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WITCHER [35]
3 years ago
13

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.

6 0
2 years ago
Dion ran 3.75 kilometers each day to prepare for a race.
Sladkaya [172]

Answer:

105 km

Step-by-step explanation:

3.75 x 28 = 105 km

5 0
3 years ago
Read 2 more answers
A psychologist takes an SRS of 404040 people in their twenties and 606060 people in their fifties and surveys them about their a
Leto [7]

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:

3 0
2 years ago
15/13 as a mixed number!!
stepan [7]

Answer:

1 and 2/13

Step-by-step explanation:

15 can go into 13 once with 2 left over.

8 0
2 years ago
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g There are 3 signal transmitters T1,T2 and T3. Each one sends a signal to a receiver R and R sends three signals back to the th
ANEK [815]

Answer:

Recall that probability is given as; the number of required outcome over the number of total possible outcome.

The probability that a transmitter receives the signal being sent by itself is given as \frac{1}{3}.

when there are n transmitters, the probability will be given as \frac{1}{n}

Step-by-step explanation:

Probability simply the likelihood of an event occurring or not occurring.

Probability therefore is given as; the number of required outcome over number of possible outcome.

In the case of the first part above we have the number of required outcome to be at least one divided by the number of possible outcome which is 3.

while in the second part we have the number o possible outcome to be n.

7 0
3 years ago
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