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vlabodo [156]
3 years ago
12

4 questions 20 points

Mathematics
1 answer:
Dvinal [7]3 years ago
3 0
1. Cross multiply
35x = 5(11)
35x = 55
Divide both sides by 35
x = 55/35
x = 11/7

2.  (x - 2)/x = 3/8
Cross multiply
3x = 8(x - 2)
3x = 8x - 16
Subtract 8x from both sides
-5x = -16
divide both sides by -5
x = -16/-5
x = 16/5 OR  3 1/5

3.  (a + 1)/(a - 1) = 5/6
cross multiply
6(a + 1) = 5(a - 1)
distribute
6a + 6 = 5a - 5
subtract 5a from both sides
a + 6 = -5
subtract 6 from both sides
a = -11

4.  (1/3)x - 4 = (2/3)x + 6
multiply each term by 3 to clear the fractions
x - 12 = 2x + 18
subtract x from both sides
-12 = x + 18
subtract 18 from both sides
-30 = x


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\frac{1+\tan x}{\sin x+\cos x}=\sec x is proved

<h3><u>Solution:</u></h3>

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\frac{1+\tan x}{\sin x+\cos x}=\sec x  ------- (1)

First we will simplify the LHS and then compare it with RHS

\text { L. H.S }=\frac{1+\tan x}{\sin x+\cos x}  ------ (2)

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=\frac{1+\frac{\sin x}{\cos x}}{\sin x+\cos x}

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Solve the initial-value problem<br><br> y' = x^4 - \frac{1}{x}y, y(1) = 1.
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