A concrete planter is formed from a square-based pyramid that was inverted and placed inside a cube.
A. What is the slant height of the pyramid?
B. What is the surface area of the composite figure?
C. How many cubic yards of concrete are needed to make the planter?
Answers
Answer:
Notice that each edge of the cube is 2 yards long, and the height of the pyramid is 2 yards long too.
The slant height refers to the height of a triangle on its face, which forms a right triangle with the height of the pyramid and half side. Using Pythagorean's Theorem, we have
[tex]s^{2}=1^{2} +2^{2}\\ s=\sqrt{5}[/tex]
Therefore, the slant height is the square root of 5, in yards units. (A)
The surface of the composite figure is the sum of the surface area of both volumes.
[tex]S_{composite}=S_{cube} +S_{pyramid}\\ S_{composite}=5(2)^{2} +(2)^{2} +\frac{1}{2} (8)(\sqrt{5} )=20+4+4\sqrt{5} \\ S_{composite}\approx 32.9 yd^{2}[/tex]
Therefore, the surface of the composite figure is 32.9 square yards. (B)
The concrete needed will fill the empty space between the cube and the pyramid, so we have to find the difference between their volumes.
[tex]V_{concrete}=V_{cube} -V_{pyramid}=2^{3}-\frac{1}{3}(2)^{2} (2)=8-\frac{8}{3} \\V_{concrete} \approx 5.33 yd^{3}[/tex]
Therefore, we need 5.33 cubic yards of concrete to make the planter. (C)
Answer:
A. 2.24 yd
B. 53.67 yd²
C. 5.33 yd³
Step-by-step explanation:
Here we have;
Height of the pyramid = 2 yd
Side length of pyramid base = 2 yd
Therefore, the slant height forms a right triangle with the height of the pyramid and half the base hence;
(Slant height)² = (2·yd)² + (2·yd/2)² = 4·(yd)² + (yd)² = 5·(yd)²
∴ Slant height = √5 yards = 2.24 yd
B. The surface area of the cube with one side open is found as follows;
Surface area of container cube = 5 × (2·yd)² = 20 yards²
The surface area of the pyramid = Base area + 1/2 perimeter of base × Slant height
Since the base is open, we have;
The surface area of the pyramid = 1/2 perimeter of base × Slant height
= 1/2 × (4 × (2·yd))×yd·√5 = 4·yd×yd·√5 = 4·√5·(yd)²
Hence total surface area of the planter = Surface area of container cube + surface area of the pyramid
total surface area of the planter = 20·yd² + 4·√5 yd² = 24·√5 yards²
C. The volume of concrete needed to make the planter is the volume of the cube concrete container less the volume of the inverted pyramid
Volume of the cube = 2 × 2 × 2 = 8 yd³
Volume of the inverted pyramid = 1/3 × Base area × Height
Volume of the inverted pyramid = 1/3 × 2 × 2 × 2 = 8/3 yd³
Therefore, volume of the concrete needed = 8 yd³ - 8/3 yd³ = 16/3 yd³ = 5.33 yd³.
Related Questions
The volume of a cone with a radius of 7 cm is 147 pi cubic centimeters. Which expression can be used to find h, the height of the cone?
A. 147 pi = one-third (7) (h) squared
B. 147 pi = one-third pi (7 squared) (h)
C. 147 pi = one-third pi h
D. 147 pi = one-third pi (7) (h)
Answers
Answer:
B
Step-by-step explanation:
Volume = ⅓ pi × r² × h
147pi = ⅓ × pi × 7² × h
Step-by-step explanation:
Step 1: Find the expression that can be used to find h
[tex]V = \pi * r^2 * \frac{h}{3}[/tex]
[tex]147 \pi = \pi * (7)^2 * \frac{h}{3}[/tex]
[tex]147\pi = \frac{1}{3} * \pi * 7^2 * h[/tex]
147 pi = one-third pi (7 squared) (h)
Answer: Option B
What is the values of x?
Answers
X = 4
Answer:Answer is 4
15x-5+125=180°
15x=60
x=4
Step-by-step explanation:I don't say you have to mark my ans as brainliest but my friend don't forget to thank me if it has really helped you..
Mrs. Ellis determines that 5 gallons of water flow from a faucet in 3 minutes. The water continues to flow at the same rate. Which equation can be used to represent the number of gallons, y, that flow through the faucet in x
Answers
Answer:
y=5/3x
Step-by-step explanation:
The equation can be used to represent y = (5/3)x.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
We have been given that Mrs. Ellis determines that 5 gallons of water flow from a faucet in 3 minutes.
Since the water continues to flow at the same rate.
Using represent the number of gallons, y, that flow through the faucet in x
In 3 minutes, 5 gallons of water come out of a faucet.
So the equation can be used to represent y = (5/3)x
Learn more about the equation here:
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what is the answer for this question below
7 (4u – 2v + w)
Answers
Answer:
28u-14v+7w
Step-by-step explanation:
Answer: 28u−14v+7w
Step-by-step explanation:
Hope that helps
Georgianna wants to use the linear model associated with the data in the table to make a prediction.
A 2-column table with 5 rows. The first column is labeled time (minutes) with entries 0, 5, 10, 15, 30. The second column is labeled distance (miles) with entries 0, 4, 9, 13, 18.
Which range of time values describes the entire interval over which she would be interpolating?
0 to 5 minutes
0 to 18 minutes
0 to 30 minutes
18 to 30 minutes
Answers
Answer:
0 to 30 minutes on edg.
Step-by-step explanation:
Answer:
c on e 2020
Step-by-step explanation:
Jamal and Cleo mow lawns together, Jamal can mow an average lawn in 60 minutes by
himself. Cleo would take 90 minutes for the same job. How long would it take both of
them together to mow one (1) lawn
Answers
Hope this helps
The leaning Tower of Pisa was completed in 1372 and makes 86 degree angle with the ground. The tower is 50 meters tall, measured vertically from the ground to the highest point. If you were to climb to the top then accidentally drop your keys, where would you start looking for them?
How far from the base of the tower would they land?
I made having no luck in figuring this out.
Answers
Answer:
The distance where the keys would drop from the base is 3.5m
Step-by-step explanation:
Height of the tower = 50m
Angle it makes to the ground = 86°
To solve this question, you have to understand that the tower isn't vertically upright and the height of the tower is different from the distance from the top of the tower to the ground.
The tower makes an angle 86° to the ground and that makes it not vertically straight because a vertically straight building is at 90° to the ground.
See attached document for better illustration.
The distance from where the keys drop to the base of the tower can be calculated using SOHCAHTOA
We have to use cosθ = adjacent / hypothenus
θ = 86°
Adjacent = ? = x
Hypothenus = 50m
Cos θ = x / hyp
Cos 86 = x / 50
X = 50 × cos 86
X = 50 × 0.06976
X = 3.488 = 3.5m
The distance where the keys would drop from the base of the tower is approximately 3.5m
Determine if the question posed is a statistical question (yes) or not (no). What is 2 plus 2?
Answers
Answer:yes?
Step-by-step explanation:
it has #s in it lol
Answer:
no it isnt
Step-by-step explanation:
pls helllllllllllllp
Answers
Answer:
40
Step-by-step explanation:
24 divided by = 8
8 times 5 = 40
can i have brainliest please
Answer:
40
Step-by-step explanation:
there is a 5 to 3 ratio for ice cream cones to brownies
ice cream: brownies
5:3
x:24
three times eight is 24
five times eight is 40
help meeeeeeeeeeeeeeeeee pplllzzzzzzzzz asap
Answers
Answer: 16
Step-by-step explanation:
8+6+2
Answer:
2
Step-by-step explanation:
Under 13 min - that means at least at 07:13 am, and this is the first column, which shows Two People.
Secant TP and tangent TR intersect at point 7. Chord SR and chord PQ intersect
at point V. Find the values of x and y. If necessary, round to the nearest tenth.
AN
x = 11.6
y = 11.6
= 11.6
y= 23.2
x = 18.3
y = 36.6
Answers
Answer:
(C)x=11.6, y=23.2
Step-by-step explanation:
Using Theorem of Intersecting Secant and Tangent
Applying this theorem in the diagram, we have:
[tex]TQ$ X TP=TR^2[/tex]
[tex]10(10+x+4)=16^2\\10(14+x)=256\\140+10x=256\\10x=256-140\\10x=116\\$Divide both sides by 10\\x=11.6[/tex]
Next, we apply Theorem of Intersecting Chords
PV X VQ=SV X VR
4 X x= 2 X y
Recall earlier we got: x=11.6
2y=4 X 11.6
2y=46.4
Divide both sides by 2
y=46.4/2=23.2
Therefore: x=11.6, y=23.2
Ben I love kids then with a speed of 51 miles per hour Melanie also left at the same time in the opposite direction at a speed of 42 my husband our find how many hours mowing must travel to of course they are 360 miles apart
Answers
Answer:
Time when Ben and Melanie are 360 miles apart = 3.871 hours.
Step-by-step explanation:
The question seems unclear, but the sense that could be made from this question is that
Ben leaves with a speed of 51 miles per hour and Melanie also left at the same time in the opposite direction at a speed of 42 miles per hour. My husband wants to find how many hours they both must have been moving to be 360 miles apart.
Let the required time be t.
Let the distance covered by Ben in t hours be x miles.
Let the distance covered by Melanie in t hours be y miles.
Total distance covered = x + y = 360 (eqn 1)
speed = (distance/time)
For Ben
51 = (x/t)
x = (51t) miles
For Melanie
42 = (y/t)
y = (42t) miles
Substituting for x and y in eqn 1
x + y = 360
51t + 42t = 360
93t = 360
t = (360/93) = 3.871 hours.
Ben would have travelled x = 51t = 51 × 3.871 = 197.42 miles
Melanie would have travelled y = 42t = 42 × 3.871 = 162.58 miles
Hope this Helps!!!!
Find the value of e/a. Just read the variables and numbers.
(50 points)
Answers
Answer:
35
Step-by-step explanation:
solve the equation 18=n-18
n=_____
Answers
Answer:
36
Step-by-step explanation:
A car odometer showed 6,437.5 miles at the end of a trip. How many miles did the odometer show at the beginning of the trip if the car was driven 422.3 miles?
Answers
Answer:
The odometer showed 6,015.2 miles at the beginning of the trip.
Step-by-step explanation:
The odometer increases according to the number of miles traveled.
Before the trip, it showed x miles.
During the trip, the car was driven 422.3 miles.
After the trip, it showed 6,437.5 miles.
So
x + 422.3 = 6437.5
x = 6437.5 - 422.3
x = 6,015.2
The odometer showed 6,015.2 miles at the beginning of the trip.
I need help with these plzzz
Answers
Answer:
1. C 2. B
Step-by-step explanation:
1. find the total circumference, d times pi, then put 42 over 360 and multiply them to get that section
2. The actual value of x is 33.2
So I plugged in that value for all of them
i need help asap! anyone know this?
Answers
Answer:
1 = 0
12x12 = 4
100=1
I think the last one is also 1
Step-by-step explanation:
The 8 in both sides gets cancelled out.
x=0
100^x=100
The hundred in both sides gets cancelled out.
x=1
12^x times 12^4=12^8
When the bases (numbers) are same and are multiplied together, you add the powers together.
12^x+4=12^8
The 12 in both sides get cancelled out.
x+4=8
x=8-4
x=4
(7^2)^9=7^3)^x
When there are powers both inside and outside the brackets, they’re multiplied with each other.
7^18=7^3x
The seven in both sides gets cancelled out.
18=3x
3x=18
x=18/3
x=6
Please help me now I will mark you brainliest
Answers
Answer:
Out side the circle
Step-by-step explanation:
This is because the center is 0 and if the point 6, square root seven is on the circle that mean that as far as the circle goes on each side.
HELP - WILL MAKE BRAINLIEST IF CORRECT - a chunk of lava flies out of a volcano from a height of 12,447 feet a velocity of 608 feet per second. Find the highest point the lava reaches and how long it takes to reach it using the equation y= -16t^2 + 608t + 12,447.
Answers
Answer:
18,223 feet
Step-by-step explanation:
y= -16t^2 + 608t + 12,447.
y = -16(t² - 38t) + 12447
y = -16[t² - 2(t)(19) + 19² - 19²] + 12447
y = -16(t - 19)² - 16(-19²) + 12447
y = -16(t - 19)² + 18223
Vertex: (19, 18223)
Max height is 18,223 at t = 19
The parabolas are:
a = -16
b = 608
c = 12,447
x_v = -b/2a
t_v = -608/2(-16)
t_v = -608/-32
t_v = 19
Plug in t_v = 19 to find y_v
y = -16(19)^2 + 608(19) + 12,447
y = -16(361) + 11,552 + 12,477
y = -5,776 + 11,552 + 12,477
y = 18,253
We have the point (19, 18,253)
The max height is at 18,253 when t = 19
Best of Luck!
please Help it’s urgent
Answers
Answer:
Angle IAJ
Step-by-step explanation:
X idea again. They are opposite to each other in the immediate area around them.
Two gongs strike at intervals of 24 and 40minutes respectively. At twist time will they strike together again if they start simultaneously at 12 noon? Hint: 60 minutes = 1 hour
Answers
Answer:
They will sound together at 2pm
Step-by-step explanation:
Now, the first thing we need to calculate is , in how many minutes will the two gongs strike together.
To be able to do this, we need to calculate the least common multiple of the two numbers 24 and 40
The lowest common multiple between both is 120
This means that the two gongs will sound together at exactly 120 minutes
Now since 1 hour is 60 minutes, this means that 120 minutes will be = 120/60 = 2 hours
Since they both sounded together at 12 noon and the next time they will be sounding is next two hours, their sounding time will thus be 12 noon + 2 hours = 2 pm
The ratio of the leg opposite to an angle to the leg adjacent to the angle in a right
triangle is called the ___ of the angle.
A. sine
B. tangent
C. cotangent
D. secant
Answers
Answer:
the answer is b. tangent
Step-by-step explanation:
The ratio of the leg opposite to an angle to the leg adjacent to the angle in a right triangle is called the tangent of the angle.
On which triangle can we apply trigonometric ratios?The trigonometric ratio can be defined in terms of ratios of perpendicular, bases, and hypotenuse.
Trigonometric ratios for a right-angled triangle are from the perspective of a particular non-right angle.
In a right-angled triangle, two such angles are there which are not right-angled(not of 90 degrees).
The slanted side is called the hypotenuse.
From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called the base.
The tangent of the angle is
[tex]\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}[/tex]
Learn more about trigonometric ratios here:
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Given that x+1 is a factor of 2x^3-3x^2-8x-3 , solve 2x^3-3x^2-8x-3=0. This means find all the roots for the function.
Answers
Answer:
x=-1, -1/2, 3
Step-by-step explanation:
Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -36 and 2304, respectively.
Answer Choices:
A) an = 9 • 4n
B) an = 9 • (-4)n + 1
C) an = 9 • 4n - 1
D) an = 9 • (-4)n - 1
Answers
Which of the following options have the same value as %25, percent of 64? Choose 2 answers:
A 25⋅64
B 25/100⋅64
C 0.25⋅64
D 64÷ 25/100
E 25÷ 64/100
Answers
Answer:
B and C
Step-by-step explanation:
25% of 64 is 16. So find the two answers that are equivalent to 16.
A: 25*64 = 1600 [tex]\neq[/tex] 16
B: [tex]\frac{25}{100}[/tex]*64 = 16
C: 0.25 * 64 = 16
D: 64/[tex]\frac{25}{100}[/tex] =256 [tex]\neq[/tex] 16
E: 25/[tex]\frac{64}{100}[/tex] = 39.06 [tex]\neq[/tex] 16
Answer:
its b and c. had the same problem.
There are 70,000 bacteria present in a culture. An antibiotic is introduced to the culture and the number of bacteria is reduced by half every 4 hours. Which of the following statements are true? Select all that apply.
A.) two hours after the antibody is introduced , there are 35000 bacteria present in the culture
B.) 24 hours after the antibiotic is introduced , the number if bacteria in the culture is reduced to 1093
C.) the number of present in the culture during the 24 hours after the the antibiotic is introduced is an example of exponential decay
D.) the half-life of the bacteria after the antibiotic is introduced is 2 hours
E.)the function B(x)=70000(0.5)^x where x is the number of 4 hour periods represents the amount of bacteria present after the antibiotic is introduced
Answers
Answer:
c
Step-by-step explanation:
the number of bacteria is introduced
The function B(x) = 70000(0.5)ˣ, where x represents the number of 4 hour periods, represents the amount of bacteria present after the antibiotic is introduced. Therefore, option D is the correct answer.
What is the exponential function?Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).
In any situation where an amount grows or declines by a set percent every time period can be represented using an exponential function. Since the amount of bacteria is reduced by half, or 50%, every 4 hours, this is exponential decay.
Exponential functions such as this are of the form
y = a(1+r)ˣ, where a represents the initial population, r is the percent of growth or decrease, and x is the number of time periods. In this situation, the initial population, a, is 70000. Since the number of bacteria decreases by half, r = -0.50. This gives us
y = 70000(1+-0.50)ˣ, or y = 70000(0.50)ˣ.
In 24 hours, there are 6 4-hour periods. This means x = 6; this gives us
y = 70000(0.50)⁶ = 1093.75.
Therefore, option D is the correct answer.
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EMERGENCY!!!! EXTRA POINTS! I HAVE POSTED THIS QUESTION 5 TIMES AND HAD TO REPORT ALL RESPONSES! I ACTUALLY NEED HELP!
The amusement park in Riverdale charges a $10 entrance fee plus $1 per ride. The amusement park in Esterdamb charges a $5 entrance fee and $2 per ride. For how many rides will the cost be the same for both amusement parks? x= # of rides
Number of rides_____?
Cost_____?
Answers
Answer:
the price will be the same for either amusement park
Step-by-step explanation:
10+1(x)=?
5+2(x)=?
ex; x=5
10+1(5)= 5+2(5)=
10+5= 5+10=
15 15
Answer:
5 rides, cost of $15
Step-by-step explanation:
With the information given we have two expressions:
10 + 1x and 5 + 2x
Using these expressions we can create this equation:
10 + 1x = 5 + 2x
Knowing some information we can can simply analyze some information:
The closest number each of these equations could equal is 15,
1(5) is 5 + 10 = 15, and 2(5) is 10 + 5 = 15
15 = 15 this is a true statement, so we know this is answer
Hope this helps! Have a good day!
What is the radius and diameter of the following circle?
111 cm
Radius
cm
Diameter =
cm
Answers
Answer:
Diameter = 212 cm
Step-by-step explanation:
D= 2r
What is the slope of the line ?
Answers
Answer:
-3
Step-by-step explanation:
In a classroom of 20 students, 70% of them have brown eyes. If a teacher picks two students
at random to pass out supplies, what is the probability he chooses two students without brown
eyes?
49
A)
100
B)
91
190
3
C)
38
9
D)
100
Answers
Answer:
The probability is 9/100
Step-by-step explanation:
First, we know that 70% of the students are with brown eyes. Since we have a total of 20 students, this corresponds to 70/100 * 20 = 14 students
The number of students without brown eyes is thus 20 -14 = 6 students
Now, the probability of selecting a student without brown eyes is 14/20 = 7/10 while the probability of selecting a student with brown eyes is 6/20 = 3/10
Now the probability of selecting two students without brown eyes mean, the first selected is without brown eyes and also the second selected is without brown eyes.
In probability, once we have the work and, we multiply.
So our answer here is 3/10 * 3/10 = 9/100
