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1 year ago

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:

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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How to factorise 5h^2-12hg

bonufazy [111]

Answer:

$h(5h-12g)$

Step-by-step explanation:

$5h^2-12hg$

When we factor expressions, we look for factors within the terms that are alike, or in other words, we look for common factors. Here, $5h^2$ and $12hg$ only have one common factor: $h$ . Therefore, to factorize this expression, divide both terms by $h$ .

$= h(\frac{5h^2}{h}-\frac{12hg}{h} )\\= h(5h-12g)$

Now, we've "carried" $h$ out of the expression and have therefore factored it.

I hope this helps!

7 0

1 year ago

One state leads the country in tart cherry production, producing 74 out of every 100 tart cherries each year.

Anarel [89]

A. The percent of cherries that are produced in the state is calculated by dividing the number of cherries produced in the state by the total number of cherries and multiplying the quotient by 100%.
r = (74 / 100) x 100% = 74%

B. The percent of cherries not produced in the state is equal to difference of the 100 and the answer in letter A. This is shown below.
s = 100% - 74%
s = 26%.

3 0

1 year ago

The formula that relates the length of a ladder, L, that leans against a wall with distance d from the base of the wall and the

Ulleksa [173]

Answer:

Step-by-step explanation:

The formula that relates the length of a ladder, L, that leans against a wall with distance d from the base of the wall and the height h that the ladder reaches up the wall is L = StartRoot d squared + h squared EndRoot. What height on the wall will a 15-foot ladder reach if it is placed 3.5 feet from the base of a wall?

L = √d² + h²

4 0

1 year ago

Read 2 more answers

The total length of two ribbons is 13 meters. If one ribbion is 7 5/8 meters long what is the length of the other ribbon

Liono4ka [1.6K]

Perhaps the easiest way to solve this problem is to convert 13 into a fraction that has the same denominator as 7 5/8.
Convert both to improper fractions:
7 5/8 turns into 61/8, and
13 turns into 104/8.

Then, subtract 61/8 from 104/8:
104/8-61/8=43/8.
Simplify (mixed fraction):
5 3/8.

The second ribbon has a length of 5 3/8 meters.

5 0

1 year ago

Read 2 more answers

Two cross sections of a right hexagonal pyramid are obtained by cutting the pyramid with planes parallel to the hexagonal base.

Tanya [424]

Answer:

The larger cross section is 24 meters away from the apex.

Step-by-step explanation:

The cross section of a right hexagonal pyramid is a hexagon; therefore, let us first get some things clear about a hexagon.

The length of the side of the hexagon is equal to the radius of the circle that inscribes it.

The area is

$A=\frac{3\sqrt{3} }{2} r^2$

Where $r$ is the radius of the inscribing circle (or the length of side of the hexagon).

Now we are given the areas of the two cross sections of the right hexagonal pyramid: $A_1=216\:ft^2\: \:\:\:A_2=486\:ft^2$

From these areas we find the radius of the hexagons:

$r_1=\sqrt{\frac{2A_1}{3\sqrt{3} } } =\sqrt{\frac{2*216}{3\sqrt{3} } }=\boxed{9.12ft}$

$r_2=\sqrt{\frac{2A_2}{3\sqrt{3} } } =\sqrt{\frac{2*486}{3\sqrt{3} } }=\boxed{13.68ft}$

Now when we look at the right hexagonal pyramid from the sides ( as shown in the figure attached ), we see that $r_1$ $r_2$ form similar triangles with length $H$

Therefore we have:

$\frac{H-8}{r_1} =\frac{H}{r_2}$

We put in the numerical values of $r_1$ , $r_2$ and solve for $H$ :

$\boxed{H=\frac{8r_2}{r_2-r_1} =\frac{8*13.677}{13.68-9.12} =24\:feet.}$

8 0

1 year ago