A cube has a surface area of 54 square centimeters, what is the side length?

Answer:

[tex]x=\log_3{(15+ 4\sqrt{14})}\approx3.0949\text{ or } \\x=\log_3{(15- 4\sqrt{14})}\approx-3.0949[/tex]

Step-by-step explanation:

So we have the equation:

[tex]3^{1-x}+3^{1+x}=90[/tex]

First, note that this is the same as:

[tex]3\cdot 3^{-x}+3\cdot 3^x=90[/tex]

Factor out a 3:

[tex]3(3^{-x}+3^{x})=90[/tex]

Divide both sides by 3:

[tex]3^{-x}+3^x=30[/tex]

Change the negative exponent into a fraction:

[tex]\frac{1}{3^x}+3^x=30[/tex]

Multiply both sides by 3^x:

[tex]3^x(\frac{1}{3^x}+3^x)=(30)(3^x)[/tex]

Distribute:

[tex](1)+(3^x)^2=30(3^x)[/tex]

Let u equal 3^x. So:

[tex]1+u^2=30u[/tex]

Subtract 30u from both sides:

[tex]u^2-30u+1=0[/tex]

This is a quadratic. Solve using the quadratic formula. A is 1, b is -30, and c is 1. So:

[tex]u=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Substitute:

[tex]u=\frac{-(-30)\pm \sqrt{(-30)^2-4(1)(1)}}{2(1)}[/tex]

Simplify:

[tex]u=\frac{30\pm \sqrt{900-4}}{2}[/tex]

Subtract:

[tex]u=\frac{30\pm \sqrt{896}}{2}[/tex]

Simplify:

[tex]u=\frac{30\pm 8\sqrt{14}}{2}[/tex]

Simplify:

[tex]u=15\pm 4\sqrt{14}[/tex]

Substitute back u:

[tex]3^x=15\pm 4\sqrt{14}[/tex]

Take the log to base 3 of both sides:

[tex]\log_3{3^x}=\log_3{15\pm 4\sqrt{14}}[/tex]

The left side cancels:

[tex]x=\log_3{15\pm 4\sqrt{14}}[/tex]

So, our solutions are:

[tex]x=\log_3{(15+ 4\sqrt{14})}\approx3.0949\text{ or } \\x=\log_3{(15- 4\sqrt{14})}\approx-3.0949[/tex]

And we're done!

Answer:

ii) curved surface area =2 pie rh

2*22/7*14*21

1548 cm2

iii) total surface area=2 pie r(r+h)

2*22/7*14(14+21)

2780

iv) volume of cylinder=pie r2h

22/7*14*14*21

12936 ans

Step-by-step explanation:

Answer:

As = 2112 cm²

Step-by-step explanation:

given:

A cylinder has a circular base radius 14cm and height of 10cm.

find:

the total surface area of the cylinder. [take pie 22/7] *​

solution:

surface area (As) = 2πrh + 2πr²

where r = 14 cm;    h = 10 cm;   π = 22/7

plugin values into the formula:

As = 2 (22/7) 14 (10) + 2 (22/7) 14²

As = 880 + 1232

As = 2112 cm²

Answer:

x = 15

Step-by-step explanation:

Use the direct variation equation, y = kx

Plug in the values of x and y to find k

y = kx

104 = k(8)

13 = k

So, the direct variation equation will be y = 13x

Plug in 195 as y to find x

y = 13x

195 = 13x

15 = x

So, x = 15 when y = 195

As The value of y varies directly with x, when y = 195, x will be 15.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, The value of y varies directly with x.

∴ y = kx.

If x = 8, then y = 104.

104 = 8k.

k = 104/8.

k = 13.                                  (constant of proportionality)

Now,  y =195.

∴ 195 = 13x.

x = 195/13.

x = 15

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Answer:

There is no picture, my sweetheart.

Step-by-step explanation:

Answer:

a+62=65

Step-by-step explanation:

if a=3 then 62+3=65

Answer:

76

Step-by-step explanation:

140-56= 84

140-84=56

160-84=76

Answer:

150

Step-by-step explanation:

125/2.5=50

50x3 =150

Answer:

150

Step-by-step explanation:

I took the Practice/Instruction :)

d. 1440

I'm guessing you mean hours in a school yr

8 hrs in a day x 180 days = 1440 hrs in 1 school yr

how many 'hours' are there in a school year?

answer: D

8 hours a day x 180 days ( one school year)

8 x 180

= 1440 hours

Answer:

it is 5/2

Step-by-step explanation:

Answer:

7.07

Step-by-step explanation:

See image for explanation

Answer:

Step-by-step explanation:

Perimeter= 46

Area of rectangle= Length * Width

Ratio                    =       2 : 1

= Length= 2/3 * 46 = 30.6/2 = 15.3

Width = 1/3 * 46 = 15.3/2 = 7.65

Area= 117.045

Answer:

8

Step-by-step explanation:

2 (2)(2)

2 times itself 3 times.

Answer: 8

Step-by-step explanation: Since 2 is to the power of 3 that means multiply by itself 3 times, so 2 x 2 x 2 = 8.

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Answer: What is the volume of a book when the length is 42 cm, the width is 12 cm and the height is 4 cm?  2016 (length x width x height)

What is the mass of a rock if the volume is 54 ml and the density is 3.2 g/ml?  172.8 (when finding the mass you always multiply the volume and density so 54ml x 3.2 g/ml = 172.8)

What is the density of a block of wood that has a mass of 38 g and a volume of 19 cm3?  2cm3 (38g/19cm3=2cm3

What is the density of a box if the mass is 160 g and the volume is 12 ml?  13.3 (160/12=13.3)

What is the volume of a shark’s tooth when you start with 75 ml of water in a graduated cylinder and when the shark’s tooth is placed in the water, the water level rises to 90 ml? (use water displacement) 15 (If you measure the amount the water level increases, you can find the volume of the water pushed out of the way.)

The mass of a pencil is 8 g and the density is 1.24 g/ cm3. What is the volume of the pencil? 6.45cm3  (8/1.24/cm3=6.45

Step-by-step explanation:

Answer:

[tex] m\angle L = 111\degree \\

m\angle M = 69\degree [/tex]

Step-by-step explanation:

Since, angle L and angle M are supplementary.

[tex]\therefore m\angle L + m\angle M= 180\degree \\ \therefore \: 12x + 45 + 18x - 30 = 180 \degree \\ \therefore \: 30x + 15= 180 \degree\\ \therefore \: 30x= 180 \degree - 15 \degree\\ \therefore \: 30x= 165 \degree \\ x = \frac{165 \degree}{30} \\ x = 5.5 \degree \\ \\ m\angle L = 12x + 45 \\ m\angle L = 12 \times 5.5 + 45 \\ m\angle L = 66 + 45 \\ \huge \red{ \boxed{ m\angle L = 111 \degree}} \\ \\ m\angle M=18x - 30 \\ m\angle M=18 \times 5.5 - 30 \\ m\angle M=99 - 30 \\ \huge \purple{ \boxed{ m\angle M=69 \degree}} \\ [/tex]

Answer:

4^3 and 8^2

Step-by-step explanation:

Answer:

12

2

Step-by-step explanation:

4 × 4 × 4 × 8 x 8

Solution:

2 2 2 3 3 2+2+2+3+3

2 x 2 x 2 x 2 x 2 = 2

12

2

2 raised to the 12 power

Answer:

266

Step-by-step explanation:

Answer:34.00-29.99=4.01. 4.01÷0.17=

Step-by-step explanation:

Answer:

-6 and -4

Step-by-step explanation:

-6 + -4 = -10

-6- - 4 = -2

Answer:

C. reflection across the x-axis

Answer:

C

Step-by-step explanation:

This is a reflection across the x-axis because it is the same thing but reflected.

Hope this helps.

Answer:

-11=x

Step-by-step explanation:

2/5x-3.6 is the simplified when you DISTRIBUTE 2/5 multiplying both parts of the parentheses. Add 3.6 to both sides 2/5x=-4.4 then 2x=-22, x=-11

Answer:

Two.

Step-by-step explanation:

In algebra, a term is either a single number or variable, or numbers and variables multiplied together. In any equation, all of the numbers there that aren't divided by a mathematical operation (times or divide symbols) are terms.

3x2 isn't a term, it's an expression - but 5x and 9 are, so therefore there are 2 terms.

Answer:

não sei....................

Answer:

1,298

Step-by-step explanation:

Step 1:

1,278 + 20

Answer:

1,298

Hope This Helps :)

Answer:

1298

Step-by-step explanation:

20+1278=1298

Answer:

0.07

Step-by-step explanation:

Answer:

Step-by-step explanation:

(x - 3)/2= 1

x - 3 = 2

x = 5

(y - 8)/2 = -2

y - 8 = -4

y = 4

(5, 4) coordinates for B

The coordinates of B are (5, 4) if the midpoint of AB is M(1,-2). If the coordinates of A are (-3, -8),

It is defined as a representation of coordinates in a two-dimensional coordinate plane. It has a list of two elements in it, such as (x, y).

[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]

It is given that:

The midpoint of AB is M(1,-2). If the coordinates of A are (-3, -8).

Let the coordinate of B is (x, y)

From the midpoint theorem:

(x - 3)/2= 1

x - 3 = 2

x = 5

For y coordinate:

(y - 8)/2 = -2

y - 8 = -4

y = 4

(5, 4) coordinates for B

Thus, the coordinates of B are (5, 4) if the midpoint of AB is M(1,-2). If the coordinates of A are (-3, -8),

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Answer: The answer is x = -19

Answer:

-19

Step-by-step explanation:

9x - 5x -3x = -14 -5

1x = -19

Answer:

8/2

Step-by-step explanation:

n = 2

My picture shows my work :)

Answer:

A.  12

Step-by-step explanation:

a = -7

b = -4

c = 5

ignore B. counting should be till the desired grid which is C

AC = 7 + 5

AC = 12

Answer: 12

Step-by-step explanation: just count their distance by 1