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choli [55]
3 years ago
12

1.5(−2.4+(−5.3)) ​= ?

Mathematics
2 answers:
ddd [48]3 years ago
4 0
1.5(-2.4+(-5.3))=1.5(-2.4-5.3)=1.5(-7.7)=-11.55
FinnZ [79.3K]3 years ago
3 0
-11.55 is the answer. 
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Step-by-step explanation:

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If sinA+cosecA=3 find the value of sin2A+cosec2A​
Irina18 [472]

Answer:

\sin 2A + \csc 2A = 2.122

Step-by-step explanation:

Let f(A) = \sin A + \csc A, we proceed to transform the expression into an equivalent form of sines and cosines by means of the following trigonometrical identity:

\csc A = \frac{1}{\sin A} (1)

\sin^{2}A +\cos^{2}A = 1 (2)

Now we perform the operations: f(A) = 3

\sin A + \csc A = 3

\sin A + \frac{1}{\sin A} = 3

\sin ^{2}A + 1 = 3\cdot \sin A

\sin^{2}A -3\cdot \sin A +1 = 0 (3)

By the quadratic formula, we find the following solutions:

\sin A_{1} \approx 2.618 and \sin A_{2} \approx 0.382

Since sine is a bounded function between -1 and 1, the only solution that is mathematically reasonable is:

\sin A \approx 0.382

By means of inverse trigonometrical function, we get the value associate of the function in sexagesimal degrees:

A \approx 22.457^{\circ}

Then, the values of the cosine associated with that angle is:

\cos A \approx 0.924

Now, we have that f(A) = \sin 2A +\csc2A, we proceed to transform the expression into an equivalent form with sines and cosines. The following trignometrical identities are used:

\sin 2A = 2\cdot \sin A\cdot \cos A (4)

\csc 2A = \frac{1}{\sin 2A} (5)

f(A) = \sin 2A + \csc 2A

f(A) = \sin 2A +  \frac{1}{\sin 2A}

f(A) = \frac{\sin^{2} 2A+1}{\sin 2A}

f(A) = \frac{4\cdot \sin^{2}A\cdot \cos^{2}A+1}{2\cdot \sin A \cdot \cos A}

If we know that \sin A \approx 0.382 and \cos A \approx 0.924, then the value of the function is:

f(A) = \frac{4\cdot (0.382)^{2}\cdot (0.924)^{2}+1}{2\cdot (0.382)\cdot (0.924)}

f(A) = 2.122

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3 years ago
A square and a triangle have equal perimeters. The square has a perimeter of 4(x + 9), and the triangle has a perimeter of 3(x +
cricket20 [7]

Answer: x=36

4(x+9)=3(x+24)

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