Answer:
The volume of pyramid B is 81 cubic units
Step-by-step explanation:
Given
Pyramid A
[tex]s = 4[/tex] -- base sides
[tex]V = 36[/tex] -- Volume
Pyramid B
[tex]s = 6[/tex] --- base sides
Required
Determine the volume of pyramid B [Missing from the question]
From the question, we understand that both pyramids are equilateral triangular pyramids.
The volume is calculated as:
[tex]V = \frac{1}{3} * B * h[/tex]
Where B represents the area of the base equilateral triangle, and it is calculated as:
[tex]B = \frac{1}{2} * s^2 * sin(60)[/tex]
Where s represents the side lengths
First, we calculate the height of pyramid A
For Pyramid A, the base area is:
[tex]B = \frac{1}{2} * s^2 * sin(60)[/tex]
[tex]B = \frac{1}{2} * 4^2 * \frac{\sqrt 3}{2}[/tex]
[tex]B = \frac{1}{2} * 16 * \frac{\sqrt 3}{2}[/tex]
[tex]B = 4\sqrt 3[/tex]
The height is calculated from:
[tex]V = \frac{1}{3} * B * h[/tex]
This gives:
[tex]36 = \frac{1}{3} * 4\sqrt 3 * h[/tex]
Make h the subject
[tex]h = \frac{3 * 36}{4\sqrt 3}[/tex]
[tex]h = \frac{3 * 9}{\sqrt 3}[/tex]
[tex]h = \frac{27}{\sqrt 3}[/tex]
To calculate the volume of pyramid B, we make use of:
[tex]V = \frac{1}{3} * B * h[/tex]
Since the heights of both pyramids are the same, we can make use of:
[tex]h = \frac{27}{\sqrt 3}[/tex]
The base area B, is then calculated as:
[tex]B = \frac{1}{2} * s^2 * sin(60)[/tex]
Where
[tex]s = 6[/tex]
So:
[tex]B = \frac{1}{2} * 6^2 * sin(60)[/tex]
[tex]B = \frac{1}{2} * 36 * \frac{\sqrt 3}{2}[/tex]
[tex]B = 9\sqrt 3[/tex]
So:
[tex]V = \frac{1}{3} * B * h[/tex]
Where
[tex]B = 9\sqrt 3[/tex] and [tex]h = \frac{27}{\sqrt 3}[/tex]
[tex]V = \frac{1}{3} * 9\sqrt 3 * \frac{27}{\sqrt 3}[/tex]
[tex]V = \frac{1}{3} * 9 * 27[/tex]
[tex]V = 81[/tex]
Answer:
81
Step-by-step explanation:
Consider the equation: X^2+16x-2=11 1) Rewrite the equation by completing the square
Answer:
[tex](x+8)^{2}[/tex] =77
x= -8 +/- [tex]\sqrt\\ 77[/tex]
From Khan Academy
What is i^34?
A. -1
B. -i
C. 1
D. 1
Answer:
A.-1 all you had to do was look up the answer
Step-by-step explanation:
1/6-9/8 as a fraction in simplest form
Four laps around the track is equal to one mile. It takes Taylor 8 minutes to run 3 laps.
How many minutes would it take Taylor to run 6 miles?
A. 16 minutes
B. 36 minutes
C. 48 minutes
D. 64 minutes
Answer:
D
Step-by-step explanation:
8x60=480
480÷3=160
160x4=640
640 is 10 Minutes 40 Seconds
6 Miles is 24 Laps
640x6=3840
3840÷60=64
The Answer Will be 64 Minutes.
-2c^2 -9c -2 = -3c^2
its very important, please help asap
2 Doctors is _______________% of 25 Doctors what is it.
Answer:
8%
Step-by-step explanation:
if you divide 2 by 25, you would get 0.08, which is equal to 8%
Answer:
8%
Step-by-step explanation:
Let a and b be rational numbers.
Answer:
Ok, let me guess... 4 and 5
Step-by-step explanation:
Gary goes to the grocery store to buy hot dogs and hamburgers for a cookout. He buys a total of 8 packages for a total of $28.52. A package of hot dogs costs $2.29 and a package of hamburgers costs $5.69.
Answer:
3 hamburger packs
5 hot dog packs
Step-by-step explanation:
The system of equations that corresponds to the situation is:
1. x + y = 8
2. 2.29x + 5.69y = 28.52
Let's use variables to represent the unknowns in the problem.
Let:
x = number of packages of hot dogs purchased
y = number of packages of hamburgers purchased
We are given the following information:
1. Gary buys a total of 8 packages: x + y = 8
2. The total cost of the packages is $28.52: 2.29x + 5.69y = 28.52
So, the system of equations that corresponds to the situation is:
1. x + y = 8
2. 2.29x + 5.69y = 28.52
To know more about equations:
https://brainly.com/question/10724260
#SPJ2
Complete question is:
Write a system of equations that corresponds to the situation. Do not solve. Gary goes to the grocery store to buy hot dogs and hamburgers for a cookout. He buys a total of 8 packages for a total of $28.52. A package of hot dogs costs$2.29 and a package of hamburgers costs $5.69.
If you can create 1 item in 3/4 hr how many can you create in 8 hrs
Answer:
10.6, or 10 entire items
Step-by-step explanation:
Answer:
[tex]\frac{32}{3}[/tex] items
Step-by-step explanation:
Please see the attached image.
I hope this helps!
Which Equation Is equivalent To Log2y =x+7
Answer:
the second one
Step-by-step explanation:
I NEED HELP PLEASE !
Answer:
x = 4, -2 1/2
Step-by-step explanation:
factors:
(2x + 5) (x - 4)
set each factor equal to zero:
2x + 5 = 0
2x = -5
x = -5/2
x - 4 = 0
x = 4
show dis and i will mark you correcr
Answer:
A and DStep-by-step explanation:
The area of the combined rectangle is:
t(5 + 4) = 5t + 4t = 9tIncorrect choices are:
A. 4*5*tD. t + 5 + 4Answer:
Solution :-Second option is correct because t is the breadth and 5 and 4 are length. So, Option B is correct 5t + 4t
On adding both we get 9t. Option C is correct
We may also take t as common and may be written as
t(5 + 4)
Correct option are B,C,E
[tex] \\ [/tex]
which expression is equivalent to 3 to the power of 9
Answer:
3^9
Step-by-step explanation:
Also 3 to the power of 9 is 19,683
Hope This Helps :b
Answer:
What he said which is the answer I just want to get more points
If the radius of a circle is 8 inches, what is the area. Use the formula shown below, and round the answer to the nearest hundredth, please.
A = π r² π ≈ 3.14
A≈201.06in²
A=πr2=π·82≈201.06193in²
Answer:
A=πr2=π·82≈201.06193
this is your answer.
201.1 — estimated.
Have a great day!!
Compare |-2/5| and |-3/8|
Answer:
2/5 and 3/8
2/5 is greater than 3/8
Step-by-step explanation:
Those parallel lines mean absolute value which means no signs no positive nor negative.
Find the surface area of the regular hexagonal prism.
Answer:
I think the surface is
Step-by-step explanation:
3.5
x/12-5>-2 please help
Answer:
The inequality for x is x > 36
(In interval notation form it is (36, ∞)
Step-by-step explanation:
Multiply to remove the fraction, then set equal to zero and solve.
Hope this helped you!
Please consider giving brainliest!
Dont forget to give a rating and leave a thanks.
10 = g - 19. Please help!!!
Answer: g = 29
10 = g - 19
add 19 to both sides:
29 = g
flip if u want
g = 29
hope this helped :)
The americans with disabilities act sets a maximium angle for a wheelchair ramp entering a business at 4.76 degrees. Determine the horizontal distance needed to occomidate a ramp that goes up to a door.
Answer:
d = 48.03 feet
Step-by-step explanation:
Given that,
The maximum angle for a wheelchair ramp entering a business at 4.76 degrees.
We need to find the horizontal distance needed to accomidate a ramp that goes up to a door 4 feet of the ground.
We can solve it using trigonometry.
[tex]\tan\theta=\dfrac{h}{d}[/tex]
Where
h is height
d is the angle of elevation
[tex]d=\dfrac{h}{\tan\theta}\\\\d=\dfrac{4}{\tan(4.76)}\\\\d=48.03\ ft[/tex]
So, the horizontal distance is equal to 48.03 feet.
Evaluate: 2-^4=
A.1/16
B.1/8
c. -8
D.-16
Answer:
A. 1/16
Step-by-step explanation:
[tex] {2}^{ - 4} = \frac{1}{ {2}^{4} } = \frac{1}{16} \\ [/tex]
Given that h varies inversely with respect to g, and that h= -24 when g= 3, write an
equation that describes the relationship between h and g. Then find h when g=-1,
Answer:
h = 72
Step-by-step explanation:
Given that h varies inversely with g then the equation relating them is
h = [tex]\frac{k}{g}[/tex] ← k is the constant of variation
To find k use the condition h = - 24 when g = 3 , then
- 24 = [tex]\frac{k}{3}[/tex] ( multiply both sides by 3 )
- 72 = k
h = - [tex]\frac{72}{g}[/tex] ← equation of variation
When g = - 1 , then
h = - [tex]\frac{72}{-1}[/tex] = 72
A unicycle wheel has a diameter of 30 inches. How many inches will the unicycle travel in 5 revolutions? Use π = 3.14 and round your answer to the nearest hundredth of an inch.
Answer:
471.3inches
Step-by-step explanation:
Given data
Diameter= 30in
Radius= D/2= 30/2= 15in
The circumference is the same as the distance covered in one revolution
C= 2πr
Hence the distance covered in 5 revolutions is
C= 2*5*πr
Substitute
C=10*3.142*15
C= 471.3inches
In the diagram to the right, a right circular cone has a diameter of 8 inches and a height of 12 inches.What is the volume of the cone to the nearest cubic inch? A. 201 in3 B. 481 in3 C. 603 in3 D. 804 in3
Answer:
(A) 201
Step by step explanation :
Volume of a cone is approximately equal to [tex]\boldsymbol{201}[/tex] inches.
So, option A. is correct.
Volume of coneA cone is a three-dimensional geometric object with a smooth trans-ition from a flat base to the ap-ex or vertex.
Radius of a cone is half of the diameter.
Radius of a cone [tex](r)=\frac{8}{2}[/tex]
[tex]=4[/tex] inches
Height of a cone [tex](h)=12[/tex] inches
Volume of a cone [tex]=\frac{1}{3}\pi r^2 h[/tex]
[tex]=\frac{1}{3}(\frac{22}{7} ) (4)^2 (12)[/tex]
[tex]\approx 201[/tex] inches
So, volume of a cone is approximately equal to [tex]\boldsymbol{201}[/tex] inches.
So, option A. is correct.
Find out more information about cone here:
https://brainly.com/question/2920315?referrer=searchResults
Examine the sequence of integers below.
−16, −10, −4, 2, 8, 14
Which algebraic expression represents the nth integer in this sequence?
A.
6n − 16
B.
−6n − 10
C.
−6n + 2
D.
6n − 22
Answer: D
6n-22
Step-by-step explanation:
(This is for my Algebra ll project all you need to do is answer this question) How many siblings do you have?
Answer:
I have two Sisters
Step-by-step explanation:
The point C(-2, -4) is rotated 270° clockwise around the origin. What are the coordinates of the resulting point, C′?
Answer:
(2,4)
Step-by-step explanation:
Rewrite 3log(4) in the form log(c)
Step-by-step explanation:
this is the answer of this question
Answer:
log(64)
Step-by-step explanation:
3 log (4) = log (4^3) = log (64)
Hope this helps!
4(5-2x)+3=7 step by step pls
Answer: x = 2
The step by step is attached to this answer, hope it helped!
Triangle ABC is graphed on a coordinate plane with vertices at A (-3,7), B (9,-8), and
C(-5, -6). If triangle ABC is dilated by a scale factor of m with the origin as the center
of dilation to create triangle A'B'C', what will be the coordinates of the dilated vertex
B?
Answer:
Step-by-step explanation:
how do you know of an exponential fuction is reflected across the x-axis?
Answer:
Step-by-step explanation:
A reflection over the x-axis changes all the y-values. The reflection is modeled as -f(x)
For example:
[tex]\sqrt{x}[/tex] would look like --[tex]\sqrt{x}[/tex] .
If the negative sign is outside of the bracket ( what it's called sorry), then it is a reflection over the x-axis
However if the negative sign was inside the bracket: [tex]\sqrt{-x}[/tex] then this would be a reflection over the y axis.
Hope this helps!