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Black_prince [1.1K]
2 years ago
15

Peyton is going to invest $9,700 and leave it in an account for 16 years. Assuming the interest is compounded continuously, what

interest rate, to the nearest tenth of a percent, would be required in order for Peyton to end up with $14,100?
Mathematics
1 answer:
Mariulka [41]2 years ago
5 0

Answer: r ≈ 2.3%

Step-by-step explanation:

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Steve likes to entertain friends at parties with "wire tricks." Suppose he takes a piece of wire 60 inches long and cuts it into
Alex_Xolod [135]

Answer:

a) the length of the wire for the circle = (\frac{60\pi }{\pi+4}) in

b)the length of the wire for the square = (\frac{240}{\pi+4}) in

c) the smallest possible area = 126.02 in² into two decimal places

Step-by-step explanation:

If one piece of wire for the square is y; and another piece of wire for circle is (60-y).

Then; we can say; let the side of the square be b

so 4(b)=y

         b=\frac{y}{4}

Area of the square which is L² can now be said to be;

A_S=(\frac{y}{4})^2 = \frac{y^2}{16}

On the otherhand; let the radius (r) of the  circle be;

2πr = 60-y

r = \frac{60-y}{2\pi }

Area of the circle which is πr² can now be;

A_C= \pi (\frac{60-y}{2\pi } )^2

     =( \frac{60-y}{4\pi } )^2

Total Area (A);

A = A_S+A_C

   = \frac{y^2}{16} +(\frac{60-y}{4\pi } )^2

For the smallest possible area; \frac{dA}{dy}=0

∴ \frac{2y}{16}+\frac{2(60-y)(-1)}{4\pi}=0

If we divide through with (2) and each entity move to the opposite side; we have:

\frac{y}{18}=\frac{(60-y)}{2\pi}

By cross multiplying; we have:

2πy = 480 - 8y

collect like terms

(2π + 8) y = 480

which can be reduced to (π + 4)y = 240 by dividing through with 2

y= \frac{240}{\pi+4}

∴ since y= \frac{240}{\pi+4}, we can determine for the length of the circle ;

60-y can now be;

= 60-\frac{240}{\pi+4}

= \frac{(\pi+4)*60-240}{\pi+40}

= \frac{60\pi+240-240}{\pi+4}

= (\frac{60\pi}{\pi+4})in

also, the length of wire for the square  (y) ; y= (\frac{240}{\pi+4})in

The smallest possible area (A) = \frac{1}{16} (\frac{240}{\pi+4})^2+(\frac{60\pi}{\pi+y})^2(\frac{1}{4\pi})

= 126.0223095 in²

≅ 126.02 in² ( to two decimal places)

4 0
3 years ago
Pls tell me the answer with an explanation how you got it!
Flura [38]

Answer:

25 degrees

Step-by-step explanation:

40 + 50 = 90

2 x 25 = 5

8 0
3 years ago
Kimberly drives at a rate of 50 miles per hour on her trip across the country. If it takes Kimberly 200 gallons of gasoline to d
ipn [44]

Answer:

3x

Step-by-step explanation:

50 mi/hr × (1 hr / 60 min) × (200 gal / 500 mi) = ⅓ gal/min

(⅓ gal/min) × (t min) = x gal

t = 3x

3 0
3 years ago
Which function is the inverse of f(x) = –5x – 4?
mixas84 [53]

y=-5x-4

x=-5y-4

5y=-x-4

y= -1/5x - 4/5

7 0
3 years ago
Read 2 more answers
100 POINTS IF U GET THIS RIGHT!
iVinArrow [24]

Answer:

That is the answer

Hope this helps!

3 0
2 years ago
Read 2 more answers
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