Prove that the following equation is an identity.
esou
sin 4t/8= 1/2(cos^3tsint-sin^3tcost)
Answers
I suspect you mean
1/8 sin(4t ) = 1/2 (cos³(t ) sin(t ) - sin³(t ) cos(t ))
On the right side, pull out a factor of cos(t ) sin(t ):
1/2 (cos³(t ) sin(t ) - sin³(t ) cos(t )) = 1/2 cos(t ) sin(t ) (cos²(t ) - sin²(t ))
Recall the double angle identities for sin and cos :
sin(2t ) = 2 sin(t ) cos(t )
cos(2t ) = cos²(t ) - sin²(t )
Then
… = 1/4 (2 cos(t ) sin(t )) (cos²(t ) - sin²(t ))
… = 1/4 sin(2t ) cos(2t )
… = 1/8 (2 sin(2t ) cos(2t ))
… = 1/8 sin(4t )
Related Questions
anyone can solve this?
\( \sqrt[4] {a}^{3 \:} to \: power\)
Answers
The value of the expression \(\sqrt[4]{a}^3\) when evaluated is \(a^\frac34\)
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
\(\sqrt[4]{a}^3\)
Consider an expression expressed as xⁿ
The expression can be expanded as
xⁿ = x * x * x .... in n places
Using the above as a guide, we have the following:
\(\sqrt[4]{a}^3 = \sqrt[4]{a} * \sqrt[4]{a} * \sqrt[4]{a}\)
Apply the exponent rule of indices
\(\sqrt[4]{a}^3 = a^\frac14 * a^\frac14 * a^\frac14\)
Apply the power rule of indices
\(\sqrt[4]{a}^3 = a^\frac34\)
Hence, the expression \(\sqrt[4]{a}^3\) when evaluated is \(a^\frac34\)
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10. Prime numbers from 1 to 100 are running a restaurant - PRIME SPOT, near a tourist point. On a winter holiday, 1 and the composite numbers up to 100 enter the restaurant for dinner after their picnic at the same point. The dining hall has tables with seating capacity 15 for each. If they occupy tables without leaving any chair free, how many tables are required? If each prime number attender has to serve equal number of customers, how many customers should each one get to serve?
Answers
6 tables are required. Each prime number attender should serve 3 customers each.
The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
All the numbers other than prime numbers are composite numbers.
The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.
Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.
Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables
Therefore, 6 tables are required.
Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.
Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.
Thus, each prime number attender should serve 3 customers each.
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Translate the following written expression into an algebraic expression:
"The difference of y and 5, divided by 2"
Answers
Answer:
(y-5) ÷ 2
Step-by-step explanation:
f(x) is a direct variation function f(3)= 12 f(x)= ? f(2)= ?
Answers
The function f(x) will be : f(x) = 4x and f(2) = 8.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that f(x) is a direct variation function .
Direct variation of {y} with {x} means that as {x} increases, {y} increases uniformly with it. Mathematically -{K} = y/x = constant
Scale factor {K} is a dimensionless value that indicates the constant ratio value indicating direct variation.It is given that -
f(3) = 12
We can write the slope of f(x) as -
m = (12 - 0)/(3 - 0)
m = 12/3
m = 4
So, f(x) will be -
f(x) = 4x
and
f(2) will be -
f(2) = 8
Therefore, the function f(x) will be : f(x) = 4x and f(2) = 8.
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Marca con aquellas que sí lo sean y justifica porqué sí son funciones exponenciales o porqué no. 1 punto cada espacio correcto. Total 22 puntos
FUNCIÓN
JUSTIFICACIÓN
f(x)=( 1/( 2) )^x
g(x)=2^x
h(x)=1-2x
j(x)=x^3-1
k(x)=5^x
EJERCICIO 2: Identifique el valor de la base de cada una de las siguientes funciones exponenciales y además indique su monotonía diciendo si la función es creciente o decreciente.
FUNCIÓN
BASE
MONOTONÍA
f(x)=( 3/( 2) )^x
g(x)=〖1,1〗^x
h(x)=( 2/( 3) )^x
k(x)=〖0,75〗^x
m(x)=3^x
n(x)=e^x
Answers
Answer:
Ejercicio 1
Las funciones exponenciales son;
\(f(x)= \left (\dfrac{1}{\left (2 \right )} \right )^{x}\)
\(g(x)= 2^{x}\)
\(h(x)= 1- 2^{x}\)
\(k(x)= 5^{x}\)
La función que no es exponencial se da de la siguiente manera;
\(j(x)= x^3- 1\)
Exercise 2
a) \(La \ base= \dfrac{3}{2 }\)
La función está aumentando ya que la base> 1
b) La base = (1,1)
La función aumenta a medida que la base> 1 es igual a 1
c) \(La \ base = \dfrac{2}{3 }\)
La función está disminuyendo ya que la base <1
d) La base = 0,75
La función está disminuyendo ya que la base <1
e) La base = 3
La función aumenta a medida que la base> 1
f) La base = e
La función aumenta a medida que la base> 1
Step-by-step explanation:
Una función exponencial es una función en la que la variable independiente está presente en el exponente de la función
Las funciones se expresan de la siguiente manera;
\(f(x)= \left (\dfrac{1}{\left (2 \right )} \right )^{x}\)
La función tiene la variable independiente en el exponente, por lo tanto, es una función exponencial
\(g(x)= 2^{x}\)
Del mismo modo, la función anterior tiene la variable independiente en el exponente, por lo tanto, es una función exponencial
\(h(x)= 1- 2^{x}\)
La función anterior tiene la variable independiente en el exponente, por lo tanto, es una función exponencial
\(j(x)= x^3- 1\)
En la función anterior, la variable independiente no está en el exponente, por lo tanto, no es una función exponencial
\(k(x)= 5^{x}\)
La función anterior tiene la variable independiente en el exponente, por lo tanto, es una función exponencial.
Exercise 2
a)
\(f(x)= \left (\dfrac{3}{\left (2 \right )} \right )^{x}\)
\(La \ base = \dfrac{3}{2 }\)
La función está aumentando ya que la base> 1
b) g(x) = (1,1)ˣ
The base = (1,1)
La función aumenta a medida que la base> 1
c)
\(h(x)= \left (\dfrac{2}{\left (3 \right )} \right )^{x}\)
\(La \ base = \dfrac{2}{3 }\)
La función está disminuyendo ya que la base <1
d) k (x) = (0,75) ˣ
La base = 0,75
La función está disminuyendo ya que la base <1
e) m (x) = 3ˣ
La base = 3
La función aumenta a medida que la base> 1
f) n (x) = eˣ
La base = e
La función aumenta a medida que la base> 1
Find the slope of a line perpendicular to the line whose equation is x + 6y = -24.
Fully simplify your answer.
Answers
Answer:
\(m_{perpendicular}\) = 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
x + 6y = - 24 ( subtract x from both sides )
6y = - x - 24 ( divide through by 6 )
y = - \(\frac{1}{6}\) x - 4 ← in slope- intercept form
with slope m = - \(\frac{1}{6}\)
given a line with slope m then the slope of a line perpendicular to it is
\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-\frac{1}{6} }\) = 6
Polygon KLMN is drawn with vertices at K(0, 0), L(5, 2), M(5, −5), N(0, −3). Determine the image vertices of K′L′M′N′ if the preimage is rotated 270° clockwise.
K′(0, 0), L′(−2, 5), M′(5, 5), N′(3, 0)
K′(0, 0), L′(−2, −5), M′(−5, 5), N′(−3, 0)
K′(0, 0), L′(−5, −2), M′(5, −5), N′(3, 0)
K′(0, 0), L′(−5, −2), M′(−5, −5), N′(0, 3)
Answers
The image vertices of K′L′M′N′ under a rotation of 270° clockwise are:
K′(0, 0), L′(−2, 5), M′(5, 5), N′(3, 0).
What is coordinates?
Coordinates are numerical values used to represent the position of a point in a particular space or system. coordinates are used to identify the position of a point in a given plane or space. Typically, two or three numbers are used to describe the location of a point in a two-dimensional or three-dimensional space, respectively.
To rotate a point by 270° clockwise about the origin, we can swap the coordinates and negate the new x-coordinate. Let's apply this transformation to each vertex of the polygon:
For point K(0, 0), we have K′(0, 0) (since the origin is its own image under any rotation).
For point L(5, 2), we have L′(−2, 5) (swapping the coordinates gives (2, 5), and negating the x-coordinate gives (−2, 5)).
For point M(5, −5), we have M′(5, 5) (swapping the coordinates gives (−5, 5), and negating the x-coordinate gives (5, 5)).
For point N(0, −3), we have N′(3, 0) (swapping the coordinates gives (−3, 0), and negating the x-coordinate gives (3, 0)).
Therefore, the image vertices of K′L′M′N′ under a rotation of 270° clockwise are:
=> K′(0, 0), L′(−2, 5), M′(5, 5), N′(3, 0)
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help......................
Answers
Where the above relations are given, note that Options A, D, and E are the relations that represents a function. The others are just relations.
How do you identify the relation that represents a function?To distinguish a function from a relation, look to see if any of the x values are repeated; if not, the relationship is a function. If some x values are repeated but the accompanying y values differ, we have a relation rather than a function.
Note that where you are given domain and range, only the range is represented on the x-axis.
Some of the x values may be seen repeated in B, and C.
How is this so?
B) In a coordinate system, values are represented as (x, y). so
In relations, B 2 is repeated twice to in connection with -5, and -6. That is:
(2, -5) , (2, -6)
Since two is x, then its repetition nullified the relation as a function.
C) On table indicated on C, it is much easier to identify the x and y values. As is seen, -3 is repeated twice in connection with 4 and 2. Thus, its repetition nullified the relation as a function.
As a result, Options A, D, and E are the relations that represent a function.
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Solve the following math problem. Show your work.
My mom gave me 25 cents. I shared 10 cents with my brother. How much money do I have left?
Answers
Answer:
15
Step-by-step explanation:
25-10=15
You take out 10 cents and u have 15 left
WILL GIVE 5 STAR IF CORRECT: Amelia uses her credit card to buy some clothes for $678.34. She can pay off up to $235 per month. The card has an annual rate of 21.7% compounded monthly. How much total interest will she pay? (4 points)
$11.93
$12.27
$24.65
$29.72
Answers
Answer:
chetta es polla airemeris di quana premeria
Step-by-step explanation:
Answer:
Month 1:
Calculate Balance (by adding interest to existing balance): 678.34*(1 + 0.217/12) = 690.606648333333 = 690.61
Make payment: 690.61 - 235 = 455.61
Old Balance: 690.61
New Balance: 455.61
--------------------------------------------------------------
Month 2:
Calculate Balance (by adding interest to existing balance): 455.61*(1 + 0.217/12) = 463.8489475 = 463.85
Make payment: 463.85 - 235 = 228.85
Old Balance: 463.85
New Balance: 228.85
--------------------------------------------------------------
Month 3:
Calculate Balance (by adding interest to existing balance): 228.85*(1 + 0.217/12) = 232.988370833333 = 232.99
Make payment: 232.99 - 232.99 = 0
Old Balance: 232.99
New Balance: 0
--------------------------------------------------------------
Payments Made: 235, 235, 232.99
Number of Payments Made: 3
Total Cost: 235 + 235 + 232.99 = 702.99
Total Cost: $702.99
Total Interest: 702.99 - 678.34 = 24.65
Total Interest: $24.65
Which item below has the lowest cost per piece of pizza?
A a 12 piece pizza for $13.00
B. an 8 piece pizza for $9.00
C. a 16 piece pizza for $18.75
D. a 6 piece pizza $7.50
Answers
Answer:
C
Step-by-step explanation:
1.08333333333 , 1.125 ,1.171875, 1.25
and c =1.171875 which is the lowest cost per slice so its c
use an appropriate taylor series to find the first four nonzero terms of an infinite series that is equal to ln(5/3).
Answers
The appropriate Taylor series for an infinite series with the first four nonzero terms equal to ln(5/3) is 0/1!, 0/2!, 0/3!, and 0/4! .......
What is taylor series?An infinite sum of words that are expressed in terms of a function's derivatives at a single point is known as the Taylor series or Taylor expansion of a function in mathematics. Near this point, the function and the sum of its Taylor series are equivalent for the majority of common functions. The polynomial or function of an infinite sum of terms is the Taylor series. The exponent or degree of each succeeding term will be greater than the exponent or degree of the one before it.
The formula is:
∑n=0 to ∞(fⁿ(a)(x-a)ⁿ)/n!
Here,
∑n=0 to ∞(fⁿ(a)(x-a)ⁿ)/n!
at n=1,
=0/1!
at n=2,
=0/2!
at n=3,
=0/3!
at n=4,
=0/4!
Appropriate taylor series for first four nonzero terms of an infinite series that is equal to ln(5/3) is 0/1!, 0/2!, 0/3!, 0/4!.......
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Two rectangles of the same shape have areas of 676 and 3,457 square centimetres. If the shorter side of the larger rectangle is 41 centimetres, what are the dimensions of the smaller one?
Answers
The dimensions of the smaller rectangle are 13 centimeters by 52 centimeters.
Let's assume the dimensions of the smaller rectangle are length L and width W (in centimeters).
We know that the area of the smaller rectangle is 676 square centimeters:
L * W = 676 ----(1)
We also know that the larger rectangle has a shorter side of 41 centimeters. Let's say the corresponding longer side of the larger rectangle is H centimeters.
The area of the larger rectangle is 3457 square centimeters:
41 * H = 3457 ----(2)
Our current set of equations contains two unknowns. In order to get the smaller rectangle's dimensions, we can simultaneously solve these equations.
In order to find H, we can use equation (2):
H = 3457 / 41
H ≈ 84.22
Now we can substitute this value of H into equation (1):
L * W = 676
We need to find the dimensions (L and W) that multiply to give 676. We can start by looking for factors of 676.
Factors of 676: 1, 2, 4, 13, 26, 52, 169, 338, 676
By trial and error, we can see that the factors that give a close match to the dimensions of the larger rectangle (41 and 84.22) are 13 and 52:
L = 13
W = 52
Therefore, the smaller rectangle has measurements of 13 by 52 centimetres.
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The large of 2 numbers is 1 less than 3 times the smaller if 3 times the larger is 5 more than 8 times the smaller
Answers
The smaller number is 8 and the larger number is 23.Let's denote the larger number as L and the smaller number as S. We are given two pieces of information:
The larger number is 1 less than 3 times the smaller: L = 3S - 1.
Three times the larger number is 5 more than 8 times the smaller: 3L = 8S + 5.
From the first equation, we can express L in terms of S: L = 3S - 1.
Substituting this value of L into the second equation, we get:
3(3S - 1) = 8S + 5.
Expanding the equation, we have:
9S - 3 = 8S + 5.
Simplifying further, we find:
S = 8.
Now that we know the value of S, we can substitute it back into the first equation to find L:
L = 3(8) - 1 = 23.
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Find the radius and diameter of each of the circles .
Answers
Answer:
Step-by-step explanation:
Diameter of the Circle refer to a line passing through the centre and meets the circumference at opposite ends. And it twice as long as Radius.
1) Radius is given 3yd
so, diameter is double of radius 2*3=6yd
Radius= 3yd
Diameter=6yd
2) Diameter is given 92 in
so, radius is half of diameter 92/2= 46 inch
Radius= 46 in
Diameter= 92 in
3) Radius is given 23 ft
so, diameter is double of radius 23*2 = 46 ft
Radius = 23 ft
Diameter = 46 ft
4) Diameter is given 36 in
so, radius is half of diameter 36/2 = 18 in
Radius = 18 in
Diameter = 36 in
5) Radius is given 19 ft
so, diameter is double of radius 19*2 = 38 ft
Radius = 19 ft
Diameter = 38 ft
6) Diameter is given 12yd
so, radius is half of diameter 12/2 = 6yd
Radius = 6yd
Diameter = 12yd
Find the amount (future value) of the ordinary annuity. (Round your answer to the nearest cent.)
$300/week for 9 1/2
years at 5.5%/year compounded weekly
Answers
Answer: $227,226.51
Step-by-step explanation:
First, we need to convert the period to weeks.
9 1/2 years = 9.5 years
1 year = 52 weeks
9.5 years = 494 weeks
Next, we can use the formula for the future value of an annuity:
FV = (PMT x (((1 + r/n)^(n*t)) - 1)) / (r/n)
where:
PMT = payment amount per period
r = annual interest rate
n = number of compounding periods per year
t = number of years
Plugging in the given values:
PMT = $300
r = 0.055 (5.5% expressed as a decimal)
n = 52 (compounded weekly)
t = 9.5 years = 494 weeks
FV = ($300 x (((1 + 0.055/52)^(52*494)) - 1)) / (0.055/52)
FV = $227,226.51
Therefore, the future value of the annuity is approximately $227,226.51.
A college alumni office is choosing a new alumni board of 12 people. They have 25 total applicants.
How many different combinations without repetition of 12 people are there?
Answers
Answer:
5200300
Step-by-step explanation:
Use Combination
25C12=25!/12!(25-12)!The different combinations without repetition of 12 people will be equal to 5,200,300.
What is a Factorial?When a whole number is multiplied by each natural number underneath it, the result is known as its factorial. The symbol "!" can represent the idea of a factorial. As a result, "n factorial" is just n and is defined as the sum of the first n natural integers.
As per the given information in the question,
Total number of people chosen by the board = 12
Total number of applicants = 25
Then the number of combinations without repetition will be = ²⁵C₁₂
= \(\frac{25 !}{12!(25-12)!}\)
= 25!/(12! × 13!)
= 5,200,300
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Graph the solution to the inequality on the number line.
q<69.5
Answers
The graph of the solution to the given inequality on the number line plotted is attached.
Inequalities are the mathematical expressions in which both sides are not equal.
In inequality, unlike in equations, we compare two values.
The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is q < 69.5.
The result can be shown in multiple forms.
Inequality Form:q<69.5
Interval Notation:(−∞,69.5)
Therefore, the graph the solution to the given inequality on the number line plotted below.
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Jack leaves home for school on his bike every day at 6 a.m., travelling at 32 km/h.
One day he forgot his homework, which his mother discovered in the car 15 minutes after he had left.
She immediately left home and chased after Jack, travelling at 52 km/h.
At what time did she catch up to him?
Answers
Let's break down the information given:
- Jack's speed: 32 km/h
- Jack left at 6 a.m.
- Jack's mother's speed: 52 km/h
- Jack's mother discovered the homework 15 minutes after Jack had left.
First, we need to convert the 15 minutes of delay into hours. There are 60 minutes in an hour, so 15 minutes is equal to 15/60 = 0.25 hours.
Now, let's calculate the time it took for Jack's mother to catch up to him:
Distance traveled by Jack in 0.25 hours = Jack's speed * time
Distance traveled by Jack in 0.25 hours = 32 km/h * 0.25 hours = 8 km
Since Jack's mother is traveling at a faster speed than Jack, she will cover this distance faster. To determine the time it takes for her to catch up, we divide the distance by her speed:
Time taken for Jack's mother to cover 8 km = Distance / Speed
Time taken for Jack's mother to cover 8 km = 8 km / 52 km/h ≈ 0.154 hours
Now, we can add this time to the initial delay of 0.25 hours to find out when Jack's mother catches up to him:
Time when Jack's mother catches up to him = 6 a.m. + 0.25 hours + 0.154 hours
To simplify the calculation, we can convert the minutes into hours:
0.25 hours + 0.154 hours = 0.404 hours
Converting back to minutes:
0.404 hours * 60 minutes/hour ≈ 24.24 minutes
Adding this to the initial time of 6 a.m.:
Time when Jack's mother catches up to him ≈ 6:24 a.m.
Therefore, Jack's mother catches up to him at approximately 6:24 a.m.
please help meeeeeeee due in 5 minutessssssssssssss
Answers
Answer:
I think it would be 6. But im not 100% sure
Step-by-step explanation:
Answer:
40
Step-by-step explanation:
Mean x¯¯¯ 12.875
Median x˜ 11.5
Mode 15
Range 34
Minimum 6
Maximum 40
Count n 16
Sum 206
Quartiles Quartiles:
Q1 --> 8.5
Q2 --> 11.5
Q3 --> 14.5
Interquartile
Range IQR 6
Outliers 40
In the last year, a total of 16,674 earthquakes occurred in a country. Of these, 89.1% were minor tremors with magnitudes of 4.9 or less on the Richter scale. How many minor earthquakes occurred in the country in the last year?
Answers
Answer: 1,817 minor earthquakes
Step-by-step explanation: First you make 89.1% and change it to a decimal. You do that by moving the decimal point over 2 spaces to the left. Next you take 16,674 and divide it by 0.891. Once you get that number you subtract 16,674 by your new number from when you divided to get your answer.
graph PQR with vertices P(-2,3),Q (1,2), and R (3,-1) and its image after the translation ( x,y) -> ( x-2, y - 5)
Answers
Answer:
(x,y)(x-2,yt)
Step-by-step explanation:
(x,t)(x-2,yt)
we sniled it to the lete by 2 and then we snifted it down by
The prize of a television was reduced from $250 to $200.
By, what percentage was the price of the telivision
reduced?
F 20%
G 25%
H 80%
J 50%
Answers
Answer: F 20%
Step-by-step explanation:
50 is 20% of 250
Three pizza are shared equally among 12 people.what fraction of a pizza will each person get?
A
4/1
B
3/1
Answers
Answer:
d) 1/12
Step-by-step explanation:
I need Help please!!!
Answers
Step-by-step explanation:
it seems you solved the tricky part yourself already.
just to be sure, let's do the first derivative here again.
the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...
f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =
= 3t⁴ + 18t³ + 24t² + 18t + 21
f'(t) = 12t³ + 54t² + 48t + 18
and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).
we simply put the input number (2) at every place of the input variable (t).
so,
f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =
= 426
Wasting all my points. How to find the area of a triangle
Answers
Answer:
multiply the base by the height, and then divide by 2
Step-by-step explanation:
Answer:
See below.
Step-by-step explanation:
1. Find the base and height. (or, depending on the situation, calculate them)
2. Multiply the base by the height.
3. Divide by 2.
2. What will be the extension of this spring if the load is a) 4N and b) 75 g?
Answers
Answer:
I think is 75 because is the only one that has a weight letter in the variable
Step-by-step explanation:
Show what a monomial expression looks like
Give me a monomial expression and solve it, step-by-step, thoroughly, show your work and explain with each step how your doing it
(New to this, thanks in advance for the extra help!!!)
Answers
Answer:
Refer to the step-by-step explanation.
Step-by-step explanation:
Come up with a monomial expression and solve it.
What is a monomial expression?A monomial expression is an algebraic expression that consists of a single term. It is an expression that can contain variables, constants, and non-negative integer exponents, but there should be no addition or subtraction between different terms.
Here are a few examples of an monomial expression:
5x-2xy²3a⁵7m³n²\(\hrulefill\)
Let's work with the monomial expression, 3x²y³z.
To solve this expression, I assume you would like to evaluate it for specific values of the variables x, y, and z. So let x=3, y=2, and z=1.
Plug these values into the expression:
3x²y³z
=> 3(3)²(2)³(1)
=> 3(9)(8)(1)
=> 27(8)(1)
=> 216(1)
=> 216
Thus, the expression is solved.
Jonas received a gifted $35 to use for an online App Store to buy apps for his née iPhone all apps cost $1.75 each which table represents the relationship between x the number of apps Jonas can buy and y the balance remains in his gift card.
Answers
Answer:
1.75x = 35
Step-by-step explanation:
I got a brain bro
Compare the investment below to an investment of the same principal at the same rate compounded annually.
principal: $5,000, annual interest: 9%, interest periods: 4, number of years: 18
After 18 years, the investment compounded periodically will be worth $? more than the investment compounded annually.
(Round to two decimal places as needed.)
Answers
After 18 years, the investment compounded periodically (quarterly) will be worth $1,230.23 more than the investment compounded annually.
What is compounded interest?Compounded interest refers to the interest system that charges interest on both principal and accumulated interest.
The period of compounding in a year determines the worth of the future value.
The future value can be ascertained using an online finance calculator as follows:
Interest periods: = 4 times yearly (Quarterly)
Principal = $5,000
Annual interest rate = 9%
Number of years: 18
N (# of periods) = 72 quarters (18 years x 4)
I/Y (Interest per year) = 9%
PV (Present Value) = $5,000
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $24,815.83
Total Interest = $19,815.83
Interest periods: = Annually
N (# of periods) = 18 years
I/Y (Interest per year) = 9%
PV (Present Value) = $5,000
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $23,585.60
Total Interest = $18,585.60
Difference in Future Values $1,230.23 ($24,815.83 - $23,585.60)
Thus, an investment compounded periodically earns more than an investment compounded annually.
Learn more about compounded interest at https://brainly.com/question/28020457.
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