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alekssr [168]
3 years ago
12

Joseph invested $16,000 in an account paying an interest rate of 5.7% compounded

Mathematics
2 answers:
Natasha_Volkova [10]3 years ago
5 0

Answer: 34767.2

Step-by-step explanation:

given p = $16,000, n = 14 years, y = 5.7%

amount in bank after 14 years = p ( 1 + </100)

= 16,000 (1 + 5.7/ 100) 14

= 34767.2

Taya2010 [7]3 years ago
3 0

Answer:

  • $35537.51

Step-by-step explanation:

<u>Required formula:</u>

  • P(t) = P₀e^{rt}

<u>Substitute values and solve:</u>

  • P(14) = 16000e^{0.057*14}
  • P(14) = 35537.51
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\bold{\huge{\orange{\underline{ Solution }}}}

<h3><u>Given </u><u>:</u><u>-</u></h3>

  • <u>We </u><u>have </u><u>given </u><u>in </u><u>the </u><u>question </u><u>that</u><u>, </u><u> </u><u>Robin </u><u>is </u><u>flying </u><u>a </u><u>kite</u><u>. </u>
  • <u>She </u><u>ties </u><u>the </u><u>5</u><u>0</u><u> </u><u>foot </u><u>kite </u><u>string </u><u>to </u><u>the </u><u>ground </u><u>.</u>
  • <u>The</u><u> </u><u>kite </u><u>is </u><u>flying </u><u>at </u><u>4</u><u>0</u><u> </u><u>feet </u><u>high </u>

<h3><u>To </u><u>Find </u><u>:</u><u>-</u></h3>

  • <u>We </u><u>have </u><u>to </u><u>find </u><u>the </u><u>measure </u><u>of </u><u>the </u><u>angle </u><u>the </u><u>string </u><u>forms </u><u>with </u><u>the </u><u>group </u><u>that </u><u>is </u><u>angle </u><u>of </u><u>elevation</u><u>. </u>

<h3><u>Let's </u><u>Begin </u><u>:</u><u>-</u></h3>

<u>According </u><u>to </u><u>the </u><u>given</u><u> </u><u>question</u><u>, </u>

  • Hypotenuse AC ( Distance of string from the ground) = 50 ft.
  • Perpendicular height AB ( Distance of the kite from the ground) = 40 ft.

<h3><u>Therefore</u><u>, </u></h3>

<u>By </u><u>using </u><u>trigonometric </u><u>ratios</u><u>,</u><u> </u>

{ \bold{\pink{ Sin Φ = }}{\bold{\pink{\dfrac{Perpendicular}{Hypotenuse }}}}

\bold{\red{ Cos Φ = }}{\bold{\red{\dfrac{Base}{Hypotenuse }}}}

\bold{\purple{ Sin Φ = }}{\bold{\purple{\dfrac{Perpendicular}{Base }}}} }

<u>The </u><u>Angle </u><u>of </u><u>elevation </u><u>will </u><u>be </u>

<u>[</u><u> </u><u>The </u><u>angle </u><u>that </u><u>is </u><u>formed </u><u>between </u><u>the </u><u>line </u><u>of </u><u>sight </u><u>and </u><u>base </u><u>of </u><u>the </u><u>triangle </u><u>is </u><u>called </u><u>angle </u><u>of </u><u>elevation </u><u>]</u>

\bold{\pink{Sin Φ = }}{\bold{\pink{\dfrac{AB}{AC }}}}

\sf{ Sin Φ = }{\sf{\dfrac{40}{50 }}}

\sf{ Sin Φ = }{\sf{\dfrac{4}{5}}}

\sf{ Sin Φ = 0.8 }

\bold{\green{  Φ = 45.83° }}

Hence, The measure of the angle the string forms with the ground is 45.83° .

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