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Butoxors [25]
3 years ago
8

Let f(x)=16x^2-x. Find f(x+1)-f(x)

Mathematics
1 answer:
olasank [31]3 years ago
8 0

f(x+1) = 16(x+1)² - (x+1) = 16(x²+2x+1) - x - 1

= 16x² + 32x + 16 - x - 1 = 16x²+31x+15

so

f(x+1)-f(x) = 16x²+31x+15 - (16x² - x)

= 16x²+31x+15 - 16x² + x

= 32x + 15

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If breadth of a cuboid is one-fourth of its length,height is 5cm and total surface area is 328 cm²,find the length and breadth o
velikii [3]

The length of cuboid is 16 cm and breadth of cuboid is 4 cm.

<h3>How to find the Surface Area of Cuboid?</h3>

A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (L), Breadth (B), and Height (H) of the cuboid and use the formula, SA=2 x ( LB + BH + HL ) , to find the surface area.

Here, We have given that height of the cuboid is 5cm.

Let length of the cuboid = X cm

so, the breadth of the cuboid = \frac{X}{4} cm

also, we have given that total surface area is 328 cm²

Now, put all the values in the formula of Surface Area (SA):

SA = 2 x ( LB + BH + HL )

SA = 2 x ( X²/4 + 5X/4 + 5X )

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using Quadratic Formula: see the attached figure for the formula.

here Discriminant D = b² - 4ac

D = 625 - 4(-656)

D = 3249

on putting value of D or b² - 4ac in the formula we get

X =  ( -25 + 57 ) / 2 and ( -25 - 57 ) /2

length can not be negative so we eliminate the second answer.

now, X = 16 cm

breadth = X /4 = 4 cm

Hence, The length of cuboid is 16 cm and breadth of cuboid is 4 cm.

Learn more about " Quadratic Formula " from here: brainly.com/question/2615966

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Answer:

its \: dimensions \: are \to \\\boxed{w = 17.6cm}  \: \boxed{l = 78.4cm}

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