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3 years ago

What is 54 divided 6 equal blank times 3

Mathematics

1 answer:

Nonamiya [84]3 years ago

5 0

$54:6=\fbox{3}\times3\\\\Check:\\\\54:6=9\\\\3\times3=9$

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A lampshade has a height of 12cm and upper and lower diameters of 10cm and 20cm A)what area of material is required to cover tha

netineya [11]

Answer:

$(a)\ Area = 195\pi$

$(b)\ Volume = 700\pi$

Step-by-step explanation:

Given

$h = 12$

$d_1 = 10$ --- lower diameter

$d_2 = 20$ --- upper diameter

Solving (a): The curved surface area

This is calculated as:

$Area = \pi l(r_1 + r_2)$

Where

$r_1 = 0.5 * d_1 = 0.5 * 10 = 5$ --- lower radius

$r_2 = 0.5 * d_2 = 0.5 * 20 = 10$ --- upper radius

And

$l = \sqrt{h^2 + (r_1 - r_2)^2$ ---- l represents the slant height of the frustrum

$l = \sqrt{12^2 + (5 - 10)^2$

$l = \sqrt{12^2 + (-5)^2$

$l = \sqrt{144 + 25$

$l = \sqrt{169$

$l = 13$

So, we have:

$Area = \pi l(r_1 + r_2)$

$Area = \pi * 13(5 + 10)$

$Area = \pi * 13(15)$

$Area = 195\pi$

Solving (b): The volume

This is calculated as:

$Volume = \frac{1}{3}\pi * h * (r_1^2 + r_2^2 + (r_1 * r_2))$

This gives:

$Volume = \frac{1}{3}\pi * 12 * (5^2 + 10^2 + (5 * 10))$

$Volume = \frac{1}{3}\pi * 12 * (25 + 100 + (50))$

$Volume = \frac{1}{3}\pi * 12 * (175)$

$Volume = \pi *4 * 175$

$Volume = 700\pi$

6 0

2 years ago

Which is the completely factored form of 12x^3-60x^2+4x-20

Shkiper50 [21]

Answer:

(12x²+4)(x-5)

Step-by-step explanation:

To factor the expression factor by grouping.

(12x³ - 60x²) + (4x - 20)

12x²(x - 5) 4(x-5)

(12x²+4)(x-5)

6 0

3 years ago

What is a scale factor?

Blababa [14]

Answer:

Here is some helpful information from my mini lessons.

Step-by-step explanation:

If two objects have the same shape, they are called "similar." When two figures are similar, the ratios of the lengths of their corresponding sides are equal. To determine if the triangles shown are similar, compare their corresponding sides. Here you'll learn that the ratio of the perimeters of similar figures is equal to their scale factor and that the ratio of their areas is equal to the square of their scale factor. If two polygons are similar, then the ratio of the lengths of any two corresponding sides is called the scale factor. This means that the ratio of all parts of a polygon is the same as the ratio of the sides.

3 0

2 years ago

Iven that f(x) = 5x − 10 and g(x) = x + 3, solve for f(g(x)) when x = −1

irina1246 [14]

G(-1) = -1+3
= 2
F(2) = 5(2) - 10
= 0

5 0

3 years ago

A circle has a diameter of 5. What is the area and circumference.

Aloiza [94]

Answer:

Area= 19.63 units squared Circumference= 15.71 units

Step-by-step explanation:

Area= π r ^2

Circumference= 2π r

3 0

3 years ago

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