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:
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:
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!
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!
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Dont forget to give a rating and leave a thanks.
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.
Let a and b be rational numbers.
Answer:
Ok, let me guess... 4 and 5
Step-by-step explanation:
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!!
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
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!
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
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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.
1/6-9/8 as a fraction in simplest form
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.
(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:
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
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
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
Find the surface area of the regular hexagonal prism.
Answer:
I think the surface is
Step-by-step explanation:
3.5
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:
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:
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 :)
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.
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
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:
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]
4(5-2x)+3=7 step by step pls
Answer: x = 2
The step by step is attached to this answer, hope it helped!
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:
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]
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!
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
-2c^2 -9c -2 = -3c^2
its very important, please help asap
Which Equation Is equivalent To Log2y =x+7
Answer:
the second one
Step-by-step explanation: