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3 years ago

Solve similar triangles solve for x can someone answer please help

Mathematics

1 answer:

zlopas [31]3 years ago

8 0

Answer:

Step-by-step explanation:

ΔABC & ΔADE are similar triangles

$\frac{AD}{AB}=\frac{DE}{BC}\\\\\frac{12}{4}=\frac{12}{x}\\$

Cross multiply,

12*x = 12*4

$x=12*\frac{4}{12}\\$

x = 1 * 4

x = 4

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Help please calculus

VLD [36.1K]

Let x, y, and z denote the side lengths of the box, with the bottom face having dimensions x-by-y and z is the height. Naturally this means each of x, y, and z must be greater than 0.

The box has a fixed volume of 252 cm³, so

xyz = 252

The surface area of the box is

2xy + 2xz + 2yz

and we're told that the material cost for each face is different. The total cost of the material needed to make the box is given by

C (x, y, z) = ($5/cm²) xy + ($2/cm²) xy + 2 ($3/cm²) (xz + yz)

or, omitting units and simplifying,

C (x, y, z) = 7xy + 6 (x + y) z

In the volume constraint, solve for any one variable; I'll do z.

z = 252/(xy)

Substitute this into the cost function:

C (x, y, 252/(xy)) = 7xy + 1512 (x + y)/(xy)

Since this is now a function of 2 variables, I'll rewrite this as

C* (x, y) = 7xy + 1512 (1/y + 1/x)

Compute the partial derivatives of C and find the critical points:

∂C/∂x = 7y - 1512/x² = 0 ⇒ x² y = 216

∂C/∂y = 7x - 1512/y² = 0 ⇒ x y² = 216

It follows that

x² y = x y² ⇒ x = y

Just like before, we can think about C* as yet another function but only of 1 variable,

C** (x) = 7x² + 3024/x

Now find the critical points of C** :

dC**/dx = 14x - 3024/x² = 0 ⇒ x = 6

All of this tells us that C (x, y, z) has a critical point when x = y = 6 and z = 252/6² = 7. So the box that costs the least has dimensions 6 × 6 × 7 cm, which gives the box a surface area of 240 cm² and a total cost of $756.

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Answer:

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Step-by-step explanation:

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Answer: Approximately normal, because we expect 19.2 successes and 20.8 failures from people in their twenties, and 16.8 and 43.2 from people in their fifties, and all of these counts are at least 10.

Step-by-step explanation:

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2 years ago

15/13 as a mixed number!!

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Answer:

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Step-by-step explanation:

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