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My name is Ann [436]
3 years ago
8

What is the midpoint of the vertical line segment graphed below? (2, 4), (2, -9) A. (4, -5). B. (2, -5/2). C. (2, -5). D. (4, 5/

2)

Mathematics
1 answer:
omeli [17]3 years ago
8 0

Answer:

B. (2, -\frac{5}{2})

Step-by-step explanation:

Given:

(2, 4) and (2, -9)

Required:

Midpoint of the vertical line with the above endpoints

Solution:

Apply the midpoint formula, which is:

M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})

Where,

(2, 4) = (x_1, y_1)

(2, -9) = (x_2, y_2)

Plug in the values into the equation:

M(\frac{2 + 2}{2}, \frac{4 + (-9)}{2})

M(\frac{4}{2}, \frac{-5}{2})

M(2, -\frac{5}{2})

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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:

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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

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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)}

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8 0
3 years ago
When solving negative one over eight (x + 35) = −7, what is the correct sequence of operations?
Maksim231197 [3]
<span>The answer is:  [C]:  
__________________________________________________________
Multiply each side by −8, subtract 35 from each side.

___________________________________________________________
Explanation:
___________________________
Given: You have (-1/8)*(x + 35) = -7
________________________________________
Note that all the answer choices given start with: "Multiply each side by...."; 
</span>____________________
Given the choices, multiplying EACH SIDE of the equation by "(-8)" would make sense, since doing would cancel the "(-1/8)" on the "right-hand side" of the equation above to a "1" (i.e "cancel out" that ("-1/8") value); and would result in making the "right side" of the equation above ("-7") a positive integer number. 
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Subtract: "(35)" from each side of the question [hence the answer choice] to isolate "x" on one side of the equation; and to solve for "x".
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6 0
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