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valkas [14]
3 years ago
12

Did I do this right?

Mathematics
1 answer:
vagabundo [1.1K]3 years ago
3 0
\bf f(x)=|x+2|\implies f(x)=\pm\sqrt{(x+2)^2}\implies f(x)=\left[ (x+2)^2 \right]^{\frac{1}{2}}
\\\\\\
\cfrac{dy}{dx}=\stackrel{chain~rule}{\cfrac{1}{2}[(x+2)^2]^{-\frac{1}{2}}\cdot 2(x+2)^1\cdot 1}\implies \cfrac{dy}{dx}=[(x+2)^2]^{-\frac{1}{2}}(x+2)
\\\\\\
\cfrac{dy}{dx}=\cfrac{x+2}{[(x+2)^2]^{\frac{1}{2}}}\implies \left. \cfrac{dy}{dx}=\cfrac{x+2}{\pm \sqrt{(x+2)^2}} \right|_{x=1}\implies \cfrac{3}{\pm 3}

check the picture below. the point 1,3 is on the increasing slope side, so will be 3/3 or 1.

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What is the side length of a 36 inch cube
Vladimir [108]

The side length is 3 inches

<h3>What is the perimeter of a cube?</h3>

The formula for perimeter of a cube is given as:

Perimeter = 12 × side length

We have that;

  • Perimeter = 36 inches
  • Side length be x

Substitute into the formula

12x = 36

Divide both sides by 12

12x/12 = 36 / 12

x = 3 inches

The side length is x and equal to 3 inches.

Hence, the side length is 3 inches

Learn more about a cube here:

brainly.com/question/1972490

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8 0
1 year ago
After heating up in a teapot, a cup of hot water is poured at a temperature of 204°F.
laila [671]

Answer:

  • Question 1: 0.081 min⁻¹
  • Question 2: 168ºF

Explanation:

The missing equation is:

             T=T_a+(T_0-T_a)e^{-kt}

You are given:

  • Ta = the temperature surrounding the object = 73ºF
  • T₀ = the initial temperature of the object = 204ºF
  • t = 2.5 min
  • T after 2.5 min = 180ºF

Question 1: Find the the value of k.

Substitute the data into the equation and solve for k:

          180\º=73\º+(204\º-73\º)e^{-k\cdot 2.5min}\\ \\ 107\º=131\ºe^{-k\cdot 2.5min}\\\\-k\cdot 2.5min=\ln (107/131)\\\\k=0.081min^{-1}

Question 2: Find the Fahrenheit temperature of the cup of water, to the nearest degree, after 4 minutes.

Subsititute into the formula and compute:

            T=73\ºF+(204\ºF-73\ºF)e^{-0.081min^{-1}\times 4min}\\ \\ T=73\ºF+(131\ºF)(0.72325024)\\\\T=168\ºF

4 0
3 years ago
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-7 ÷ 2 1/2
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-7/1 ÷ 5/2
Then, take the reciprocal of 5/2 and multiply it by -7/1
-7/1 × 5/2
Which would be -35/2
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3 years ago
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3 years ago
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Elza [17]
2x² - 4x - 30
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