³ 21.5 cm 25 cm
The volume of the cylinder is 9071.65 cubic centimeters.
We have to find the volume of the cylinder with a height of 25 cm.
The base has a diameter of 21.5 cm.
Radius of cylinder = 21.5/2
=10.75 cm
The formula for Volume =πr²h
Where r is the radius and height is 25 cm.
Plug in the values of radius and height in to the volume formula.
=3.14×10.75²×25
=9071.65 cubic centimeters.
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help meee im so confusedddd
h can be written as the composition of:
f(x) = x⁴ and g(x) = 8x - 6
How to decompose the function h(x)?We know that the function h is written as:
h(x) = (8x - 6)⁴
And we want to write h(x) as a composition of other two functions, such that:
h(x) = f(g(x))
Then we can define f(x) as a quartic power, f(x) = x⁴, and g(x) as the argument g(x) = 8x - 6, then we will get:
f(g(x)) = g(x)⁴ = (8x - 6)
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Mrs alvares rents skis and poles for 3 days what is the total cost of rental
The total cost of rents is $180.
In the given table,
The cost of skis per day = $48
The cost of pole per day = $12
Now since given that,
Alveres rents for 3 days
Therefore,
The cost of skis for 3 days = $48 x 3
= $144
The cost of pole for 3 days = $12 x 3
= $36
To find the total cost of rental,
Adding the cost of 3 days of skis and cost of 3 days of poles,
Hence,
Total cost of rents = $144 + $36
= $180
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A piece of wire is bent into the shape of a triangle. Two sides have length 16 inches and 23 inches. The angle between these two sides is 40°. What is the length of the third side to the nearest hundredth of an inch?
Answer:
The length of the third side is approximately ≈ 14.79 inches
Step-by-step explanation:
A piece of wire is bent into the shape of a triangle. Two sides have lengths of 16 inches and 23 inches. The angle between these two sides is 40°. What is the length of the third side to the nearest hundredth of an inch?
Use the law of cosines to find the length of the missing side.
Let C be the third side.
A = 18
B = 23
Angle C = 40^∘
c^2 = a^2 + b^2 - 2ab cos C
c = √a^2 + b^2 - 2ab cos C
c = √18^2 + 23 ^2 - 2 (18) (23) cos 40^∘
c = √583 - 828 cos40^∘
≈ 14.79
Thus, The length of the third side is approximately 14.79 inches.
Hope this helps!
can someone help me with number 2! i’ll give brainly
Answer: Order of operations
a. Plastics vary in density when they are manufactured; therefore, their volumes are variable for a given mass. A tablet of polystyrene (a manufactured plastic) sinks in water and alcohol solution and floats in calcium chloride solution. The tablet has a mass of 0.4 grams. What is the most its volume can be?
b. What is the least its volume can be?
The most its volume can be is approximately 0.286 cm³
The least the volume of the tablet can be is approximately 0.4 cm³.
How to solve for the volumeThe density of calcium chloride solution depends on its concentration. Let's assume a saturated solution, which has a density of about 1.4 g/cm³ (this value could be slightly different depending on temperature and exact concentration).
Given:
mass (m) = 0.4 grams
density (ρ) = 1.4 grams/cm³
We can rearrange the density formula to solve for volume:
ρ = m/V --> V = m/ρ
So, substituting in our values:
V = 0.4 g / 1.4 g/cm³
= 0.286 cm³
The tablet must have a volume less than or equal to 0.286 cm³ to float in the calcium chloride solution. Therefore, the most its volume can be is approximately 0.286 cm³.
b. Since the tablet sinks in water and alcohol, its density is greater than these liquids. Assuming the alcohol is ethanol, the density of ethanol is about 0.789 g/cm³, and the density of water is 1 g/cm³. As the tablet sinks in both, its density must be higher than 1 g/cm³.
Using the same volume formula and considering the density of water:
V = m/ρ
= 0.4 g / 1 g/cm³
= 0.4 cm³
Therefore, the least the volume of the tablet can be is approximately 0.4 cm³.
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Given the following system of equations and its graph below, what can be determined about the slopes and y-intercepts of the system of equations? A line includes points 1 comma negative 3 and 3 comma negative 7. A line includes points 3 comma negative 7 and 6 comma negative 6. 4x + 2y = −2 x − 3y = 24 The slopes are different, and the y-intercepts are different. The slopes are different, and the y-intercepts are the same. The slopes are the same, and the y-intercepts are different. The slopes are the same, and the y-intercepts are the same.
The following can be determined about the slopes and y-intercepts of the system of equations: A. The slopes are different, and the y-intercepts are different.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + b
Where:
m represent the slope or rate of change.x and y are the points.b represent the y-intercept or initial value.Based on the information provided above, we have the following system of equations in standard form:
4x + 2y = −2
x − 3y = 24
By rewriting system of equations in slope-intercept form, we have:
y = -2x - 1 ⇒ m = -2, b = -1
y = x/3 - 8 ⇒ m = 1/3, b = -8
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Help please I need it bad
The equation of the axis of symmetry of the quadratic function in this problem is given as follows:
x = -4.
How to obtain the equation of the axis of symmetry?The equation of the axis of symmetry of the quadratic function is a vertical line given as follows:
x = xv.
In which xv is the x-coordinate of the vertex of the quadratic function.
The vertex of a quadratic function is the turning point of the quadratic function, hence it has a x-coordinate of 4 and the equation of the axis of symmetry of the quadratic function in this problem is given as follows:
x = -4.
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1
2
3
4
5
5
3 points
A rectangular prism and a cylinder have the same height. The length of each side of the prism base is equal to the diameter of the cylinder. Which shape has a greater
volume? Use the drop-down menus to explain your answer.
Volume of a Rectangular Prism: V = wh
Volume of a Cylinder: V = ²h
The choose your answer....
extra
choose your answer...
cylinder
rectangular prism
has the greater volume because the choose your answer....
fits within the choose your answer.....
V
The rectangular prism has a greater volume than the cylinder.
Here, we have,
Volume of shapes:
The rectangular prism has a greater volume than the cylinder. This is because the rectangular prism fully occupies the space within its boundaries, while the cylinder has empty space above and below it.
The cylinder's rounded shape leaves gaps between its curved surface and the boundaries of the rectangular prism.
Therefore, the rectangular prism can hold more volume than the cylinder as it utilizes the entire space within its shape efficiently.
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Determine the amplitude and the period of the graph shown.
5
3
(0,4)
The amplitude is
k
4T
2
4
(2T, 0)
2T 3T
Choose....
4T
and the period is
Choose...
4T
2π
4
The period and the amplitude of the given function is 4π and 2.
To find the amplitude and period of a function using its graph, you can follow these steps:
Identify the highest point and the lowest point on the graph. These points represent the maximum and minimum values of the function.
The amplitude is equal to half the difference between the maximum and minimum values of the function. In other words, it is the distance from the midline (average value) of the function to either the highest or lowest point on the graph.
Locate two consecutive peaks or troughs on the graph. A peak is a point where the graph reaches its highest point, and a trough is a point where the graph reaches its lowest point.
Measure the horizontal distance between these two consecutive peaks or troughs. This distance is called the period of the function.
If the distance between the two peaks or troughs is not explicitly marked on the graph, you can estimate it by counting the grid lines or using the scale of the x-axis.
Hence the period and the amplitude of the given function is 4π and 2.
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Determine the length of side AB and BC in triangle ABC.
A. AB= 10.065, BC = 8.388
B. AB = 8.8, BC = 6.4
C. AB = 10.56, BC = 7.68
D. AB = 7.425, BC = 5.954
Answer:
C. AB=10.56, BC=7.68
Step-by-step explanation:
AB) 8.8x7.32÷6.1=10.56
BC) 6.4x7.32÷6.1=7.68
Which points labeled shows the solution? Thank you all
The point (x, y) = (- 1, 2) (Point A) is the solution to the system of linear equations.
Which point does represent the solution to a system of linear equations?
In this problem we find the representation of two linear equations set on Cartesian plane, the system consists in two equations with two variables. We are asked to find the solution to the system of linear equations. Graphically speaking, the solution to the system of linear equations is represented by a point of intersection.
Then, by direct inspection, we find that the solution to the system of linear equations is (x, y) = (- 1, 2). (Point A)
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below is trapezoid ABCD with mid segment EF. What is the value of x?
The value of x is:
x = -32/3
Here, we have,
EF = ½(BC + AD) => Trapezoid Midsegment theorem
Substitute
21 = ½(24 + (-3x-14))
21 = ½(10 -3x)
Multiply both side by 2
42 = 10 -3x
Collect like terms
- 3x = 42 - 10
-x = 32/3
Divide both sides by -1
x = -32/3
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Melody bought a fish tank in the shape of a rectangular prism for her living room. Which statement will help her figure out how much water she will need to fill the tank
The statement that will help Melody determine the amount of water needed to fill the tank is D . Find the volume by using the formula V = lwh
How to find the amount of water ?The amount of water that Melody needs to be able to fill up the tank would be the volume of the tank .
To find the volume of a rectangular prism, the formula is:
V = L × W × H
Which is length x width x height. This is the exact formula shown in option D so this is the correct option .
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Options include:
A Find the surface area by using the formula SA = 2hw + 2lh + 2wh
B Find the surface area by using the formula SA = pi * r ^ 2 * h
C. Find the volume by using the formula V = 2lw + 2lh + 2wh
D Find the volume by using the formula V = lwh
A grocery store has 10 cartons of yogurt for sale, of which 4 are raspberry. What is the probability that a randomly selected carton of yogurt will be raspberry? Write your answer as a fraction or whole number.
Answer:
2/5
Step-by-step explanation:
4 raspberry / 10 total
4/10
2/5
Find the missing length x. Round your answer to the nearest tent
61°
21
X
The missing length x = 18. 4
How to determine the valueTo determine the value of the missing side, we need to take note of the following;
The different trigonometric identities are expressed as;
sinecosinetangentcotangentsecantcosecantThe sine identity is represented with the fraction;
sin θ = opposite/hypotenuse
From the information given, we have;
θ = 61 degrees
x is the opposite side
21 is the hypotenuse
Substitute the values, we have;
sin 61 = x/21
cross multiply the values, we have;
x = 0.8746(21)
Multiply the values, we have;
x = 18. 4
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The complete question:
Find the missing length x. Round your answer to the nearest tent
theta = 61°
Hypotenuse = 21
Opposite = X
what is equivalent to [tex]\sqrt{-25} ?[/tex]
The equivalent to √-25 is 5i.
How to find what is equivalent to √-25?A complex number is a number of the form a + bi, where a and b are real numbers, and i is an imaginary number.
Where i² = -1 or i =√(-1)
A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane.
Thus, we can find the equivalent to √-25 as follow:
√-25 = √(-1 * 25)
= √(-1)* √(25)
= i * 5
= 5i
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What’s is the surface area of a circle with a radius of 6
Answer: 113.04
Step-by-step explanation:
btw, the question is
What's the surface area of a circle with a radius of 6.
Grammar XD
Anyways, the formula for an area of a circle is [tex]\pi r^2[/tex], where [tex]\pi[/tex] is approx 3.14
6 square is 36
36*3.14 is 113.04
Please mark brainliest! :)
12. Mary wants to calculate the area of APOR. Q O draw PW so that PW || RQ and PW = V=RQ Odraw PS so that PS IRQ and point S is on RQ draw QV so that point Vis on PR and PV = VR 35° 5 cm What would be the first step in deriving the formula to calculate the area of APOR? Odraw RT so that RT bisects LPRQ and point Tis on PQ 6 cm P R
The area of APT by the given data is 0.65 m^2.
We are given that;
PV = VR 35° 5 cm
Now,
The formula to calculate the area of APOR is to draw RT so that RT bisects ∠PRQ and point T is on PQ. This will create two congruent triangles, PRT and QRT, by the ASA criterion. Then, the area of APOR can be found by subtracting the area of QRT from the area of APT.
The length of the bottom base of APT is 2(1.5) = 3 m and the length of the top base of APT is 2(1.5 - 0.4) = 2.2 m.
You are also given that each step is 0.25 m higher than the previous one. This means that the height of APT is 0.25 m.
Using these values, you can plug them into the formula for the area of a trapezoid:
A = 0.5(a + b)h A = 0.5(3 + 2.2)(0.25) A = 0.5(5.2)(0.25) A = 0.65 m^2
Therefore, by the area answer will be 0.65 m^2.
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Mr. and Mrs. Davis hope to send their son to college in 12 years. How much mo eh should they invest now at an interest rate of 9.5%per year, compounded continuously, in order to be able to contribute $9500 to his education
Find the components of a vector with magnitude 8 and a direction angle of 210°
Please have your answer be in coordinates.
The components of the vector with magnitude 8 and a direction angle of 210° are
(-4√3, -4)
How to find the componentsTo find the components of a vector with magnitude 8 and a direction angle of 210°, we can use the following formulas
x-component = magnitude * cos(angle)
y-component = magnitude * sin(angle)
given that:
magnitude = 8
angle = 210°
convert the angle from degrees to radians:
angle in radians = angle * π / 180
= 210° * π / 180
= 7π/6 radians
calculate the components:
x-component = magnitude * cos(angle in radians)
= 8 * cos(7π/6)
= 8 * (-√3/2)
= -4√3
y-component = magnitude * sin(angle in radians)
= 8 * sin(7π/6)
= 8 * (-1/2)
= -4
Therefore, the components of the vector with magnitude 8 and a direction angle of 210° are (-4√3, -4).
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Which of the following is NOT equal to log subscript 3 25
log 25 divided by log 3
log 25 over 3
fraction numerator log 25 over denominator log 3 end fraction
fraction numerator ln 25 over denominator ln 3 end fraction
The two expressions are not equivalent.
log 25 divided by log 3 is equal to log subscript 3 25.fraction numerator ln 25 over denominator ln 3 end fraction is not equal to log subscript 3 25.The expression "fraction numerator log 25 over denominator log 3 end fraction" is equal to log 25 divided by log 3.
This is because the numerator represents the logarithm of 25 and the denominator represents the logarithm of 3, resulting in the ratio of the two logarithms.
On the other hand, the expression "fraction numerator ln 25 over denominator ln 3 end fraction" is not equal to log subscript 3 25. The numerator represents the natural logarithm (ln) of 25, and the denominator represents the natural logarithm of 3.
The natural logarithm uses the base e (2.71828), whereas the logarithm with subscript 3 uses the base 3.
Therefore, these two expressions are not equivalent.
log 25 divided by log 3 is equal to log subscript 3 25.
fraction numerator ln 25 over denominator ln 3 end fraction is not equal to log subscript 3 25.
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