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Semmy [17]
3 years ago
6

1. A catering company’s recipe for salad uses a ratio of 2 c of dressing to 4 lb of vegetables. (a) Draw a model for the ratio.

(b) Write the ratio of dressing to vegetables as a reduced fraction. Answer:
Mathematics
1 answer:
IRISSAK [1]3 years ago
3 0
1. ratio = 2 c of dressing / 4 lb of vegetables

Use two variables: d for the number of c of dressing and v for the number of pounds of vegetables.

Then d / v = 2/4 = 1/2 => d = v/2

Now you can make a table

v     d  

2    1

4    2

6    3

8    2

And you can draw a line for the points (2,1); (4,2); (6,3), (8,4) ... the slope of the graph is the ratio = 1/2

b) I already did it above as part ot the explanation: d/v = 1/2
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Help with 30 please. thanks.​
Svet_ta [14]

Answer:

See Below.

Step-by-step explanation:

We have the equation:

\displaystyle  y = \left(3e^{2x}-4x+1\right)^{{}^1\! / \! {}_2}

And we want to show that:

\displaystyle y \frac{d^2y }{dx^2} + \left(\frac{dy}{dx}\right) ^2 = 6e^{2x}

Instead of differentiating directly, we can first square both sides:

\displaystyle y^2 = 3e^{2x} -4x + 1

We can find the first derivative through implicit differentiation:

\displaystyle 2y \frac{dy}{dx}  = 6e^{2x} -4

Hence:

\displaystyle \frac{dy}{dx} = \frac{3e^{2x} -2}{y}

And we can find the second derivative by using the quotient rule:

\displaystyle \begin{aligned}\frac{d^2y}{dx^2} & = \frac{(3e^{2x}-2)'(y)-(3e^{2x}-2)(y)'}{(y)^2}\\ \\ &= \frac{6ye^{2x}-\left(3e^{2x}-2\right)\left(\dfrac{dy}{dx}\right)}{y^2} \\ \\ &=\frac{6ye^{2x} -\left(3e^{2x} -2\right)\left(\dfrac{3e^{2x}-2}{y}\right)}{y^2}\\ \\ &=\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\end{aligned}

Substitute:

\displaystyle y\left(\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\right) + \left(\frac{3e^{2x}-2}{y}\right)^2 =6e^{2x}

Simplify:

\displaystyle \frac{6y^2e^{2x}- \left(3e^{2x} -2\right)^2}{y^2} + \frac{\left(3e^{2x}-2\right)^2}{y^2}= 6e^{2x}

Combine fractions:

\displaystyle \frac{\left(6y^2e^{2x}-\left(3e^{2x} - 2\right)^2\right) +\left(\left(3e^{2x}-2\right)^2\right)}{y^2} = 6e^{2x}

Simplify:

\displaystyle \frac{6y^2e^{2x}}{y^2} = 6e^{2x}

Simplify:

6e^{2x} \stackrel{\checkmark}{=} 6e^{2x}

Q.E.D.

6 0
2 years ago
This is how dora subtracts 73-26. 73-3=70. 70-?=50. ?-?=? fill in the blanks to solve
olganol [36]

Answer:

73-3=70

70-20=50

50-24=26

7 0
3 years ago
Write a ratio for each situation 310 beats per minute
MakcuM [25]

The obvious one is (310 beats)/(1 minute).

4 0
3 years ago
U divided by 25 =13 please do step by step and show work thanks :))
Anna71 [15]
Answer U/25=13
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             U=325
6 0
3 years ago
In Volleyball , players serve the ball to the opposing team . If the opposing team fails to hit the ball , the services is calle
choli [55]
To solve, I would write an equation like this: 0.3=x/70 , where x is the number of aces divided by 70 games and 0.3 is his ace average.

0.3=x/70
x=70x0.3
  =21

The player has served 21 aces.

Check:
21/70
=0.3


6 0
3 years ago
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