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Alexxx [7]
3 years ago
10

Help my sister step by step show work so she can understand because I forgot how to do this stuff

Mathematics
1 answer:
nikdorinn [45]3 years ago
8 0
The volume of this shape is 960

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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

8 0
3 years ago
Ok no one at my school can get it, who has the crown to get this right 1st out of my whole class lolllll plus ill give brainiest
FrozenT [24]

Answer:

A.y=(t-1998)+b

B. 13,720 Vehicles

Step-by-step explanation:

N/A

7 0
3 years ago
Help me please on this question .....!.!.!.!.!.!.!.!.!.!.
Zigmanuir [339]

If you look through the chart, you'll see that in each column,
the amount of money donated is 1/5 the number of lunch
specials sold.

The equation is:

Donation amount = (1/5) · (lunch specials sold) .

The constant of proportionality in money per lunch special sold
is $1/5 or 20 cents.
7 0
3 years ago
Tickets to a science museum cost $19.95 each. there is a $3 charge for each order no matter how many tickets are ordered. write
cestrela7 [59]
$19.95x +$3
x stands for number of tickets purchased.
$19.95(5) + $3
$99.75 + $3
$102.75 for 5 tickets
5 0
3 years ago
Read 2 more answers
Twenty-seven minus 2/3 of a number (x) is not more than 36. What is the number?
Nuetrik [128]

 

The number is  D. xs-6

4 0
3 years ago
Read 2 more answers
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