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svp [43]
3 years ago
7

Write a story problem using mixed numbers that need to be scaled up.

Mathematics
1 answer:
Rudik [331]3 years ago
7 0
[Insert generic name here] is trying to bake a yellow cake because [reasons]. This recipe will make one whole cake.

3\frac{1}{4}\ cups\ of\ flour\\ 2\frac{1}{2}\ teaspoons\ of\ baking\ soda\\ \frac{1}{2}\ teaspoon\ of\ salt \\ 1\frac{3}{4}\ cups\ of\ sugar \\ \frac{2}{3}\ cup\ of\ butter \\ 2\ eggs\\ 1\frac{1}{2}\ teaspoons\ of\ vanilla\ \\ 1\frac{1}{4}\ cups\ of\ milk

He wants to make three cakes instead of one. How much of each item should be used in the new (scaled-up) recipe?

3\frac{1}{4}*3=9\frac{3}{4}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ cups\ of\ flour\\ 2\frac{1}{2}*2=4\frac{2}{2}=4+1=5\ \ \ \ \ teaspoons\ of\ baking\ soda\\ \frac{1}{2}*3=\frac{3}{2}=1\frac{1}{2}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ teaspoons\ of\ salt \\ 1\frac{3}{4}*3=3\frac{9}{4}=3+2\frac{1}{4}=5\frac{1}{4}\ cups\ of\ sugar

\frac{2}{3}*3=\frac{6}{3}=2\ \ \ \ \ \ cups\ of\ butter\\ 2*3=6 \ \ \ \ \ \ \ \ \ \ \ \ eggs\\ 1\frac{1}{2}*3 = 3\frac{3}{2} = 4\frac{1}2\ teaspoons\ of\ vanilla\ \\ 1\frac{1}{4}*3=3\frac{3}{4}\ \ \ \ \ \ \ \ cups\ of\ milk

I don't know exactly how your teacher wants you to write out the work, but I have it pretty simple there. It's not like math is tailored to a specific process; any sort of reasonable work should do.

Good luck!
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The function C(h)=(2h^2+5h)/(h^3+8) models the concentration of medication in the bloodstream (as a percent) h hours after its i
salantis [7]

Answer:

  1. h ≥ 0
  2. C = 0; concentration eventually decays to nothing
  3. (0, 0) is the only intercept in the domain. It means the concentration in the bloodstream is zero at the time the drug is injected.
  4. 1.95 hours

Step-by-step explanation:

1. a. The domain of the function in the context of this problem is h ≥ 0. The maximum value of h will correspond to the time at which the concentration is considered to be negligible. If that time is when the concentration decays to 1% of its peak value, then perhaps the suitable domain is 0 ≤ h ≤ 180.

b. The equation of the vertical asymptote of this function is where the denominator of C(h) is zero, that is ...

  h^3 +8 = 0

  h = ∛(-8)

  h = -2 . . . . the equation of the vertical asymptote

This is not a concern for a medical professional because it is outside the domain of the function.

__

2. As h gets large the value of the function approaches 2/h, which is to say the horizontal asymptote is C = 0. It means the concentration of medication in the blood eventually decays to zero.

__

3. C(0) = 0 is the only intercept in the domain of the function. (h, C(h)) = (0, 0)

In the context of this problem, it means the blood concentration of medication is zero at the time of the injection.

__

4. About 1.95 hours after injection, a maximum concentration of the drug occur in the bloodstream. This value is easily found using a graphing calculator.

Taking the derivative of the function gives you ...

  C'(h) = -2(h^4 +5h^3 -16h -20)/(h^3 +8)^2

This has two real zeros and two complex zeros. The positive real zero is near h = 1.94527, about 1.95.

That is, the concentration in the bloodstream reaches a maximum about 1.95 hours after injection into the muscle.

5 0
3 years ago
What is the length of segment CD question mark
blagie [28]

Answer:

CD = two square root of 10 end square root

Step-by-step explanation:

To find the length of a segment, use the distance formula. Substitute the order pairs for the endpoints of the segment. CD has the end points (-7, -4) and (-1, -2).

d = \sqrt{(y_2-y_1)^2 + (x_2-x_1)^2} \\\\d = \sqrt{(-4--2)^2 + (-7--1)^2} \\\\d = \sqrt{-2^2 + -6^2}\\\\d = \sqrt{4 + 36}\\\\d=\sqrt {40} = 2\sqrt{10}

8 0
3 years ago
16-25(b+3) square
Andre45 [30]
Since 16 and 25 are perfect squares you can factor the first part.
4^2-5^2(b+3)^2
=(4-5(b+3))(4+5(b+3))
=(4-5b-15)(4+5b+15)
=(-11-5b)(19+5b)

Which can be expanded if necessary,
= -209+150b-25b^2
4 0
3 years ago
the lenths of the sides of a triangle are in the extended ratio 5:9:10. the perimeter of the triangle is 48 cm. what are the len
dezoksy [38]

Answer:

What's my age im 1300

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Find the distance between (2,7) and (-6,-2)
stepladder [879]

Answer: \sqrt{145}

Step-by-step explanation:

1. use the distance formula!

distance = \sqrt{(x_{2} - x_{1})^{2}  +{(y_{2} - y_{1})}^2

2. then using the distance formula with (2, 7) and (-6, -2) you get...

distance= \sqrt{2 -(-6)^2 +(7 - (-2)^2}

distance= \sqrt{8^2 +9^2}

distance=  \sqrt{64 +81}

distance= \sqrt{145}

\sqrt{145} is the simplest radical form

:D

6 0
3 years ago
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