Find the indicated sides of the right triangle. b = 5600, c = 6500, a = ?

Even on a cloudy day, you can get sunburned outside. However, inside a glass greenhouse, you won’t get sunburned. Which type of electromagnetic waves will pass through clouds, but not glass?

A spring hangs from the ceiling. Describe how a single coil moves as a longitudal wave passes through the spring.

Plot each complex number in the complex plane and write it in polar form. Express the argument in degrees. $-2+3 i$

The improper fraction 3/2 equals what mixed number?

If P is a polynomial of degree k, then $\int{P(x)e^x}dx=[P(x)-P'(x)+\cdots\pm P^{(k)}(x)]e^x+C$ Verify this statement. For simplicity, take k = 4.

Decompose v into two vectors, one parallel to w and the other orthogonal to w. $\mathbf{v}=-\mathbf{i}+2 \mathbf{j} ; \mathbf{w}=3 \mathbf{i}-\mathbf{j}$

Combine each pair of simple sentences to form a compound sentence. Use a comma and coordinating conjunction or a semicolon to separate the independent clauses. Odysseus yelled insults at Polyphemus. The Cyclops hurled a rock at the ship.

John has a balance of $3000 on his Discover card that charges 1% interest per month on any unpaid balance. John can afford to pay$100 toward the balance each month. His balance each month after making a $100 payment is given by the recursively defined sequence$B_{0}=$3000 \quad B_{n}=1.01 B_{n-1}-100.$ Determine John’s balance after making the first payment. That is, determine $B_{1}.$

Use a graphing utility to graph $f(x)=\frac{2 x+3}{1-3 x}$ and f'(x) on the same set of coordinate axes. Use TRACE and ZOOM to find where f'(x) = 0.

The price p (in dollars) and the quantity x sold of a certain product obey the demand equation $p=-\frac{1}{6} x+100.$ What quantity x maximizes revenue? What is the maximum revenue?

State where the power series is centered. Σ_(n=1)^∞ (x-2)^n / n³

A coin is tossed three times. Suppose you lose $3 if 3 heads appear, lose$2 if 2 heads appear, and win $3 if 0 heads appear. How much should you win or lose if 1 head appears in order for the game to be fair?

Give (a) the additive inverse and (b) the absolute value of each number. 0.13