Una espira de radio \( \mathrm{R}=5 \mathrm{~cm} \) por la que circula una corriente eléctrica en sentido horario de 30 a se encuentra situada en el plano de la pantalla. ¿Cuál es el campo magnético en el centro de la espira? ¿Que cara de la espira estariamos viendo?

The three numbers have a sum of 30 and therefore a mean of 10 . Use software to determine the standard deviation. Use the function for sample standard deviation. Give your answer precise to two decimal places. standard deviation = Now suppose a fourth value equal to the mean, 10, were added to the data set. What would happen to the standard deviation? The standard deviation would remain the same because the fourth value is equal to the mean. The standard deviation would increase because the data get more spread out relative to the mean. The statiation would decrease because the data get less spread out relative to the mean.

3. (1,0 punto) Calcular el valor de a para que la función siguiente \( \quad f(x)=\left\{\begin{array}{ll}x+1 & \text { si } x \leq 1 \\ \text { sea continua: } & \text { si } x>1\end{array}\right. \)

A Bernoulli differential equation (named after James Bernoulli) is of the form \[ \frac{d y}{d x}+P(x) y=Q(x) y^{n} \] Observe that, if \( n=0 \) or 1 , the Bernoulli equation is linear. For other values of \( n \), the substitution \( u=y^{1-n} \) transforms the Bernoulli equation into the linear equ \[ \frac{d u}{d x}+(1-n) P(x) u=(1-n) Q(x) \text {. } \] Use the substitution \( u=y^{1-n} \) to solve the following differential equation. \[ x y^{\prime}+y=-8 x y^{2} \]

From a hang-glider 1 km from a beach, the angle of depression of the beach is estimated at \( 10^{\circ} \). What is its altitude? Draw the suitable diagram to help answer the question.

Let \( P(x)=2 x^{4}+a x^{2}-5 x-7 \). If \( P(3)=68 \), determine the value of \( P(x)=x^{4}+x^{3}-2 x+c \). If \( P(1)=6 \), determine the value of d Let \( P(x)=3 x^{6}-5 x^{3}+a x^{2}+b x+10 \). If \( P(-1)=P(2)=0 \), find the values of