Determine whether the infinite geometric series is convergent or divergent. If it is convergent, find its sum. 0.1 + 0.01 + 0.001 + 0.0001 + · · ·

Evaluate each integral using any algebraic method or trigonometric identity you think is appropriate. When necessary, use a substitution to reduce it to a standard form.

$$\int _ { - 1 } ^ { 1 } \sqrt { 1 + x ^ { 2 } } \sin x\ d x$$

Determine whether the series is convergent or divergent. If it is convergent, find its sum. summation n=1 to infinity ln(n^2+1/2n^2+1)

A student finds a species of autotrophic algae with a long filament that propels it through the water. The filament is a ____. A. flagellum. B. pseudopod. C. cilium. D. microtubule.

Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.summation n=1 to infinity n-1/3n-1

Write the matrix with the given elements. In each case, specify the dimensions of the matrix.

$$\left. \begin{array} { l } { a _ { 11 } = 1 , a _ { 31 } = 2 , a _ { 42 } = - 1 , a _ { 32 } = 7 , a _ { 13 } = - 2 }, \\ { a _ { 23 } = 0 , a _ { 33 } = 4 , a _ { 21 } = 3 , a _ { 41 } = - 4 , a _ { 12 } = - 3 }, \\ { a _ { 22 } = 6 , a _ { 43 } = 5 }. \end{array} \right.$$

Solve for

$$\theta , 0 ^ { \circ } \leq \theta < 360 ^ { \circ }$$

, or for x,

$$0 \leq x < 2 \pi$$

.

$$\sin \left( 3 \theta - 25 ^ { \circ } \right) = \frac { \sqrt { 3 } } { 2 }$$

Match the trigonometric expression with its simplified form. (a) sec x, (b) -1 (c) cot x, (d) 1, (e) -tan x, (f) sin x. $\frac{\sin (-x)}{\cos (-x)}$

Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. 3-4+16/3-64/9+........

Why is the weather in New York State consistently cooler in January than it is in July? (1) Earth is closer to the sun in July (2) Cloudy weather is more common in January (3) The Northern Hemisphere is tilted away from the sun in January. (4) Sunlight is reflected away from Earth by ice and snow during January

(a) Show that

$$\| \mathbf { u } + \mathbf { v } \| ^ { 2 } + \| \mathbf { u } - \mathbf { v } \| ^ { 2 } = 2 \left( \| \mathbf { u } \| ^ { 2 } + \| \mathbf { v } \| ^ { 2 } \right)$$

for any vectors u and v. (b) What does this say about parallelograms?

Jean owned x shares of a corporation and received a quarterly dividend check for y dollars. Express the annual dividend for one share algebraically.

Determine the amplitude of each function. Then graph the function and y = sin x in the same rectangular coordinate system for

$$0 \leq x \leq 2 \pi.$$

y = 5 sin x

Solve the equation.

$$( 2 b + 29 ) ^ { 1 / 3 } = 3$$