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dezoksy [38]
3 years ago
10

It takes the hot water faucet 4 times as long to fill a bathtub as it does the cold water faucet. Left on together, the cold and

hot water faucets take 3 minutes to fill the tub. How long will it take the cold water faucet to fill the tub by itself
Mathematics
1 answer:
Debora [2.8K]3 years ago
3 0

If it takes the cold water faucet x minutes to fill 1 tub, then its flow rate is (1 tub)/(x min).

The hot water faucet takes 4 times as long, so its flow rate is (1 tub)/(4x min).

Together, the total flow rate is (1 tub)/(3 min), so we have

\dfrac1x+\dfrac1{4x}=\dfrac13

\implies\dfrac5{4x}=\dfrac13

\implies15=4x

\implies x=\dfrac{15}4\,\text{min}=3\,\text{min}\,45\,\text{sec}

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How is 3/5 and 8/10 Are equivalent fractions?
olya-2409 [2.1K]
Hi!

These are not <span>equivalent fractions because 8/10 reduces to 4/5, not 3/5, therefore, they are not </span>equivalent.
4 0
3 years ago
The volume of a cone with a radius of 6 and height of 15
alexandr402 [8]
565.487 units cubed
hope this helps:)

4 0
3 years ago
F(x) = e^-x . Find the equation of the tangent to f(x) at x=-1​
natima [27]

Answer:

The <em>equation</em> of the tangent line is given by the following equation:

\displaystyle y - \frac{1}{e} = \frac{-1}{e} \bigg( x - 1 \bigg)

General Formulas and Concepts:

<u>Algebra I</u>

Point-Slope Form: y - y₁ = m(x - x₁)

  • x₁ - x coordinate
  • y₁ - y coordinate
  • m - slope

<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

Derivative Property [Multiplied Constant]:
\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)

Derivative Rule [Basic Power Rule]:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]:
\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)

Step-by-step explanation:

*Note:

Recall that the definition of the derivative is the <em>slope of the tangent line</em>.

<u>Step 1: Define</u>

<em>Identify given.</em>

<em />\displaystylef(x) = e^{-x} \\x = -1

<u>Step 2: Differentiate</u>

  1. [Function] Apply Exponential Differentiation [Derivative Rule - Chain Rule]:
    \displaystyle f'(x) = e^{-x}(-x)'
  2. [Derivative] Rewrite [Derivative Rule - Multiplied Constant]:
    \displaystyle f'(x) = -e^{-x}(x)'
  3. [Derivative] Apply Derivative Rule [Derivative Rule - Basic Power Rule]:
    \displaystyle f'(x) = -e^{-x}

<u>Step 3: Find Tangent Slope</u>

  1. [Derivative] Substitute in <em>x</em> = 1:
    \displaystyle f'(1) = -e^{-1}
  2. Rewrite:
    \displaystyle f'(1) = \frac{-1}{e}

∴ the slope of the tangent line is equal to  \displaystyle \frac{-1}{e}.

<u>Step 4: Find Equation</u>

  1. [Function] Substitute in <em>x</em> = 1:
    \displaystyle f(1) = e^{-1}
  2. Rewrite:
    \displaystyle f(1) = \frac{1}{e}

∴ our point is equal to  \displaystyle \bigg( 1, \frac{1}{e} \bigg).

Substituting in our variables we found into the point-slope form general equation, we get our final answer of:

\displaystyle \boxed{ y - \frac{1}{e} = \frac{-1}{e} \bigg( x - 1 \bigg) }

∴ we have our final answer.

---

Learn more about derivatives: brainly.com/question/27163229

Learn more about calculus: brainly.com/question/23558817

---

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

Unit: Differentiation

3 0
2 years ago
Please help me with this?
Alenkasestr [34]

Answer:

  A)  The population in the year that she was born.

Step-by-step explanation:

The multiplier of an exponential function is the value that function has when the exponent is zero -- the initial value. The initial value of population in this context is the population in the year Adriana was born.

3 0
3 years ago
Is 6.52 grater then 6.520
stich3 [128]
No 6.52 is equal to 6.520.
The reason for this is because even if you add more ceros to the othe side of 6.52 it would not matter unless there is another number other than 0, Like 6.52000000000000001 is bigger than 6.52 ans smaller tahn 6.5200000000000000000000
8 0
3 years ago
Read 2 more answers
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