Payroll functions. Let the social security tax function $SSTAX$ be defined as $\operatorname{SSTAX}(x)=0.0765 x$, where $x \geq 0$ is the weekly income. Let $ROUND2$ be the function that rounds a number to two decimal places. Find the value of $( ROUND2 \circ SSTAX)(525)$.

If a particle moves along a coordinate line with a constant acceleration a (in centimeter per square second), then at time t (in seconds) its distance s(t) (in centimeters) from the origin is

$$s(t)=\frac{1}{2} a t^2+v_0 t+s_0$$

for velocity $v_0$ and distance $s_0$ from the origin at t=0. If the distances of the particle from the origin at t=1/2, t=1, and t=3/2 are 7, 11, and 17 , respectively, find a, $v_0$, and $s_0$.

Particle acceleration If a particle moves along a coordinate line with a constant acceleration $a$ (in $\mathrm{cm} / \mathrm{sec}^2$ ), then at time $t$ (in seconds) its distance $s(t)$ (in centimeters) from the origin is

$$s(t)=\frac{1}{2} a t^2+v_0 t+s_0$$

for velocity $v_0$ and distance $s_0$ from the origin at $t=0$. If the distances of the particle from the origin at $t=\frac{1}{2}, t=1$, and $t=\frac{3}{2}$ are $7,11$, and $17$, respectively, find $a, v_0$, and $s_0$.

In electrical circuits, the formula 1/R=(1/$R_1$)+(1/$R_2$) is used to find the total resistance R if two resistors $R_1$ and $R_2$ are connected in parallel. Given three resistors, A, B, and C, suppose that the total resistance is 48 ohms if A and B are connected in parallel, 80 ohms if B and C are connected in parallel, and 60 ohms if A and C are connected in parallel. Find the resistances of A, B, and C.

यदि R प्रतिरोधों R1 , R2 , R3 , के साथ समानांतर में जुड़े तीन प्रतिरोधकों का कुल प्रतिरोध है, तो 1/R=1/R1+1/R2+1/R3 यदि प्रतिरोधों को ओम में R1=25ohm के रूप में मापा जाता है, R2=40ohm और R3=50ohm, प्रत्येक मामले में 0.5% की संभावित त्रुटि के साथ, R के परिकलित मान में अधिकतम त्रुटि का अनुमान लगाएं।

The total resistance R produced by three conductors with resistances R1, R2 , R3 connected in a parallel electrical circuit is given by the formula 1/R=1/R1+1/R2+1/R3 Find curlR/ curlR1

The total resistance for a parallel circuit is given by (1/R) = (1/R1) + (1/R2) + (1/R3). a. If R = 1 ohm, R2 = 6 ohms, and R3 = 8 ohms, find R1. b. If R1 = 3 ohms, R2 = 4 ohms, and R3 = 6 ohms, find R.

Blending coffees A shop specializes in preparing blends of gourmet coffees. From Colombian, Costa Rican, and Kenyan coffees, the owner wishes to prepare $1$-pound bags that will sell for $\$ 12.50$. The cost per pound of these coffees is $\$ 14, \$ 10$, and $\$ 12$, respectively. The amount of Colombian is to be three times the amount of Costa Rican. Find the amount of each type of coffee in the blend.

If f(x)=ax$^3$+bx$^2$+cx+d, find a, b, c, and d if the graph of f is to pass through (-1,2),(0.5,2),(1,3), and (2,4.5).

Write the equation of the parabola that meets each set of conditions. Then graph the equation. The parabola has a vertical axis and passes through points at (1, -7), (5, -3), and (7, -4).

Find an equation for the parabola that has a vertical axis and passes through the given points.

P(-1,9), Q(1,7), R(2,15)

Solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.

$$\left\{\begin{array}{l}{2 x+y-z=4} \\ {-x+y+3 z=1}\end{array}\right.$$

Solve each system of equations using matrices. If the system has no solution, say that it is inconsistent.

$$\left\{\begin{aligned} 3 x-2 y &=1 \\ 10 x+10 y &=5 \end{aligned}\right.$$

Use matrices to solve the system.

$$\left\{\begin{aligned} 5 x+2 y-z &=10 \\ y+z &=-3 \end{aligned}\right.$$