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2 years ago

Simplify the following expression: (66)4

Mathematics

1 answer:

lina2011 [118]2 years ago

8 0

Answer:

46656 to the power 4

Step-by-step explanation:

6 to the power 6 = 6 × 6 × 6 × 6 × 6 × 6 = 46656

(46656) to the power 4 = 46656 × 46656 × 46656 × 46656

This answer is undefined, so we will leave it at 46656 to the power 4.

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Prove by mathematical induction that 1+2+3+...+n= n(n+1)/2 please can someone help me with this ASAP. Thanks

Iteru [2.4K]

Let

$P(n):\ 1+2+\ldots+n = \dfrac{n(n+1)}{2}$

In order to prove this by induction, we first need to prove the base case, i.e. prove that P(1) is true:

$P(1):\ 1 = \dfrac{1\cdot 2}{2}=1$

So, the base case is ok. Now, we need to assume $P(n)$ and prove $P(n+1)$ .

$P(n+1)$ states that

$P(n+1):\ 1+2+\ldots+n+(n+1) = \dfrac{(n+1)(n+2)}{2}=\dfrac{n^2+3n+2}{2}$

Since we're assuming $P(n)$ , we can substitute the sum of the first n terms with their expression:

$\underbrace{1+2+\ldots+n}_{P(n)}+n+1 = \dfrac{n(n+1)}{2}+n+1=\dfrac{n(n+1)+2n+2}{2}=\dfrac{n^2+3n+2}{2}$

Which terminates the proof, since we showed that

$P(n+1):\ 1+2+\ldots+n+(n+1) =\dfrac{n^2+3n+2}{2}$

as required

4 0

2 years ago

‼️GEOMETRY‼️

ella [17]

Answer:

A.) 1018 square inches

Step-by-step explanation:

The largest sphere will have a diameter equaling the length of the cube (see picture).

If the side length of the cube is 18 inches, the diameter of the sphere is also 18 inches. Use the surface area formula for a circle:

$SA=4\pi r^2$

For this formula, we need the radius of the sphere. Divide the diameter by 2:

$\frac{18}{2}=9$

The radius is 9 inches. Plug this into the equation:

$SA=4\pi *9^2$

Simplify the equation:

$SA=4\pi *81\\\\SA=324\pi \\\\SA=1017.87$

Round the result to the nearest whole number:

$1017.87$ → $1018$

The surface area is 1,018 inches².

:Done

Picture:

In a 2D version, we can clearly see that if the circle fits snuggly inside of the square, the diameter of a sphere is the same as the length of a side of the cube.

6 0

2 years ago

Miss Hernandez has 17 tomato plants that she wants to plant in Rose she will put two plants and some rolls and one plant and the

Papessa [141]

She can plant 34 plants in all. If you multiply 34 and 2 you will get 34 and I think that is the answer.

5 0

2 years ago

Read 2 more answers

5. Ms. Lee has 220 students in all her classes. If her classes collected 2860 pounds of food, how many meals did each student pr

jarptica [38.1K]

Answer:

Each students provides 13 pounds of meal

Step-by-step explanation:

Total students in Ms. Lee class = 220

Total pounds of food collected = 2,860

how many meals did each student provide?

Meals provided by each student = Total pounds of food collected / total number of students

= 2,860 / 220

= 13 pounds

Each students provides 13 pounds of meal

Note: 1.2 pounds of food equals one meal

1.2 pounds : 1 meal = 13 pounds : x meals

1.2/1 = 13/x

1.2 * x = 1 * 13

1.2x = 13

x = 13 / 1.2

= 10.83 meals

Approximately 11 meals to the nearest number

Note:1 kilogram is 2.2 pounds

1 kg : 2.2 pounds = x kg : 13 pounds

1/2.2 = x / 13

1 * 13 = 2.2 * x

13 = 2.2x

x = 13/2.2

= 5.91 kilogram

Approximately x = 6 kilograms

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2 years ago

Use the strategy of your choice to multiply the following expression.

Digiron [165]

Find answer showing detailed workings in the image

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2 years ago