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2 years ago

14

HURRY please answer thisWhich expression is represented by the model?

1 answer:

Irina18 [472]2 years ago

3 0

Respuesta:

es una operacion aritmetica de sustraccion. sustraes la variante o la pones en negativo.

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A closed, rectangular-faced box with a square base is to be constructed using only 36 m2 of material. What should the height h a

kkurt [141]

Answer:

$b=h=\sqrt{6}$ m

Step-by-step explanation:

Let

Bas length of box=b

Height of box=h

Material used in constructing of box=36 square m

We have to find the height h and base length b of the box to maximize the volume of box.

Surface area of box= $2b^2+4bh$

$2b^2+4bh=36$

$b^2+2bh=18$

$2bh=18-b^2$

$h=\frac{18-b^2}{2b}$

Volume of box, V= $b^2h$

Substitute the values

$V=b^2\times \frac{18-b^2}{2b}$

$V=\frac{1}{2}(18b-b^3)$

Differentiate w. r.t b

$\frac{dV}{db}=\frac{1}{2}(18-3b^2)$

$\frac{dV}{db}=0$

$\frac{1}{2}(18-3b^2)=0$

$\implies 18-3b^2=0$

$\implies 3b^2=18$

$b^2=6$

$b=\pm \sqrt{6}$

$b=\sqrt{6}$

The negative value of b is not possible because length cannot be negative.

Again differentiate w.r.t b

$\frac{d^2V}{db^2}=-3b$

At $b=\sqrt{6}$

$\frac{d^2V}{db^2}=-3\sqrt{6}$

Hence, the volume of box is maximum at $b=\sqrt{6}$ .

$h=\frac{18-(\sqrt{6})^2}{2\sqrt{6}}$

$h=\frac{18-6}{2\sqrt{6}}$

$h=\frac{12}{2\sqrt{6}}$

$h=\sqrt{6}$

$b=h=\sqrt{6}$ m

7 0

3 years ago

Factor completely, then place the answer in the proper location on the grid. 6x ^2 - 3x - 30

seraphim [82]

Factor out the GCF first
3(2x² - x - 10)
3(2x - 5)(x + 2)

3 0

3 years ago

Read 2 more answers

Traveling math word problem - thank you! :)

Anni [7]

<u>We are given:</u>

car and train leave at the same time

average velocity of car = 50 miles/hour

average velocity of train = 70 miles/hour

train arrives 2 hours early

<u>Assuming variables and making equations!</u>

let the time taken by the train = t hours

since the car arrived late, it took more time as compared to the train

time taken by the car = t + 2 hours

since the distance from Pasadena to Sacramento doesn't change, both the vehicles covered the same distance, d

<u>Distance travelled by the car:</u>

d = 50 $\frac{miles}{hour}$ * (t+2) hours [distance = velocity * time]

d = 50(t+2) miles

rewriting in terms of t

$t = \frac{d-100}{50}$

<u>Distance travelled by the train:</u>

d = 70 $\frac{miles}{hour}$ * t hours

d = 70t miles

rewriting in terms of t

$t = \frac{d}{70}$

now we have two expressions for t, both of which are equal because t is just the time taken by the train

<u>Finding the distance:</u>

<u></u> $t = \frac{d-100}{50}$ <u></u>

<u></u> $t = \frac{d}{70}$ <u></u>

because t is the same:

$\frac{d-100}{50} = \frac{d}{70}$

$\frac{d-100}{5} = \frac{d}{7}$

7(d - 100) = 5(d)

7d - 700 = 5d

(7d - 5d) - 700 = 0 [subtracting 5d from both sides]

2d = 700 [adding 700 on both sides]

d = 350 miles [dividing both sides by 2]

The distance between Pasadena and Sacramento is 350 miles!

7 0

2 years ago

Evan used half of his pay check for his car payment, then $125 for groceries. If he has $215 left, how much was his paycheck?

elena-s [515]

680 because if 125+215=340 then that’s the car payment. Multiply that by two and you get your answer.

7 0

3 years ago

Which of the following is the multiplicative inverse of 12x/5? a)5/12x b)12x/5 c)- 5/12x d)- 12x/5

fgiga [73]

The product of a number and its multiplicative inverse is 1.
12x/5 * 5/12x = 1

Therefore, the multiplicative inverse of 12x/5 is 5/12x

7 0

3 years ago