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Vesna [10]
2 years ago
7

A convex lens has a diameter of 30 mm and a depth of 5 mm at the center. How far from the vertex is the focus?

Mathematics
1 answer:
natima [27]2 years ago
8 0
The formula for determining the distance of the focus from the vertex is as follows,

     f = x² / 4a

where f is focus, x is the radius (half the value of diameter), and a is the depth. Substituting the known values to the given equation,

   f = (30/2 mm)² / (4)(5 mm)

    f = 11.25 mm

<em>ANSWER: 11.25 mm</em>
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Which equation could be used to calculate the sum of the geometric series?
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A

Step-by-step explanation:

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2 years ago
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Find the range of y=3/2cos4x-1
MrRissso [65]

Answer:

Range = [- 2.5, 0.5] = [ - 5/2, 1/2]

Step-by-step explanation:

Smallest value of cos α = - 1,

largest value of cos α = 1.

When cos 4x = - 1,  y=3/2cos4x-1 = 3/2*(-1) - 1 = - 5/2 = - 2 1/2 = - 2.5

When cos 4x = 1,  y=3/2cos4x-1 = 3/2*1 - 1 = 1/2 = 0.5

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5 0
2 years ago
What is the minimum number of points needed to determine the equation of a line containing those points?. The choices are the fo
vodomira [7]
I believe the correct answer among the choice presented above is the second option. The minimum number of points needed to determine the equation of a line containing those points is two. This is because two points is also needed to make or define a line.
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2 years ago
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Triangle XYZ is rotated to create the image triangle X'Y'Z'.
Solnce55 [7]

Answer:

The correct option is;

R0, 180°

Step-by-step explanation:

The coordinates of ΔXYZ are given as follows;

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The coordinates of ΔX'Y'Z' are given as follows;

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Whereby, the coordinates of the point Y' is (-1, -2), we have the rule that describe the transformation of ΔXYZ to ΔX'Y'Z', given as follows

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7 0
2 years ago
Caleb has 20 more books than Danica. If Caleb gives Danica half of his books, Danica will have 4 more books than Caleb. How many
wariber [46]

Answer:

Option E: 24.

Step-by-step explanation:

When Caleb (C) has 20 more books than Danica (D), we have:

C = 20 + D   (1)

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C' = C - \frac{C}{2}   (2)

Danica will have 4 more books than Caleb, so:

D' = D + \frac{C}{2}     (3)    

Also we have that:

D' = C' + 4   (4)  

By entering equation (2) and equation (3) into equation (4) we have:

D + \frac{C}{2} = C - \frac{C}{2} + 4   (5)

From (1) we have:

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By entering (6) into (5):

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And, from (6):

D = C - 20 = 24 - 20 = 4  

Therefore, the correct option is E, Caleb had to start with 24 books.

I hope it helps you!          

3 0
2 years ago
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