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2 years ago

Find the length of a 90° arc of a circle with a diameter of 10 m

Mathematics

1 answer:

Ray Of Light [21]2 years ago

6 0

Answer:

7.85 m (3 significant figures)

Step-by-step explanation:

Formula: arc length = $2\pi r(\frac{\theta}{360} )$

The radius of a circle is half the diameter, so r = 10 ÷ 2 = 5

Therefore, arc length = 2 x $\pi$ x 5 x $(\frac{90}{360} )$

= $\frac{5}{2}\pi$

= 7.853981634...

= 7.85 m (3 significant figures)

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Find x so that x, X +2, X'+3 are the first three terms of a geometric sequence. Then find the 5" term of the

velikii [3]

Answer:

The fifth term is -1/4.

Step-by-step explanation:

We know that the first three terms of the geometric sequence is x, x + 2, and x + 3.

So, our first term is x.

Then our second term will be our first term multiplied by the common ratio r. So:

$x+2=xr$

And our third term will be our first term multiplied by the common ratio r twice. Therefore:

$x+3=xr^2$

Solve for x. From the second term, we can divide both sides by x:

$\displaystyle r=\frac{x+2}{x}$

Substitute this into the third equation:

$\displaystyle x+3=x\Big(\frac{x+2}{x}\Big)^2$

Square:

$\displaystyle x+3 = x\Big( \frac{(x+2)^2}{x^2} \Big)$

Simplify:

$\displaystyle x+3=\frac{(x+2)^2}{x}$

We can multiply both sides by x:

$x(x+3)=(x+2)^2$

Expand:

$x^2+3x=x^2+4x+4$

Isolate the x:

$-x=4$

Hence, our first term is:

$x=-4$

Then our common ratio r is:

$\displaystyle r=\frac{(-4)+2}{-4}=\frac{-2}{-4}=\frac{1}{2}$

So, our first term is -4 and our common ratio is 1/2.

Then our sequence will be -4, -2, -1, -1/2, -1/4.

You can verify that the first three terms indeed follow the pattern of x, x + 2, and x + 3.

So, our fifth term is -1/4.

4 0

3 years ago

Jane is planting a mixture of flowers. For every ounce of Marigold seeds she uses 2/5 of an ounce of lupine seeds how many ounce

dusya [7]

Answer:

$\frac{5}{2}$ ounces of marigold seeds.

Step-by-step explanation:

We have been given that Jane uses 2/5 of an ounce of lupine seeds for every ounce of Marigold seeds. We are asked to find the ounces of Marigold seeds, which Jane will use, if she used one ounce of lupine seeds.

We will use proportions to solve our given problem.

$\frac{\text{Marigold seeds}}{\text{Lupine seeds}}=\frac{1}{\frac{2}{5}}$

Let us simplify our proportion as shown below:

$\frac{\text{Marigold seeds}}{\text{Lupine seeds}}=\frac{1\cdot 5}{2}$

$\frac{\text{Marigold seeds}}{\text{Lupine seeds}}=\frac{5}{2}$

Since Jane used 1 pounce of lupine seeds, so we will substitute this value in our proportion as:

$\frac{\text{Marigold seeds}}{1}=\frac{5}{2}$

$\text{Marigold seeds}}=\frac{5}{2}$

Therefore, Jane will use $\frac{5}{2}$ ounces of marigold seeds, if she used one ounce of lupine seeds.

6 0

3 years ago

What happens when you multiply 2 negative numbers?

dalvyx [7]

1) either you'll get a negative number
Or
2) You'll get a positive Number..
But I'm guess you'll get a positive number

3 0

3 years ago

Read 2 more answers

A set of stacked plates for serving weighs 12kg . If each plate weighs 1/2 kg how many plates are in the stack?

Nutka1998 [239]

Answer:

Step-by-step explanation:

12 divided by 1/2 = 24

Hope this helped! :)

7 0

2 years ago

Please HELP!!!!!

Stels [109]

Can you explain it more clear because my english is not very good, I want to easy to help you

3 0

2 years ago

Find the length of a 90° arc of a circle with a diameter of 10 m​

Find the length of a 90° arc of a circle with a diameter of 10 m