Find the area of a regular pentagon with an apothem of 2.75 cm and a side length of 4 cm. (round to the nearest whole number)

The volume of the pyramid shown in the figure is cubic centimeters. If the slant height of the pyramid increases by 4 centimeter

Nostrana [21]

Answer:

Part a) The volume of the original pyramid is $15\ cm^{3}$

Part b) The volume of the pyramid increases by $6\ cm^{3}$

Step-by-step explanation:

The complete question is

Part 1) The volume of the pyramid shown in the figure is 9,15,21, or 63 cubic centimeters?. Part 2) If the slant height of the pyramid increases by 4 centimeters and its height increases by 2 centimeters, the volume of the pyramid increases by 6,9,12 or 21 cubic centimeters?

we know that

The volume of the pyramid is equal to

$V=\frac{1}{3}Bh$

where

B is the area of the base

h is the height of pyramid

see the attached figure to better understand the problem

Step 1

Find the volume of the original pyramid

the area of the base B is equal to

$B=3^{2}=9\ cm^{2}\\h=5\ cm$

substitute

$V=\frac{1}{3}(9)(5)=15\ cm^{3}$

Step 2

Find the volume of the new pyramid

$B=9\ cm^{2}$ -------> the area of the base is the same

$h=5+2=7\ cm$ ------> the height increase by

substitute

$V=\frac{1}{3}(9)(7)=21\ cm^{3}$

Subtract the original volume from the new volume

$21\ cm^{3}-15\ cm^{3}=6\ cm^{3}$

5 0

2 years ago

How do I solve this I don't know how to solve this i dont under stand this

k0ka [10]

Use Pythagoras theorem
${13}^{2} + {x}^{2} = {26}^{2} \\ { {x}^{2} = 507} \\ x = 22.52$

3 0

3 years ago

Help me with one and two plz

agasfer [191]

Answer:

1. parental function is g(x)=√x

2. parental function is g(x)=3√x

Step-by-step explanation:

1. To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Parent Function: g(x)=√x

Horizontal Shift: None

Vertical Shift: Down 9 Units

Reflection about the x-axis: None

Vertical Stretch: Stretched

2. Parent Function: g(x)=3√x

Horizontal Shift: Left 5 Units

Vertical Shift: Up 3 Units

Reflection about the x-axis: Reflected

Vertical Compression: Compressed

6 0

2 years ago

A coffee shop charges $2.50 for each cup of coffee and $1.50 for a cupcake. Your mom gives you $10 and ask you to buy 5 cupcakes

Dominik [7]

Answer:

$\frac{10-7.50}{2.50}$ $\geq$ c

1 cup of coffee

Step-by-step explanation:

Let's say c = coffee

5 cupcakes would cost 5*1.50 = 7.50

We can make an inequality :

$\frac{10-7.50}{2.50}$ $\geq$ c

Now we can solve the inequality

10 - 7.50 = 2.50

2.50/2.50 = 1

The maximum cup of coffee you can buy is 1

Hope this helps :)

5 0

1 year ago

Read 2 more answers

SOMEONE HELP ME PLEASE

Alina [70]

9514 1404 393

Answer:

log4(2) = 0.5000

Step-by-step explanation:

You are being asked to figure out how to make the value 2 from the values 6 and 3. Your familiarity with arithmetic facts tells you ...

2 = 6/3

Taking logs base 4, you have ...

log4(2) = log4(6/3) = log4(6) -log4(3)

log4(2) = 1.2925 -0.7925

log4(2) = 0.5000

__

Additional comment

This is consistent with your knowledge of factors of 4:

√4 = 4^(1/2) = 2

log4(2) = 1/2

__

Here, we're using "log4" to mean the base-4 logarithm.

4 0

2 years ago