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3 years ago

Cindy works at Jurassic Park and has been tasked to design a container in the shape of a

Mathematics

1 answer:

vichka [17]3 years ago

8 0

The amount Cindy should increase for each dimension of the scaled model will be 12 meters.

<h3>What is the scale factor?</h3>

The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.

Given that:-

The scaled model of the container has dimensions of 2m by 4m by 6m. Cindy has decided to increase each dimension of the scaled model by the same amount in order to produce a container with a volume of 84 times the volume of the scale model.

The scale model will be solved as follows:-

Present volume = 2 x 4 x 6 = 48 cubic meters

Let the lengths be increased by x meters now the new volume will be:-

( 2 + x ) ( 4 + x ) ( 6 + x ) = 48 x 84

( x² + 6x + 8 ) ( 6 + x ) = 48 x 84

( x³ + 44x + 12x² - 3984 ) = 0

By solving the cubic equation we will get the value of x = 12 meters.

Therefore the amount Cindy should increase for each dimension of the scaled model will be 12 meters.

To know more about scale factors follow

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gregori [183]

Huy b yan alam ko na yan matagal na ako nyan

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3 years ago

The function f(x,y)=2x + 2y has an absolute maximum value and absolute minimum value subject to the constraint 9x^2 - 9xy + 9y^

deff fn [24]

Answer:

the minimum is located in x = -5/3 , y= -5/3

Step-by-step explanation:

for the function

f(x,y)=2x + 2y

we define the function g(x)=9x² - 9xy + 9y² - 25 ( for g(x)=0 we get the constrain)

then using Lagrange multipliers f(x) is maximum when

fx-λgx(x)=0 → 2 - λ (9*2x - 9*y)=0 →

fy-λgy(x)=0 → 2 - λ (9*2y - 9*x)=0

g(x) =0 → 9x² - 9xy + 9y² - 25 = 0

subtracting the second equation to the first we get:

2 - λ (9*2y - 9*x) - (2 - λ (9*2x - 9*y))=0

- 18*y + 9*x + 18*x - 9*y = 0

27*y = 27 x → x=y

thus

9x² - 9xy + 9y² - 25 = 0

9x² - 9x² + 9x² - 25 = 0

9x² = 25

x = ±5/3

thus

y = ±5/3

for x=5/3 and y=5/3 → f(x)= 20/3 (maximum) , while for x = -5/3 , y= -5/3 → f(x)= -20/3 (minimum)

finally evaluating the function in the boundary , we know because of the symmetry of f and g with respect to x and y that the maximum and minimum are located in x=y

thus the minimum is located in x = -5/3 , y= -5/3

4 0

4 years ago

Which expression is a factor of 10 x 2 + 11 x + 3

Eduardwww [97]

Answer: the two factors are (5x + 3) and (2x + 1)

Explanation:

I will find the two factors of 10x² + 11x + 3.

You can use either the quadratic formula of factor.

I will use the quadratic formula:

1)

$x= \frac{b^2 +/- \sqrt{b^2-4ac} }{2a}$

$x= \frac{-11+/- \sqrt{11^2-4(10)(3)} }{(2)(10)}$

x = -3/5 and x = -1/2

2) the factors are: x - (-3/5) = 0 and x - (-1/2) = 0

Simplify them.

3) x - (-3/5) = 0

5x + 3 = 0

4) x - (-1/2) = 0

2x + 1 = 0

5) Then the two factors are: (5x + 3) and (2x + 1).

6) verify:

(5x + 3)(2x + 1) = 10x² + 5x + 6x + 3 = 10x² + 11x + 3 which is the original expression.

7 0

3 years ago

Determine whether the series is convergent or divergent. 1 2 3 4 1 8 3 16 1 32 3 64 convergent divergent Correct:

Vanyuwa [196]

Answer:

This series diverges.

Step-by-step explanation:

In order for the series to converge, i.e. $\lim_{n \to \infty} a_n =A$ it must hold that for any small $\epsilon$ >0, there must exist $n_0\in \mathbb{N}$ so that starting from that term of the series all of the following terms satisfy that $|a_n-A|n_0$ .

It is obvious that this cannot hold in our case because we have three sub-series of this observed series. One of them is a constant series with $a_n=1$ , the other is constant with $a_n=3$ , and the third one has terms that are approaching infinity.

Really, we can write this series like this:

$a_n=\begin{cases} 1 \ , \ n=4k+1, k\in \mathbb{N}_0\\ 2^{k}\ , \ n=2k, k\in \mathbb{N}_0\\3\ , \ n=4k+3, k\in \mathbb{N}_0\end{cases}$

If we denote the first series as $b_n=1$ , we will have that $\lim_{k \to \infty} b_k=1$ .

The second series is denoted as $c_k=2^k$ and we have that $\lim_{k \to \infty} c_k=+\infty$ .

The third sub-series $d_k=3$ is a constant series and it holds that $\lim_{k \to \infty} d_k=3$ .

Since those limits of sub-series are different, we can never find such $n_0\\$ so that every next term of the entire series is close to one number.

To make an example, if we observe the first sub-series if follows that A must be equal to 1. But if we chose $\epsilon =1$ , all those terms associated with the third sub-series will be out of this interval $(A-1, A+1)=(0, 2)$ .

Therefore, the observed series diverges.

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4 years ago

A train leaves a station at 10:40 a.m. and arrives at its destination at 1:20 p.m. Find the distance between the stations if the

Katena32 [7]

Average speed = distance / time

60 = distance / (13.20 - 10.40)

13.20 - 10.40 = 2 hours 40 minutes = 2 2/3 hours

60 = distance / 8/3 = 3 d / 8 (where d = distance)

3d = 480

d = 480/3 = 160 miles Answer

4 0

4 years ago