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2 years ago

A drink is made from orange juice and lemonade in the ratio 3 : 7. How much lemonade is needed if 60 ml of orange juice is used?

Mathematics

1 answer:

lina2011 [118]2 years ago

8 0

Answer:

140 ml

Step-by-step explanation:

60/3 = 20

20x7 = 140

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Find the derivative.

krek1111 [17]

Answer:

$\displaystyle f'(x) = \bigg( \frac{1}{2\sqrt{x}} - \sqrt{x} \bigg)e^\big{-x}$

General Formulas and Concepts:

Algebra I

Terms/Coefficients

Expanding/Factoring

Calculus

Differentiation

Derivatives
Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Quotient Rule]: $\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle f(x) = \frac{\sqrt{x}}{e^x}$

Step 2: Differentiate

Derivative Rule [Quotient Rule]: $\displaystyle f'(x) = \frac{(\sqrt{x})'e^x - \sqrt{x}(e^x)'}{(e^x)^2}$
Basic Power Rule: $\displaystyle f'(x) = \frac{\frac{e^x}{2\sqrt{x}} - \sqrt{x}(e^x)'}{(e^x)^2}$
Exponential Differentiation: $\displaystyle f'(x) = \frac{\frac{e^x}{2\sqrt{x}} - \sqrt{x}e^x}{(e^x)^2}$
Simplify: $\displaystyle f'(x) = \frac{\frac{e^x}{2\sqrt{x}} - \sqrt{x}e^x}{e^{2x}}$
Rewrite: $\displaystyle f'(x) = \bigg( \frac{e^x}{2\sqrt{x}} - \sqrt{x}e^x \bigg) e^{-2x}$
Factor: $\displaystyle f'(x) = \bigg( \frac{1}{2\sqrt{x}} - \sqrt{x} \bigg)e^\big{-x}$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

7 0

2 years ago

The perimeter of a rectangular garden is 346. if the width of the garden is 79 feet, what is its length?

Nostrana [21]

Perimeter = L + L + W + W
346 = L + L + 79 + 79
346 = L + L + 158
346 - 158 = L + L 158 -158
188 = L + L
So im gonna square root 188
188 ( square rooted) = 13.7113092.....
Im gonna round it so the lengths gonna be
≈ 13.7

6 0

3 years ago

In a dance competition, a participant has to score a total of at least 30 points in the first four rounds combined to move on to

Anvisha [2.4K]

Answer:

5 + 3p ≥ 30

Step-by-step explanation:

"at least" means greater than are equal to. ≥

So we already know he has 5 points, but the other 3 rounds we don't. 5 + 3p

30 is the overall points he has.

5 + 3p ≥ 30

4 0

3 years ago

Using a white-board with graph paper or graphing technology such as Geogebra be able to perform a reflection for a pre-image ove

Marta_Voda [28]

Explanation:

The line of reflection is the perpendicular bisector of the segment joining a point with its reflected image.

___

The segment joining a point with its reflection is as short as possible consistent with the requirement that the reflected point be the same distance from the line that the original is. That means it is perpendicular to the line of reflection. Since the distance from that line is the same on either side, the line of reflection bisects the joining segment.

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2 years ago

What’s the y-intercept for 10/-5

irinina [24]

Answer:

-2

Step-by-step explanation:

3 0

3 years ago