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svet-max [94.6K]
3 years ago
10

John is 30 years old. He will receive two payments of $2500 each. The first payment will be an unknown number of years in the fu

ture. The second payment will be five years after the first payment. At an annual effective interest rate of I=5%, the present value of the two payments is $2606. Determine at what age John will receive the second payment.
Mathematics
1 answer:
Bogdan [553]3 years ago
7 0

Answer:

16 years

Step-by-step explanation:

Let us assume that he would received the first payment after t years

So

The following formula should be used

PV = P ÷ (1 + r)^t + P ÷ (1 + r)^t+5

$2,606 = $2,500 ÷ (1 + 0.05)^t + $2,500 ÷ (1 + 0.05)^t + 5

$2,606 = $2,500 ÷ 1.05^t (1 + 1 ÷ (1.05)^5)

1.05^t = $2,500 ÷ $2,606 (1.7835) = 1.71098

t = ln(1.71098) ÷ ln(1.05)

= 11

Therefore he would be received the second payment after

= 11 + 5

= 16 years

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ollegr [7]

Answer:

CE = 21.2

Step-by-step explanation:

CE = CD + DE = 14 + 7.2 = 21.2

7 0
2 years ago
NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h ( t ) = − 4.
Oliga [24]

Answer:

\displaystyle 1)48.2    \:  \: \text{sec}

\rm \displaystyle  2)3021.6 \: m

Step-by-step explanation:

<h3>Question-1:</h3>

so when <u>flash down</u><u> </u>occurs the rocket will be in the ground in other words the elevation(height) from ground level will be 0 therefore,

to figure out the time of flash down we can set h(t) to 0 by doing so we obtain:

\displaystyle  - 4.9 {t}^{2}  + 229t + 346 = 0

to solve the equation can consider the quadratic formula given by

\displaystyle x =  \frac{ - b \pm  \sqrt{ {b}^{2} - 4 ac} }{2a}

so let our a,b and c be -4.9,229 and 346 Thus substitute:

\rm\displaystyle t =  \frac{ - (229) \pm  \sqrt{ {229}^{2} - 4.( - 4.9)(346)} }{2.( - 4.9)}

remove parentheses:

\rm\displaystyle t =  \frac{ - 229 \pm  \sqrt{ {229}^{2} - 4.( - 4.9)(346)} }{2.( - 4.9)}

simplify square:

\rm\displaystyle t =  \frac{ - 229 \pm  \sqrt{ 52441- 4( - 4.9)(346)} }{2.( - 4.9)}

simplify multiplication:

\rm\displaystyle t =  \frac{ - 229 \pm  \sqrt{ 52441- 6781.6} }{ - 9.8}

simplify Substraction:

\rm\displaystyle t =  \frac{ - 229 \pm  \sqrt{ 45659.4} }{ - 9.8}

by simplifying we acquire:

\displaystyle t = 48.2  \:  \:  \: \text{and} \quad  - 1.5

since time can't be negative

\displaystyle t = 48.2

hence,

at <u>4</u><u>8</u><u>.</u><u>2</u><u> </u>seconds splashdown occurs

<h3>Question-2:</h3>

to figure out the maximum height we have to figure out the maximum Time first in that case the following formula can be considered

\displaystyle x _{  \text{max}} =  \frac{ - b}{2a}

let a and b be -4.9 and 229 respectively thus substitute:

\displaystyle t _{  \text{max}} =  \frac{ - 229}{2( - 4.9)}

simplify which yields:

\displaystyle t _{  \text{max}} =  23.4

now plug in the maximum t to the function:

\rm \displaystyle  h(23.4)- 4.9 {(23.4)}^{2}  + 229(23.4)+ 346

simplify:

\rm \displaystyle  h(23.4)  =  3021.6

hence,

about <u>3</u><u>0</u><u>2</u><u>1</u><u>.</u><u>6</u><u> </u>meters high above sea-level the rocket gets at its peak?

5 0
2 years ago
Can someone please help me :)
gavmur [86]

Answer:

<em>90 degree</em>

Step-by-step explanation:

Three points A, B, and C are added and shown in attached picture.

As the property of inscribed angle in circle:

angle BAC = (1/2) x 88 = 44 deg

As the property of complement angle:

angle ABC = 180 - 89 = 91 deg

As the property of sum of three angles in a triangle:

angle ACB + angle ABC + angle BAC = 180 deg

=> angle ACB = 180 - angle ABC - angle BAC = 180 - 44 - 91 = 45 deg

One more time, we use the property of inscribed angle in circle:

x = 2 x angle ACB = 2 x 45 = 90 deg

Hope this helps!

7 0
3 years ago
A recipe for cookies uses ½ cup of sugar for every 1 cup of flour. How much flour would you need to add to 1 ¾ cups of sugar so
kherson [118]

Answer:

2 1/4

Step-by-step explanation:

1 3/4 = 7/4

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3 years ago
Can someone answer my questions please ._.
tekilochka [14]

Answer:

wheres the question?

Step-by-step explanation:

6 0
2 years ago
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