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3 years ago

14

ou invested 7000 between two accounts paying 4% and 9% annual interest, respectively. If the total interest earned for the year

was $430 how much was invested at each rate? $ nothing was invested at and $ nothing was invested at

1 answer:

lana [24]3 years ago

7 0

9514 1404 393

Answer:

$3000 at 9%
$4000 at 4%

Step-by-step explanation:

Let x represent the amount invested at 9%. Then 7000-x was invested at 4% and the interest earned was ...

9%·x +4%(7000-x) = 430

5%·x +280 = 430 . . . . . . . . . simplify

0.05x = 150 . . . . . . . . . . . subtract 280

x = 3000 . . . . . . . . . . divide by 0.05

$3000 was invested at 9%; $4000 was invested at 4%.

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Let:

<em /> $I \to$ <em> I-Beam</em>

<em /> $d_I \to$ <em> distance between I beam and the bridge</em>

<em /> $b \to$ <em> distance between each I beam</em>

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Given that:

$I = \frac 34 ft\\$

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From the diagram (see attachment), there are: 6 I-beams.

So, the length of the 6 I-beams is:

$L_1 = 6 \times I$

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$L_1 = \frac {18}4$

$L_1 = 4.5ft$

There are 2 I-beams beside the bridge

So, the distance between the 2 I-beams and the bridge is:

$d_1 =2 \times d_I$

$d_1 =2 \times 3ft$

$d_1 =6ft$

There are 5 spaces between the I-beams

So, the length of the total spaces is:

$L_2 = 5 \times b$

$L_2 = 5b$

The total length is:

$Length = L_1 + d_1 + L_2$

So, we have:

$4.5ft + 6ft + 5b = 55ft\ 6in$

Collect like terms

$5b = 55ft\ 6in - 4.5ft - 6ft$

$5b = 44.5ft\ 6in$

Convert inches to feet

$5b = 44.5ft\ + \frac{6}{12}ft$

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$5b = 45ft$

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$b = 9ft$

<em>Hence, the distance (b) between each beam is 9ft.</em>

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This question is incomplete because it lacks the diagram of the right angled triangle. Find attached to this answer the diagram of the right angle triangle.

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Step-by-step explanation:

Looking at the attached diagram, the only way to solve for this is the use of the trigonometric function. The trigonometric function to be used is the cosine function.

From the diagram, we are given

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