The span of 3 vectors can have dimension at most 3, so 9 is certainly not correct.
Check whether the 3 vectors are linearly independent. If they are not, then there is some choice of scalars [tex]c_1,c_2,c_3[/tex] (not all zero) such that
[tex]c_1 (2,-1,1) + c_2 (3,1,1) + c_3 (1,2,0) = (0,0,0)[/tex]
which leads to the system of linear equations,
[tex]\begin{cases} 2c_1 + 3c_2 + c_3 = 0 \\ -c_1 + c_2 + 2c_3 = 0 \\ c_1 + c_2 = 0 \end{cases}[/tex]
From the third equation, we have [tex]c_1=-c_2[/tex], and substituting this into the second equation gives
[tex]-c_1 + c_2 + 2c_3 = 2c_2 + 2c_3 = 0 \implies c_2 + c_3 = 0 \implies c_2 = -c_3[/tex]
and in turn, [tex]c_1=c_3[/tex]. Substituting these into the first equation gives
[tex]2c_1 + 3c_2 + c_3 = 2c_3 - 3c_3 + c_3 = 0 \implies 0=0[/tex]
which tells us that any value of [tex]c_3[/tex] will work. If [tex]c_3 = t[/tex], then [tex]c_1=t[/tex] and [tex]c_2 = -t[/tex]. Therefore the 3 vectors are not linearly independent, so their span cannot have dimension 3.
Repeating the calculations above while taking only 2 of the given vectors at a time, we see that they are pairwise linearly independent, so the span of each pair has dimension 2. This means the span of all 3 vectors taken at once must be 2.
Fill in the missing amounts. July Aug. Sept. Oct. Nov. Dec. Receipts $500 $550 $700 $850 $795 $715 Expenses $490 $550 $600 $795 $ $650 Net Cash Flow $ $0 $ $55 $45 $ Cumulative Balance $10 $ $110 $ $210 $275
July Aug. Sept. Oct. Nov. Dec. Receipts $500 $550 $700 $850 $795 $715 Expenses $490 $550 $600 $795 $ $650 Net Cash Flow $ $0 $ $55 $45 $ Cumulative Balance $10 $ $110 $ $210 $275 the missing values are 750, 10, 100, 65, 10, 165
This is further explained below.
What is Cumulative Balance?Generally, The term "cumulative balance" refers to the total amount of money left over at the end of a fiscal year after all surplus amounts have been subtracted from deficit amounts. If there is a negative amount in the Cumulative Balance at the conclusion of a fiscal year, then that balance will be carried forward and used as the opening balance for the next fiscal year.
The term "cumulative account" refers to the total amount of an employee's account under a defined contribution plan (for an unaggregated plan) or the total amount of an employee's account under all defined contribution plans included in an Aggregation Group (for aggregated plans), both of which are determined as of the most recent plan valuation date within the most recent 12-month period that ends on the...
In conclusion, for the following data July Aug. Sept. Oct. Nov. Dec. Receipts $500 $550 $700 $850 $795 $715 Expenses $490 $550 $600 $795 $ $650 Net Cash Flow $ $0 $ $55 $45 $ Cumulative Balance $10 $ $110 $ $210 $275 the missing values are 750, 10, 100, 65, 10, 165
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Suppose that you repeated questions 5 and 6 using two line segments of your choice. The line segments could be any length and in any
orientation as long as the midpoints were marked correctly and coincided with each other. Would you reach the same conclusion that you
reached in question 7? How does your conclusion relate to the diagonals of a parallelogram?
A line segment can be defined as the part of a line in a geometric figure such as a parallelogram, that is bounded by two (2) distinct points and it typically has a fixed length.
In Geometry, a line segment can be measured by using the following measuring instruments:
A scale (ruler).A divider.What is a parallelogram?A parallelogram refers to a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.
Based on the previous experiment conducted in question 5, 6 and 7, we can logically conclude that the opposite sides of quadrilateral ABCD have the same (equal) slopes, which implies that the opposite sides are parallel. Hence, quadrilateral ABCD is simply a parallelogram by definition.
In this context, yes I would you reach the same conclusion that I reached in question 7 because the line segments that I drew represent the diagonals of a parallelogram.
Therefore, if the point of intersection of the diagonals divide each diagonal in half, then, the quadrilateral belonging to these diagonals forms a parallelogram.
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What expression is equivalent to (9x^2 + 2x -7)(x - 4)
Answer: C
Step-by-step explanation:
We can use the expanding rule to get that one if the expressions is
(9x^2 + 2x - 7)x + (9x^2 + 2x - 7)(-4)
A DC10 airplane travels 3000 km with a tailwind in 3 hr. It travels 3000 km with a headwind in 4 hr. Find the speed of the plane and the speed of the wind.
The speed of the plane will be 875km/h and the speed of the wind will be 125km/h.
How to calculate the speed?It should be noted that the speed is calculated as:
= Distance/Time
Based on the information, the DC10 airplane travels 3000 km with a tailwind in 3 hr. It travels 3000 km with a headwind in 4 hr.
Therefore, (v + w) = 3000/3
v + w = 1000 .... I
(v - w) = 3000/4
v - w = 750 .... ii
We'll then add both equations together. Therefore, the speed of the plane will be 875km/h and the speed of the wind will be 125km/h.
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Determine the five-number summary for this data set, taking into account any outliers. 10 13 15 12 12 4 12 17 12 13 15 18 10 11 20 19 Tiles 11.5 13 16 20 10 12.5 17
The value of the median, lower and upper quartile
Median = 21.5lower quartile = 12upper quartile = 29What is the five-number summary for this data set?
The minimum value = 10
The maximum value = 38
The median is the value that is found in the center of the data when it is ordered from lowest to highest. In the event that there is no value that precisely corresponds to the center, the value will be determined by taking the average of the values that are located on each side of the middle.
10 11 12 15 19 24 27 29 33 38
Median = 21.5
The intermediate value of the data that is located to the left of the median is known as the lower quartile.
10 11 12 15 19
lower quartile = 12
The intermediate value of the data that is located to the right of the median is known as the upper quartile.
24 27 29 33 38
upper quartile = 29
In conclusion, the 5 number summary is 10, 12, 21.5, 29, 38 → A
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Answer: minimum 10 first quartile 11.5 median 12.5 third quartile 16 maximum 20
Step-by-step explanation:
At the given point, find the slope of the curve, the line that is tangent to the curve, or the line that is normal to the curve, as
requested.
y5+ x3 = y2 + 12x, slope at (0, 1)
0-2
02
04
The slope of the curve described by the equation at the given point (0,1) as in the task content is; 4.
What is the slope of the curve, the line tangent to the curve at the given point; (0, 1)?According to the task content, it follows that the slope of the curve can be determined by means of implicit differentiation as follows;
y⁵+ x³ = y² + 12x
5y⁴(dy/dx) -2y(dy/dx) = 12 - 3x²
(dy/dx) = (12 -3x²)/(5y⁴-2y)
Hence, since the slope corresponds at the point given; (0, 1); we have;
(dy/dx) = (12 -3(0)²)/(5(1)⁴-2(1))
dy/dx = 12/3 = 4.
Hence, slope, m = 4.
Consequent to the mathematical computation above, it can then be concluded that the slope of the curve, the line tangent to the curve at the given point is; 4.
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After descending 8.25 feet, a bird is now
at a height of 16.5 feet. What was the initial
height of the bird?
compare the discounts you would receive with a 10% off coupon versus a 510 off coupon. Which one is better? Are there situations in which the other one is better? Will they get you the same amount of discount? Show All the work.
1. To determine the better option between a 10% off coupon versus a $10 off coupon, it is necessary to determine the coupon price.
2. On the other hand, the $10 off coupon becomes better when the coupon price is less than $100.
3. The 10% off coupon and the $10 off coupon do not give the same amount of discount unless the coupon or list price is $100 in both situations.
What is a discount?A discount is a monetary reduction in the cost of a good or service offered to customers to increase trade.
Offering discounts enhances sales but not profitability. So, there is a trade-off that must be considered properly.
Calculations:Ordinarily, if the coupon price is more than $100, the 10% off coupon becomes better than the $10 off coupon.
For instance, if the coupon price is $110, the 10% off coupon will yield a discount amount of $11 ($110 x 10%), which is more than $10.
For instance, if the coupon price is $99, the discount amount will be $9.90, which is less than $10.
Thus, a 10% off coupon and a $10 off coupon do not offer the same discount amount unless the list price is $100, no more, no less.
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Question Completion:Compare the discounts you would receive with a 10% off coupon versus a $10 off coupon.
(1 point) Find y as a function of x if
y" - 12y" + 32y' = 0,
y(0) = 5, y'(0) = 2, y" (0) = 1.
0
y(x) =
Find the points of intersection of the equation: xy=2 and x+y =4
Answer:[tex]\Large\boxed{(2+\sqrt{2},~2-\sqrt{x} )~~and~~ (2-\sqrt{2},~2+\sqrt{x} )}[/tex]
Step-by-step explanation:
Given the system of equations
[tex]1)~xy=2[/tex]
[tex]2)~x+y=4[/tex]
Divide x on both sides of the 1) equation
[tex]xy=2[/tex]
[tex]xy\div x=2\div x[/tex]
[tex]y=\dfrac{2}{x}[/tex]
Current system
[tex]1)~y=\dfrac{2}{x}[/tex]
[tex]2)~x+y=4[/tex]
Substitute the 1) equation into the 2) equation
[tex]x+(\dfrac{2}{x} )=4[/tex]
Multiply x on both sides
[tex]x\times x+\dfrac{2}{x}\times x=4\times x[/tex]
[tex]x^2+2=4x[/tex]
Subtract 4x on both sides
[tex]x^2+2-4x=4x-4x[/tex]
[tex]x^2-4x+2=0[/tex]
Use the quadratic formula to solve for the x value
[tex]x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(1)(2)} }{2(1)}[/tex]
[tex]x=2\pm\sqrt{2}[/tex]
Substitute the x value into one of the equations to find the y value
[tex]xy=2[/tex]
[tex](2+\sqrt{2} )y=2[/tex]
[tex]y=2-\sqrt{2}[/tex]
[tex]OR[/tex]
[tex]xy=2[/tex]
[tex](2-\sqrt{2} )y=2[/tex]
[tex]y=2+\sqrt{2}[/tex]
Therefore, the points of intersection are
[tex]\Large\boxed{(2+\sqrt{2},~2-\sqrt{x} )~~and~~ (2-\sqrt{2},~2+\sqrt{x} )}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
(2 - [tex]\sqrt{2}[/tex] , 2 + [tex]\sqrt{2}[/tex] ) and (2 + [tex]\sqrt{2}[/tex], 2 - [tex]\sqrt{2}[/tex] )
Step-by-step explanation:
xy = 2 → (1)
x + y = 4 ( subtract x from both sides )
y = 4 - x → (2)
substitute y = 4 - x into (1)
x(4 - x) = 2
4x - x² = 2 ( multiply through by - 1 )
x² - 4x = - 2
using the method of completing the square
add ( half the coefficient of the x- term)² to both sides
x² + 2(- 2)x + 4 = - 2 + 4
(x - 2)² = 2 ( take square root of both sides )
x - 2 = ± [tex]\sqrt{2}[/tex] ( add 2 to both sides )
x = 2 ± [tex]\sqrt{2}[/tex] , that is
x = 2 - [tex]\sqrt{2}[/tex] , x = 2 + [tex]\sqrt{2}[/tex]
substitute these values of x into (2) for corresponding values of y
x = 2 - [tex]\sqrt{2}[/tex] , then
y = 4 - (2 - [tex]\sqrt{2}[/tex])
= 4 - 2 + [tex]\sqrt{2}[/tex]
= 2 + [tex]\sqrt{2}[/tex] ⇒ (2 - [tex]\sqrt{2}[/tex] , 2 + [tex]\sqrt{2}[/tex] ) ← 1 point of intersection
x = 2 + [tex]\sqrt{2}[/tex] , then
y = 4 - (2 + [tex]\sqrt{2}[/tex] )
= 4 - 2 - [tex]\sqrt{2}[/tex]
= 2 - [tex]\sqrt{2}[/tex] ⇒ (2 + [tex]\sqrt{2}[/tex] , 2 - [tex]\sqrt{2}[/tex] ) ← 2nd point of intersection
Please help me with this question <3
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
For two lines to be parallel, there should be angles that follow some specific properties that is usually observed with parallel lines.
We can clearly see that :
[tex] \qquad❖ \: \sf \: \angle7 \cong \angle16[/tex]
( by Alternate interior angle pair )
[tex] \qquad \large \sf {Conclusion} : [/tex]
Lines l and m are parallel to each other.
Consider the functions below. f(x)=8x^2+x+3, g(x)=4x-1, h(x)=3x+6. Which of the following statements is true?
A.
As x approaches infinity, the value of g(x) eventually exceeds the values of both f(x) and h(x).
B.
Over the interval [3, 5], the average rate of change of g and h is more than the average rate of change of f.
C.
Over the interval [0, 2], the average rate of change of f and h is less than the average rate of change of g.
D.
As x approaches infinity, the values of g(x) and h(x) eventually exceed the value of f(x).
The functions f(x)=8x^2+x+3, g(x)=4x-1, h(x)=3x+6 C.Over the interval [0, 2], the average rate of change of f and h is less than the average rate of change of g is true.
What is increasing function?
⇒ The function is said to be increasing if the y value increases as the x value increase over a given range
What is average rate of change?
⇒An average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another
As x approaches infinity the value of f(x) eventually exceeds the value of both g(x) and h(x)
And it is true for the interval [0,2]
The faster the growth rate higher the average rate of change
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Answer:
C.
Over the interval [0, 2], the average rate of change of f and h is less than the average rate of change of g.
Find the length indicated
Find SR (image)
Answer:
SR = 5
Step-by-step explanation:
We know that the two lines are equal to each other and thus TS + SR = 13
So, we can simply set the two equations of the first line equal to 13:
x + 2 + 2x - 7 = 13
3x - 5 = 13
3x = 18
x = 6
Now we plug in 6 for x in the SR equation:
2 * 6 = 12 - 7 = 5
5. Write the following inequality in slope-intercept form. −8x + 4y ≥ −52 y ≤ 2x − 13 y ≥ 2x − 13 y ≤ 2x + 13 y ≥ 2x + 13
Answer:35443
Step-by-step explanation:
P: 2,012
1) El volumen de un cubo de arista 1 es Vc = 1³ y el
Volumen de una esfera de radior es
JE
V₁ = πr ²³ Entonces si en un cubo de arista 4cm
3
y se introduce una pelota de diametro 4 cm, al Calcular
aproximación con cuatro cifras decimales, por exceso.
Calcular el volumen que queda entre la esfera y el cubo.
(toma π =
3,141592654)
El volumen remanente entre la esfera y el cubo es igual a 30.4897 centímetros cúbicos.
¿Cuál es el volumen remanente entre una caja cúbica vacía y una pelota?
En esta pregunta debemos encontrar el volumen remanente entre el espacio de una caja cúbica y una esfera introducida en el elemento anterior. El volumen remanente es igual a sustraer el volumen de la pelota del volumen de la caja.
Primero, se calcula los volúmenes del cubo y la esfera mediante las ecuaciones geométricas correspondientes:
Cubo
V = l³
V = (4 cm)³
V = 64 cm³
Esfera
V' = (4π / 3) · R³
V' = (4π / 3) · (2 cm)³
V' ≈ 33.5103 cm³
Segundo, determinamos la diferencia de volumen entre los dos elementos:
V'' = V - V'
V'' = 64 cm³ - 33.5103 cm³
V'' = 30.4897 cm³
El volumen remanente entre la esfera y el cubo es igual a 30.4897 centímetros cúbicos.
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Find the variance of 24,30,17,22,22
Answer:
22
Step-by-step explanation:
An airplane is heading north at an airspeed of 640 km/hr, but there is a wind blowing from the southwest at 90 km/hr. How many degrees off course will the plane end up flying, and what is the plane's speed relative to the ground? Round your answers to 2 decimal places.
An airplane is heading north at an airspeed of 640 km/hr, but there is a wind blowing from the southwest at 90 km/hr. degrees off course will be 6.25°
How many degrees off course will the plane end up flying, and what is the plane's speed relative to the ground?Generally, the equation for the velocity of the plane with reference to the ground is mathematically given as
Vp= velocity of the plane with reference to wind+ velocity of the wind with reference to ground
Therefore
Vp=Vp'+Vw
[tex]mVp=\sqrt{(640)^2+(90)^2-2*640*90cos45}[/tex]
mVp=579.8km/h
where
[tex]\frac{sintheta}{90}=\frac{sin45}{Vp'}[/tex]
[tex]sin \theta=\frac{90}{579.8}*sin45[/tex]
sin[tex]\theta=0.109[/tex]
[tex]\theta=sin^{-1}(0.109)=6.25[/tex]
In conclusion, degrees off course will be 6.25
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Which of the following are polynomials?
A. x^2 + x + 1/x^2 + 1
B. 2/x^3 + x + 1/2
C. 2/3x^2 + x + 1
D. x^2/3 + 0x + 1
E. x^3 + 2x + square root of 2
Answer: C, E
Step-by-step explanation:
These are polynomials by the definition of a polynomial.
A student says that 3% is equal to 0.3 when written as a decimal. Is their thinking correct? Explain.
The answer is no.
Always remember when converting from percent to decimal, divide by 100%.
3% ÷ 100%0.03 ≠ 0.3Hence, the student's thinking is not correct.
Answer:
no
Step-by-step explanation:
0.3 = 30% not 3%
to change a percentage to a decimal fraction, divide by 100
3% = [tex]\frac{3}{100}[/tex] = 0.03
What is the simplified form of i^86?
A. 1
B. i
C. -1
D. -i
please help urgently
Answer: no real solution
Thus, the function has no x- intercept
Step-by-step explanation:
A drawer contains loose socks. There are 2 blue and 4 black socks in the drawers. What is the probability that you choose a sock without looking, then choose a second sock (keeping the first in your hand) without looking, and end up with a pair of black socks?
The probability is p = 2/5, the correct option is the third one.
How to find the probability?
There is a total of 6 socks, such that 4 are black and 2 are blue.
Then the probability of first getting a black sock is the quotient between the number of black socks and the number of blue socks, which gives:
P = 4/6
Now there are 5 socks in total, such that 3 are black and 2 blue.
Then the probability of getting another black one is:
Q = 3/5
The joint probability (getting the two black socks) is given by the product of the individual probabilities:
p = (4/6)*(3/5) = 2/5
The correct option is the third one.
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Please select the best answer from the choices provided .
Answer: B: (1-5x²)³, all real numbers
Step-by-step explanation:
The notation [tex]f\circ g(x)[/tex] is called function composition, which is where you pass one function in as the value of another function. In other words, [tex]\( f\circ g(x)=f(g(x)) \)[/tex].
Since we have the values for f(x) and g(x), let's plug them in.
[tex]f(g(x))\\f(1-5x^2)\\(1-5x^2)^3[/tex]
Hence, the best answer choice is B, as all real numbers would work and it is the cube of 1 - 5x².
Let σ(n) be the sum of all positive divisors of the integer n and let p be any prime number.
Show that σ(n) < 2n holds true for all n of the form n = p²
The statement that "σ(n) < 2n holds true for all n of the form n = p²" has been proved.
Let p be any prime number, and let σ(n) be the sum of all positive divisors of the integer n.
As p is a prime number, and 2 is the smallest prime number, so, p[tex]\geq[/tex]2
So, the positive divisors of the integer n are: 1,p,p².
As σ(n) represents the sum of all positive divisors of the integer n.
σ(n)=1+p+p²
In order to prove that σ(n) < 2n,for all n of the form n = p².
1+p+p²<2p²
p²-p-1>0
It is know that, p[tex]\geq[/tex]2.
So, p²-p-1[tex]\geq[/tex]1
Thus, σ(n) < 2n holds true for all n of the form n = p².
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A baseball travels d meters t seconds after being dropped from the top of the building
Considering the given function, it is found that:
When t = 0, d = 0 meters.When t = 0.5, d = 1.25 meters.When t = 1, d = 5 meters.When t = 1.5, d = 11.25 meters.When t = 2, d = 20 meters.Since the changes for each 5 second interval are not the same, the ball is not traveling at a constant speed.
What is the function for the distance traveled by the ball?The function is:
d = 5t².
Hence:
When t = 0, d = 5 x 0² = 0 meters.When t = 0.5, d = 5 x 0.5² = 1.25 meters.When t = 1, d = 5 x 1 = 5 meters.When t = 1.5, d = 5 x 1.5² = 11.25 meters.When t = 2, d = 5 x 2² = 20 meters.Since the changes for each 5 second interval are not the same, the ball is not traveling at a constant speed.
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Find two positive numbers whose difference is 9 and whose product is 2950.
The two positive numbers whose difference is 9 and whose product is 2950 are 50 and 59
How to determine the positive numbers?As a general rule, it should be noted that positive numbers are numbers that have their value greater than 0
So, we start by representing the two positive numbers with x and y.
So, we have the following equations
x - y = 9
xy = 2950
Make x the subject in the first equation x - y = 9
x = y + 9
Substitute y + 9 for x in the second equation
(y + 9) * y = 2950
Expand the equation
y^2 + 9y - 2950 = 0
Using a graphing tool, we have the solution of the above equation to be
y = 50
Recall that:
x = 9 + y
So, we have:
x = 9 + 50
Evaluate
x = 59
Hence, the two positive numbers whose difference is 9 and whose product is 2950 are 50 and 59
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evaluate the following using powers of ten rules: 10 to the 4th times the square root of 1.042
The value of the given expression is approximate equal to 1.021 × 10⁴ OR 10207.8
Evaluating an expressionFrom the question, we are to determine the value of the given expression
The given expression is
10 to the 4th times the square root of 1.042
That is,
10⁴ × √1.042
The expression can be evaluated as shown below
10⁴ × √1.042
= 10⁴ × 1.02078
= 1.02078 × 10⁴
≈ 1.021 × 10⁴
OR
= 1.02078 × 10⁴ = 10207.8
Hence, the value of the given expression is approximate equal to 1.021 × 10⁴ OR 10207.8
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Remy obtains a 30-year mortgage in the amount of $625,000 for a co-op. She secures a 7/1 ARM at an initial interest rate of 3%. Her initial monthly payment is $2,635.03. After 7 years, the interest rate on her loan changes to 4.925%. Calculate her new monthly payment in year 8 of the loan. (Round your answer to the nearest cent.)
The new monthly payment is $3,181.53
What is ARM?
ARM stands adjustable rate mortgage, which means that the interest rate applicable to the mortgage would change during the life of the mortgage, in this case, 7/1 ARM means that interest rate of 3% is applicable for the first 7 years and the rate would change in year 8 to another interest rate, which is 4.925% as hinted at in the question.
To determine the monthly payment in year 8 , we need to compute the outstanding balance at the end of year 7, which is the opening balance in year 8 using the present value formula of an ordinary annuity since monthly payments would occur at the end of each month
PV(balance at the end of year 7)=PMT*(1-(1+r)^-N/r
PMT=initial monthly payment=$2,635.03
r=initial monthly interest rate=3%/12=0.0025
N=number of monthly payments in the remaining 23 years(i.e 30-7)=23*12
N=number of monthly payments in the remaining 23 years(i.e 30-7)=276
PV=$2,635.03*(1-(1+0.0025)^-276/0.0025
PV=$2,635.03*(1-0.502008144755209)/0.0025
PV=$2,635.03*0.497991855244791/0.0025
PV=$ 524,889.39
With the balance at the end of year 7, we can now compute monthly payment in year 8 using the same formula as above where the unknown is the PMT, PV=$ 524,889.39 and r= 4.925%.
$524,889.39=PMT*(1-(1+4.925%/12)^-276/4.925%/12)
$524,889.39=PMT*(1-(1.00410416666666667
)^-276/0.00410416666666667
$524,889.39=PMT*(1-0.32289378683267300
)/0.00410416666666667
$524,889.39=PMT*164.98019407122700000
PMT=$524,889.39/164.98019407122700000
PMT=$3,181.53
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1. a) Sajina deposited Rs 20,000 at the rate of 8% p.a. in her saving account. After 2 years, she withdrew Rs 5,000 and the total interest of 2 years. How long should she keep the remaining amount to get total interest of Rs 6,800 from the beginning?
6,800 to get a total interest of Rs 6,800 and keep the balance for 3 years.
What is meant by total interest?Total interest is the sum of all interest payments made during the course of an account or loan, including compounded amounts on accumulated interest that has not yet been paid.The equation [Total Loan Amount] = [Principle] + [Interest Paid] + [Interest on Unpaid Interest] can be used to calculate it.Under Section 24, you may deduct up to Rs 2 lakh from your total income for the interest component of the EMI you paid during the year.
How long should she keep the remaining amount to get a total interest of Rs 6,800 from the beginning:
The rate of 8% p.a. in her saving account.
20,000 at 8% interest for 2 years:
= 20,000*2*8/100
= 3200
5000 was withdrawn after 2 years and earned interest.
After 2 years, the new principal:
= 20000- 5000
=15000
She needs to get interested of 6800–3200 =3600 for the next N years.
N= 100* I /PR
= 100*3600/(15000*8)
=3
6,800 to get a total interest of Rs 6,800 and keep the balance for 3 years.
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Sajina should keep the remaining amount for 3 years to get a total interest of Rs 6,800 from the beginning.
What is the formula for total interest?For the principal [tex]P[/tex] and the rate of interest [tex]r\%[/tex] per annum, the total interest after [tex]t[/tex] years is given by the formula: [tex]I=\dfrac{Prt}{100}[/tex].
Given that Sajina deposited Rs 20,000 at the rate of 8% p.a. in her savings account.
So, [tex]P=20,000[/tex] and [tex]r=8[/tex].
Thus, after t=2 years the total interest would be
[tex]I=\dfrac{Prt}{100}\\\Longrightarrow I=\dfrac{20000\times 8\times 2}{100}\\\therefore I=3200[/tex]
So, the total interest after 2 years would be Rs 3,200.
Given that Sajina withdrew Rs 5,000 and the total interest of 2 years.
So, the new principal will be [tex]P'=20,000-5,000=\test{Rs}\hspace{1mm}15,000[/tex].
The total interest she wanted to gain is Rs 6,800. She had already gained Rs 3,200.
so, the remaining interest [tex]I'=6,800-3,200=\text{Rs}\hspace{1mm}3,600[/tex].
Let the required time be [tex]t'[/tex] years after how many years she got a total interest of Rs 6,800 from the beginning.
For principal [tex]P'=15,000[/tex], rate of interest [tex]r=8\%[/tex]; the total interest after [tex]t'[/tex] years would be [tex]I'=\dfrac{P'rt'}{100}=\dfrac{15000\times 8\times t'}{100}=1200t'[/tex]. But given that [tex]I'=3600[/tex].
So, we must have
[tex]1200t'=3600\\\Longrightarrow t'=\dfrac{3600}{1200}\\\therefore t'=3[/tex]
Therefore, Sajina should keep the remaining amount for 3 years to get a total interest of Rs 6,800 from the beginning.
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The three circles in the diagram have the same centre and have radii 3cm, 4cm and 5cm.
What percentage of the area of the largest circle is shaded?
Answer:
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