39. The difference between simple and compound interest on Rs. 500 for 3 years in yearly rate of interest is Rs. 2.432. What is the rate of interest ?
Answers
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Answer:
4%
Step-by-step explanation:
The multiplier for computing simple interest over a 3-year period is ...
I = Prt . . . . . interest on principal P at rate r for t years
I/P = rt = 3r
The multiplier for computing compound interest over a 3-year period is ...
A = P(1 +r)^t . . . . amount with interest
A/P -1 = (1 +r)^3 -1 . . . . multiplier for computing interest only
Then the multiplier for the difference in amounts of interest is ...
((1 +r)^3 -1) -3r = (1 +3r +3r^2 +r^3) -1 -3r = r^2(3 +r)
This means we need to solve the cubic ...
r^2(3 +r) = 2.432/500
__
This can be solved a variety of ways. Perhaps my favorite is a graphical solution. For that, we would rewrite the equation to the form ...
f(x) = x^2(3 +x) -0.004864
so the solution is found where f(x) = 0. The graph shows the solution to be ...
x = 0.04
The rate of interest is 0.04 = 4%.
_____
Additional comment
Using the above f(x) to develop a Newton's Method iterator, we find it to be ...
x' = (x²(2x +3) +0.004864)/(3x(x +2))
This needs a starting value, so we need an initial clue as to the approximate interest rate.
That can be offered by rearranging the cubic we first developed:
r = √(0.004864/(r +3))
Starting with r=0, this gives r ≈ 0.0402. At this point, we can either use this equation as an iterator, or use the Newton's method iterator above. Both will give an interest rate accurate to 4 or 5 decimal places in one iteration.
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You may be aware from the development above that the polynomial that must be solved will have a degree equal to the number of years over which interest is computed. That is, solving the same question for a 10-year period would involve finding the root of a 10th-degree polynomial.
Related Questions
Draw the image of quadrilateral ABCD when translated by the directed line segment v. Label the image of A as A', the image of B as B', the image of C as C' and the image of D as D'.
Answers
Answer:
Try this on for size.
Step-by-step explanation:
The image of quadrilateral ABCD translated as A'B'C'D' is given below.
What is a transformation of a shape?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the structure and/or location of the object. From before the refers to the object's initial condition, and Picture, after transformation, refers to the object's ultimate structure and location.
The translation does not change the shape and size of the geometry. But changes the location.
The image of quadrilateral ABCD translated as A'B'C'D' is given below.
The graph of the quadrilateral and its translated new quadrilateral is attached below.
More about the transformation of the shape link is given below.
https://brainly.com/question/27224339
#SPJ2
An unknown fraction is between 0 and 1. Which is true about the equivalent percent and decimal?
Answers
Answer:
D
Step-by-step explanation:
"The percent is greater than 0 and less than 100, and the decimal is between 0 and 1."
1. A basketball player made 12 out of 15 free throws she attempted. She wants to know how many consecutive free throws she would have to make to raise the percent of successful free throws to 85%. (a) Write an equation to represent this situation. (b) Solve the equation. How many consecutive free throws would she have to make to raise her percent to 85%?
Answers
Step-by-step explanation:
[tex] \frac{85}{100} \times 15[/tex]
=12.75≈13
someone please help!!
Answers
Jonas selects two numbers from this list and adds them for a sum of 392.03.
Which two numbers does he select? *put smallest decimal first
:: 174.97
:: 289.10
:: 217.06
:: 164.16
Answers
3)Calcular la distancia entre los puntos A = (2,1) y B =(-3,2)
Answers
Answer:
Step-by-step explanation:
You use the distance formula
d = √ (x1-x2) ² + (y1- y2) ²
d = √ (2 - (-3)) ² + (1 - 2) ²
d = √ (25 + 1)
d = √26
d = 5.2
What’s the domain and range of the exponential growth function?
Answers
Answer:
Recall that the domain of a function is the set of input or x -values for which the function is defined, while the range is the set of all the output or y -values that the function takes. A simple exponential function like f ( x) = 2 x has as its domain the whole real line.
Step-by-step explanation:
okay na yan
at what ordered pair do the lines x=-2 and y=5 intersect?
Answers
Answer: (-2, 5)
Step-by-step explanation:
The line x = -2 is simply a vertical line with an x-intercept of -2.
The line y = 5 is simply a horizontal line with a y-intercept of 5.
Can someone help me with this
Answers
Answer:
The answer is 39.2
Step-by-step explanation:
The first thing you want to do is multiply both numbers by them selves like this: 9x8 and 4x8. Then after you do that, add the sum of those equations and you have your answer. Think about it like this, for 8x4, all it is is just 8+8+8+8. If solving it that way is easier for you, go for it! Hope I could help!
You could have used a calculator
what are the steps for using a compass and straightedge
Answers
Answer:
Step-by-step explanation:
ESTA GOOGEL N
find the derivative of (3x+1)(x+5)
Answers
Hope this helps!
Have a great day!
Answer:
6x+16
Step-by-step explanation:
[tex]\frac{d}{dx} [(x+5)(3x+1)]\\=\frac{d}{dx} [x+5]*(3x+1)+(x+5)*\frac{d}{dx} [3x+1]\\=(\frac{d}{dx} [x]+\frac{d}{dx} [5])(3x+1)+(x+5)(3*\frac{d}{dx} [x]+\frac{d}{dx} [1])\\=(1+0)(3x+1)+(x+5)(3*1+0)\\=3(x+5)+3x+1\\Simplify/Rewrite\\=6x+16[/tex]
Graph the equation. y=−1/2(x−3)(x−7)
Answers
Answer:
x y
3 0
4 3
2 5
2 6
3 2
7 0
Step-by-step explanation:
simplify 8x+10x-5y+3+9y
Answers
Answer:
18x + 4y + 3
Step-by-step explanation:
8x + 10x - 5y + 3 + 9y(8x + 10x) + (-5y + 9y) + (3)18x + 4y + 3Therefore, the answer is 18x + 4y + 3.
Answer:
[tex]18x+4y+3[/tex]
Step-by-step explanation:
Add the like terms.
[tex]8x+10x=18x[/tex]
[tex]-5y+9y=4y[/tex]
⇒ [tex]18x + 4y+3[/tex]
Thus, the answer is [tex]18x + 4y + 3[/tex]
Need answer on this one Please !!
Answers
Answer:
It should be [tex]\frac{3}{14}[/tex]
Step-by-step explanation:
[tex]\frac{1}{2}=\frac{7}{14}[/tex]
[tex]\frac{2}{7} =\frac{4}{14}[/tex]
[tex]\frac{4}{14}+ \frac{7}{14}=\frac{11}{14}[/tex]
what is 4 7/9 as improper fraction
Answers
Answer:
43/9
Step-by-step explanation:
4 • 9 = 36
36 + 7 = 43
Keep the original denominator
PLEASE HELP IF YOU CAN ASAP PLEASE THIS IS ALGEBRA
1. What is the domain of the following points? (picture will be added
a) {-7, 3, 7} b) {-3, 3, 7} c) {-7, -3, 3, 7} d) {3,7}
2. What is the slope of the line through the points (-2, -1) and (4, 3)?
a) ⅖ b) 3/2 c) 5/2 d) ⅔
Answers
Answer:
1. (I need the picture for this one)
2. m=2/3 / Slope = 2/3
Step-by-step explanation:
Solving Steps: Reasoning:
1.) m=(y2-y1)/(x2-x1) [Slope Formula]
2.) m=(x1=-2, y1=-1) (x2=4, y2=3) [Assign Value to ordered pairs]
3.) m=(3-(-1))/(4-(-2)) [Substitution P.O.E.]
4.) m=(3+1)/(4+2) [Negative minus negative = positive]
5.) m=4/6 [Addition]
6.) m=2/3 [Simplification]
Therefore, the slope (m) = 2/3. To find the Domain, you will need to list all the X-coordinates from your ordered pairs. To find the range, you will need to list all the Y-coordinates from your ordered pairs.
You can use these formula:
Domain={x1, x2, x3, x4, x5…}
Range={y1, y2, y3, y4, y5…}
You just have to input your values into these formulas. An ordered pair looks like this: (5, 4). The left value is the x-coordinate (5), and the right value is the y-coordinate (4).
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4.153) If the area of the shaded area in the drawing below is 56 inches square and the volume is 1400 inches cubed what is the height.
Answers
9514 1404 393
Answer:
25 inches
Step-by-step explanation:
The volume of a prism is given by the formula ...
V = Bh
Filling in the given values, we have ...
1400 in³ = (56 in²)h
h = (1400 in³)/(56 in²) = 25 in . . . . . . divide by the coefficient of h
The height of the triangular prism is 25 inches.
Answer: The answer is 25 inches, I hope my answer is very helpful to your own question and have the rest of the day! :D
Sincerely,
Jason Ta,
The ambitious of Brainly and the role of the TDSB and WHCI Student of the high school.
Step-by-step explanation:
? : 11 = 1/3 : 6
I need help
Answers
Answer:
11/18
Step-by-step explanation:
let n represent the number to be found
simplify the ratio on the right by multiplying both parts by 3
we now have
n/11 =11/18 ( cross-multiply )
18n = 11 ( divide both sides by 18 )
n = 11/18
Using f(x) = 2x + 7 and g(x) = x - 3, find f(g(-2)
PLEASEEEEEEE HELP OR ELSE I WILL DIE
Answers
Answer:
Step-by-step explanation:
g(-2) = -2 - 3 = -5
f(-5)= 2(-5) + 7 = -10 + 7 = -3
Maths Question here.
Please answer - for homework
10 points available.
Answers
Answer:
a)first 3 terms =5, 8,11
b) 10th term is 32
Una secretaria puede hacer 3 escritos del mismo tamaño en 4 horas. Que tiempo le llevará realizar 5 trabajos de la misma longitud?
Answers
Answer:
Um I don’t know to to speak Spanish
Step-by-step explanation:
no se hablar espanol perdon
(2+a+b)²
Include how you solved the problem
Answers
Answer:
=[tex]4+a^{2} +b^{2}[/tex]
Step-by-step explanation:
=[tex]2^{2} +a^{2} +b^{2}[/tex]
=[tex]4+a^{2} +b^{2}[/tex]
Divide 54 in to two parts so that four times the greater equals five times the less
Answers
Answer:
Let the both the parts be 'x' and 'y'
x>y
We know that 4x = 5y
so x = 5y/4
x + y = 54
Replacing x we get
(5y/4) + y = 54
(5y +4y)/4 = 54
9y = 216
y = 24
Replacing y in ' x+y = 54'
we get x = 30
Step-by-step explanation:
Hence the larger part is 30 whereas the smaller part is 24
Find the value of x from the figure given below:
Answers
Answer:
[tex]sinB = \frac{x}{34}=\frac{5}{17} => \frac{x}{34}=\frac{5}{17}\\\\<=> x= \frac{5}{17}.34 =10[/tex]
Step-by-step explanation:
Question 9 Annabelle lives at Bermondsey in London. She has to speak at a conference in Birmingham at 10.30am. It will take her an hour from her home to get to Euston Rail Station, from where she will get a train to Birmingham. The train journey from Euston to Birmingham is an hour and 10 minutes. Trains to Birmingham run at the following times: 5 minutes past the hour, 25 minutes past the hour and 45 minutes past the hour. The meeting venue in Birmingham is a 5-minute walk from the station. What is the latest time that Annabelle can leave home, if she is to make it on time for the meeting in Birmingham? Show your working. (8 marks)
Answers
Answer:
Step-by-step explanation:
working backwards
the five minute walk
10:30 - 0:05 = 10:25
train ride to Birmingham
10:25 - 1:10 = 9:15
Next earliest train departure time
9:05
Getting to Euston Station
9:05 - 1:00 = 8:05 am
Probably wise to leave a couple of minutes earlier to allow for minor emergencies on the way to Euston Station or to account for potential clock synchronization errors.
The train schedule already allows an additional 10 minutes of buffer time after boarding.
A piece of wood is 12 feet long, and a nail is 3 inches long. The piece of wood is how many times as long as the nail?
Answers
Answer:
the piece of wood is 48 times as long as the nail.
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
you take the length of the wood and divide it by the length of the nail, so 12 divided by 3 well you can also skip-count until you reach 12, regardless you get 4
What is the equation of a line perpendicular to y= -3x+4 that passes through (-1, 6)
Answers
Given the linear equation, y = -3x + 4 and the point, (-1, 6):
We can assume that the slope of the other line must be 1/3, because if you multiply 1/3 by -3, the product will be -1.
Substitute the values if the given point, (-1, 6) and the slope of the other line, m = 1/3 into the slope-intercept form to solve for the y-intercept (b) of the other line:
y = mx + b
6 = 1/3(-1) + b
6 = -1/3 + b
Add 1/3 to both sides
6 + 1/3 = -1/3 + 1/3 + b
19/3 = b
Therefore, given the slope of 1/3 and the y-intercept, b = 19/3, the equation of the other line is:
y = 1/3x + 19/3
Attached is a screenshot of the graph of both equations, proving that both lines are perpendicular from each other, and that y = 1/3x + 19/3 passes through point (-1, 6).
Please mark my answers as the Brainliest if you find this helpful :)
For the equation
y + 2 = 6(x - 5),
the line has a slope of 6 and contains what point?
Answers
Answer:
(5, -2)
Step-by-step explanation:
1. The equation "y + 2 = 6(x - 5)" is in the form of point-slope. Point slope form is [tex]y-y_1=m(x-x_1)[/tex] where y_1 = y-coordinate of point, m = slope, and x_1 = x-coordinate of point.
2. Given the information above, the point (5, -2) and slope of 6 makes the equation y + 2 = 6(x - 5) because:
[tex]y - y_1 = m(x-x_1)[/tex] [tex]y - (-2) = 6(x-5)[/tex] [tex]y + 2=6x-5[/tex]Therefore, the point is (5,-2).
Select all polynomial expressions that are equivalent to 6X^4 + 4X^3 - 7X^2 + 5X +8.
A. 16x^10
B. 6X^5+ 4X^4 - 7X^3+ 5X^28.
C. 6X^4 + 4X^3 - 7X. ^2 + 5X +8.
D. 8 + 5X 7x^2 _ 4x^3 + 6x^4
E. 8 + 5X - 7x^2 + 4x^3 + 6x^4
Answers
A pet store has 15 dogs and 6 cats, which is a ratio of _____?
Answers
Answer:
5:2
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Answer:
15:6 or 5:2
Step-by-step explanation:
The number of dogs and cats can be simplified by dividing the two values by 3.