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3 years ago

What is the surface area of this right rectangular prism with dimensions of 5 centimeters by 5 centimeters by 12 centimeters?

1 answer:

4 0

The formula I like to use is
A = 2(LW + H(L+W))
For your dimensions, this is
A = 2((5 cm)(5 cm) + (12 cm)(5 cm + 5 cm))
A = 2(25 cm² + 120 cm²)
A = 290 cm²

The surface area of your right rectangular prism is 290 cm².

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Calculate the distance between (8 - 2i) and (4- 2i)

kifflom [539]

Answer:

The Problem:

Compute the distance between 8-2i and 4-2i.

Step-by-step explanation:

This is equivalent to asking the distance from point (8,-2) to point (4,-2).

The nice thing about this problem is that the y-coordinates are the same which means it is just a horizontal distance. It can either be counted or just find the distance between the x's by finding the positive difference; that is do larger minus smaller.

8-4=4.

The distance between the points is 4.

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3 years ago

Exponential growth can anyone give the answers to me? I’m completely lost!

PilotLPTM [1.2K]

Answer:

The exponential growth model for frogs:

F(x) = 100(1.22)ˣ,

F- number of frogs, x- number of years, 1.22 - growth factor

Calculations:

F(5) = 100(1.22)⁵ = 270
a) F(10) = 100(1.22)¹⁰ = 730
b) F(20) = 100(1.22)²⁰ = 5335

All numbers rounded

The exponential growth model for bacteria:

B(x) = 10(1.8)ˣ

B- number of bacteria, x- number of hours, 1.8 - growth factor

Calculations:

a) B(5) = 10(1.8)⁵ = 189
b) B(24) = 10(1.8)²⁴ = 13382588
c) B(168) = 10(1.8)¹⁶⁸ = 7.68 * 10⁴³

All numbers rounded

Q3.

The exponential growth model for fish:

F(x) = 821(1.02)ˣ,

F- number of fish, x- number of months, 1.02 - growth factor

Calculations:

a) F(12) = 821(1.02)¹² = 1041
b) F(120) = 821(1.02)¹²⁰ = 8838

All numbers rounded

3 0

3 years ago

Read 2 more answers

Nirmala graphed the relationship between the duration (in hours) of using an oil lamp and the volume (in milliliters) of oil rem

mariarad [96]

Answer:

Nirmala can use the lamp for 31.66 hours before it runs out of oil.

Step-by-step explanation:

From the graph,

Take any two points, let say

(15, 25)

(25, 10)

$\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(15,\:25\right),\:\left(x_2,\:y_2\right)=\left(25,\:10\right)$

$m=\frac{10-25}{25-15}$

$m=-\frac{3}{2}$

The equation of line in slope-intercept form

$y = mx + b$

Putting $m=-\frac{3}{2}$ and any point, let say (25, 10), to find the y-intercept 'b'

$10=-\frac{3}{2}\left(25\right)+b$

$-\frac{3}{2}\left(25\right)+b=10$

$-\frac{75}{2}+b=10$

$\mathrm{Add\:}\frac{75}{2}\mathrm{\:to\:both\:sides}$

$-\frac{75}{2}+b+\frac{75}{2}=10+\frac{75}{2}$

$b=\frac{95}{2}$

$b=47.5$

So the equation of line will be:

$y = mx + b$

$y=-\frac{3}{2}x+47.5$

In order to find how long Nirmala can use the lamp before it runs out of oil, we need to find x-intercept which can be obtained by putting y = 0, and solve for x, as duration lies on x-axis.

$y=-\frac{3}{2}x+47.5$

Putting y = 0

$0=-\frac{3}{2}x+47.5$