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2 years ago

What dimensions will produce a square-based box, of minimum surface area, with volume of

Mathematics

1 answer:

Mashutka [201]2 years ago

3 0

Answer:

the total surface of the box is 486 cm 2

.......

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the measure of one angle of the angles in a linear is 30 less than one-half the measure of the other angle. Find the measure of

SVETLANKA909090 [29]

Answer:

140° and 40°

Step-by-step explanation:

let x be one angle then the other is $\frac{1}{2}$ x - 30

Since the angles are a linear pair, theis sum is 180° , then

x + $\frac{1}{2}$ x - 30 = 180, that is

$\frac{3}{2}$ x - 30 = 180 ( add 30 to both sides )

$\frac{3}{2}$ x = 210 ( multiply both sides by 2 to clear the fraction )

3x = 420 ( divide both sides by 3 )

x = 140

and $\frac{1}{2}$ x - 30 = $\frac{1}{2}$ (140) - 30 = 70 - 30 = 40

The 2 angles are 140° and 40°

7 0

3 years ago

Which statement about the dilation of these triangles is true?

alexandr402 [8]

B) I believe it’s b

6 0

3 years ago

The base of a solid is the region enclosed by the graphs of y=e^x, y=0, x=0, and x = 1. If each cross-section perpendicular to t

yanalaym [24]

Answer:

Step-by-step explanation:

The base of a solid in the region enclosed by the graphs of y = eˣ, y = 0, x = 0, and x = 1. Each cross-section perpendicular to the x-axis is an equilateral triangle. We want to find the volume of the solid.

Please refer to the graph below. We are concerned with the red region.

In order to find the volume, we essentially sum up the area of the figure at each x value. So, we integrate from x = 0 to x = 1.

The area for an equilateral triangle is given by:

$\displaystyle A=\frac{\sqrt{3}}{4}s^2$

Where s is the side length of the triangle.

Since the triangle lies perpendicular on the region, the side length of the triangle at x is simply y, which is eˣ.

Therefore, our volume is:

$\displaystyle V=\int_0^1\frac{\sqrt3}{4}(y)^2\, dx$

Substitute:

$\displaystyle V=\int_0^1\frac{\sqrt3}{4}(e^x)^2\, dx$

Evaluate the integral. Simplify:

$\displaystyle V=\frac{\sqrt3}{4}\int_0^1e^{2x}\, dx$

Integrate using u-substitution:

$\displaystyle V=\frac{\sqrt3}{8}\left(e^{2x}\Big|_0^1\right)$

Evaluate:

$\displaystyle V=\frac{\sqrt3}{8}\left(e^{2(1)}-e^{2(0)} \right)$

Therefore, the volume of the solid is:

$\displaystyle V=\frac{\sqrt3}{8}\left(e^2-1\right)$

Our answer is A.

3 0

3 years ago

Read 2 more answers

1. Which equation is equivalent to the equation 6x + 9 = 12?

yanalaym [24]

Answer:

Step-by-step explanation:

if we divide both sides of 6x + 9 = 12 by 3

(6x + 9)/3 = 12/3

2x + 3 = 4 ---> which matches choice B

4 0

4 years ago

Read 2 more answers

In kite WXYZ, mZWY = 41° and mXYW = 11° What is mWZY?

olchik [2.2K]

Answer:

128°

Step-by-step explanation:

In kite WXYZ, WY and XZ are longer and smaller diagonals respectively.

Longer diagonal bisects the opposite angles.

$\therefore m\angle ZYW =m\angle XYW$

$\because m\angle XYW = 11\degree... (given)$

$\therefore m\angle ZYW =11\degree$

$In\: \triangle WYZ$

$m\angle ZYW + m\angle ZWY + m\angle WZY=180\degree$

$11\degree + 41\degree+ m\angle WZY=180\degree$

$52\degree+ m\angle WZY=180\degree$

$m\angle WZY=180\degree - 52\degree$

$\purple{\bold {m\angle WZY=128\degree}}$

8 0

3 years ago