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3 years ago

Here are the first five terms of a sequence:

Mathematics

1 answer:

levacccp [35]3 years ago

3 0

Answer:

2n² + n + 1

Step-by-step explanation:

4, 11, 22, 37

Difference between: 7, 11, 15

7,11,15 are all 4 apart. You divide the 4 by 2 to get 2n² (it is squared because you needed a second level to find the difference)

And then I knew you needed to put the original 2n² with the sequence we are trying to work out.

2, 8, 18, 32

4, 11, 22, 37

difference between the 2 sequences 2, 3 ,4 ,5 (which all has a difference of 1) which means 1n or just n.

So that's 2n² + n

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Write 7.75 x 10^-3 in standard notation

Natasha_Volkova [10]

Answer:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

7.75 × 10^−3

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3 years ago

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What is the inverse of the function

Angelina_Jolie [31]

Answer:

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3 years ago

The volume of a right circular cone is 2,279.64 in cubed. If the height of the cone is 18 in, what is the diameter of the cone?

Aleksandr [31]

ANSWER

A. 22 in

EXPLANATION

The volume of a cone is calculated using the formula:

$Volume = \frac{1}{3} \times \pi {r}^{2} h$

It was given that: the volume is 2,279.64 in³

The height of the cylinder is also given as: h=18 in.

We substitute, the given values into the formula to get:

$2279.64= \frac{1}{3} \times (3.14) \times {r}^{2} \times 18$

$2279.64= 18.84 {r}^{2}$

${r}^{2} = \frac{2279.64}{18.84}$

${r}^{2} = 121$

We take positive square root to get;

$r = \sqrt{121}$

$r = 11in$

Therefore the diameter is 2(11) which is equal to 22 inches.

5 0

3 years ago

How do I put y=90-15x in standard form

lisabon 2012 [21]

The standard form: Ax + By = C

y = 90 - 15x <em>add 15x to both sides</em>

8 0

3 years ago

The length of a rectangle is 6 more than twice the width. if the area is 40 cm^2, find the length and breadth of the rectangle

ra1l [238]

Answer: 3.217 & 12.434

Step-by-step explanation:

If we use <em>w</em> to represent the width, the length will be 6 more than 2 times w.

Hence, the length is $2w+6$ .

The area of a rectangle would be its length times its width, so let's make an equation to represent it's area.

$A=w(2w+6)$

We can also substitute 40 in for A as it's given in the question.

$40 = w(2w+6)$

Distributing <em>w</em> by multiplying it by both terms in the parentheses, we get

$40 = 2w^2+6w$

We can make the equation simpler by dividing both sides by 2.

$20 = w^2+3w$

Subtracting both sides by 20 will make the left-hand side 0.

$0=w^2+3w-20$

Now that we have put this <em>quadratic equation</em> into standard form (ax²+bx+c), we can find its solutions using the quadratic formula.

For reference, the quadratic formula is

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

In this case, a is 1, b is 3, and c is -20.

Substituting, we get

$w=\frac{-3\pm\sqrt{3^2-4(1)(-20)}}{2(1)}$

$w= \frac{-3\pm\sqrt{9+80}}{2}$

$w=\frac{-3+\sqrt{89}}{2}\hspace{0.1cm}or\hspace{0.1cm}\frac{-3-\sqrt{89}}{2}$

Since the second solution results in a negative number, it cannot be the length of w.

$w=\frac{-3+\sqrt{89}}{2}\approx3.217$

The width/breadth of the rectangle is 3.217 cm.

To calculate the length, let's substitute the width into the expression for the length:

$l=2(3.217)+6$

$l=12.434$

The length of this rectangle is 12.434 cm.

6 0

2 years ago