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zloy xaker [14]
3 years ago
10

Lisa invests $4,000 in two types of bonds, bond A and bond B. Bond A offers a 10% return, and bond B offers a 6% return. Lisa in

vests $x in bond A and $y in bond B. Her total return on the investment is $340. The system of linear equations defining the situation is x+y=4,000 and .1x=.06y=340. The amount Lisa invested at the rate of 10% is ___ , and the amount she invested at the rate of 6% is ___ .
Mathematics
1 answer:
NikAS [45]3 years ago
4 0
Lisa invests $4,000 in two types of bonds, bond A and bond B. A + B = 4000 Bond A offers a 10% return, and bond B offers a 6% return. .10 A + .06 B = 340 Her total return on the investment is $340. <span>since the relationship A+B=4000 must satisfy the setup for all values A and B we can state that A = 2000 + n, and B = 2000 -n afterall: 2000 +n + 2000 - n = 4000 for all n .10(2000+n) + .06(2000-n) = 340, once we know n we know A and B</span>
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Suppose that a spherical droplet of liquid evaporates at a rate that is proportional to its surface area: where V = volume (mm3
Alex

Answer:

V = 20.2969 mm^3 @ t = 10

r = 1.692 mm @ t = 10

Step-by-step explanation:

The solution to the first order ordinary differential equation:

\frac{dV}{dt} = -kA

Using Euler's method

\frac{dVi}{dt} = -k *4pi*r^2_{i} = -k *4pi*(\frac {3 V_{i} }{4pi})^(2/3)\\ V_{i+1} = V'_{i} *h + V_{i}    \\

Where initial droplet volume is:

V(0) = \frac{4pi}{3} * r(0)^3 =  \frac{4pi}{3} * 2.5^3 = 65.45 mm^3

Hence, the iterative solution will be as next:

  • i = 1, ti = 0, Vi = 65.45

V'_{i}  = -k *4pi*(\frac{3*65.45}{4pi})^(2/3)  = -6.283\\V_{i+1} = 65.45-6.283*0.25 = 63.88

  • i = 2, ti = 0.5, Vi = 63.88

V'_{i}  = -k *4pi*(\frac{3*63.88}{4pi})^(2/3)  = -6.182\\V_{i+1} = 63.88-6.182*0.25 = 62.33

  • i = 3, ti = 1, Vi = 62.33

V'_{i}  = -k *4pi*(\frac{3*62.33}{4pi})^(2/3)  = -6.082\\V_{i+1} = 62.33-6.082*0.25 = 60.813

We compute the next iterations in MATLAB (see attachment)

Volume @ t = 10 is = 20.2969

The droplet radius at t=10 mins

r(10) = (\frac{3*20.2969}{4pi})^(2/3) = 1.692 mm\\

The average change of droplet radius with time is:

Δr/Δt = \frac{r(10) - r(0)}{10-0} = \frac{1.692 - 2.5}{10} = -0.0808 mm/min

The value of the evaporation rate is close the value of k = 0.08 mm/min

Hence, the results are accurate and consistent!

5 0
3 years ago
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lawyer [7]

Answer:

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Step-by-step explanation:

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55° is also in the second triangle.

Let's check with the second triangle:

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Therefore, both triangles are similar as the angles in both triangles are the same - 82°, 43° and 55°.

Hence, C.

7 0
3 years ago
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