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Bess [88]
3 years ago
14

You split $2000 between two savings accounts. Account a pays 2% annual interest and account b pays 5% annual interest. After one

year, you have earned a total of $77.50 in interest. How much did you invest in each account?
Mathematics
1 answer:
sdas [7]3 years ago
8 0
0.05x+0.02(2000-x)=77.5
0.05x+40-0.02x=77.5
(0.05-0.02)x=77.5-40
0.03x=37.5
X=37.5/0.03=1250 at 2%
2000-1250=750 at 5%
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Answer:

29 feet in length, 5 feet in width and 12 feet in height

Step-by-step explanation:

We have that for the volume of a quadrangular prism is:

V = l * w * h

Ie length times width times height

In this case, the height is determined by the squares that you put in each corner, taking into account that a square has all the same sides, the height is 12 inches. h = 12

they tell us that the length is 24 inches more than the width, that is, l = 24 + w

replacing we have:

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3 years ago
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A 140 kg camera is suspended by two wires over a 40 metre wide football field to get shots of the action from above. At one poin
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Answer:

Please red the answer below

Step-by-step explanation:

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T2: tension of the second cable = 800N

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θ2: angle between the horizontal and the first cable

For the y component you have:

T_1sin\theta_1+T_2sin\theta_2-W=0               (2)

W: weight of the camera = Mg = (140kg)(9.8m/s^2) = 1372N

You can squared both equations (1) and (2) and the sum the two equations:

T_1^2cos^2\theta_1=T_2^2cos^2\theta_2\\\\T_1^2sin^2\theta_1=T_2^2sin^2\theta_2-2WT_2sin\theta_2+W^2

Then, you sum the equations:

T_1^2(cos^2\theta_1+sin^2\theta_1)=T_2^2(sin^2\theta_2+cos^2\theta_2)-2Wsin\theta_2+W^2        (3)

Next, you use the following identity:

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T_1^2=T_2^2-2WT_2sin\theta_2+W^2\\\\sin\theta_2=\frac{T_2^2-T_1^2+W^2}{2WT_2}=\frac{(800N)^2-(1500)^2+(1372N)^2}{2(800N)(1372N)}=0.066\\\\\theta_2=sin^{-1}0.066=27.23\°

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l_1cos\theta_1=40-d\\\\l_2cos\theta_2=d\\\\

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By using the cosine law you can fins a system of equation and then you can calculate the values of l1 and l2.

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