The vertices A, B, and C of a triangle in $\mathbb{R}^{3}$ are given. Find the lengths of the sides of the triangle and determine whether it is a right triangle, an isosceles triangle, both, or neither.

$$A(1,1,1), B(3,3,2), C(3,-3,5)$$

Saturn's average distance from the Sun is about 900 million miles. Write that distance in scientific notation.

The Trieste research submarine traveled $10.9 \mathrm{km}$ below the ocean surface while exploring the Mariana Trench in the South Pacific, the deepest place in the ocean. Determine the force needed to prevent a $0.10-\mathrm{m}-$diameter window on the side of the submarine from imploding. The density of the water is $1025 \mathrm{kg} / \mathrm{m}^{3}$.

Evaluate the definite integral. ∫_0^1 xe^(-x²) dx

Simplify the expression

$$3 x ^ { 2 } - 5 x - 4 + x y - \left( 2 x y + 2 x ^ { 2 } \right)$$

. Then evaluate the result if x=-1 and y=6.

Why did Churchill believe the Munich Pact was the "beginning of the reckoning"?

Solve $3x + 7y = 2$ for $y$

Find the open intervals where the below function is concave upward or concave downward. Find any inflection points.

$$f(x) = 18x - 18e^{-x}$$

What main demands did the Mongols make on their Russian subjects?

If the statement is true, write true. If it is false, change the underlined word or words to make the statement true. -An

$$\underline {\text{Amniotic egg}}$$

is a characteristic of reptiles.

Let P be the point in 3-space with rectangular coordinates

$$( \sqrt { 2 } , - \sqrt { 2 } , 2 \sqrt { 3 } )$$

. (a) Cylindrical coordinates for P are

$$( r , \theta , z )$$

=___, (b) Spherical coordinates for P are

$$( \rho , \theta , \phi )$$

=___

Find the interest rate per year, r. Use the simple interest formula. $2350 for 1 year 9 months,$378.35 interest

Explain the following observation. When 3-methyl-2-butanol is treated with HBr, a single alkyl bromide is isolated, resulting from a 1,2-shift. When 2-methyl-1-propanol is treated with HBr, no rearrangement occurs to form an alkyl bromide.

Replace the

$$\circ$$

with <, >, or = to make a true sentence.

$$-18 \circ -8$$