With the current housing market situation in the United States, iths estimated that the number of houses built, \( H(t) \) (in millions) over the next 5 years, is related to the mortgage rate, \( r(t) \) (percent per year), and can be modeled by the equation: \[ 7 H(t)^{2}+r(t)=32 \] Find the rate of change of the number of houses being built with respect to time when the mortgage rate is \( 8 \% \) per year and is increasing at \( 0.1 \% \) per year. (Round your answer to the nearest whole number.)

Найдите периметр ромба, у которого один из углов равен \( 150^{\circ} \), а меньшая диагональ равна \( 4,5 \mathrm{~cm} \). \( \begin{array}{llll}\text { А) } 27 \mathrm{~cm} ; & \text { Б) } 18 \mathrm{~cm} ; & \text { В) } 13 \mathrm{~cm} ; & \text { Г) } 21,5 \mathrm{~cm}\end{array} \)

If \( \$ 3500 \) is invested in an account that pays interest compounded continuously, how long will it take to grow to \( \$ 7000 \) at \( 4 \% \) ?

\( \int _{}^{}\sec (x)^{3} d x \)

Multiply \( (3+8 i)(5-4 i) \)

The radioactive substance uranium-240 has a half-life of 14 hours. The amount \( A(t) \) of a sample of uranium-240 remaining (in grams) after \( t \) hours is given by the following exponential function. \( A(t)=2400\left(\frac{1}{2}\right)^{\frac{t}{14}} \) Find the initial amount in the sample and the amount remaining after 60 hours. Round your answers to the nearest gram as necessary. Initial amount: