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3 years ago

Solve 5n – 7p + 3n = 25p for n.

Mathematics

2 answers:

jekas [21]3 years ago

8 0

Simplifying:

5n + -7p + 3n = 25p

Reorder the terms:

5n + 3n + -7p = 25p

Combine like terms: 5n + 3n = 8n

8n + -7p = 25p

Solving:

8n + -7p = 25p

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '7p' to each side of the equation.

8n + -7p + 7p = 25p + 7p

Combine like terms: -7p + 7p = 0

8n + 0 = 25p + 7p

8n = 25p + 7p

Combine like terms: 25p + 7p = 32p

8n = 32p

Divide each side by '8'.

n = 4p

Simplifying:

n = 4p

Hope this helps!

saul85 [17]3 years ago

7 0

5n – 7p + 3n = 25p

Combine like terms

8n - 7p = 25p

Add (7p) to both sides

8n - 7p + 7p = 25p + 7p

Simplifying

8n = 32p

Divide both sides by 8

8n / 8 = 32p / 8

Simplifying

n = 4p

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3 years ago

Find the distance between the line 1.2x − 0.5y + 1.1=0 and the origin.

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Answer:

The answer to your question is: d = 0.85 units

Step-by-step explanation:

Data

Line equation: 1.2 x − 0.5 y + 1.1 = 0 A = 1.2; B = -0.5; C = 1.1

Point (0, 0) x = 0; y = 0

Formula

d = | Ax + By + C | / √(A² + B²)

Process

d = |(1.2)(0) + (-0.5)(0) + 1.1 | / √ (1.2)² + (0.5)²

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2 years ago

Rational number between - 4/7 and 8/4

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Step-by-step explanation:

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2 years ago

A box with a square base and an open top is being constructed out of A cm2 of material. If the volume of the box is to be maximi

viktelen [127]

Answer:

Side length = $\sqrt{\frac{A}{3} }$ cm , Height = $\frac{1}{2} \sqrt{\frac{A}{3} }$ cm , Volume = $\frac{A\sqrt{A}}{6\sqrt{3} }$ cm³

Step-by-step explanation:

Assume

Side length of base = x

Height of box = y

total material required to construct box = A ( given in question)

So it can be written as

A = x² + 4xy

4xy = A - x²

$y = \frac{A - x^{2} }{4x}$

Volume of box = Area x height

V = x² ₓ y

V = x² ₓ ( $\frac{A - x^{2} }{4x}$ )

V = $\frac{Ax - x^{3} }{4}$

To find max volume put V' = 0

So taking derivative equation becomes

$\frac{A - 3 x^{2} }{4} = 0$

A = 3 $x^{2}$

$x^{2}$ = $\frac{A}{3}$

x = $\sqrt{\frac{A}{3\\} }$

put value of x in equation 1

y = $\frac{A - \frac{A}{3} }{4\sqrt{\frac{A}{3} } }$

y = $\frac{2 \sqrt{\frac{A}{3} } }{4 \sqrt{\frac{A}{3} } }$

y = $\frac{1}{2} \sqrt{\frac{A}{3} }$

So the volume will be

V = $x^{2}$ × y

Put values of x and y from equation 2 & 3

V = $\frac{A}{3} (\frac{1}{2} \sqrt{\frac{A}{3} } )$

V = $\frac{A\sqrt{A}}{6\sqrt{3} }$

8 0

3 years ago