Evelyn is making a candy that contains 25% dark chocolate and the rest milk chocolate. The candy has 3 pounds of milk chocolate.

Mathematics

1 answer:

Vitek1552 [10]3 years ago

4 0

Let c represent the total amount of chocolate there is in lbs.

c = 0.25c + 0.75c

0.75c represents milk chocolate, and we know that there are 3 lbs of milk chocolate, so you can replace the 0.75c with 3 (representing 3 lbs):

c = 0.25c + 3

Divide all the terms by c:

1 = 0.25 + 3/c

Subtract 0.25 from both sides to combine the like terms:

0.75 = 3/c

Multiply all the terms by c to make the equation easier to work with:

0.75c = 3

Divide both sides by 0.75 to isolate the c and find the total amount of chocolate in pounds.

c = 4

Substitute c for 4 in the term that defines dark chocolate (which was 0.25c)

0.25(4) = 1 pound

Therefore, there was exactly 1 pound of dark chocolate present in the chocolate.

This makes sense, as 1 pound of dark chocolate + 3 pounds of milk chocolate = 4 pounds of chocolate in total, and 1 is 25% of 4 and 3 is 75% of 4.

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a firefighter dives at 7.5 m/sec from window to net. If window is 34 m above net, what speed does firefighter hit net. ACCELRATI

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Answer:

Step-by-step explanation:

This is more physics than math, but since "The book of nature is written in the language of mathematics"...

Anyway, the one-dimesional motion equation you want to use here resembles the quadratic we use to model parabolic motion. It is

$v^2=v_0^2+2a$ Δx

where v is the final velocity of the firefighter, v₀ is the initial velocity of the firefighter, a is -9.8 m/s/s (negative because the motion is in the downward direction), and Δx is -34 m. This is also negative because where the firefighter lands is below the point at which he started. This is important, because if you leave the 34 as positive, you end up with a negative radicand...and that's not gonna work. Filling in the formula:

$v^2=(7.5)^2+2(-9.8)(-34)$

Paying close attention to significant digits here is important (at least it is when I teach physics in school!). Since there are 2 significant digits in 7.5, we need 2 in the product. 7.5 squared is 56.25 which will round to 56. Then on the right side of the plus sign, we need 2 significant digits as well since the number 2 is part of the equation. We don't count it as significant if it is part of the equation. 2(-9.8)(-34) = 666.4 but that will round to 670. NOW, since the rules for significant digits are different in multiplication and addition, you have to round each first, then take the square root of the sum, rounding at the end. In this case we will round to the place that holds the least significance between the 2 numbers. In our case that is the tens place, since the tens place is less significant than is the 1's place. The number 7 is in the tens place. (Following that rule is super tricky, and also quite maddening!)

What we have here is

$v^2=56+670$ and