Answer:
Step-by-step explanation:
To calculate the volume of sand needed to fill the long jump pit to a depth of 0.07 meters, we need to know the length and width of the pit.
Assuming that the long jump pit is a rectangular prism, we can use the formula:
Volume = length x width x depth
Let's say the length of the pit is 8 meters and the width is 3 meters. Then the volume of sand needed to fill the pit to a depth of 0.07 meters would be:
Volume = 8m x 3m x 0.07m
Volume = 1.68 cubic meters
Therefore, we would need 1.68 cubic meters of sand to fill the long jump pit to a depth of 0.07 meters.
If the federal reserve decreases the reserve rate from 5% to 2% how does this affect the amount of money that would result because of fractional reserve banking from an into Al deposit in a bank of 25000
The decrease in reserve rate from 5% to 2% would increase the amount of money that results from fractional reserve banking on a $25,000 deposit in a bank.
What is percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
According to given information :If the Federal Reserve decreases the reserve rate from 5% to 2%, it means that banks are required to hold a lower percentage of deposits as reserves and can lend out more money. This can lead to an increase in the amount of money that results from fractional reserve banking.
Assuming a fractional reserve ratio of 10%, which means that banks are required to hold 10% of deposits as reserves, here's how the change in the reserve rate can affect the amount of money that would result from a $25,000 deposit in a bank:
Initially, the bank would hold $2,500 (10% of $25,000) as reserves and can lend out $22,500 ($25,000 - $2,500).
After the decrease in the reserve rate to 2%, the bank would only be required to hold $500 (2% of $25,000) as reserves and can now lend out $24,500 ($25,000 - $500).
If this process continues through multiple rounds of lending and deposits, the total amount of money that can be created through fractional reserve banking can increase significantly.
However, it's important to note that the actual impact of a change in the reserve rate on the money supply depends on a variety of other factors, such as the demand for loans and the willingness of banks to lend out money.
Therefore, the decrease in reserve rate from 5% to 2% would increase the amount of money that results from fractional reserve banking on a $25,000 deposit in a bank.
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Given m+1/m =3
Determine the value of
m^2-1 +1/m^2
Answer:
8
Step-by-step explanation:
square the whole equation to get
[tex] {m}^{2} + \frac{1}{ {m}^{2} } = 9[/tex]
then minus one from both sides of the equation to get 8
Write a polynomial function of the least degree with integral coefficients that have the given zeros. 4,-2+root5
If the given zeros are 4 and -2+√5, then the polynomial function of the least degree with integral coefficients that has these zeros can be obtained by using the fact that if a polynomial has a root at x=a, then it has a factor of (x-a).
Therefore, the polynomial function with these zeros can be written as:
(x - 4)(x - (-2+√5))(x - (-2-√5))
Expanding the factors using the difference of squares, we get:
(x - 4)((x + 2) - √5)((x + 2) + √5)
Simplifying the expression further, we get:
(x - 4)((x + 2)^2 - 5)
Expanding the square, we get:
(x - 4)(x^2 + 4x - 1)
Therefore, the polynomial function of the least degree with integral coefficients that has the zeros 4 and -2+√5 is:
f(x) = (x - 4)(x^2 + 4x - 1)
Expanding the factors, we get:
f(x) = x^3 + 4x^2 - x - 16
The height (metres) of an object is given by h(t) = -2t² + 9t + 56 where t is time is seconds. When does the object hit the ground?
Answer: 8 seconds
Answer:
8 seconds
Step-by-step explanation:
-2t^2+9t+56=0
-2t^2+16t-7t+56=0
-2t(t-8)-7(t-8)=0
(-2t-7)(t-8)=0
-2t-7=0 or t-8=0
t-8=0
t=8
The growth rate for a population is 0.66. The carrying capacity of the environment is 6,400,500. If the initial population is 660,000, what Is the differential equation that represents logistic growth for this situation?
Answer:
6,400,500 = 660,000(0.66)^t
Step-by-step explanation:
Find the value of m.
6200=200^m
Answer:
The value of m that satisfies the equation 6200 = 200^m is approximately 1.94.
Step-by-step explanation:
To find the value of m, we can take the logarithm of both sides of the equation:
log(6200) = log(200^m)
By the laws of logarithms, we can simplify this to:
log(6200) = m log(200)
Now we can solve for m by dividing both sides by log(200):
m = log(6200) / log(200)
Using a calculator, we can evaluate this expression to find:
m ≈ 1.94
Therefore, the value of m that satisfies the equation 6200 = 200^m is approximately 1.94.
Hopefully this helps! I'm sorry if it doesn't. If you need more help, ask me! :]
please help me I am in a pinch with an over due assignment and I already knows how to solve but I don't have time and just need answers please.
Answer:
Step-by-step explanation:
The first question is 3 * 2x which equals 6x + 15. That's your answer
Answer:
[tex]\tt \: Hope \: it \: helps \: you \\[/tex]
Find the length of y=1/3x^3/2-x^1/2 from (1, -2/3) to (4, 2/3)
The length of the curve y=1/3x³/2-x⁻¹/² from (1, -2/3) to (4, 2/3) is approximately 0.236 units.
what is curve?
In mathematics, a curve refers to a continuous and smooth line or a geometric object that is formed by joining an infinite number of points. Curves can be defined algebraically or geometrically, and they can have different shapes and properties. Some examples of curves include lines, circles, ellipses, parabolas, hyperbolas, and spirals.
Curves are often used in various fields of mathematics, science, and engineering to represent real-world phenomena, such as the trajectory of a moving object, the shape of a surface, or the behavior of a system over time. They are also important in computer graphics and design, where they are used to create visual effects, animations, and models.
In calculus, the study of curves is an essential part of differential and integral calculus. The concepts of limits, derivatives, integrals, and differential equations are used to analyze the properties and behavior of curves, such as their slope, curvature, area, and length.
To find the length of the curve y=1/3x³/2-x¹/² from (1, -2/3) to (4, 2/3), we can use the formula for arc length:
L = ∫[a,b] √(1 + (dy/dx)²) dx
where a and b are the x-coordinates of the starting and ending points of the curve.
First, we need to find the derivative of y:
dy/dx = (d/dx) (1/3 x^³/²- x¹/²) = (1/2) x⁻¹/² - (1/2) x⁻¹/²= x⁻¹/²
Next, we need to find the definite integral of the square root of 1 + (dy/dx)² from 1 to 4:
L = ∫[1,4] √(1 + (x⁽⁻¹/²⁾⁾²) dx
L = ∫[1,4] √(1 + 1/x) dx
To evaluate this integral, we can use the substitution u = 1 + 1/x, which gives du/dx = -1/x²and dx = (1/u) du.
Substituting, we get:
L = ∫[u(1),u(4)] √u (1/u²) du
L = ∫[u(1),u(4)] u⁻¹/² du
L = 2(u(4)¹/²- u(1)¹/²
To find u(1) and u(4), we substitute x=1 and x=4 into the equation for u:
u = 1 + 1/x
u(1) = 2 and u(4) = 1.25
Substituting these values into the expression for L, we get:
L = 2(1.118 - 1)
L = 0.236
Therefore, the length of the curve y=1/3x³/²-x¹/²from (1, -2/3) to (4, 2/3) is approximately 0.236 units.
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WHAT PERCENTAGE OF 27.5 IS 17.6
Answer:64
Step-by-step explanation:
27.5------100%
17.6--------x
x=64
How many milliliters are there in 0.5 liter's
Answer:
500 Milliliters
Step-by-step explanation:
Because a liter is 100x a milliliter so 0.5x100=500
I need help with this question! (For 55 points)
Answer:
1.65 inches
Step-by-step explanation:
3.63/2.2= 1.65
Check
2.2 x 1.65 x 1/2 = 1.815
Repeat for the other half of the triangle
2.2 x 1.65 x 1/2 = 1.815
Add
1.815 + 1.815= 3.63
Answer:
1.65"
Step-by-step explanation:
I did the test
Hope this helps :)
Use a sketch to find the exact value of the following expression.
Therefore , the solution of the given problem of expressions comes out to be the expression's precise number is 8/15.
What does a expression actually mean?There is a need for calculations like variable multiplication, dividing, joining, and currently removing. If you combined them, you'd get the following: A mathematical formula, some data, and an equation. Values, elements, mathematical operations like equation additions, deductions, errors, and subdivisions, as well as mathematical formulas, make up a statement of truth. It is possible to assess and analyse words and sentences.
Here,
A right triangle with an opposite side of 8 and a hypotenuse of 17 can be completed by adding the missing side using the Pythagorean equation. Make x the neighbouring side. Then:
=> x² + 8² = 17²
=> x² = 17² - 8²
=> x² = 225
=> x = 15
The triangle therefore has edges of 8, 15, and 17. As a result, the neighbouring angle's tangent is 15/8 and the sine of the angle across from the side of length 8 is 8/17. (since tangent is opposite over adjacent). In order to determine the cotangent, we can take the inverse of this tangent:
Coefficient
=> [sin⁻¹ 8/17] = 8/15
As a result, the expression's precise number is 8/15.
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If the adult dosage of a drug is 257mL , how much should a 2-year old child receive? Round your answer to the nearest hundredth.
In this particular case, a 2-year old child should receive a dosage of approximately 16.15mL of the drug. This figure is calculated by using the following formula: (adult dosage/150) x (child's weight in kg).
What is dosage?Dosage is a term used to describe the amount of medicine or drug prescribed for a particular individual to take at a given time. It is usually prescribed by a doctor or healthcare provider based on the patient's age, weight, and medical condition. Dosage may vary from person to person depending on their health condition and other factors.
The appropriate dosage of a drug for a 2-year old child is calculated by taking into account the weight, age and health status of the child. Before administering any medications, it is important to consult with a doctor or a pharmacist to ensure that the appropriate dosage is used.
The adult dosage of 257mL is divided by 150 to obtain the base dosage of 1.71mL. This is then multiplied by the child's weight in kilograms (which is usually around 9 kg) to obtain the final dosage of 16.15mL.
It is important to note that the dosage should be rounded to the nearest hundredth. Therefore, the recommended dosage for the 2-year old child in this case would be 16.2mL. It is important to ensure that the dosage is not rounded up, as this could lead to an overdose of the drug, which could have serious consequences.
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Anyone know how to solve this?, it’ll help a lot
The total feet of steel wire needed to secure the pole is 26 using Pythagoras Theorem.
What is Pythagorean Theorem?
A fundamental idea in mathematics pertains to the lengths of the sides of a right triangle and is known as the Pythagorean theorem. It claims that the hypotenuse's square length, which is the side that faces the right angle, equals the sum of the squares of the lengths of the other two sides of any right triangle. The Pythagorean theorem, which is named after the ancient Greek mathematician Pythagoras who originally proved the theorem, has extensive applications in areas including geometry, trigonometry, and physics.
Let the length of the wire = x.
Using Pythagoras Theorem we have:
x² = 12² + 5²
x² = 144 + 25
x² = 169
x = √(169)
x = 13
For two steel wires:
2(13) = 26 ft.
Hence, the total feet of steel wire needed to secure the pole is 26.
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given the coordinate of the foci to be (0,2) and (0,-2) and the length of the major axis is 6 find the vertices, the centre and equation of the ellipse
The vertices are (0,3) and (0,-3). The center of the ellipse is (0,0). the equation of the ellipse is (x²)/9 + (y²)/5 = 1.
How to find entre and equation of the ellipse?The center of the ellipse is at the midpoint of the foci, which is (0,0).
The distance between the center and each focus is 2, so we know that c = 2.
The length of the major axis is 6, so we know that a = 3.
The formula for the distance between the center and each vertex is a, so we can find the vertices at (0,3) and (0,-3).
The formula for the minor axis is b² = a² - c², so we have b² = 5. Therefore, b = √(5).
The equation of the ellipse is (x - h)²/a² + (y - k)²/b² = 1, where (h,k) is the center. Plugging in our values:
(x - 0)²/3² + (y - 0)²/5 = 1
Simplifying:
(x²)/9 + (y²)/5 = 1
So the equation of the ellipse is (x²)/9 + (y²)/5 = 1.
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To help pay for culinary school, Keiko borrowed money from her credit union.
She took out a personal, amortized loan for $50,000, at an interest rate of 5.5%, with monthly payments for a term of 10 years.
For each part, do not round any intermediate computations and round your final answers to the nearest cent.
If necessary, refer to the list of financial formulas.
(a) Find Keiko's monthly payment.
$0
(b) If Keiko pays the monthly payment each month for the full term,
find her total amount to repay the loan.
$0
(c) If Keiko pays the monthly payment each month for the full term,
find the total amount of interest she will pay.
$0
X
Ś
(a) Keiko's monthly payment is $536.82. (b) The total amount Keiko will repay is approximately $64,419.19 over the 10-year term. c. (c) The total amount is approximately $14,419.19 in interest.
How to Calculate Total Amount of Interest?(a) To find Keiko's monthly payment, we can use the formula for the monthly payment of an amortized loan:
P = (r * A) / (1 - (1+r)^(-n))
where:
P = monthly payment
A = loan amount
r = monthly interest rate (annual interest rate / 12)
n = total number of payments
Plugging in the values we have:
A = $50,000
r = 0.055 / 12
n = 10 * 12 = 120
P = (r * A) / (1 - (1+r)^(-n))
P = (0.055/12 * $50,000) / (1 - (1+0.055/12)^(-120))
P ≈ $536.82
Therefore, Keiko's monthly payment is $536.82.
(b) If Keiko pays the monthly payment each month for the full term of 10 years (120 months), her total amount to repay the loan will be:
Total amount = P * n
Total amount = $536.82 * 120
Total amount ≈ $64,419.19
Therefore, Keiko will repay a total amount of approximately $64,419.19 over the 10-year term.
(c) If Keiko pays the monthly payment each month for the full term of 10 years (120 months), the total amount of interest she will pay can be calculated as:
Total interest = P * n - A
= $536.82 * 120 - $50,000
Total interest ≈ $14,419.19
Therefore, Keiko will pay a total of approximately $14,419.19 in interest over the 10-year term.
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i’ve been struggling for hours and i still can’t figure it out!!! someone please help
The side length of the unknown segment x in the triangle has a value of 40.1cm
How to find the unknown side.To find the unknown side x, we use the sine rule
The Law of Sines (or Sine Rule) is very useful for solving triangles:
a/sin A = b/sin B = c/sin C
It works for any triangle and it says that:
When we divide side a by the sine of angle A it is equal to side b divided by the sine of angle B, and also equal to side c divided by the sine of angle C
To find the third angle in the triangle, we use the known rule of the sum of angles in a triangle which is equal to 180°
unknown angle = 180° - 90°- 55° = 35°
Using the sine rule let us find the side x
23/sin35 = x/sin90
23/0.5736 = x/1
from here we cross multiply to get
0.5736x = 23
We can find the value of x by dividing both sides by 0.5736
x = 23/0.5736
x = 40.1cm
Hence, the value is 40.1 cm
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A recipe calls for 2 1/4 teaspoons of baking powder per serving. You have 9 teaspoons of baking powder. You want to make 4 1/4 servings. Do you have enough baking powder?
You do not have enough baking powder.
Do you have enough baking powder?A mixed number is a value that is made up of a whole number and a proper fraction. A proper fraction is a fraction in which the numerator is less than the denominator. An example of a mixed number is 1 1/2.
In order to determine if you have enough baking powder, multiply 2 1/4 by 9. The teaspoons of baking powder that is needed for 4 1/4 servings = teaspoons needed for one serving x number of serving
2 1/4 x 4 1/4
= 9/4 x 17/4 = 153 / 16 = 9 9/16
9 9/16 is greater than 9 so you do not have enough baking powder.
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Help please I need help
Answer:
[tex]2\frac{7}{24}[/tex]
Step by step explanation:
just do the math it aint hard tbh
Answer:
[tex]2\frac{7}{24}[/tex]
Step-by-step explanation:
To work this out, we first need to change the fractions into mixed numbers...
[tex]2\frac{3}{4} = \frac{11}{4}[/tex][tex]1\frac{1}{5}=\frac{6}{5}[/tex]Now we have to flip the second fraction around so our question will turn into a multiplication...
[tex]\frac{11}{4}[/tex] × [tex]\frac{5}{6}[/tex]Now solve...
[tex]\frac{11}{4}[/tex] × [tex]\frac{5}{6}[/tex] = [tex]\frac{55}{24}[/tex] = [tex]2\frac{7}{24}[/tex]Hope this helps, have a lovely day! :)
The volume of a cube is 64 cubic meters. Find the length of an edge.
FIND THE LENGTH IN METERS!!!!
Answer:
Below
Step-by-step explanation:
Volume = L X W X H For a CUBE, all of the dimesions L, W, and H are the same ...so this becomes volume =L x L x L = L^3
Volume = L^3
64 = L^3 take the cube root of both sides of the equation:
L = 4 meters
find the domain of the function f(x)=7x+5/3x-1
Answer:
the answer is (-infinity,1/3)Union (1/3,infinity)
Match the polynomial expression on the left with the simplified version on the right.
6x³+11x²-5x-12
3x+4
2x² + x - 8
6x +7x³-9x²+13x-12
3x²-x+3
2x² + 3x - 4
2x²+x-3
2-2
S
6
The simplified form of each rational equation is:
Case 1: f(x) = (6 · x³ + 11 · x² - 5 · x - 12) / (3 · x + 4) → f(x) = 2 · x² + x - 3
Case 2: f(x) = (6 · x⁴ + 7 · x³ - 9 · x² + 13 · x - 12) / (3 · x² - x + 3) → f(x) = 2 · x² + 3 · x - 4
How to simplify a rational equationHerein we find two rational equations, whose simplified form has to be found. Rational equations are algebraic equations of the form:
R(x) = P(x) / Q(x)
Where:
R(x) - Rational equationP(x) - Numerator polynomial.Q(x) - Denominator polynomial.The procedure to simplify a rational equation is summarized below:
Factor the numerator polynomial.Factor the denominator polynomial.Cancel common binomials.Expand the resulting expression.Case 1
f(x) = (6 · x³ + 11 · x² - 5 · x - 12) / (3 · x + 4)
f(x) = [(x - 1) · (3 · x + 4) · (2 · x + 3)] / (3 · x + 4)
f(x) = (x - 1) · (2 · x + 3)
f(x) = 2 · x² - 2 · x + 3 · x - 3
f(x) = 2 · x² + x - 3
Case 2
f(x) = (6 · x⁴ + 7 · x³ - 9 · x² + 13 · x - 12) / (3 · x² - x + 3)
f(x) = [6 · (x + 3 / 4 - √41 / 4) · (x + 3 / 4 + √41 / 4) · (x - 1 / 6 - i √ 35 / 6) · (x - 1 / 6 + i √35 / 6)] / [3 · (x - 1 / 6 - i √ 35 / 6) · (x - 1 / 6 + i √35 / 6)]
f(x) = 2 · (x + 3 / 4 - √41 / 4) · (x + 3 / 4 + √41 / 4)
f(x) = 2 · [x² + (3 / 2) · x + [(3 / 4)² - (√41 / 4)²]]
f(x) = 2 · [x² + (3 / 2) · x - 2]
f(x) = 2 · x² + 3 · x - 4
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Determine whether y varies directly with x if so, solve for the constant of variation k. 3y= -7x-18
Therefore , the solution of the given problem of equation comes out to be ratio of y to x is not constant in this situation, y does not directly change with x.
What is equation?The use of the same variable word in mathematical formulas frequently ensures agreement between two assertions. Mathematical equations, also referred to as assertions, are used to demonstrate expression the equality of many academic figures. Instead of dividing 12 into 2 parts in this instance, the normalise technique adds b + 6 to use the sample of y + 6 instead.
Here,
Checking whether there is a fixed ratio between y and x will help us determine whether y directly changes with x.
In general, straight variation is calculated as follows:
=> y = kx
where k is the variational constant.
Let's split both sides by x to check if the equation 3y = -7x - 18 can be expressed in this way:
=> 3y/x = -7 - 18/x
Now, 3y/x ought to equal some constant k if the relation between y and x is constant:
=> 3y/x = k
When we add this to the solution we previously determined, we get:
=> k = -7 - 18/x
Since the ratio of y to x is not constant in this situation, y does not directly change with x.
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Which of the following would most likely reduce the monthly premium a policyholder pays for automobile insurance?
1. Buying a minivan
II. Maintaining an accident-free driving record over time
III. Paying a speeding ticket
IV. Taking a job with a longer commute by car
O I, II
O III, IV
O II, III
OI, IV
The factors that would most likely reduce the monthly premium a policyholder who pays for automobile insurance is -
Option A: I, II
What is insurance?
Insurance is a legal agreement, evidenced by a policy, under which a policyholder receives financial security or compensation from an insurance provider against losses. In order to make payments to the insured more manageable, the company pools the risks of its clients.
The factors that can affect the monthly premium a policyholder pays for automobile insurance include the type of vehicle, driving record, and other personal factors.
Out of the options given, buying a minivan and maintaining an accident-free driving record over time would most likely reduce the monthly premium a policyholder pays for automobile insurance.
Minivans are generally considered safer and less expensive to repair than other types of vehicles, and having an accident-free driving record indicates that the policyholder is a lower risk for filing a claim in the future.
Paying a speeding ticket and taking a job with a longer commute by car are unlikely to reduce the monthly premium a policyholder pays for automobile insurance.
Paying a speeding ticket indicates a violation of traffic laws and a higher risk for accidents, and a longer commute by car increases the risk of accidents and damages.
Therefore, the answer is buying a minivan and maintaining an accident-free driving record over time.
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Answer: option a (I, II)
Step-by-step explanation: Person above is correct!
Find the area of the figure below.
The area of the triangle in the diagram is 87.55 squared centimeters.
What is the area of the triangle?A triangle is simply a two-dimensional polygon with 3 sides and 3 interior angles.
The area of a triangle is expressed as;
Area A= 1/2 × b × h
Where b is the base and h is the height of the trinagle.
From the image;
Base = 17cmHeight = 10.3cmArea A = ?Plug the given values into the above formula and solve for the area of the triangle.
Area = 1/2 × base × height
Area = 1/2 × 17cm × 10.3cm
Area = 87.55 cm²
Therefore, the area is 87.55 squared centimeters.
Option D) 87.55 cm² is the correct answer.
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Help me solve this please !! X^2+6x+y^2+8y=52
Graph the equation-5 < x < -3
A graph of the equation -5 < x < -3 is shown in the image attached below.
What is an inequality?In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;
Less than (<).Greater than (>).Greater than or equal to (≥).Less than or equal to (≤).Next, we would rewrite the given compound inequality in pairs as follows;
-5 < x < -3 ≡ x > -5 or x < -3
In this scenario, we would use an online graphing calculator to plot the inequality as shown in the graph attached below.
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You can model a particular stock investment using the formula $12000(1.05)* where x represents the number of years that you have held your investment.
a. (1 point) Complete the following table to show various investment outcomes.
Investment Balance
Years
3
5
10
20
b. (1 point) What was your total return on investment after 20 years?
The tοtal return οn investment after 20 years is $55,275.00.
Hοw thοrοughly are stοcks selected?By dividing the tοtal number οf shares οutstanding by the number οf shares that a sharehοlder οwns, and multiplying the result by 100, a sharehοlder can determine hοw much οf a firm they οwn.
a. Tο cοmplete the table, we plug in the values οf x and evaluate the fοrmula:
Investment Balance
Years (x)
3 $14,157.00
5 $18,564.38
10 $32,435.85
20 $67,275.00
b. Tο find the tοtal return οn investment after 20 years, we need tο calculate the difference between the investment balance after 20 years and the initial investment οf $12,000:
Tοtal return = Investment balance after 20 years - Initial investment
Tοtal return = $67,275.00 - $12,000
Tοtal return = $55,275.00
Therefοre, the tοtal return οn investment after 20 years is $55,275.00.
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CAN SOMEONE HELP WITH THIS QUESTION?✨
the rate of change of the angle of elevation teta is ∅ = tan⁻¹ 2.1275
What is angle of elevation?Angle of Elevation is an equation used in math to describe the angle formed between the horizontal line and the line of sight when an observer looks upwards. It is always at a height that is greater than the height of the observer
Using ∅ = tan⁻¹ (x/2000)
Then we are to find the angle teta
Where x = 4255 ( substitution)
∅ = tan⁻¹ (4255/2000)
∅ = tan⁻¹ 2.1275
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Simplify to a single trig function or constant with no fractions.
We can simplify cosec(t)tant(t) to sec(t). A trigonometric function is a mathematical function that relates the angles of a triangle to the ratios of its sides.
The most common trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).
To simplify the expression cosec(t)tant(t), we need to use the trigonometric identity:
cosec(t) = 1/sin(t)
tant(t) = sin(t)/cos(t)
Substituting these expressions into the original expression, we get:
cosec(t)tant(t) = (1/sin(t))(sin(t)/cos(t))
The sin(t) term in the numerator and denominator cancel out, leaving:
cosec(t)tant(t) = 1/cos(t)
Recalling the definition of secant, sec(t) = 1/cos(t), we can express the simplified expression as:
cosec(t)tant(t) = 1/sec(t)
Therefore, we can simplify cosec(t)tant(t) to sec(t).
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