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3 years ago

Find the missing term in the equation

Mathematics

1 answer:

Anika [276]3 years ago

7 0

Answer:

Step-by-step explanation:

4x² - 8x + 8 - x² + 2x - 4 - 3x² + <u>6x</u> = 4

You might be interested in

If 5x - 8 = 37, then x = 9.

lyudmila [28]

Answer:

true

Step-by-step explanation:

5x-8=37

5(9)-8=37

45-8=37

37=37

8 0

3 years ago

A7-ft ladder is placed against a wall with its base 3 ft from the wall. How high above the ground is the top of the ladder? Roun

Firdavs [7]

Answer:

6.3 feet

Step-by-step explanation:

use pythagorean theorem

a² + b² = c²

a² + 3² = 7²

a² + 9 = 49

Subtract 9 from both side

a² = 40

Take the square root of both sides

a = 6.324555320336759

Rounded

a = 6.3

4 0

3 years ago

A right circular cylinder is inscribed in a sphere with diameter 4cm as shown. If the cylinder is open at both ends, find the la

SOVA2 [1]

Answer:

$8\pi\text{ square cm}$

Step-by-step explanation:

Since, we know that,

The surface area of a cylinder having both ends in both sides,

$S=2\pi rh$

Where,

r = radius,

h = height,

Given,

Diameter of the sphere = 4 cm,

So, by using Pythagoras theorem,

$4^2 = (2r)^2 + h^2$ ( see in the below diagram ),

$16 = 4r^2 + h^2$

$16 - 4r^2 = h^2$

$\implies h=\sqrt{16-4r^2}$

Thus, the surface area of the cylinder,

$S=2\pi r(\sqrt{16-4r^2})$

Differentiating with respect to r,

$\frac{dS}{dr}=2\pi(r\times \frac{1}{2\sqrt{16-4r^2}}\times -8r + \sqrt{16-4r^2})$

$=2\pi(\frac{-4r^2+16-4r^2}{\sqrt{16-4r^2}})$

$=2\pi(\frac{-8r^2+16}{\sqrt{16-4r^2}})$

Again differentiating with respect to r,

$\frac{d^2S}{dt^2}=2\pi(\frac{\sqrt{16-4r^2}\times -16r + (-8r^2+16)\times \frac{1}{2\sqrt{16-4r^2}}\times -8r}{16-4r^2})$

For maximum or minimum,

$\frac{dS}{dt}=0$

$2\pi(\frac{-8r^2+16}{\sqrt{16-4r^2}})=0$

$-8r^2 + 16 = 0$

$8r^2 = 16$

$r^2 = 2$

$\implies r = \sqrt{2}$

Since, for r = √2,

$\frac{d^2S}{dt^2}=negative$

Hence, the surface area is maximum if r = √2,

And, maximum surface area,

$S = 2\pi (\sqrt{2})(\sqrt{16-8})$

$=2\pi (\sqrt{2})(\sqrt{8})$

$=2\pi \sqrt{16}$

$=8\pi\text{ square cm}$

4 0

3 years ago

Find the area of a space figure is its a rectagle with triangle on each end

vladimir1956 [14]

Formula for surface area of a triangular prism: bh+2ls+lb
(7*4)+2(8*5)+(8*7)
28+80+56
=164 cm^2

5 0

3 years ago

Compared to last year, the population of boom town has increased by 24%. The population is now 6,600. What was the population la

CaHeK987 [17]

Answer:

1,584

Step-by-step explanation:

6,600 multiplied by 24%(or 0.24) is 1,584

8 0

3 years ago