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gogolik [260]
2 years ago
9

John Smith made a one year investment that generated a nominal return of 6% or $3000. The real return was $2000. What was the or

iginal investment amount? what was the annual inflation rate? Macroeconomic
Mathematics
1 answer:
nata0808 [166]2 years ago
3 0

The nominal value - without discounting the inflation rate - of income was $ 3000.

If the interest rate was 6%, a rule of three is enough to find the value of the original investment.

3000 - 6%

x - 100%

x = 50,000

The value of the investment was $ 50,000

In this case, the inflation rate also requires a simple calculation.

Inflation corroded $ 1000 dollars of income of $ 3000

Therefore the inflation rate will be 1000/3000 = 33.3%

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Write the ratio as a fraction in simplest form: 2.35 to 5.25.
Sliva [168]

Step-by-step explanation:

\frac{2.35}{5.25}  =  \frac{235}{525}  =  \frac{47}{105}  = 47 \:  : \: 105 \\

4 0
2 years ago
Find, correct to four decimal places, the length of the curve of intersection of the cylinder 16x2 + y2 = 16 and the plane x + y
Yuri [45]

Let the curve C be the intersection of the cylinder  



16x^2+y^2=16



and the plane



x+y+z=1



The projection of C on to the x-y plane is the ellipse



16x^2+y^2=16



To see clearly that this is an ellipse, le us divide through by 16, to get



\frac{x^2}{1}+ \frac{y^2}{16}=1



or  



\frac{x^2}{1^2}+ \frac{y^2}{4^2}=1,



We can write the following parametric equations,



x=cos(t), y=4sin(t)



for  



0\le t \le 2\pi



Since C lies on the plane,



x+y+z=1



it must satisfy its equation.



Let us make z the subject first,  



z=1-x-y



This implies that,



z=1-sin(t)-4cos(t)



We can now write the vector equation of C, to obtain,



r(t)=(cos(t),4sin(t),1-cos(t)-4sin(t))



The length of the curve of the intersection of the cylinder and the plane is now given by,



\int\limits^{2\pi}_0 {|r'(t)|} \, dt



But  



r'(t)=(-sin(t),4cos(t),sin(t)-4cos(t))



|r'(t)|=\sqrt{(-sin(t))^2+(4cos(t))^2+(sin(t)-4cos(t))}



\int\limits^{2\pi}_0 {\sqrt{2sin^2(t)+32cos(t)-8sin(t)cos(t)} }\, dt=24.08778184



Therefore the length of the curve of the intersection  intersection of the cylinder and the plane is 24.0878 units correct to four decimal places.

6 0
2 years ago
James has a total of 66 dollars in his piggy bank. He only has one dollar bills and two dollar bills in his piggy bank. If there
gavmur [86]

Answer:

32 one-dollar bills.

Step-by-step explanation:

Let <em>x </em>represent one-dollar bills and <em>y </em>represent two-dollar bills.

He has a total of 49 bills. Therefore:

x+y=49

The total amount of money James has is 66. <em>x</em> is worth one dollar, while <em>y</em> is worth two dollars. Therefore:

1x+2y=66\\x+2y=66

We have a system of equations. Solve by substitution:

x+2y=66\\x+y=49\\x=49-y\\(49-y)+2y=66\\y=17\\x=49-17=32

Therefore, James has 32 one-dollar bills and 17 two-dollar bills.

Checking:

32(1)+17(2)\stackrel{?}{=}66\\32(1)+17(2)\stackrel{\checkmark}{=}66\\\\32+17\stackrel{?}{=}49\\49\stackrel{\checkmark}{=}49

5 0
2 years ago
Pls help i have a test tmrw and i don't understand anything
Alex777 [14]

Answer:

Step-by-step explanation:

Go on super teacher worksheets to get the answer key

3 0
2 years ago
George had 1 sheet of paper. He cuts it into 6 inches by 5 inches, and 3 inches by 6 inches. What were the dimensions and total
Neporo4naja [7]
The answer is 48 inches ^2
5 0
2 years ago
Read 2 more answers
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