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3 years ago

The radius of a circle is 10 m. Find the circumference to the nearest tenth.

Mathematics

2 answers:

Mars2501 [29]3 years ago

6 0

Answer:

$\bf \large 60 \: m$

Step-by-step explanation:

<h2>Given that :</h2>

The radius of a circle is 10 m.

Find the circumference to the nearest tenth.

<h2>formulas used :</h2>

circumference = 2 × π × r

<h2>where,</h2>

π = 22/7

r = 10 m

<h2>explanation :</h2>

⟼ c = 2πr

⟼ c = 2 × 22/7 × 10 m

⟼ c = 2 × 3•14 × 10m

⟼ c = 6•28 × 10 m

⟼ c = 62•8 m

<h2>Round to the nearest tenth :</h2>

⟼ c = 62•8 m

⟼ c = 60 m

∴ circle circumference is 60 m.

Eva8 [605]3 years ago

5 0

The answer is: C≈62.83m

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Find all solutions of each equation on the interval 0 ≤ x < 2π.

Korvikt [17]

Answer:

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Step-by-step explanation:

How are tangents and secants related to sines and cosines?

$\displaystyle \tan{x} = \frac{\sin{x}}{\cos{x}}$ .

$\displaystyle \sec{x} = \frac{1}{\cos{x}}$ .

Sticking to either cosine or sine might help simplify the calculation. By the Pythagorean Theorem, $\sin^{2}{x} = 1 - \cos^{2}{x}$ . Therefore, for the square of tangents,

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This equation will thus become:

$\displaystyle \frac{1 - \cos^{2}{x}}{\cos^{2}{x}} \cdot \frac{1}{\cos^{2}{x}} + \frac{2}{\cos^{2}{x}} - \frac{1 - \cos^{2}{x}}{\cos^{2}{x}} = 2$ .

To simplify the calculations, replace all $\cos^{2}{x}$ with another variable. For example, let $u = \cos^{2}{x}$ . Keep in mind that $0 \le \cos^{2}{x} \le 1 \implies 0 \le u \le 1$ .

$\displaystyle \frac{1 - u}{u^{2}} + \frac{2}{u} - \frac{1 - u}{u} = 2$ .

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Solve this equation for $u$ :

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In simplest radical form, what are the solutions to the quadratic equation 6 = x2 – 10x?

vichka [17]

Answer:

$x = 5+\sqrt{31}\,\, and\,\, x=5-\sqrt{31}$

Step-by-step explanation:

We need to solve the quadratic equation

6 = x^2 -10x

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x^2-10x-6=0

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

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Putting values in the quadratic formula

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What is the value of x?<br> 6.75+ x = 131

yanalaym [24]

Answer:

x = 497/4 = 124.250

Step-by-step explanation:

Step 1 :

Simplify ——

Equation at the end of step 1 :

(—— + x) - 131 = 0

Step 2 :

Rewriting the whole as an Equivalent Fraction :

2.1 Adding a whole to a fraction

Rewrite the whole as a fraction using 4 as the denominator :

x x • 4

x = — = —————

1 4

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

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Equation at the end of step 2 :

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Step 3 :

Rewriting the whole as an Equivalent Fraction :

3.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 4 as the denominator :

131 131 • 4

131 = ——— = ———————

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Adding fractions that have a common denominator :

3.2 Adding up the two equivalent fractions

(4x+27) - (131 • 4) 4x - 497

——————————————————— = ————————

4 4

Equation at the end of step 3 :

4x - 497

———————— = 0

Step 4 :

When a fraction equals zero :

4.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, multiplys both sides of the equation by the denominator

Here's how:

4x-497

—————— • 4 = 0 • 4

Now, on the left hand side, the 4 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

4x-497 = 0

Solving a Single Variable Equation :

4.2 Solve : 4x-497 = 0

Add 497 to both sides of the equation :

4x = 497

Divide both sides of the equation by 4:

x = 497/4 = 124.250

One solution was found :

x = 497/4 = 124.250

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