In given problem, find the work done by the force field $\mathbf{F}$ in moving a particle along the curve C.

$\mathbf{F}(x, y)=\left(x^3-y^3\right) \mathbf{i}+x y^2 \mathbf{j} ; \quad C$ is the curve $x=t^2$, $y=t^3,-1 \leq t \leq 0$.

Multiply and state in standard form. $5 x^{5}\left(9 x^{3}+8 x\right)$

Multiply and state in standard form. $(6 x+7)\left(4 x^{7}-7 x\right)$

A particle of mass $m$ moves along the $x$ axis. Its position varies with time according to $x=2 t^3-4 t^2$, where $x$ is in meters and $t$ is in seconds. Find the work done by the net force from $t=0$ to $t=t_1$.

Match the questions on the left with the most appropriate response on the right. Write the letter of your choice in the space provided.

¿Dónde pago? A. No, porque pagué con tarjeta de crédito. B. Para cambiar algo. C. En efectivo. D. Está en oferta. Cuesta veinte dólares. E. Sí, es de buena calidad. F. En la caja. G. Está muy caro. H. El dependiente.

Find a general solution. (Show the details of your work.)

$$\begin{aligned} & y_1^{\prime}=y_1+y_2+5 \cos t \\ & y_2^{\prime}=3 y_1-y_2-5 \sin t \\ \end{aligned}$$

Any values that could cause a denominator to equal 0 must be excluded from the domain and, consequently, as solutions of an equation that has variable expressions in the denominators. (a) Without actually solving the equation, list all possible numbers that could have to be rejected if they appeared as proposed solution. (b) Then give the domain, using set notation. $\frac{1}{x^{2}-16}-\frac{2}{x-4}=\frac{1}{x+4}$

Susana está en el mercado. Escoge el adjetivo demostrativo correcto para completar la conversación. Luego pon las joyas en orden según su proximidad a Susana, empezando con la más cercana. (Choose the correct demonstrative adjective. Then write a list of the jewelry items in order from the closest to the farthest in relation to Susana.)

Susana: Me gustan las joyas de plata. ¿Me deja ver (aquella / aquel) collar?

Vendedora: Sí, le dejo (aquel / aquellos) collar en treinta mil colones.

Susana: Es caro. ¿Y (estas / estos) aretes de aquí? ¿Cuánto cuestan?

Vendedora: _________ (Esos / Esas) aretes de plata cuestan veinticinco mil colones. Son de buena calidad.

Susana: Me gustan (esas / esos) joyas de allí, pero cuestan demasiado.

Vendedora: ¿Le gustaría (ese / esa) anillo de plata? Sólo cuesta dieciocho mil colones.

Susana: ¡Está bien! Quisiera comprar (esa / ese) anillo.

Solve. (Show the details of your work.)

$$\begin{aligned} y_1^{\prime} & =4 y_2+5 e^t \\ y_2^{\prime} & =-y_1-20 e^{-t} \\ y_1(0) & =1, y_2(0)=0 \end{aligned}$$

State the equations below in standard form for a circle. $x^{2}+81+y^{2}-18 y=1$

Repondez a la question :

Ou aimes - tu piqueniquer ? avec qui ?

Solve the system of equations.

$$\left\{\begin{array}{r}x^2+3 y^2=7 \\ x+4 y=6\end{array}\right.$$

Explain.

f a person belongs to clan $k_i$, that person's father belongs to clan $c^{-1}\left(k_i\right)$. If a woman belongs to clan $k_j$, her husband belongs to clan $w^{-1}\left(k_j\right)$.

Continuous compound interest. Find the amount $A$ in an account after $t$ years if

$$\frac{dA}{dt}=0.03A\qquad \text{and}\qquad A(0)=1,000$$