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pychu [463]
3 years ago
11

Find the area of a circle with radius of 6 inches. (Use 3.14 for 1.)

Mathematics
1 answer:
Schach [20]3 years ago
6 0

Answer:

\pi {r}^{2}

\pi {6}^{2}  \\ 113.1

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Find the length of the hypotenuse of a right triangle whose legs are 5 and √2.
Blizzard [7]

Answer:

\sqrt{27}

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let h represent the hypotenuse, then

h² = 5² + (\sqrt{2} )² = 25 + 2 = 27 ( take the square root of both sides )

h = \sqrt{27} ← exact value

6 0
3 years ago
Read 2 more answers
What value of x satisfies the equation below?<br> 12 ( x - 2 ) + 3 x = 1 2 ( x + 6 ) + 2
Sergeu [11.5K]

Answer:

x = 32.6666667

Step-by-step explanation:

12(x - 2) + 3x = 12(x + 6) + 2

Distribute;

12x - 24 + 3x = 12x + 72 + 2

Collect like terms;

15x - 24 = 12x + 74

Subtract 12x from both sides;

3x - 24 = 74

Add 24 to both sides;

3x = 98

Divide both sides by 3;

x = 32.6666667

4 0
3 years ago
You are given the following equation.
saul85 [17]

Answer:

Step-by-step explanation:

Given the equation  4x²+ 49y² = 196

a) Differentiating implicitly with respect to y, we have;

8x + 98y\frac{dy}{dx} = 0\\98y\frac{dy}{dx}  = -8x\\49y\frac{dy}{dx}  = -4x\\\frac{dy}{dx} = \frac{-4x}{49y}

b)  To solve the equation explicitly for y and differentiate to get dy/dx in terms of x,

First let is make y the subject of the formula from the equation;

If 4x²+ 49y² = 196

49y² = 196 - 4x²

y^{2} =  \frac{196}{49}  - \frac{4x^{2} }{49} \\y = \sqrt{\frac{196}{49}  - \frac{4x^{2} }{49} \\} \\

Differentiating y with respect to x using the chain rule;

Let u=  \frac{196}{49}  - \frac{4x^{2} }{49}

y =  \sqrt{u} \\y =u^{1/2} \\

\frac{dy}{dx}  = \frac{dy}{du} * \frac{du}{dx}

\frac{dy}{du} = \frac{1}{2}u^{-1/2} \\

\frac{du}{dx} =  0 - \frac{8x}{49} \\\frac{du}{dx} =\frac{-8x}{49} \\\frac{dy}{dx} = \frac{1}{2} ( \frac{196}{49}  - \frac{4x^{2} }{49})^{-1/2} *  \frac{-8x}{49}\\\frac{dy}{dx} = \frac{1}{2} (  \frac{196-4x^{2} }{49})^{-1/2} *  \frac{-8x}{49}\\\frac{dy}{dx} = \frac{1}{2} ( \sqrt{ \frac{49}{196-4x^{2} })} *  \frac{-8x}{49}\\\frac{dy}{dx} = \frac{1}{2} *{ \frac{7}\sqrt {196-4x^{2} }} *  \frac{-8x}{49}\\

\frac{dy}{dx} = \frac{-4x}{7\sqrt{196-4x^{2} } }

c) From the solution of the implicit differentiation in (a)

\frac{dy}{dx} = \frac{-4x}{49y}

Substituting y = \sqrt{\frac{196}{49}  - \frac{4x^{2} }{49} \\ into the equation to confirm the answer of (b) can be shown as follows

\frac{dy}{dx} = \frac{-4x}{49\sqrt{\frac{196-4x^{2} }{49} } }\\\frac{dy}{dx}  =  \frac{-4x}{49\sqrt{196-4x^{2}}/7} }\\\\\frac{dy}{dx}  = \frac{-4x}{7\sqrt{196-4x^{2}}}

This shows that the answer in a and b are consistent.

6 0
3 years ago
Abdul drove 380 miles using 14 gallons of gas. At this rate, how many gallons of gas would he need to drive 418 miles?
Alex17521 [72]

Answer:

<u>15.4 gallons</u>

Step-by-step explanation:

This can be solved using a proportion. Keep in mind that "mi." is miles and "g" is gallons

\frac{14g}{380mi}=\frac{g}{418}

Cross multiply.

380g = 5852

Solve.

\frac{380g}{380}=\frac{5852}{380}  \\\\g = 15.4

Therefore, Adbul would need 15.4 gallons to drive 418 miles.


7 0
3 years ago
Which ray is oppisite to ED
Lerok [7]

You don't have a picture here , but try to see if any ray are maybe parralell .

Hope this helps!

3 0
3 years ago
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