cone is inscribed in a cylinder. A square pyramid is inscribed in a rectangular prism. The cone and the pyramid have the same volume. Part of the volume of the cylinder, 1 V 1 , is not taken up by the cone. Part of the volume of the rectangular prism, 2 V 2 , is not taken up by the square pyramid. What is the relationship of these two volumes, 1 V 1 and 2 V 2 ?
Answer:
The answer is "[tex]v_1 \ and\ v_2[/tex] are equal".
Step-by-step explanation:
Its volume could be defined both by cone as well as the cylinders
[tex]\to \text{(base area)} \times \text{(solid height)} \times (\frac{1}{3})\\\\[/tex]
We are planning to write this as [tex]V = \frac{Bh}{3}[/tex]
When we relate this formula to the cylindrical and prism volume formula, we can see that when we multiply the cone volume by 3, the cylinder size where it is registered comes in. The very same goes for the pyramid as well as the inscription of the rectangular prism. That both pyramid and the cone have the same volume V, hence it would have the same volume of a cell and rectangle prism. [tex]v_1 \ and\ v_2[/tex] are so similar.
Someone help me please?
Answer:
([tex]a^{2}[/tex] + 9 ) × (2[tex]a^{2}[/tex] + 1)
for the first one try two but im not sure
The vertices of a triangle are P(-6,1), Q(-2,-5) and R(8,1).
Find the equation of the perpendicular bisector of the side QR
Answer:
Step-by-step explanation:
Find the slope of QR. From that we can find the the slope of the line perpendicular to QR.
Q(-2, -5) & R(8,1)
[tex]Slope \ = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{1-[-5]}{8-[-2]}\\\\=\frac{1+5}{8+2}\\\\=\frac{6}{10}\\\\=\frac{-3}{5}[/tex]
So, the slope of the line perpendicular to QR = -1/m - 1÷ [tex]\frac{-5}{3} = -1*\frac{-3}{5}=\frac{3}{5}[/tex]
Bisector of QR divides the line QR to two half. We have find the midpoint of QR.
Midpoint = [tex](\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]
[tex]=(\frac{-2+8}{2},\frac{-5+1}{2})\\\\=(\frac{6}{2},\frac{-4}{2})\\\\=(3,-2)[/tex]
slope = 3/5 and the required line passes through (3 , -2)
y - y1 = m(x-x1)
[tex]y - [-2] = \frac{3}{5}(x - 3)\\\\y + 2 = \frac{3}{5}x-\frac{3}{5}*3\\\\y=\frac{3}{5}x-\frac{9}{5}-2\\\\y=\frac{3}{5}x-\frac{9}{5}-\frac{2*5}{1*5}\\\\y=\frac{3}{5}x-\frac{9}{5}-\frac{10}{5}\\\\y=\frac{3}{5}x-\frac{19}{5}[/tex]
Which graphs are the graphs of even functions?
HELP ASAP
Answer:
Step-by-step explanation:
Even functions have symmetry about the y-axis, so the graphs of even functions are the bottom 2.
Suppose you own a rowboat and sometimes go rowing in the summer. In June, you are planning to go rowing with two of your friends (three people total in the boat), and in July, you are planning to go rowing with just one friend (two people total in the boat). Will you put in more effort (row harder) on the three-person trip or on the two-person trip?
Answer:
The three-person trip require more effort (row harder) than the two person-trip
Step-by-step explanation:
The number of persons in the boat determines the mass of the boat
The mass of the boat with three people in total is more than the mass of the boat with only two person's
Mass is a measure of inertia, which is the resistance of a body to accelerate, and therefore, to the application of a force
Therefore, on the three-person trip were three people are in the boat, the boat has more mass, and therefore more inertia and will require more effort (force) than on the two-person trip that has a lesser mass
What is the word form of 1.604
Answer:
one point 4 inchs
Step-by-step explanation: yessuh
Answer:
one and six hundred four thousandths
Two square based pyramids are joined, total volume is 2700mm, perpendicular height of top pyramid is 16mm, perpendicular height of bottom pyramid is 20mm, length and width of joint base area both x, find x. Please help me
Answer: 15 m
Step-by-step explanation:
Given
Total volume of the combined pyramid is [tex]V=2700\ mm^3[/tex]
Height of top and bottom pyramid is
[tex]h_t=16\ mm[/tex]
[tex]h_b=20\ mm[/tex]
If the base has a side length of x, its area must be [tex]x^2[/tex]
Volume of square prism is given by
[tex]\Rightarrow V=\dfrac{1}{3}Bh\quad [\text{B=base area}]\\\\\text{Total volume will be the sum of the two pyramids}\\\\\Rightarrow 2700=\dfrac{1}{3}\times x^2\times 16+\dfrac{1}{3}\times x^2\times 20\\\\\Rightarrow 2700=\dfrac{1}{3}\times x^2\times (16+20)\\\\\Rightarrow x^2=225\\\Rightarrow x=15\ mm[/tex]
Thus, the value of [tex]x[/tex] is 15 m.
Help please
What value of x will ensure that the shelves are parallel?
for the to be parallel both the angle must be equal
so 7x - 20 = 3x + 20 - > 4x = 40⁰
x = 10⁰
One number is 10 less than three times a second number. If their sum is 46, find the larger of the two numbers.
Answer:
32
Step-by-step explanation:
Number 1 =x
Number 2 =(3x-10)
number 1 + number 2 =46
x+(3x-10)=46
4x=56
x=14
Number 1 =x=14
Number 2=3x-10
3(14)-10
32
Number 1 (14)+Number 2 (32)=46
Apply the distributive property to factor out 5x.
(5x · x2) + (5x · 3x) − (5x · 7) =
Answer:
5x^3+15x^2-35x
Step-by-step explanation:
Firstly, you want to combine the "x"s in the (5x*x^2) and the (5x*3x). Once you have that (you will get 5x^3 and 15x^2), you can move onto the last set of parenthesis. We can get 35x from here. Finally, the last step is to add the correct signs. Our final answer will then be 5x^3+15x^2-35x. I hope this helped and please don't hesitate to reach out with more questions!
which lines are perpendicular ?
Answer:
Lines C and D
Step-by-step explanation:
For a pair of lines to be perpendicular ,
the product of their slope must be - 1 .
Slope of A:
[tex]2x - 3y = 6\\\\-3y = -2x + 6\\\\y = \frac{-2x}{-3} + \frac{6}{-3}\\\\[/tex]
[tex]y = \frac{2}{3}x - 2\\\\slope_A = \frac{2}{3}[/tex]
Slope of B:
[tex]3x - 2y = - 9\\\\-2y = - 3x - 9\\\\y = \frac{-3x}{-2} - \frac{9}{-2}\\\\y =\frac{3x}{2} + \frac{9}{2}\\\\slope_B = \frac{3}{2}[/tex]
Slope of C:
[tex]y = - \frac{3}{2}x - 5 \\\\slope_C = -\frac{3}{2}[/tex]
Slope of D:
[tex]y = \frac{2}{3}x + 2\\\\slope_D = \frac{2}{3}[/tex]
Product of the slopes = - 1
[tex]slope_A \times slope_B = \frac{2}{3} \times \frac{3}{2} = 1 \neq - 1 \\\\Therefore, not\ perpendicular.\\\\Slope_B \times slope_C = \frac{3}{2} \times \frac{-3}{2} = \frac{-9}{4} \neq -1\\\\Therefore , not \ perpendiucalr.\\\\Slope_C \times slope_D = -\frac{3}{2} \times \frac{2}{3} = - 1\\\\Therefore , perpendicular\\\\\\Slope_A \times slope_D = \frac{2}{3} \times \frac{2}{3} = \frac{4}{9} \neq 1\\\\therefore , not \ perpendicular.[/tex]
AB = 20 cm, m∠A = 30°, and m∠C = 45°. Express the number of centimeters in the length of BC in simplest radical form.
Answer:
Step-by-step explanation:
x/Sin30 = 20/sin45 multiply both sides by sin30
x = 20*sin30 / sin45
sin30 = 1/2
sin45 = 0.7071
x = 20*1/2 / 0.7071
x = 10 / 0.7071
x = 10 * sqrt(2)
Carlos and Maria drove a total of 197 miles In 3.8 hours. Carlos drove the first part of the trip and averaged 55 miles per hour. Maria drove the
remainder of the trip and averaged 47 miles per hour. For approximately how many hours did Maria drive? Round your answer to the nearest tenth if
necessary.
Answer:
1.5 hours
Step-by-step explanation:
Carlos = x
Maria = y
55x + 47y = 197
x + y = 3.8
x = 3.8 - y
55(3.8 - y) + 47y = 197
209 - 55y + 47y = 197
-8y = -12
y = 3/2 = 1.5
PLS HELP (algebra 1)
solve -19d + 8(7d - 14)
Answer:
[tex]\huge\boxed{-19d + 8(7d - 14)=37d-112}[/tex]
Step-by-step explanation:
[tex]-19d + 8(7d - 14)[/tex]
use the distributive property: a(b + c) = ab + ac
[tex]-19d + (8)(7d)+(8)(- 14)=-19d+56d-112[/tex]
combine like terms
[tex]=(-19d+56d)-112=37d-112[/tex]
Suppose a triangle has sides a, b, and c, and that a2 + b2 > c2. Let 0/ be the
measure of the angle opposite the side of length c. Which of the following
must be true? Check all that apply.
A. 0/ is an acute angle.
B. cos 0/ > 0
C. The triangle is a right triangle.
D. The triangle is not a right triangle.
Hello,
Answer A
Indeed:
[tex]c^2=c^2+b^2-2ab*cos(\theta) < a^2+b^2\\\\-cos(\theta)<0\\\\cos(\theta)>0\ \Longrightarrow \theta < 90^o[/tex]
True statements are:
A. [tex]\theta[/tex] is an acute angle.
C. The triangle is a right triangle.
D. The triangle is not a right triangle.
What is angle?An angle is a combination of two rays (half-lines) with a common endpoint.
Given:
a² + b² > c²
as, the triangle with sides a, b and c.
If this is a right triangle, then the condition a² + b² > c² apply.
Using cosine law.
angle> 90 degrees which is an obtuse angle.
Also, cos [tex]\theta[/tex] is negative.
Hence, the conditions that are true are A, C and D.
Learn more about this concept here:
https://brainly.com/question/1619127
#SPJ2
using the diagram below, what is the measure of ∠E?
Step-by-step explanation:
angle e = 50 degree,,,,,,,
If function fhas zeros at -3 and 4, which graph could represent function ?
Answer:
Graph A
Step-by-step explanation:
Zeroes mean the x intercepts so the only graph that has points at -3 and 4 is GRAPH A. You can also come to the conclusion by using process of elimination.
Given the function (Image below) [Algebra ll]
Can someone help with questions 5 -9
Answer:
THE ANSWER IS UNLIMITED
Step-by-step explanation:
THE REASON IT'S UNLIMITED IS BECAUSE YOU CAN HAVE ALL TYPES OF SHIRTS, FROM JERSEYS TO DRESS SHIRTS, TO T-SHIRTS.
Can someone ask me about this, which is algebra, please
Answer:
The correct answer is not shown in your picture. You must get a = 60.
Step-by-step explanation:
(1/2)a + (2/3)b = 50
b = 30
(1/2)a + (2/3)(30) = 50
(1/2)a + 20 = 50
(1/2)a + 20 - 20 = 50 - 20
(1/2)a = 30
2 * (1/2)a = 2 * 30
a = 60
The correct answer is not shown in your picture. You must get a = 60.
Examine the linear functions that represent Abel and Neal's mountain biking scenario. Abel: d = 14t, Neal: d = 11t + 6 How will you inspect the equations to determine the number of solutions? Compare the slopes. If they are the same, there will be one solution. Compare the slopes. If they are different, there will be one solution. Compare the y-intercepts. If they are the same, there will be one solution. Compare the y-intercepts. If they are different, there will be one solution.
Answer:
B: Compare the slopes. If they are different, there will be one solution.
Step-by-step explanation:
I gottchu guys :)
Answer:
Step-by-step explanation:
What is the length of the hypotenuse of the right angle triangle, keep your answer to 1 decimal place a is 9cm and b is 13cm
Answer:
15.8cm
Step-by-step explanation:
\sqrt{9^2+13^2} =15.8113883008
15.8cm
The total profit P of manufacturing x hundred DVD's is given by the equation below.
P = 600 + 1,500x − 100x2
Find x if the total profit is $5,600.
Answer:
x = -7.5
Step-by-step explanation:
P = 600 + 1,500x − 100x^2
P = − 100x^2 + 1,500x + 600
x = -b/2a
1500/ (2 x -100)
x = -7.5
plz help by telling the answer. I will rate u 5 star and give u branist and also like plus I will follow u plz help me
Answer:
The simple answer is we round the square root of the number of data points. For example: 25 data points = 5 bars. 100 data points = 10 bars
PLEASEEE HELPPPPPPP
A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:
f(d) = 9(1.04)d
What is the average rate of change of the function f(d) from d = 3 to d = 9, and what does it represent?
Answer:
0.4476
Step-by-step explanation:
11. Write a compound inequality that represents each situation. Graph your solution.
all real numbers that are greater than 8 but less than 8
85x<8
8 SXS 8
-8 < x <8
8
its the third choice
PLEASE HELP ME ILL MARK YOU BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
B
Step-by-step explanation:
speed = [tex]\frac{distance }{time}[/tex]
Then
speed = [tex]\frac{2}{9}[/tex] ÷ [tex]\frac{4}{5}[/tex]Leave the first fraction, change division to multiplication, turn the second fraction upside down.
speed = [tex]\frac{2}{9}[/tex] × [tex]\frac{5}{4}[/tex] = [tex]\frac{5(2)}{9(4)}[/tex] = [tex]\frac{10}{36}[/tex] = [tex]\frac{5}{18}[/tex] mile per hour → B
Jacob and sumalee each improved their yards by planting daylilies and geraniums. They bought their supplies from the same store. Jacob spent $107 on 11 daylilies and 4 geraniums. Sumalee spent $60 on 4 daylilies and 12 geraniums. Find the cost of one daylilies and the cost of one geranium.
Answer:
Daylily: $9
Geranium: $2
Step-by-step explanation:
1 daylily costs x.
1 geranium costs y.
11x + 4y = 107
4x + 12y = 60
Multiply the first equation by 3 and subtract the second equation from it.
29x = 261
x = 9
4x + 12y = 60
4(9) + 12y = 60
12y = 24
y = 2
Answer:
Daylily: $9
Geranium: $2
Answer:
1) Set up a system of equations. Assign each plant a variable. I used X for Daylillies and Y for Geraniums. In this case:
11x + 4y = 107
4x + 12y = 60
2) Get one variable by itsef. You can choose to either get the X or the Y by itself. For the sake of ease, I'll go with achieving X.
3) Using the equation 4x + 12y = 60, isolate the 4x.
4x = -12y + 60
4) Divide both sides by 4.
x = -3y + 15
5) X is isolated. Now plug in that isolated X into another remaining equation in order to isolate Y. Don't forget to combine like terms.
11(-3y + 15) + 4y = 107
-33y + 165 + 4y = 107
-29y + 165 = 107
-29y = -58
y = 2
6) You have your Y, which means that each Geranium costs $2 each. Now, you need to find X. Plug in Y into any of the first two equations that we started with.
4x + 12(2) = 60
4x + 24 = 60
4x = 36
x = 9
7) You now have both X and Y. Daylillies cost $9 each, and Geraniums cost $2 each.
8) You can double-check your answers by plugging in your final X and Y values into any of the first equations you wrote. If it comes out equal, it works.
I need help with all of em please
Answer:5/4
Step-by-step explanation: i think this is the answer
Answer:
The area is 30 units squared, the perimeter is 17 units, and the answer to the question below is 9
Step-by-step explanation:
whch of the following can be usefiul when finding the vaue of a variable
Answer:
i don't see anything so i cant help you sorry
Step-by-step explanation: