Supongamos que 14 centímetros de alambre cuestan 70 pesos. A esta tasa. ¿cuántos centímetros de alambre podemos comprar con 45 pesos

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 \( 1+3+5+7+9+\cdots+(2 n-1) \).

Directions: Write the linear equation in Standard Form. \( y=-\frac{2}{7} x-\frac{11}{7} \) Incorrect Answer Given: \( \frac{2}{7} x+y=-\frac{11}{7} \) Why is this incorrect? Answer fails to be in the form: Answer fails to make sure \( A, B, C \) are not fractions (or decimals). Answer fails to make sure \( A \) is positive.

Determine the difference quotient \( \frac{f(x+h)-f(x)}{h} \) \( f(x)=x^{2}-14 x \)

Given that the errors in the measurements are as follows: Length of bar magnet \( =0.1 \mathrm{~cm} \) Breath of bar magnet \( =0.1 \mathrm{~cm} \) Mass of bar magnet \( =0.1 \mathrm{~g} \) Time \( =0.01 \) seconds Calculate the errors in \( M \) and Bo Mass of bar magnet \( =78.7 \mathrm{~g} \) Breath of bar magnet \( =1.5 \mathrm{~cm} \) Time \( =5.062 \) seconds Length of bar magnet \( =7.5 \mathrm{~cm} \) Mes

The cost function for a cartain company is \( c=60 x+300 \) and the revenue is given by \( R=100 x-0,5 x^{2} \). Recall that profit is revenue minus cost, Set up a quadratic equation ond find two values of \( x \) (production level) that will create a profit of \( \leq 300 \). \( x= \)