6.
Which expression represents the volume of the composite figure
formed by a hemisphere with radius r and a cube with side length 2r?
Answers
Answer:
A. [tex]r^{3}[/tex]([tex]\frac{2}{3}[/tex][tex]\pi[/tex] + 8)
Step-by-step explanation:
A composite figure is formed by two or more shapes in contact.
Volume of a cube = [tex]l^{3}[/tex]
where l is the length of its sides.
Given that l = 2r, then;
volume of the cube = [tex](2r)^{3}[/tex]
= 8[tex]r^{3}[/tex]
volume of the cube = 8[tex]r^{3}[/tex]
For a hemisphere, volume = [tex]\frac{2}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]
Also,
volume of the hemisphere = [tex]\frac{2}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]
So that,
volume of the composite figure = volume of the cube + volume of the hemisphere
= 8[tex]r^{3}[/tex] + [tex]\frac{2}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]
= [tex]r^{3}[/tex](8 + [tex]\frac{2}{3}[/tex][tex]\pi[/tex])
volume of the composite figure = [tex]r^{3}[/tex]([tex]\frac{2}{3}[/tex][tex]\pi[/tex] + 8)
Related Questions
Jill bought a lamp for $40. She sold it at a garage sale for $12. What was the approximate decrease?
Answers
Answer:
she was left with 28$ I'm in high school i think I'm right
Step-by-step explanation:
Need help i suck at mathh
Answers
Please help as soon as possible
Answers
Answer:
Step-by-step explanation:
the answer is No its not similar
because the factors don't work
Given that GJ=70.2, JH=26, and GK=70.2, find the measure of JK
Answers
Answer:
52
Step-by-step explanation:
The two sides (GJ and GK) are congruent, and the angle of ∠GHJ is 90°.
It means JH ≅ HK.
JH = 26 so you multiply 2.
26 x 2 = 52
JK = 52
The measure of the side JK is 52 units if the GJ=70.2, JH=26, and GK=70.2 after applying the Pythagoras theorem.
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
It is given that:
GJ=70.2, JH=26, and GK=70.2,
In the right angle triangle JHG:
GH = √(GJ² - JH²)
GH = √(70.2² - 26²)
GH = 65.20
Similarly, applying Pythagoras' theorem in the triangle GHK:
HK = √(GK² - GH²)
HK = √(70.2² - 65.20²)
HK = 26.01
JK = JH + HK
JK = 26 + 26.01
JK = 52.01 = 52
Thus, the measure of the side JK is 52 units if the GJ=70.2, JH=26, and GK=70.2 after applying the Pythagoras theorem.
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Anne is playing golf. On the first tee, she hits a slow shot down the Y = x -0.0 4X squared, we are why is the balls hide in the air and eggs is a horizontal distance in his drawer from the tea. The distance or measured in feet how far from the tea does the ball hit the ground
Answers
Answer:
25 ft
Step-by-step explanation:
The path of the golf ball is given by the equation.
[tex]y=x-0.04x^2[/tex]
The point on the ground where the ball will land on the ground is the point where [tex]y=0[/tex].
[tex]x[/tex] is horizontal distance
So
[tex]0=x-0.04x^2\\\Rightarrow x(1-0.04x)=0\\\Rightarrow 1-0.04x=0\\\Rightarrow x=\dfrac{1}{0.04}\\\Rightarrow x=25[/tex]
So, the ball will land 25 ft away from the tee.
1/9x=5
solve for x
please show step by step
Answers
Answer:
x=1/45
Step-by-step explanation:
do the inverse
please mark it as brainliest!!<3
A sphere has a Volume of 972 cubic feet. Find the radius of the sphere.
Answers
Answer:
6.15
Step-by-step explanation:
Please help ASAP Tysm guys!
Answers
Answer:
it would be 3
Step-by-step explanation:
Factor this trinomial.
x² + 3x - 4
A. (x-4)(x-1)
B. (x - 4)(x + 1)
C. (x + 4)(x + 1)
D. (x+4)(x - 1)
Answers
Answer:
(x-1)(x+4), so D.
Step-by-step explanation:
Multiply (x+2)(x2−3x +4)
2x2−6x+8
x3+5x2+10x+8
x2−2x+6
x3−x2−2x+8
Plz help i mark brainliest
Answers
Step-by-step explanation:
Using FOIL, we have
(x + 2)(x² - 3x + 4)
= (x³ - 3x² + 4x) + (2x² - 6x + 8)
= x³ - x² - 2x + 8.
giving points and brainly
Answers
Answer:
A 159.25 to the second power
Step-by-step explanation:
he simplest (and most commonly used) area calculations are for squares and rectangles. To find the area of a rectangle, multiply its height by its width. For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area.
The temperature was 75° Fahrenheit. The temperature dropped at a rate of 10° per hour.
What was the temperature in degrees 8 hours later?
Answers
Answer:
-5 degrees
Step-by-step explanation:
you started at 75 degrees. it dropped at a rate of 10 degrees per hour. It's been eight hours. 8 times 10 equals 80. It dropped a total of 80 degrees. the starting 75 degrees minus the current 80 degrees equals -5 degrees.
At a dinner, the meal cost $22 and a sales tax of $1.87 was added to the bill. At the same restaurant, another family had a meal and the meal cost $66.00. How much would the sales tax be on a $66 meal?
Answers
Answer:
71.61
Step-by-step explanation:
hope this helps good luck
what are the like terms in these?
3+5y-2g+7y
9g+5-2g+8x
Answers
Answer:
so the first one is 3+12y−2g
and the second one is 7g+5+8x
Step-by-step explanation:
im rlly rlly sorry if its wrong !!
g(x) = 4f(x)
Is this a vertical or a horizontal translation
Answers
Answer:
this is a vertical
Step-by-step explanation:
Which value of n makes the equation true?
1/2(n+4)=6
Answers
Answer:
8
Step-by-step explanation:
1/2(12)=6
Answer:
8
Step-by-step explanation:
1/2(8+4)=6
Mindy needs to rake a rectangular part of her yard that is 9 feet by 8 feet. It takes her 10 minutes to rake an area that is 12 feet square. How long will it take Mindy to rake the rectangular part of her yard?
Answers
Answer:
60 minutes
Step-by-step explanation:
Time taken to rake 12ft² = 10 minutes
Area of Mindy's rectangular path :
Area of rectangle = Length * Width
Dimension of Mindy's rectangular path = 9ft by 8ft
Area = 9ft * 8ft
Area = 72ft²
Hence, it will take Mindy;
(Area of Mindy's path / 12 ft) * time taken
(72ft² / 12ft²) * 10 minutes
6 * 10 = 60 minutes
Graph the line that passes through the points (2,8) and (-5,8) and determine the equation of the line.
Answers
Answer: y=7
Step-by-step explanation:
First, graph the points, and you get a horizontal line. You see that the line is on the Y-Axis, and hits the y-axis at (0,7). Since it is horizontal, you get y=7
3.
If the volume of cylinder of height 7 cm is 448 cm², then the total surface area of cylinder is
(1) 2041 cm?
(2) 2241 cm?
(3) 2481 cm?
(4) 240 cm?
Answers
Answer:
A = 240π cm²
Step-by-step explanation:
Given that,
Height of a cylinder, h = 7 cm
Volume of the cylinder, V = 448π cm³
We need to find the total surface area of the cylinder.
The formula for the volume of the cylinder is given by :
[tex]V=\pi r^2 h\\\\r=\sqrt{\dfrac{V\pi }{\pi h}} \\\\r=\sqrt{\dfrac{448\pi }{\pi \times 7}} \\\\r=8\ cm[/tex]
The formula for the total surface area of the cylinder is given by :
[tex]A=2\pi r(r+h)\\\\A=2\pi \times 8\times (8+7)\\\\A=240\pi \ cm^2[/tex]
So, the total surface area of the cylinder is 240π cm².
Use the domain (1/2, 1, 2, 4, 8) to plot the points on the graph for the given equation. The grid marks represent one unit,
the horizontal red line represents the x-axis, and the vertical red line represents the y-axis.
y = log 2 x
Answers
According to values of a function we can plot the points on a graph.
What is domain?
Domain is the value which we used to enter in a function to get the value of a function.
How to plot the points on the graph?
We have been given the domain of the function and we have to plot the value in the graph.
F(1/2)=log1=0
F(1)=log2=0.3
F(2)=log4=0.6
F(4)=log8=0.9
F(8)=log16=1.2
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what is equivalent to 8+3•12
Answers
Answer:
Step-by-step explanation:
There are infinity equivalent fractions to 812. See some examples: 23, 46, 69, 812, 1015, 1218, 1421, 1624, 1827, 2030, 2233, 2436, 2639, 2842, 3045, 3248, 3451, 3654, 3857, 4060...
help me with this thanks for anyone who helps! :D
Answers
Answer:
x= 90-60
x=30
Step-by-step explanation:
Answer:
30° is the answer because its a right angle
Step-by-step explanation:
can you mark me brainliest? thank you
(r - 3)(3r + 6)= ? .....
Answers
3r² +6r-9r-18
3r²-3r-18
Find the prime factorization of 120.
23 × 3 × 5
2 × 32 × 5
2 × 3 × 5
2 × 32 × 52
Answers
Answer:
(7/8 - 4/5)^2 = 9/
1600
= 0.005625
Step-by-step explanation:
Subtract: 7/
8
- 4/
5
= 7 · 5/
8 · 5
- 4 · 8/
5 · 8
= 35/
40
- 32/
40
= 35 - 32/
40
= 3/
40
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(8, 5) = 40. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 5 = 40. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - seven eighths minus four-fifths = three fortieths.
Exponentiation: the result of step No. 1 ^ 2 = 3/
40
^ 2 = 32/
402
= 9/
1600
In words - three-fortieths squared = nine one-thousand six-hundredths.
#21 pls help!!!!! would greatly be appreciated
Answers
3x2+2
-5x - 4
2x - 7
-2x2+10
Hint: To find the perimeter of a polygon, add all the sides
Answers
Answer:
The perimeter of a 4-sided polygon: P = x²-3x+1
Step-by-step explanation:
Given the lengths of the sides of a given polygon
3x²+2-2x²+102x-7-5x-4The perimeter of a 4-sided polygon can be determined by adding the lengths of all 4 sides.
Perimeter = (3x²+2) + (-2x²+10) + (2x-7) + (-5x-4)
Remove the parentheses
=3x²+2-2x²+10+2x-7-5x-4
Group like terms
=3x²-2x²+2x-5x+2+10-7-4
Add similar elements: 3x²-2x²=x²
=x²+2x-5x+2+10-7-4
Add similar elements: 2x-5x=-3x
=x²-3x+2+10-7-4
=x²-3x+1
Therefore, the perimeter of a 4-sided polygon: P = x²-3x+1
For each graph shown below, select the correct description for slope and y-intercept. In the fourth column, create an equation that can be used to describe the function shown in the graph.
Answers
Use the linear combination method to solve this system of equations. What is the value of x? 3 x + 7 y = 31. Minus 3 x minus 2 y = negative 1 Negative 6 Negative 3 and two-thirds 3 and two-thirds 6
Answers
Answer:
x = -3 2/3
Step-by-step explanation:
Given the simultaneous equations;
3 x + 7 y = 31 ..... 1
-3x - 2y = -1 ..... 2
Add both expressions
7y - 2y = 31-1
5y = 30
y = 30/5
y = 6
Substitute y = 6 into equation 2
From 2;
-3x - 2y = -1
-3x - 2(6) = -1
-3x - 12 = -1
-3x = -1 + 12
-3x = 11
x = -11/3
x = -3 2/3
Hence the value of x is -3 2/3
Answer:
x = -3 2/3
Step-by-step explanation:
A bag has one red ball, three blue balls and twice as many green balls as blue balls. if one ball is drawn (without looking) from the bag what are the chances that the ball will be blue?
Answers
Answer:
3/10 or three tenths or 0.3 or 0.30
Step-by-step explanation:
Plz brainliest
Answer: 30% or 3/10
Step-by-step explanation:
First you need to figure out how many balls are in the bag. There is 1 red, 3 blue, and 2x (x=# of blue balls) green balls. since there is 3 blue balls you double 3 to get how many green balls there are, which is 6. Then you do 1+3+6 to give you 10. Since there is 3 blue balls in a bag that consists of 10 balls, you have a probability of 3/10 or 30% or .3 to draw a blue ball.
The measures of the angles of A ABC are given by the expressions in the table.
Angle
Measure
A
(4x – 13)
B
15
С
(x +18)
What is the measure of ZA and ZC?
Enter your answers in the boxes
mZA =D
mZC=
Answers
Answer:
m∠A = 115°
m∠C = 50°
Step-by-step explanation:
By triangle sum theorem,
Sum of measures of all interior angles of a triangles equals to 180°.
m∠A + m∠B + m∠C = 180°
By substituting the values of the angles from the given table,
(4x - 13) + 15 + (x + 18) = 180
(4x + x) + (-13 + 15 + 18) = 180
5x + 20 = 180
5x = 180 - 20
x = [tex]\frac{160}{5}[/tex]
x = 32
m∠A = (4x - 13)° = 4(32) - 13
= 115°
m∠C = (x + 18)° = 32 + 18
= 50°
Based on the properties of the internal angles in triangles, the measure of the angles A and C from the triangle ABC are equal to 115° and 50°, respectively. #SPJ5
What are the measures of the internal angles of the triangle ABC?According to geometry, triangles are figures formed by three sides and three internal angles and, likewise, the sum of the measures of the internal angles equals 180°. Based on the latter property, we should solve the following expression for x:
(4 · x - 13) + 15 + (x + 18) = 180
5 · x + 20 = 180
5 · x = 160
x = 32
Finally, the measure of the angles A and C from the triangle ABC are, respectively:
m ∠ A = 4 · 32 - 13 = 115°
m ∠ C = 32 + 18 = 50°
Based on the properties of the internal angles in triangles, the measure of the angles A and C from the triangle ABC are equal to 115° and 50°, respectively. #SPJ5
To learn more about triangles, we kindly invite to check this verified question: https://brainly.com/question/2773823 #SPJ5