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3 years ago

Factorise x squared - 12x + 36

Mathematics

1 answer:

slava [35]3 years ago

3 0

Answer:

(x-6)(x-6) or (x-6)^2

Step-by-step explanation:

x^2-12x+36=(x-6)(x-6)

Just find two numbers that when they multiply, you get the third term,

which is 36 in this case. And when they add up, you get the second term,

which is -12 in this case. You can also check the answer by multiplying.

(x-6)(x-6)=x^2-6x-6x+36=x^2-12x+36

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Find the volume of the composite figure to the nearest tenth. Use 3.14 for pi.

Vilka [71]

Given:

In the given fig,

The radius of the cylinder = 15 ft

The height of the cylinder = 26 ft

The height of the cone = 21 ft

The radius of the cone = 15 ft

To find the volume of the cone, the volume of the cylinder and the composite figure.

Formula

The volume of the given composite fig is

$V = V_{1} +V_{2}$

where, $V_{1}$ be the volume of the cone.

$V_{2}$ be the volume of the cylinder.

$V_{1} = \frac{1}{3} \pi r^{2} h$ , r be the radius and h be the height.

$V_{2} = \pi r^{2} h$ , r be the radius and h be the height.

Now,

Putting, r = 15, h = 21 and π = 3.14 we get,

$V_{1} = \frac{1}{3} (3.14)(15^{2} )(21)$ cube ft

$V_{1} = 4945.5$ cube ft

Again,

Putting,

$V_{2} = (3.14)(15^{2} )(26)$ cube ft

$V_{2} = 18369$ cube ft

Therefore, the volume of the composite fig = (4945.5+18369) cube ft = 23314.5 cube ft

Hence,

a) The volume of the cone is 4945.5 cube ft.

b) The volume of the cylinder is 18369 cube ft.

c) The volume of the composite figure is 23314.5 cube ft.

3 0

3 years ago

Circle A and circle B are congruent. CD is a cord of both circles. if AB = 24 inches in the radius is 13 inches how long is CD A

Nitella [24]

Option A

Length of CD is 10 inches

Solution:

The diagram is attached below

Given that, Circle A and circle B are congruent

CD is a cord of both circles

AB = 24 inches

Radius = 13 inches

To find: length of CD

Draw a straight line connecting A and C

AC represents the radius of circle. Also given that radius is 13 inches, So AC = 13 inches

Given in question that AB = 24 inches

Therefore from figure, AO = AB/2 = 24/2 = 12

AO = 12

Let "b" be the length of CO

Therefore, CD = CO + OD = b + b

AOC forms a triangle, so we can use pythogoras theorem

Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

By above definition for triangle AOC

$AC^2 = AO^2 + OC^2$

Substituting AC = 13 and AO = 12 and OC = b

$13^2 = 12^2 + b^2\\\\b^2 = 169 - 144\\\\b^2 = 25\\\\b = 5$

Thus length of CD is:

CD = b + b = 5 + 5 = 10

Thus length of CD is 10 inches

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A pebble is dropped from a bridge into a river. Its height, h meters, above the river t seconds after it is released is modelled

snow_tiger [21]

I’m not sure but I think the answer is 7

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patriot [66]

Answer:

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Step-by-step explanation:

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padilas [110]

Answer:

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3 years ago