(1 point) Use the given magnitude and direction to find the vector \( \mathbf{v} \) in standard position. \( |\mathbf{v}|=8, \theta=\frac{\pi}{4} \) \( \mathbf{v}=\square \) help (vectors)

The size of a certain insect population is given by \( \mathrm{P}(\mathrm{t})=400 e^{.03 \mathrm{t}} \), where t is measured in days. At what time will the population equal 1600 ?

Find an equation for the hyperbola described. Graph the equation. Center at \( (-1,-7) ; \) focus at \( (-1,-10) ; \) vertex at \( (-1,-9) \) Write an equation for the hyperbola. \( \square-\square=1 \) (Type exact answers for each term, using fractions as needed.)

Argumen dari \( 1-i \sqrt{3} \) adalah...

What is the magnitude of a vector with a horizontal component of 5 and a vertical component of \( 12 ? \)

The function \( f(t)=60,000(2)^{\frac{1}{40}} \) gives the number of bacteria in a population \( t \) minutes after an initial observation. How much time, in minutes, does it take for the number of bacteria in the population to double?