[100 POINTS!!] Consider this cone and pyramid, which have the same height, h. Planes parallel to the base cut through each solid at equal heights, as shown.
![[100 POINTS!!] Consider This Cone And Pyramid, Which Have The Same Height, H. Planes Parallel To The](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/8rYIf0DuNf7tVRpiJrEw9ckfCXv6IqM1.png)
Answers
#Circle 1
π12²144πunits²#Circle 2
6²π36πunits²#Circle 3
3²π9πunits²#Triangle 1
1/2(12π)(24)6π(24)144πunits²#Triangle 2
1/2(6π)(12)36π units²#Triangle 3
1/2(3π)(6)9π units²The area of each cross section of the cone and pyramid is the same which is 2[tex]\pi[/tex].
This is because the cone and pyramid are similar solids, and the cross sections are taken at equal heights.
The similarity of the cone and pyramid can be seen by comparing the triangles formed by the apex, a point on the base, and the intersection of the plane with the solid. These triangles are similar because they have the same angles.
The fact that the cross sections are taken at equal heights means that the triangles are similar in size as well. This means that the areas of the triangles are also the same.
Therefore, the area of each cross section of the cone and pyramid is the same.
[tex]\pi[/tex][tex]h^2[/tex] / (1/2) h*h = 2[tex]\pi[/tex][tex]h^2[/tex] / [tex]h^2[/tex] = 2[tex]\pi[/tex]
The cross sections of the cone and pyramid are both triangles. The triangles are similar because they have the same angles. The fact that the cross sections are taken at equal heights means that the triangles are similar in size as well. This means that the areas of the triangles are also the same. Hence, the answer is 2[tex]\pi[/tex].
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Related Questions
Find the mean of the data. 20, 28, 30, 38, 39, 40, 43
Answers
Answer:
mean = 34
Step-by-step explanation:
the mean is calculated as
mean = [tex]\frac{sum}{count}[/tex] = [tex]\frac{20+28+30+38+39+40+43}{7}[/tex] = [tex]\frac{238}{7}[/tex] = 34
Answer: 34
Step-by-step explanation:
Mean is the same as average, and to find average you add all the numbers up and divide by the amount of numbers present. So, if you add all of them up, you get 238. Then, you'll divide by 7, since there are 7 numbers. And that will get you 34.
A bag contains 20 marbles: 5 red, 5 blue, and 10 yellow. What is the probability that a red is randomly selected?
4))
A)
B)
C)
12
1
D)
24
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50 points! answer ASAP!! Which of the following is the graph of y = negative (x minus 2) cubed minus 5?
On a coordinate plane, a cubic root function approaches the negative y-axis in quadrant 4, has a point of inflection at (2, negative 5), and then increases and approaches x = 4. On a coordinate plane, a cubic root function approaches x = negative 5 in quadrant 3, has a point of inflection at (negative 2, negative 5), and then approaches the y-axis in quadrant 3. On a coordinate plane, a cubic root function approaches the y-axis in quadrant 4, has a point of inflection at (2, negative 5), and then decreases and approaches x = 4. On a coordinate plane, a cubic root function approaches x = negative 4 in quadrant 3, has a point of inflection at (negative 2, negative 5), and then decreases and approaches the negative y-axis in quadrant 3.
Answers
Answer: The second image you attached (I also attached the picture of the right answer)
Step-by-step explanation:
In this equation A is negative so you know it is going downward.
the shift is down 5 units and to the right 2.
You can see this shift in the graph I attached
it is also 1 to 1
Answer:
b
Step-by-step explanation:
Students graphed the growth rate over several weeks of two plants in their classroom. The equations of both plants are given where x represents the time in weeks and y represents the heights of the plants in inches.
Plant A: y = 1.8x + 3.1
Plant B: y = 2.3x + 1.9
Approximately how many weeks will it take for both plants to reach the same height? Round your answer to the nearest tenth.
What is the solution to the system of linear equations? Round to the nearest tenth as needed.
(
,
)
Answers
Answer:
A i think
Step-by-step explanation:
Find the derivative of In( x + a) by using first principle.
Answers
Answer:
slide for von
Step-by-step explanation:
3/4 divied be 8/14. please give me answer
Answers
Answer:
1 5/16
Step-by-step explanation:
3/4 / 8/14 is the same as
3/4 * 14/8 = 42 /32 1 5/16
Using only the values given in the table for the function f(x) = –x3 + 4x + 3, what is the largest interval of x-values where the function is increasing?
Answers
An interval is made up of integers that fall between two specified provided numbers. The largest interval of x-values between which the value of f(x) is increasing is -1 to 1.
What is an interval?An interval is made up of integers that fall between two specified provided numbers. For example, the set of integers x fulfilling 0≤x≤5 is an interval including 0 and 5, as well as all values between 0 and 5.
The table has the repetitive values of f(x), therefore, the largest interval of x-values between which the value of f(x) is increasing is -1 to 1.
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What is the area, measured in square centimeters, of the green shape
pictured below? Do not include units in your answer.
Answers
Answer:
14
Step-by-step explanation
Count the whole squares and you get 12. Then count the triangles and you have four. Two triangles = 1 square so you have two squares. After add two and 12.
12. The object below is made of ten
rectangular prisms, each with
dimensions of 5 centimeters (cm) by
3 cm by 2 cm. What is the volume, in
cubic centimeters, of the object?
3 cm
2 cm
5 cm
A 100
B 150
C 250
D 300
Answers
Answer:
D 300
Step-by-step explanation:
because volume for one is [tex]2*3*5[/tex]=30 then 30*10=300
Answer:
The answer is D 300
Step-by-step explanation:
Happy to help
Find the value of x.
Answers
Answer:
x=21
Step-by-step explanation:
Following the vertical angles, we can assume that the equation that has x and 87 are equal to each other. From then, you set them equal to each other and solve for x.
87=4x+3
84=4x subtract 3 from both sides
21=x divide by 4 to get the x alone on both sides
Example : Identify the amount of Xs to Os: XXOXO
Answer is 3:2
Type the ratio which matches its corresponding image set below.
Compare the number of
to
Answers
--- 3 to 2 (3:2) ---
[50 POINTS] What is the volume of the cylindrical stack of pennies?
Answers
Radius of base=19.05/2=9.525
Volume
πr²hπ(9.525)²(38)3447.57π10825.3698 mm³A photograph with a width of 3 inches and a length of 5 inches will be enlarged so that the length is 40 inches. What will the width equal? A. 20 inches B. 24 inches C. 88 inches D. 120 inches
Answers
Answer:
B. 24inches
Step-by-step explanation:
Original photo
Width= 3inches
length= 5inches
New photo
width=
length= 40inches
3×8=24inches
5×8=40inches
Someone please explain to me
Answers
Answer:
a. simple random sampling.
im so sorry if its wrong
The diameter of a rod is required to be 1.51 inches with an acceptable variance of .015 inches. The rod would not be acceptable if the diameter measure
a.1.490 inches
b.1.500 inches
c.1.510 inches
d.1.525 inches
e.1.511 inches
Answers
The rod would not be accepted If the diameter measurement will be less than 1.495. Then the correct option is A.
What is the acceptable diameter of the rod?The compliance zone of the rod goes over the specification limits of the hole in Imperfect Fit. This indicates that the shaft is big, but the opening is little.
The diameter of a rod is required to be 1.51 inches with an acceptable variance of .015 inches.
The rod would not be accepted If the diameter measurement will be less than 1.495.
Upper limit
→ 1.51 + 0.015
→ 1.525
Lower limit
→ 1.51 - 0.015
→ 1.495
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Lucy spent $165 in December using a new credit card. In January, she began paying between $15 and $25 each month towards her account balance. The equation f(x) = 165(0.8)x describes the curve of best fit for Lucy's account balance f(x). Let x represent the number of months since December.
Month Account Balance
December $165.00
January $132.00
February $105.60
March $84.48
Using the equation for the curve of best fit, what will Lucy's account balance be in June? Round to the nearest cent.
A.
$28.25
B.
$53.95
C.
$43.25
D.
$33.25
Answers
Answer: 43 c
Step-by-step explanation: adding and multiplecation
Please solve with explanation high points
Answers
Answer:
a) angle QRP is 92 degrees, side QR is 23 cm, angle RPQ is 47 degrees
b) angle EFD is 65 degrees, side FD is 22cm, side ED is 20cm
Step-by-step explanation:
a) in the first example, you know that u are given QR, PR, and angle PRQ, and u are asked to find triangle PQR,or the rest of the lengths.
step 1-u draw an example of the triangle, i will provide one for each at the bottom of this answer
step 2-lets find the sides first with the pythagorean theorem, which will mean 25²+x²=34². Pythagorean theorem is a²+b²=c²
step 3-after solving for x, x will be 23.04, which means the third side is 23 cm (after rounding).
step 4-now that we have all the sides, we can solve for the rest of the angles, by trigonometric ratios, we are gonna use sine for angle RPQ, sine is sin(the angle u want to find)=opposite side/hypotenuse.
step 5- so sin(RPQ)=25/34, and solve for RPQ on a calculator (i used math) and angle RPQ will equal 47.3 degrees.
step 6- just subtract the sum of both angles from 180 an the last angle will be 92 degrees.
b) u are given the measure of angles FED and EDF and the side length FE, we will solve for the last angle first then we will go for the side engths
step 1- we subtract the sum of the two angles we have from 180 and we will get the measure of angle EFD to be 65 degrees, now we have the angles and we want to find he sides.
step 2-we use sine of angle 31 degrees to find the hypotenuse, but it is opposite of sine since we want to find the side, not the angle, so we will use sin(31)=11.3/x, the sine equation is written like sin(the angle u have)=opposite/hypotenuse.
step 3- after solving for arc sine in a calculator, u will find side FD to be 22cm, and now to find the last side.
step 4-i will use the sine of angle 65 degrees to solve for side ED, it will be sin(65)=x/22, which will make side ED equal 20 cm in length.
ur welcome :)
hope i helped
brainliest please?
Set C is the set of natural numbers less than 7.
Answers
Answer:
C = {1, 2, 3, 4, 5, 6}
C = {x ∈ N | x < 7}
Step-by-step explanation:
Hello!
Natural numbers are integers greater than 0 and not including it.
Lets list the natural numbers until 10: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Now, set C contains all of the natural numbers less than 7, so we select all of the numbers before 7 into our set.
C = {1, 2, 3, 4, 5, 6}The set contains numbers 1, 2, 3, 4, 5, and 6.
Set builder notation:
Keep the type of number at the start:
C = {x ∈ N | x < 7}Prove: (sin α + cos β)^2 + (cos β + sin α)(cos β − sin α) = 2 cos β(sin α + cos β)
Answers
The two terms on the left side both have a common factor of (sin(α) + cos(β)), so we can pull it out like so:
(sin(α) + cos(β))² + (cos(β) + sin(α)) (cos(β) - sin(α))
= (sin(α) + cos(β)) [(sin(α) + cos(β)) + (cos(β) - sin(α))]
= (sin(α) + cos(β)) (sin(α) + cos(β) + cos(β) - sin(α))
= 2 cos(β) (sin(α) + cos(β))
Find the perimeter and area of each figure.
Answers
Area of large rectangle : 7x16 = 112
Area of full shape: 136
Perimeter = 13+10+8+7+16=54
Hope I helped!
Suzanne buys a pair of shoes. A 9% sales tax is added to the purchase.
Which function shows the total cost for any pair of shoes with a price of x?
f(x) = 0.09x – 10
f(x) = 1.09x
f(x) = 0.9x
f(x) = 1.9x
Answers
The function which represent the total cost of pair of shoes bought by Suzanne including the 9% sales tax is,
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Suzanne buys a pair of shoes. A 9% sales tax is added to the purchase. Let any pair of shoes has a price of x when sales tax is not added.
The function which represent the total cost including the sales tax is,
[tex]f(x)=x+\dfrac{9}{100}x\\f(x)=x+0.09}x\\f(x)=1.09}x[/tex]
Hence, the function which represent the total cost of pair of shoes bought by Suzanne including the 9% sales tax is,
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You pick a card at random, put it back, and then pick another card at random
5 6 7
What is the probability of picking a 7 and then picking a 5?
Write your answer as a fraction or whole number.
Answers
Answer:
The probability is 1/9
Step-by-step explanation:
1/3 x 1/3 = 1/9
Reason:
The probability of selecting "7" is 1/3 because there's one card labeled "7" out of three cards total.
The same applies to selecting a "5" as well. When the first card is put back, effectively nothing has changed.
The probability of getting a "7", then getting a "5" is (1/3)*(1/3) = 1/9
PLEASEEEEE HURRRYYYY
Based on the given inequality statement, which statement correctly describes where the values are located on a number line relative
to each other?
-5 < 2
O -5 is located to the right of 2.
O 2 is located to the left of -5.
• -5 is located to the left of 2.
O 2 is located at the same position as -5.
Answers
Hi!~
Answer:
C) -5 is located to the LEFT of 2
Step-by-step explanation:
On a number line, of course the negatives (-) are to the left while the positives (+) are to the right, so since -5 is negative, and 2 is positive, -5 is located to the LEFT of 2.
Hope this helps! :)
Part C
In GeoGebra, label the measures of the three angles on ∆DEF. Then move point G around the coordinate plane to produce triangles with different sets of angles. Record at least five sets of angles as you move G.
Answers
The sets of angles one gets as one moves G are:
∆EFD∆ GFD∆ GDE, etc.What is a triangle?A triangle is known to be a kind of a polygon that is known to have three edges and also three vertices.
Note that the it is said to be one of the main shapes in geometry as it is often shown as triangle ABC. Therefore, the sets of angles one gets as one moves G are ∆EFD, GFD, GDE, etc.
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Find the greatest possible number of consecutive zeros at the end of the product of three positive integers if the sum of these three integers equals 939.
(The number 202100 has exactly 2 consecutive zeros at the end.)
Answers
Answer:
A. Of first 100 multiples of 10
B. 5*10*15*20*25*30*35*40*40*45
C. 100!
I would also like to know whether this kind of question is possible in GMAT and what would be the complexity level.
1. 124
2. 10
3. 24
Rewrite the equation below so that it does not have fractions. 3-3/4x=2/5
With out using decimals
Answers
Answer:
-45x=8x
this answer was gotten by simplification.
Given g(x) = x2 + 1, find g(x – 2).
Answers
Answer:
g(x)-2g
Step-by-step explanation:
g x(x-2), gx-2g
How many significant figures are there in the number 3,460?
Answers
Answer:
3 figures
Step-by-step explanation:
Just follow these steps!
Non-zero digits are always significant.
Any zeros between two significant digits are significant.
A final zero or trailing zeros in the decimal portion ONLY are significant.
The perimeter of a square is 24 feet. What is the area in square feet
Answers
Answer:
Step-by-step explanation:
Remark
You need 2 formulas to solve this. Use perimeter first and then area.
Formulas
P = 4s
Area = s^2
Givens
Perimeter = 24 feet
Solution
P = 4*s Substitute the value for P
24 feet = 4s Divide both sides by 4
24/4 = 4s/4
6 = s
Now use the area formula
Area = s^2 Substitute 6 for s
Area = 6^2
Area = 36 feet^2
Answer
Area = 36 ft^2
The perimeter of a square is 24 feet. What is the area in square feet.
Explanation -:In this question we are provided with the perimeter of the square and we are asked to calculate the area of the square. First we will calculate the side of the square and then we will calculate the area.
[tex] \small{ \underline{ \underline{ \red{\rm{ Calculating \: the \: side \: of \: the \: square}}}}}[/tex]
We know,
[tex] \star \: \small\boxed{ \rm{ Perimeter_{(square)} = 4 × side}}[/tex]
Substituting the values we get
[tex] \small\bf 24 = 4 × s[/tex]
[tex] \small\sf{ → \dfrac{24}{4} = s}[/tex]
[tex] \small\sf{ → s = 6 \: feet}[/tex]
[tex] \small{ \underline{ \underline{\rm \red{ Now, we \: will \: calculate \: the \: area }}}}[/tex]
We know,
[tex] \star \: \small \boxed{{\rm Area_{(square)} = side × side}}[/tex]
Substituting the values we get
[tex] \small\rm {Area_{(square)} = (6 × 6) feet² = 36 \: feet²}[/tex]
Hence, the area of the square is 36 feet².
Wite a differential equation in which y^2= 4(t + 1) is a solution.
Answers
Explanation:
The differential equation can be found by taking the derivative of y with respect to t of both sides of this equation.
Derivative of y^2 becomes 2y * dy/dt.
4(t+1) can be distributed to equal 4t + 4.
Derivative of 4t + 4 becomes 4.
Therefore, a possible differential equation is dy/dt * 2y = 4. Can check by separating and integrating.