Water moves into a cell due to the process of bulk transport active transport osmosis

A (allar Qrea entre Curvas \( x=3-4^{2}, x=9+1 \)

Solve: \( -8(5 b-10)+5=-115 \)

19. \( 1+2+3+4+5+\ldots+n=\frac{n(n+1)}{2} \) (a) i) Show that this formula is true for the sum of the first 8 natural numbers. ii) Find the sum of the first 400 natural numbers. (b) i) Show that \( 2+4+6+8+\cdots+2 n=n(n+1) \). ii) Find the sum of the first 200 even numbers. iii) Find the sum of the first 200 odd numbers. (c) i) Use the formula at the beginning of the question to find the sum of the first \( 2 n \) natural numbers. ii) Find a formula, in its simplest form, for \( 1+3+5+7+9+\cdots+(2 n-1) \).

(a) Calculate the magnitude of the gravitational force exerted by Venus on a 75 kg human standing on the surface of Venus. (The mass of Venus is \( 4.9 \times 10^{24} \mathrm{~kg} \) and its radius is \( 6.1 \times 10^{6} \mathrm{~m} \).) 66.5 (b) Calculate the magnitude of the gravitational force exerted by the human on Venus. 66.5 (c) For comparison, calculate the approximate magnitude of the gravitational force of this human on a similar human who is standing 2.5 meters away. 5.996e-11 × N (d) What approximations or simplifying assumptions must you make in these calculations? (Note: Some of these choices are false because they are wrong physics!) Treat Venus as though it were spherically symmetric. \( \checkmark \) Ignore the effects of the Sun, which alters the gravitational force that one object exerts on another. \( \checkmark \) Use the same gravitational constant in (a) and (b) despite its dependence on the size of the masses. Treat the humans as though they were points or uniform-density spheres.

10.- Un granjero tiene 100 mts de alambre para cercar, con el cual planea construir 2 corrales adyacentes. ¿Cuáles son las dimensiones que encierran el área máxima?