Give an algebraic proof for the triangle inequality vw v w +≤+ . draw a sketch. [hint: expand 2 vw vw vw + ≤+ ⋅+ ( )( ) . then use the cauchy-schwartz inequality ( vw v w ⋅ ≤ ).]

the arc length is found by finding the circumference of the full circle (2xpixradius) and then dividing by 4 to find just one quarter of the circle (90 degrees).

you'll have to attache the image of the bar graph in order for us to answer : )

step-by-step explanation:

a) at most means it can cost $12 or less

so the inequality sign would be ≤

you would then need to multiply the number of toppings by the 0.35 for each one and add it to the cost of the cheese pizza.

the equation would be 9.99 + 0.35x ≤ 12

b) using the above equation:

9.99 + 0.35x ≤ 12

subtract 9.99 from each side:

0.35x ≤2.01

divide both sides by 0.35:

x ≤ 2.01 / 0.35

x ≤5.74

at most you could have 5 toppings.

the 5 topping pizza would cost: 0.35 x 5 = 1.75 + 9.99 = $11.74