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Diano4ka-milaya [45]
3 years ago
15

How much principle, to the nearest dollar, should you invest at 4 percent in order to have $3000 for a vacation to Europe in 3 y

ears
Mathematics
1 answer:
KiRa [710]3 years ago
4 0

Answer:

Principle should be $2,667

Step-by-step explanation:

We need $3000 for a vacation to Europe in 3 years.

Using amount formula,

A=P(1+r)^t

Where, P is principle (P=?)

A is amount (A=3000)

r is rate of interest (r=0.04)

t is time (t=3)

Substitute the values into formula and solve for P

3000=P(1+0.04)^3

3000=P(1.04)^3

P=\frac{3000}{1.04^3}

P=2666.98

P\approx \$2667

Hence, Principle should be $2,667

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160

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A person in a balloon which is 2,000 feet above the airport finds that the angle of depression to a ship out at sea is 21°. Find
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The horizontal distance is given by the formula:
tan θ=opposite/adjacent
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A line tangent to the curve f(x)=1/(2^2x) at the point (a, f(a)) has a slope of -1. What is the x-intercept of this tangent?
kirza4 [7]

Answer:

x-intercept = 0.956

Step-by-step explanation:

You have the function f(x) given by:

f(x)=\frac{1}{2^{2x}}   (1)

Furthermore you have that at the point (a,f(a)) the tangent line to that point has a slope of -1.

You first derivative the function f(x):

\frac{df}{dx}=\frac{d}{dx}[\frac{1}{2^{2x}}]  (2)

To solve this derivative you use the following derivative formula:

\frac{d}{dx}b^u=b^ulnb\frac{du}{dx}

For the derivative in (2) you have that b=2 and u=2x. You use the last expression in (2) and you obtain:

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You equal the last result to the value of the slope of the tangent line, because the derivative of a function is also its slope.

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Next, from the last equation you can calculate the value of "a", by doing x=a. Furhtermore, by applying properties of logarithms you obtain:

-2(ln2)2^{-2a}=-1 \\\\2^{2a}=2(ln2)=1.386\\\\log_22^{2a}=log_2(1.386)\\\\2a=\frac{log(1.386)}{log(2)}\\\\a=0.235

With this value you calculate f(a):

f(a)=\frac{1}{2^{2(0.235)}}=0.721

Next, you use the general equation of line:

y-y_o=m(x-x_o)

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0=-x+0.956\\\\x=0.956

hence, the x-intercept of the tangent line is 0.956

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The correct answer is B. s = √81 in. Hope I helped!
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