I need some help with this

in circle T with m angle STU=50 and ST=3 units, find the length of arc SU. Round to the nearest hundredth.

ICE Princess25 [194]

9514 1404 393

Answer:

arc SU ≈ 2.62 . . . units

Step-by-step explanation:

The arc length is given by ...

s = rθ

where r is the radius, and θ is the central angle in radians.

arc SU = ST·STU = 3·(50°·π/180°) = 5π/6

arc SU ≈ 2.62 . . . units

6 0

3 years ago

Find the area of the rectangle. Round the answer to the nearest whole number.

Fed [463]

Answer:

The area of the given rectangle is 51

Step-by-step explanation:

First we have to find the coordinates of the vertices of the rectangle.

Then the length and breadth of it using distance formula.

The distance d between points (x₁ , y₁) and (x₂ , y₂) is given by

$d= \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

Finally calculate the area of rectangle using the formula,

Area of rectangle = Length * Breadth

From the given graph, we get the coordinates of the rectangle as

A(2,4) , B(-2,3) , C(1,-9) , D(5,-8)

Breadth, AB = $\sqrt{(-2-2)^{2}+(3-4)^{2}} = \sqrt{16+1} = sqrt{17}$

Length, BC = $\sqrt{(1+2)^{2}+(-9-3)^{2}} = \sqrt{9+144} = 3 sqrt{17}$

Now, Area of rectangle = Length * Breadth = AB * BC = √17 * 3√17 = 3 *17 = 51

∴ The area of the given rectangle is 51

7 0

4 years ago

Read 2 more answers

A rectangular swimming pool is bordered by a concrete patio. the width of the patio is the same on every side. the area of the s

andre [41]

Answer:

$x = \frac{1}{4}\left(-(l + w) + \sqrt{l^2 + 6lw + w^2} \right)$

where

l = length of the pool (w/o the patio)
w = width of the pool (w/o the patio)

Explanation:

Let

x = width of the patio
l = length of the pool (w/o the patio)
w = width of the pool (w/o the patio)

Since the pool is bordered by a complete patio,

Length of the pool (with the patio)
= (length of the pool (w/o the patio)) + 2*(width of the patio)
Length of the pool (with the patio) = l + 2x

Width of the pool (with the patio)
= (width of the pool (w/o the patio)) + 2*(width of the patio)
Width of the pool (with the patio) = w + 2x

Note that

Area of the pool (w/o the patio)
= (length of the pool (w/o the patio))(width of the pool (w/o the patio))
Area of the pool (w/o the patio) = lw

Area of the pool (with the patio)
= (length of the pool (w/o the patio))(width of the pool (w/o the patio))
= (l + 2x)(w + 2x)
= w(l + 2x) + 2x(l + 2x)
= lw + 2xw + 2xl + 4x²
Area of the pool (with the patio) = 4x² + 2x(l + w) + lw

Area of the patio
= (Area of the pool (with the patio)) - (Area of the pool (w/o the patio))
= (4x² + 2x(l + w) + lw) - lw
Area of the patio = 4x² + 2x(l + w)

Since the area of the patio is equal to the area of the surface of the pool, the area of the patio is equal to the area of the pool without the patio. In terms of the equation,

Area of the patio = Area of the pool (w/o the patio)
4x² + 2x(l + w) = lw
4x² + 2x(l + w) - lw = 0 (1)

Let

a = numerical coefficient of x² = 4
b = numerical coefficient of x = 2(l + w)
c = constant term = -lw

Then using quadratic formula, the roots of the equation 4x² + 2x(l + w) - lw = 0 is given by

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\\ = \frac{-2(l + w) \pm \sqrt{(2(l + w))^2 - 4(4)(-lw)}}{2(4)} 
\\ = \frac{-2(l + w) \pm \sqrt{(4(l + w)^2) + 16lw}}{8} 
\\ = \frac{-2(l + w) \pm \sqrt{(4(l^2 + 2lw + w^2) + 4(4lw)}}{8}
\\ = \frac{-2(l + w) \pm \sqrt{(4(l^2 + 2lw + w^2 + 4lw)}}{8}
\\ = \frac{-2(l + w) \pm \sqrt{(4(l^2 + 6lw + w^2)}}{8}$
$= \frac{-2(l + w) \pm 2\sqrt{l^2 + 6lw + w^2}}{8} \\= \frac{2}{8}(-(l + w) \pm \sqrt{l^2 + 6lw + w^2}) \\x = \frac{1}{4}(-(l + w) \pm \sqrt{l^2 + 6lw + w^2}) \\\boxed{x = \frac{1}{4}\left(-(l + w) + \sqrt{l^2 + 6lw + w^2} \right) \text{ or }}
\\\boxed{x = -\frac{1}{4}\left((l + w) + \sqrt{l^2 + 6lw + w^2} \right)}$

Since $(l + w) + \sqrt{l^2 + 6lw + w^2} \ \textgreater \ 0$ , $-\frac{1}{4}\left((l + w) + \sqrt{l^2 + 6lw + w^2}\right)$ is negative. Since x represents the patio width, x cannot be negative. Hence, the patio width is given by

$\boxed{x = \frac{1}{4}\left(-(l + w) + \sqrt{l^2 + 6lw + w^2} \right)}$

7 0

3 years ago

By what number must you multiply a quantity in order to increase it by 25% in a single step?

irina [24]

The answer will be C, 1.25

8 0

3 years ago

Simplify 2x 2 - y for x = 3 and y = -2. 20 14 16 10 i need help please

disa [49]

2x^2-y

Plug in the values.

2(3)^2-(-2)

2(3)^2+2

Exponents first.

2*9+2

18+2

20

The answer is 20.

I hope this helps!
~kaikers

6 0

3 years ago