Consider the initial value problem (t−1)x′′′ −3tx′′ +6t2x′ −(cost)x=√t+5 x(t0) = 1, x′(t0) = 0, x′′(t0) = 7. determine the values of t0 and the intervals (a, b) containing t0 for which theorem 1 guarantees the existence of a unique solution on (a, b).

The gades foundation and hbm corporation are eager to donate generously to their favorite charities. the gades foundation donated $250 in the first month, and each month afterward their cumulative donation total increases by 100$ the hbm corporation donated $64, in the first month, and each month afterward their cumulative donation total increases by 75%. in which month will the hbm corporation's cumulative donation total first exceed the gades foundations' cumulative donation total?

Witch represents the inverse of the function f(x)=1/4x-12

If m∠abc = 70°, what is m∠abd? justify your reasoning.  using the addition property of equality, 40 + 70 = 110, so m∠abd = 110°.  using the subtraction property of equality, 70 − 30 = 40, so m∠abd = 30°.  using the angle addition postulate, 40 + m∠abd = 70. so, m∠abd = 30° using the subtraction property of equality.  using the angle addition postulate, 40 + 70 = m∠abd. so, m∠abd = 110° using the addition property of equality.