An account grows at an annual interest rate of r , so it grows by a factor of x=1+r each year. The function A(x)=800x 4 +350x 3 +500x 2 +600x gives the amount in the account after 4 years when the growth factor is x . What is the total amount in the account if the interest rate for the account is 3% each year? How much money was put into the account at the beginning?
Given:
Annual interest rate = r%
Growth factor : x = 1 + r
The below function gives the amount in the account after 4 years when the growth factor is x .
[tex]A(x)=800x^4+350x^3+500x^2+600x[/tex]
To find:
The total amount in the account if the interest rate for the account is 3% each year and initial amount.
Solution:
Rate of interest = 3% = 0.03
Growth factor : x = 1 + 0.03 = 1.03
We have,
[tex]A(x)=800x^4+350x^3+500x^2+600x[/tex]
Substitute x=1.03 in the given function, to find the total amount in the account if the interest rate for the account is 3% each year.
[tex]A(1.03)=800(1.03)^4+350(1.03)^3+500(1.03)^2+600(1.03)[/tex]
[tex]A(1.03)=800(1.12550881)+350(1.092727)+500(1.0609 )+618[/tex]
[tex]A(1.03)=900.407048+382.45445+530.45+618[/tex]
[tex]A(1.03)=2431.311498 [/tex]
[tex]A(1.03)\approx 2431.31 [/tex]
Therefore, the total amount in the account is 2431.31 if the interest rate for the account is 3% each year.
For initial amount the rate of interest is 0.
Growth factor : x = 1 + 0 = 1
Substitute x=0 in the given function to find the initial amount.
[tex]A(1)=800(1)^4+350(1)^3+500(1)^2+600(1)[/tex]
[tex]A(1)=800+350+500+600[/tex]
[tex]A(1)=2250[/tex]
Therefore, 2250 was put into the account at the beginning.
PLEASE HELP ASAP What part of 6 3/5 is 3 /10 ? PLS HELP ASAP
Answer:
the 3/5 part of 6 3/5
Step-by-step explanation:
3/5 is equal to 3/10 because when you find the common denominator of 10, you multiply 3/5 by 2 and 3/10 by 1 because 10 is already 10. 3/5*2=6/10.
How do you do this question?
Answer:
dy/dx = (2t + 3t²) / (2t)
Step-by-step explanation:
y = t² + t³
dy/dt = 2t + 3t²
x = 5 +t²
dx/dt = 2t
dy/dx = (dy/dt) / (dx/dt)
dy/dx = (2t + 3t²) / (2t)
How many squares are in the 11 squares
Answer:
11 Squares are there in 11 squares
Answer:
11
Step-by-step explanation:
because take your question and realize you put, "How many squares are in the 11 squares?"
(Sry if wrong or information misunderstood!)
Find the distance between the points (-3, 5) and (7, -1), round the nearest 10th, if nessasary.
Answer:
The answer is 11.7 unitsStep-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\[/tex]
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(-3, 5) and (7, -1)
The distance between them is
[tex]d = \sqrt{ ({ - 3 - 7})^{2} + ({5 + 1})^{2} } \\ = \sqrt{( { - 10})^{2} + {6}^{2} } \\ = \sqrt{100 + 36} \: \: \: \: \: \: \: \\ = \sqrt{136} \\ = 2 \sqrt{34} \\ = 11.66190378...[/tex]
We have the final answer as
11.7 units to the nearest tenthHope this helps you
What is qualitative data? Give an example.
Answer:
it is data that you can see or describe such as he is a boy
Step-by-step explanation:
A submarine dives 20 meters each minute for 15 minutes. What is the total change in depth after 15 minutes?
Answer:
300m
Step-by-step explanation:
20 Times 15=300
evaluate the expression, (g◦f)(3), given the following functions.
f(x)=x+2 and g(x)=x
[tex]f(x) = x + 2\\g(x) = x\\(g \circ f) = g(f(x)) = x + 2\\g \circ f)(3) = 3 + 2 = 5[/tex]
How is the sentence "8 less than y is 2" written as an equation?
A. 8-y = 2
B. y - 2 - 8
C. y - 8 - 2
D. y + 8 - 2
Answer:
y - 8 = 2
thats how you would write it so idk i guess pick c because its the closest
"8 less than y" ==> y-8
"is 2" ==> =2
therefore y-8=2
what is 1/11 divided by 4?(FRACTION FORM)
Answer: 1/44
Step-by-step explanation:
6/10 as hundredths in fraction form and decimal form
Answer:
60/100 and .6
Step-by-step explanation:
Chloe bought three pounds of strawberries for $16.80. What is the price, in dollars per ounce of strawberries?
Answer:
$5.60
Step-by-step explanation:
Each pound of strawberries costs $5.60.
To solve: $16.80 divided by 3
Preview Activity 2.4.1. Consider the function f ( x ) = tan ( x ) , and remember that tan ( x ) = sin ( x ) cos ( x ) . What is the domain of f ? Use the quotient rule to show that one expression for f ′ ( x ) is f ′ ( x ) = cos ( x ) cos ( x ) + sin ( x ) sin ( x ) cos 2 ( x ) . What is the Fundamental Trigonometric Identity? How can this identity be used to find a simpler form for f ′ ( x ) ? Recall that sec ( x ) = 1 cos ( x ) . How can we express f ′ ( x ) in terms of the secant function? For what values of x is f ′ ( x ) defined? How does this set compare to the domain of f ?
Answer:
Step-by-step explanation:
Given the function f(x) = tan (x)
From trigonometry identity, tan (x) = sin(x)/cos(x)
f(x) = sin(x)/cos(x)
Using the quotient rule to find the derivative of the function, we will have;
f'(x) = cos (x)cos (x) - sin (x)[-sin (x)]/ cos²x
f'(x) = cos²x - sin²x/ cos²x
Divide through by cos²x
f'(x) = cos²x/cos²x + sin²x/cos²x / cos²x/cos²x
f'(x) = 1 + sin²x/cos²x / 1
f'(x) = 1 + (sin²x/cos²x)
f'(x) = 1 + tan²x
From trig identity, 1 + tan²x = sec²x
Hence, f'(x) = sec²x
Hence the expression f'(x) in terms of the secant function is sec²x
f'(x) = 1/cos²x
For the function to be defined, it means that cos²x ≠ 0
cos²x ≠ 0
cos x ≠ 0
x ≠ cos⁻¹0
x ≠ 90⁰
Hence the value of x must not be equal to 90 for the function to be defined. x can be defined at when x = 0 since cos 0 = 1, the equation will becomes f'(0) = 1/cos²0 = 1/1 = 1.
Hence the function is defined at 0≤x<90
PLLSSSS HEELP
Solve and graph this absolute value equation.
|x – 2| – 8 = 7
Step-by-step explanation:
y-8=7 y=15
|x-2|=15 has two solutions
17,-13
Answer:
answer
(x_2)- 8=7
2x=8-7
2x=1
that's the answer
What transformation occurs to the graph f (x) =2x + 3 if the 3 in the equation is changed to a 5?
Determine the number of real or non real solutions of the equation listed below
using the discriminant.
x2 + x + 4 = 0
Answer:
x =(-1+√-15)/2=(-1+i√ 15 )/2= -0.5000+1.9365i
Step-by-step explanation:
I got two answers
Write 0.6 as a percentage.
Answer:
60%
Step-by-step explanation:
all you need to do is multiply this by 100 (move two decimal places to the right).
0.6--> 60
60 percent
Answer: 60%
Explanation: .6 x 100 = 60
Please I need help hurry!
Answer:
Step-by-step explanation:
Team B=2.2*4.8= 10.56
Team C : 10.56 *1.5=15.84
-3.5 , 2 , -3 , -1 , -1.5
Least to greatest
Answer:
-3.5, -3, -1.5, -1, 2
Step-by-step explanation:
Answer:
-3.5, -3, -1.5, -1, 2
Step-by-step explanation:
negatives to positives
A school janitor has my 1/3 of the classroom in five minutes at what rate is he mopping
Answer:
1/15 per min
Step-by-step explanation:
3 times 5 equals 15 and so 1/15.
Try making a visual picture to see yourself.
45 2/3 + 30 1/2 + 12 3/4=?
The two triangles below are similar. Which pair are corresponding sides?
LN and MN
MN and QR
LM and QR
LM and PQ
hola estas ahi
MN and QR
Hope it helps...
If BC = XY and XY = 8, then BC = 8
A Reflexive
B Transitive
Symmetric
none of the above
Answer:
Transitive
Step-by-step explanation:
It's like a train. Since bc is equal to xy and xy is 8.Then the value of xy equals to bc.
1/2 + 2 3/4
Help please (◍•ᴗ•◍)❤
Answer:
3 1/4
Step-by-step explanation:
Answer:
3 1/4
Step-by-step explanation:
im going to change the fractions to decimals
1/2 = 0.5
2 3/4 = 2.75
0.5 + 2.75 = 3.25
now im going to switch it back to fraction
3.25 = 3 1/4
Pls help me I will give out points
Answer:
A, the first one
Step-by-step explanation:
On the left side, the graph is going closer to 0, that explains the first coordinate 0. On the right side, the graph approaches positive infinity, so that explains the infinity. I hope this helps!
Please help me answer this :)?
Math 7 A Unit 4 lesson 2 Please help quick
5/10-3/10
1/2+3/4
1/6+3/8
7/8-5/12
Answer:
2/10, 1 1/4, 13/24, 11/24
Step-by-step explanation:
1. subtract the fractions
2. add the fractions
3. add the fractions
4. add the fractions
Hi can someone pls help me on the last question (#5)
[tex]solution \: (a) \:: [/tex]
[tex] \frac{1}{7} x = 1[/tex]
[tex]x = 7[/tex]
[tex] solution \: (b) \:: \\ x \times \frac{1}{11} = 1[/tex]
[tex]x = 11[/tex]
[tex]solution \: (c) \:: [/tex]
[tex]1 \div \frac{1}{5} = x[/tex]
[tex]x = 5[/tex]
which is the product of 7/9 and 6 in a fraction number
Answer:
4 2/3
Step-by-step explanation:
7/9 multiplied by 6/1 = 42/9
Simplify: 14/3
Turn it into a mixed number: 4 2/3
-6(1/4x-2/3x+5/6x) simplified .
Answer:
[tex]-2\frac{-1}{2}[/tex]
Step-by-step explanation:
To distribute the -6, multiply every numerator by -6, this gets you
-6/4+12/3-30/6
To put these together, they all need to have a common denominator. We can make all of the denomiators 12 by multiplying the numerator by whatever we multiply the denominators by to get 12.
-18/12+48/12-60/12
This gets you -30/12
To make this a proper fraction, divide -30 by 12 and put the whole number to the left of the fraction (-2), making a mixed number. The remainder stays a fraction which is -6/12. This reduces down to -1/2. Put -2 and -1/2 together to get [tex]-2\frac{-1}{2}[/tex]