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2 years ago

7

What is the circumference of the circle that circumscribes a triangle with side lengths 3, 4, and 5?

1 answer:

djyliett [7]2 years ago

6 0

Answer:

5π, about 15.708 units

Step-by-step explanation:

A 3-4-5 triangle is a right triangle. When a circle circumscribes a right triangle, the hypotenuse is the diameter of the circle. The circumference of a circle is given by ...

C = πd

For a diameter of 5 units, the circumference is ...

C = π(5) = 5π = 15.708 . . . units

_____

<em>Additional comment</em>

The (3, 4, 5) triple is one of the first Pythagorean triples you run across. It is the smallest integer triple, and the only primitive triple with values in an arithmetic sequence. You can show this is a Pythagorean triple by ...

3² + 4² = 9 +16 = 25 = 5²

That is, these numbers satisfy the Pythagorean theorem relation for sides of a right triangle.

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How do I find the value of x

IgorC [24]

Answer:

<u><em>The value of x is 2.6</em></u>

Step-by-step explanation:

<em>Use pythagorean theorem</em>

a^2+b^2=c^2

<em>Then substitute</em>

1^2+2.4^2=c^2

<em>Then evaluate</em>

1+5.76=c^2

<em>Add</em>

c^2=6.76

<em>Isolate c by finding the sqrt of 6.76</em>

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3 0

3 years ago

Read 2 more answers

PLSSSSSS HELPPPP!!!!!Determine the area of the composite figure shown.

katrin2010 [14]

Answer: 26.13yards^2

Step-by-step explanation:

To find the area of the bottom part we can use the diameter.

6 yards. Divide it by half to have the Radius.

Now we use the formula to find the area of a circle which is

A = 3.14*R^2 Pie times radius squared.

A = 3.14*3^2

A = 3.14*9

A = 28.26 Now that we have the area of the circle divide it by 2.

14.13

Now to find the area of an isosceles triangle we use the formula

A = Base * Height Divided by 2.

A = 6*4/2

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7 0

3 years ago

Prove algebraically that r = 10/2+2sinTheta is a parabola

Xelga [282]

Answer:

$y = - \frac{ 1 }{10} {x}^{2} + \frac{5}{2}$

Step-by-step explanation:

We want to prove algebraically that:

$r = \frac{10}{2 + 2 \sin \theta}$

is a parabola.

We use the relations

${r}^{2} = {x}^{2} + {y}^{2}$

and

$y = r \sin \theta$

Before we substitute, let us rewrite the equation to get:

$r(2 + 2 \sin \theta) = 10$

Or

$r(1+ \sin \theta) = 5$

Expand :

$r+ r\sin \theta= 5$

We now substitute to get:

$\sqrt{ {x}^{2} + {y}^{2} } + y = 5$

This means that:

$\sqrt{ {x}^{2} + {y}^{2} }=5 - y$

Square:

${x}^{2} + {y}^{2} =(5 - y)^{2}$

Expand:

${x}^{2} + {y}^{2} =25 - 10y + {y}^{2}$

${x}^{2} =25 - 10y$

${x}^{2} - 25 = - 10y$

$y = - \frac{ {x}^{2} }{10} + \frac{5}{2}$

This is a parabola (0,2.5) and turns upside down.

4 0

3 years ago

Solve the inequality for u. 55 > 4u + 15 Simplify your answer as much as possible.

valentinak56 [21]

Step-by-step explanation:

55 > 4u + 15

40 > 4u

10 > u

so, this is true for all u < 10

4 0

2 years ago

HURRY PLZ ANSWER 6^2+4^2

yarga [219]

Simplify the expression.

52

4 0

3 years ago