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1 year 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?

1 answer:

natima [27]1 year 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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Find the limits of integration ly, uy, lx, ux, lz, uz (some of which will involve variables x,y,z) so that ∫uyly∫uzlz∫uxlxdxdzdy

motikmotik

Answer:

Hello your question is incomplete attached below is the complete question

Ix = 0 Ux = $\sqrt{y-9z^2}$

Iz = 0 Uz = $\frac{\sqrt{y} }{3}$

Iy = 5 Uy = 10

Step-by-step explanation:

Ix = 0 Ux = $\sqrt{y-9z^2}$

Iz = 0 Uz = $\frac{\sqrt{y} }{3}$

Iy = 5 Uy = 10

attached below is the detailed solution

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1 year ago

(p²qr + pq²r + pqr²)(-pq + qr - pr)<br>Please solve this problem as soon as possible.

Marta_Voda [28]

Answer:

−p3q2r−p3qr2−p2q3r−p2q2r2−p2qr3+pq3r2+pq2r3

Step-by-step explanation:

(p2qr+pq2r+pqr2)((−p)(q)+qr+−pr)

(p2qr)((−p)(q))+(p2qr)(qr)+(p2qr)(−pr)+(pq2r)((−p)(q))+(pq2r)(qr)+(pq2r)(−pr)+(pqr2)((−p)(q))+(pqr2)(qr)+(pqr2)(−pr)

−p3q2r+p2q2r2−p3qr2−p2q3r+pq3r2−p2q2r2−p2q2r2+pq2r3−p2qr3

−p3q2r−p3qr2−p2q3r−p2q2r2−p2qr3+pq3r2+pq2r3

4 0

1 year ago

Read 2 more answers

Drag each expression to show whether it is equivalent to (5⋅9x)+(5⋅1), 45x+15, or 15(3x−1).

JulijaS [17]

Part A: Option e: $5(9 x+1)$

Option f: $45 x+5$

Part B: Option c: $15(3 x+1)$

Option d: $(5 \cdot 9 x)+(5 \cdot 3)$

Part C: Option a: $(5 \cdot 9 x)-(5 \cdot 3)$

Option b: $45 x-15$

Explanation:

Part A: The equation is $(5 \cdot 9 x)+(5 \cdot 1)$

Simplifying, we have,

$45x+5$

Taking the term 5 common out, we have,

$5(9 x+1)$

Thus, the above two expressions are equivalent to the equation $(5 \cdot 9 x)+(5 \cdot 1)$ .

Hence, Option e and Option f are the correct answers.

Part B: The equation is $45 x+15$

Taking the term 15 common out, we have,

$15(3 x+1)$

Also, the equation can be rewritten as,

$(5 \cdot 9 x)+(5 \cdot 3)$

Thus, the above two expressions are equivalent to the equation $45 x+15$

Hence, Option c and Option d are the correct answers.

Part C: The equation is $15(3 x-1)$

Multiplying, we have,

$45 x-15$

The above expression can be rewritten as,

$(5 \cdot 9 x)-(5 \cdot 3)$

Thus, the above two expressions are equivalent to the equation $15(3 x-1)$

Hence, Option a and Option b are the correct answers.

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1 year ago

Which number produces a rational number when multiplied by 0.5

ivanzaharov [21]

10 is your answer because it is a terminating or repeating decimals

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1 year ago

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Sophie [7]

Answer:

Step-by-step explanation:

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1 year ago