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2 years ago

10

Three same-sized cubes are attached to the top of a rectangular prism as shown below. If a = 13 cm, b = 21 cm, and c = 3 cm, wha

t is the surface area of the figure?
Write your answers as square centimeters

1 answer:

aalyn [17]2 years ago

3 0

Answer:

819

Step-by-step explanation:

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If The area of a triangle is 84 square meters. What is the base if the height is 12 meters?

Delicious77 [7]

Answer:

14

Step-by-step explanation:

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2 years ago

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Help me out please :(?

Andre45 [30]

Answer:

3x2+15x=18

Step 1: Subtract 18 from both sides.

3x2+15x−18=18−18

3x2+15x−18=0

Step 2: Factor left side of equation.

3(x−1)(x+6)=0

Step 3: Set factors equal to 0.

x−1=0 or x+6=0

x=1 or x=−6

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3 years ago

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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

I need help, please..

Assoli18 [71]

Answer:

£1.31

Step-by-step explanation:

5:7:12

5x+7x+12x= 216
24x= 216
x= 9

small : medim : large = 45 : 63 : 108

45y+63*2y+108*3y= 648.45
y(45+126+324)= 648.45
495y= 648.45
y= 648.45/495
y= £1.31 profit for small cake

5 0

3 years ago

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8 − 5(3x − 7) <br><br> A 15x + 43 <br><br> B 9x-12<br><br> C -9x + 12<br><br> D -15x+43

gayaneshka [121]

8-5(3x-7)

Distribute:
8-15x+35

Combine like terms:
-15x+43

So, 'D' would be your answer.

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3 years ago