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3 years ago

Find the sum of – 52 , -36 , 42, 8 ,-22 and 46

Mathematics

1 answer:

vampirchik [111]3 years ago

6 0

-52-36-22+46+42+8 = -18

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A sheet of paper 90 cm-by-66 cm is made into an open box (i.e. there's no top), by cutting x-cm squares out of each corner and f

NNADVOKAT [17]

Answer:

$26 - \sqrt{181}$ cm

Step-by-step explanation:

The volume of the box is:

V = height * length * width

V = x*(66 - 2*x)*(90 - 2*x)

V = (66*x - 2*x^2)*(90 - 2*x)

V = 5940*x - 132*x^2 - 180*x^2 + 4*x^3

V = 4*x^3 - 312*x^2 + 5940*x

where x is the length of the sides of the squares, in cm.

The mathematical problem is :

Maximize: V = 4*x^3 - 312*x^2 + 5940*x

subject to:

x > 0

2*x < 66 <=> x < 33

In the maximum, the first derivative of V, dV/dx, is equal to zero

dV/dx = 12*x^2 - 624*x + 5940

From quadratic formula

$x = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)}$

$x = \frac{624 \pm \sqrt{(-624)^2 - 4(12)(5940)}}{2(12)}$

$x = \frac{624 \pm \sqrt{104256}}{24}$

$x = \frac{624 \pm \sqrt{2^6*3^2*181}}{24}$

$x = \frac{624 \pm 8*3*\sqrt{181}}{24}$

$x_1 = \frac{624 + 24*\sqrt{181}}{24}$

$x_1 = 26 + \sqrt{181}$

$x_2 = \frac{624 - 24*\sqrt{181}}{24}$

$x_2 = 26 - \sqrt{181}$

But $x_1 > 33$ , then is not the correct answer.

5 0

3 years ago

Identify the coefficient in the term 7x^2y^3

Advocard [28]

Answer:

<h3>LARGEST COEFFICIENT = 7</h3><h3>SMALLEST COEFFICIENT=2</h3><h3>STANDARD FORM=7,0,0,0,3,2,0,0</h3><h3>COEFFICIENTS =7,3,2</h3>

3 0

3 years ago

What equation represents the graphed function

Marina86 [1]

Answer: $y=\dfrac{-1}{3}x+3$

Step-by-step explanation:

The equation of ab line that passes through two points (a,b) and (c,d) is given by :-

$(y-b)=\dfrac{d-c}{b-a}(x-a)$

From the given picture , the line is passing through points (0,3) and (3,2).

Then, the equation of the line will be :-

$(y-3)=\dfrac{2-3}{3-0}(x-0)$

$\Rightarrow y-3=\dfrac{-1}{3}x$

$\Rightarrow y=\dfrac{-1}{3}x+3$

Hence, the required equation of the line that represents the graphed function : $y=\dfrac{-1}{3}x+3$

7 0

3 years ago

Read 2 more answers

Simplify cos(θ) − sec(θ) /<br> sin(θ)

Salsk061 [2.6K]

<span>Replace tan θ with sin θ/cos θ

= sin²θ/cos θ + cos θ

Now multiply the right-hand side by cos θ/cos θ to get the same denominator:

= sin²θ/cos θ + cos²θ/cos θ
= (sin²θ + cos²θ)/cos θ

The numerator is equivalent to 1:

= 1 / cos θ
= sec θ</span>

7 0

3 years ago

when johns age is doubled, the number is 5 more than kaylas age. if john is x years old, what is kayalas age?

Sunny_sXe [5.5K]

Answer:

Ang mga Babae sa Relihiyon at Pilosopiya sa Asya. Limang Ugnayan. emperador-mamamayan. ama-anak na lalaki.

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2 years ago