Answer:
The answer is below
Step-by-step explanation:
Show that f(x) f(y) = f(x+y)
From trigonometric:
sin(x + y) = sinxcosy + cosxsiny
sin(x - y) = sinxcosy - cosxsiny
cos(x + y) = cosxcosy - sinxsiny
cos(x - y) = cosxcosy + sinxsiny
[tex]f(x)=\left[\begin{array}{ccc}cosx&-sinx&0\\sinx&cosx&0\\0&0&1\end{array}\right] ,f(y)=\left[\begin{array}{ccc}cosy&-siny&0\\siny&cosy&0\\0&0&1\end{array}\right] \\\\\\f(x)f(y)=\left[\begin{array}{ccc}cosxcosy-sinxsiny&-cosxsiny-sinxcosy&0\\sinxcosy+cosxsiny&-sinxsiny+cosxcosy&0\\0&0&1\end{array}\right] \\\\\\f(x)f(y)=\left[\begin{array}{ccc}cos(x+y)&-sin(x+y)&0\\sin(x+y)&cos(x+y)&0\\0&0&1\end{array}\right] \\\\\\[/tex]
[tex]f(x+y)=\left[\begin{array}{ccc}cos(x+y)&-sin(x+y)&0\\sin(x+y)&cos(x+y)&0\\0&0&1\end{array}\right] \\\\\\Therefore\ f(x)f(y)=f(x+y)[/tex]
The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 38 minutes of calls is $ 25.06, and the remaining credit after 69 minutes of calls is $21.03. What is the remaining credit after 80 minutes of calls?
Answer: $19.6
Step-by-step explanation:
Linear function: f(x)=mx+c
, where m= rate of change in f(x) with respect to x.
c = Initial value.
Let c = Initial value of card , m= Charge per minute
x= Number of minutes calling time.
Then, 25.06= 38m+c (i)
21.03=69m+c (ii)
Eliminate (ii) from (i)
[tex]4.03=-31m\\\\\Rightarrow\ m=\dfrac{4.03}{-31}\\\\\Rightarrow\ m=-0.13[/tex]
Put m in (i) , we get
[tex]25.06= 38(-0.13)+c\\\\\Rightarrow\ 25.06=-4.94+c\\\\\Rightarrow\ c=25.06+4.94\\\\\Rightarrow\ c=30[/tex]
i.e. f(x)=-0.13x+30
if x=80 then
f(80)= -0.13(80)+30
=-10.4+30
=19.6
Hence, the remaining credit after 80 minutes of calls = $19.6
A kitten is born weighing 90 grams and gains 10 grams per day for 14 days.
How many days, x, will it take the kitten to double its weight? Write and solve the equation.
Answer:
9 days
Step-by-step explanation:
Answer:
180=90+10x X = 9 days
Step-by-step explanation:
does anyone know the answer
Answer:
y+8x X 5
Step-by-step explanation:
Answer:
first one and last one
Step-by-step explanation:
The temperature was -5 degrees and then fell 8 degrees. What is the temperature now?
Answer:
-13 degrees tell me if it's right
Answer:
-13 is the answer
Step-by-step explanation:
because -5-8= -13
TWENTY POINTS
PLEASE HELP ASAP DONT STEAL POINTS
Multiplying the radical by a number between 0 and 1 causes the graph of the parent function ( f(x)= √x ) to ___________.
Answer:
FOR YOU LOVE
Step-by-step explanation:
If a function is defined by a radical expression, we call it a radical function. The square root function is f(x)=√x f ( x ) = x . ... A radical function is a function that is defined by a radical expression.
THE PIC IN ABOVE IS EQUATION TRY TO ANSWER IT
PLEASS MARK ME AS BRAINLIEST LOVE YOU STAY SAFE
the difference of two numbers is 8. their sum is 17. find the two numbers?
9514 1404 393
Answer:
4.512.5Step-by-step explanation:
Let s represent the smaller number. Then s+8 is the larger number, and their sum is ...
s + (s+8) = 17
2s = 17 -8 = 9
s = 9/2 = 4.5
s+8 = 4.5 +8 = 12.5
The two numbers are 4.5 and 12.5.
_____
Comment on problems of this type
A method is shown here for solving the problem using one equation in one variable. The general solution can be seen to be ...
two numbers = (sum ± difference)/2
Here, that is ...
two numbers = (17±8)/2 = (25, 9)/2 = (12.5, 4.5)
Trevon is buying a car. He is borrowing $12,000 from the bank at a rate of 5% for 4 years. At the end of 4 years, how much interest did Trevon pay?
$24,000
$24,000
$2,400
$2,400
$4,800
$4,800
$600
I need help plz ASAP
Answer:
2nd one down
Step-by-step explanation:
Answer:
Step-by-step explanation:
Please help!!! If you can
Answer:
Im guessing its B. Im sorry of this didnt help.
Step-by-step explanation:
[tex]y = 12000 {(1.04)}^{30}[/tex]
Merton's population = 38920.77012
//
18000 + 30(500) = 33000
Hapville's population = 33000
//
38920.77012 - 33000 = 5920.77012
5920.77012 ---> 6000
The answer is B.
Madison was working at a store in the mall. She earns 7% commission for each sale that she makes. Last month, she sold a total of $1,450. How much commission did she earn?
Answer:
101.50
Step-by-step explanation:
Answer:
$101.50
Step-by-step explanation:
7% of 1450 = 0.07 × 1450 = 101.5
1, 3, 9, 27, ... What's the pattern rule and the next three numbers?
Answer:
multiply by three
Step-by-step explanation:
Step-by-step explanation:
1 x 3 = 3 x 3 = 9 x 3 = 27
=> Pattern rule = [tex]3^{n-1}[/tex]
=> The next three numbers = 81 , 243 , 729
Question 3
This table shows a linear relationship between the amount of water in a tank and time.
Time (minutes) Water (gallons)
0 30
5 20
10 10
Which of these statements is true?
Multiple choice question.
A)
The water in the tank is increasing at a rate of 2 gallons per minute.
B)
The water in the tank is increasing at a rate of 10 gallons per minute.
C)
The water in the tank is decreasing at a rate of 2 gallons per minute.
D)
The water in the tank is decreasing at a rate of 10 gallons per minute.
Answer:
C
Step-by-step explanation:
In five minutes it decreased by 10 gallons (5x2=10), In 10 minutes it decreased by 20 gallons.
Find the degree of polynomial 2x⁵-10x⁴-5x²+12x⁸-6
help
what is one astronomical unit in inches
Answer:
5.89E+12
Step-by-step explanation:
10v2 + 50
o Linear binomial
o Constant binomial
Quadratic binomial
Quadratic trinomial
Answer:
what is the question? probably describe the polynomial. okay. the polynomial 10v^2 + 50 is a quadratic (it is to the 2nd power) and a binomial (has 2 terms).
Jeffrey rented a car for spring break. It costs $100 to rent the car plus $8 per mile he was charged $1,316. How many miles did he drive.
Answer:
152 miles
Step-by-step explanation:
Answer:
he drived around 300 mile
how many centimeters are in 1 millimeter
Answer:
1 milli meter = 0.1 centi meter
Evaluate (49/64) ^1/2 write it as a fraction
Answer:
7/8
Step-by-step explanation:
Get rid of the ( )
put the 49/64 into a √ sq root and it cancels out the 1/2
49/64 whats the square root of 49? 7 Ss root of 64 is 8
7/8
How do I expand this
Step-by-step explanation:
We have
[tex](sc^2x-1)^2[/tex]
Which is the same as
[tex](sc^2x-1)(sc^2x-1)[/tex]
To expand this polynomial, we can use the FOIL method. Meaning that we multiply the Fronts, Outsides, Insides, and Lasts together and then add each of these products.
The two fronts are [tex]sc^2x[/tex] and [tex]sc^2x[/tex],
[tex](sc^2x )(sc^2x )=s^2c^4x^2[/tex]
The two Outsides are [tex]sc^2x[/tex] and [tex]-1[/tex],
[tex](sc^2x )(-1)=-sc^2x[/tex]
The two Insides are [tex]-1[/tex] and [tex]sc^2x[/tex],
[tex](-1)(sc^2x )=-sc^2x[/tex]
The two lasts are [tex]-1[/tex] and [tex]-1[/tex],
[tex](-1)(-1)=1[/tex]
Now we just need to add these together to get
[tex]s^2c^4x^2-sc^2x-sc^2x+1\\\\s^2c^4x^2-2sc^2x+1[/tex]
Answer:
[tex]cot^{4} x[/tex]
Step-by-step explanation:
I don't know this question. I REALLY NEED HELP!!!
Answer:
If it is asking what the answer is when you plug in 5 and 4 to the equation, it would be 54
Answer:
54
Step-by-step explanation:
10m + [tex]\frac{n^{2} }{4}[/tex]
First insert the m value and then multiply
10m = 10(5) =50
then the equation becomes 50 + [tex]\frac{n^{2} }{4}[/tex]
Second insert the n value
[tex]\frac{4^{2} }{4}[/tex]
4 to the second power = 16 so it becomes 16 over 4 aka 4 wholes
50+16/4
50+4=54
x and y are angles on a line l forming linear pairs . if twice of x is 30 degree less than y . Find x and y .
Answer:
hope it helped have a good day mate
plss help me il mark you brainly
Answer:
thisl give u extra credit: 2.29*20 = 45.80 and 3.49*35 = 122.15.
Step-by-step explanation:
Answer:
1. 78.54 (area)
2. 25.13 (circumference)
3. 4.5 (radius)
4. 13 (diameter)
Step-by-step explanation:
Lucy wasn't allowed to have any pets so she collected stuffed animals instead. She had 36 animals total. 3/12 of them were bears and 4/6 of them were dogs. What fraction of the animals were either dogs or bears?
Rachel found 2 quarts on the floor.what decimal represents the 2 quarters
What is the area of a square with side lengths of 3/5 units? Please explain how you know.
the total for dinner was $55 before a discount and tax there was a 10% discount and 7% sales tax
use the tiles to create and expression that could be used to find the total
55xblank x blank
use :0.10 0.9 1.07 0.07 to make the equation
Answer:
( 55 x .10 ) x .07
Hi can someone please help The inverse of a function contains the points (3,12). (-3,10). (2,6), and
(5,7). Which of the following points is contained within the original
function?
(-3,-10)
(-6,2)
(7,5)
(-12,3)
Answer:
(7,5)
Step-by-step explanation:
(7,5) inversed would be (5,7). (5,7) is one of the points contained in the function above.
Find the measure of arc BC
Answer:
The measure of the Arc BC is 80
mean median mode and range,4,8,6,4,4,1,1
please help me with this
Answer: A. 2[tex]\sqrt[3]{6}[/tex]
Step-by-step explanation: