A cubical block of side 14 cm is surmounted by a hemisphere . what is the greatest radius that the hemisphere can have?
Answers
Answer:
9.9cmStep-by-step explanation:
The hemisphere will have its greatest radius along the diagonal of the cube it was surmounted on. The base of the cubical block will be square in nature. Since a cube has all its sides equal, we can find the length of its diagonal using pythagoras theorem as shown.
[tex]hyp^{2} = adj^{2} +opp^{2}[/tex]
Note that the diagonal will be the hypotenuse of the square face which is the longest sides.
Given adjacent = 14cm and opposite = 14cm
[tex]hyp^{2} = 14^{2} +14^{2}\\hyp = \sqrt{196+196} \\hyp = \sqrt{392} \\hyp = 19.8cm[/tex]
The diagonal of the base of the cube is 19.8cm which is equivalent to the greatest diameter of the sphere.
The greatest radius that the hemisphere can have = 19.8/2 = 9.9cm
Drawing diagrams
Circles
Radius rDiameter dRelationship between r and d:[tex]\displaystyle r = \frac{d}{2}[/tex]
Cubes
Length lWidth wHeight hApplication:Let's draw a figure to supplement a visual image to further understand what we need to find. Please refer to the attached image for reference. Please excuse the poor handwriting/drawing. It is also not to scale.
We know that there is a cubical block w/ side measurements of 14 cm. "Surrmounted" means on top. So a hemisphere (half of a sphere) is on top of our block.
If we take a look at our geometrical shape from the top-down angle, we can see that the top would just look like a circle within a square, as depicted in blue.
Labeling our measurements, we can see that the length, width, and height of our cubical block are equal to 14 cm due to the definition of a cube. This extends to the definition of a square as well, so the length and width of our square are also equal to 14 cm.
With the side of the square equal to 14 cm, we know that this is equal to the circle's diameter. So d = 14 cm. We can solve for the radius of the circle/hemisphere by substituting it into the radius formula:
[tex]\begin{aligned}r & = \frac{d}{2} \\& = \frac{14 \ \text{cm}}{2} \\& = \boxed{ 7 \ \text{cm}} \\\end{aligned}[/tex]
Answer:∴ the greatest radius that the hemisphere can have is equal to 7 cm. Any r > 7 cm would result in the hemisphere being over the edge of the cube.
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Learn more about Geometry: https://brainly.com/question/27732359
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Topic: Geometry
Unit: Composition of Geometrical Shapes
Related Questions
What is the x-value of the vertex?
f(x)=(x+2)2−1
x-value of the vertex:
Answers
Step-by-step explanation:
f(x) = (x+2)(2-1)
= x(2-1)+2(2-1)
= 2x-x + 4-2
= 2x - x + 2
3w + 4u - 6
Simplify
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Step-by-step explanation:
There are many different ways to simplify this. It could be
3(w-2)+4u , 2(2u-3)+3w , or something else.
Can someone help me please??
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Answer:
B.
Step-by-step explanation:
It's just y = 2x because if you look the y is two times the x.
PLEASE ANSWR ASAP FOR BRAINLIEST!!!!
Answers
Answer:
x = 33
Step-by-step explanation:
The sum of the angles of a triangle are 180 degrees
x+114+33 = 180
Combine like terms
x+147 = 180
Subtract 147 from each side
x+147-157 = 180-147
x = 33
Answer:
x=33
Step-by-step explanation:
The interior angles of a triangle must add up to 180 degrees. Therefore, the 3 angles inside the triangle should add to 180.
x+114+33=180
Combine like terms by adding 114 and 33
x+147=180
In order to solve this equation, we must get x isolated. Perform the inverse operation to both sides.
x+147=180
147 is being added on to x. The inverse of addition is subtraction. Subtract 147 from both sides.
x+147-147=180-147
X=180-147
x=33
x is equal to 33 degrees.
A weather station reports that there is a 40% chance of rain today. What is the probability that it will not rain today?
Answers
Answer:
Since the full percentage of something is 100% thats because 1*100 = 100.
So since it has 40% chance of rain what would 100-40 be? Well it would be 60. So the probability that it will not rain is
60%Factor completely 10x2 + 2x − 8
Answers
Step-by-step explanation:
[tex]10x^2+2x-8\\2(5x^2+x-4)\\2(5x-4)(x+1)[/tex]
Answer:
[tex]2(5x-4)(x+1)[/tex]
You can check the answer by re-distributing the 2 and using the foil method :)
A bag contains eight yellow marbles, nine green marbles, three purple marbles, and five red marbles. Two marbles are chosen from the bag. What expression would give the probability that one marble is yellow and the other marble is red?
- 30%
- 40%
- 50%
- 60%
Answers
Answer:
2/15 = 13 1/3 %
Step-by-step explanation:
eight yellow marbles, nine green marbles, three purple marbles, and five red marbles = 25
P(yellow) = yellow/ total =8/25
Keep
7 yellow marbles, nine green marbles, three purple marbles, and five red marbles = 24
P(red) = red/total =5/24
P(yellow then red) = 8/25 * 5/24 = 1/15
Then we have (red, yellow) =
P(red) = red/ total =5/25 = 1/5
Keep
8 yellow marbles, nine green marbles, three purple marbles, and four red marbles = 24
P(yellow) = yellow/total =8/24 = 1/3
P(red, yellow) = 1/5*1/3 = 1/15
Add them together
1/15 + 1/15 = 2/15 =
20 points for who ever get it right someone who knows what they doing please
Answers
Answer:
F is greater than 25
F is positive
Step-by-step explanation:
You know that F must be positive, since a number is subtracted from it and then another number is multiplied by that difference. Since a positive number multiplied by a negative number is negative, F must be positive.
You also know that F is greater than 25, because a number is subtracted from it and it is multiplied by a fraction between 0 and 1, meaning that that difference is further reduced.
Hope this helps!
A park ranger standing in a 146-foot lookout tower sees the beginning of a forest fire. she measures the angle of depression from the tower to the fire to be 12 degrees. Assuming that the ground is horizontal, calculate the distance from the tower to the fire. *Round to the nearest hundredth
Answers
their gd7v7gvugvrty
Step-by-step explanation:
7yvtc
Let f(x) = 4x2 + x + 1 and g(x) = x2 − 2. Find g(f(x)). Show each step of your work.
Answers
Answer:
the answer to this question is
[tex]8x^{2} +2x[/tex]
Which graph represents an odd function? On a coordinate plane, a function has two curves. The first curve is in quadrants 2 and 3 and has a minimum value of (negative 1, negative 3). The curve intersects the x-axis at (negative 2, 0) and goes to (0, 0). The second curve is in quadrants 1 and 4 and has a minimum value of (1, negative 3). The curve starts at (0, 0) and intercepts the x-axis at (2, 0). On a coordinate plane, a curved line crosses the x-axis at (negative 4, 0), (0, 0), and (4, 0). On a coordinate plane, a v-shaped function opens up. The function goes through (0, 2), has a vertex at (2, 0), and goes through (5, 3). On a coordinate plane, a curve has a maximum point at (0.5, 1) and a minimum point at (2, 0). The curve goes through points (0, 0) and (3, 4).
Answers
Answer:
On a coordinate plane, a curved line crosses the x-axis at (negative 4, 0), (0, 0), and (4, 0)
Step-by-step explanation:
An odd function is symmetrical about the origin. It will satisfy the relation ...
f(-x) = -f(x)
Of the given points, the set that is symmetrical about the origin is found on the 3rd graph:
(-4, 0), (0, 0), (4, 0)
Answer:
B on edge
Step-by-step explanation:
took the test
100 + x = 50 ( find x)
Answers
Just subtract 100 - 50 and you get x = 50
Answer:
x = 50
Step-by-step explanation:
100 -50 = 50
50+50=100
Have a wonderful day and stay safe!
Write an integer that represents this scenario:
18-point gain
Answers
Answer:
+18
Step-by-step explanation:
A gain is a positive number
+18
Answer:
+18
Step-by-step explanation:
Neg = Drop
Pos = Gain
Gain so +
+18
Which words or variables mean OUTPUT? Select all possible answers. help me out
a. domain
b .range
c .x
d .y
e. f(x)
Answers
D. Y
E.f(x)
y is always the output, and range and f(x) mean the same thing along with Y
c. y
e. f(x)
A rocket is launched at t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t)=−4.9t2+100t+325. What is the independent variable and its units? ______ (meters, seconds, meters per second, or seconds per meters) - select the correct units What is the dependent variable and its units? _______ (seconds or meters) - select the correct units
Answers
Answer:
see below
Step-by-step explanation:
h(t)=−4.9t2+100t+325.
The independent variable is the one that we change
t which is in seconds
The dependent variable is the result
h(t) which is in meters
George gets a pay rise from £632 per week to £711 per week. What percentage pay rise was he given?
Answers
Answer:
12.5%
Step-by-step explanation:
£632 - 100%
£711 - ?%
?%= (711*100)/632 = 112.5%
112.5-100=12.5%
I will give you brainliest!!!!! Which equation models the total profit y, based on the number of T-shirts sold x?
Answers
Answer:
B. y-25=5(x-20)
-3(x+ 2y) + 5(3x - y) + y2 for x = 6 and y= 2.
Answers
Answer:
54
Step-by-step explanation:
Please help me it is only 1 question please help me I have no idea about this
Answers
Answer:
53
Step-by-step explanation:
Answer:
(540 - π60 cm²) or 350cm³(351.5)
Step-by-step explanation:
You'll have to subtract the volume of the rectangular prism with the cylinder.
We know that the prism's volume is V = s*s*h = 6*6*16 = 540 cm²
We also know the cylinder's volume: V = πr²h = π(4/2)²*15 = π*4*15 = π*60
Now the only step remaining is to subtract the volume of the prism with the cylinder: 540 - π*60 cm³
540 - π*60 cm³ is the full answer
350 is the approximate answer (rounded it down from 351.5 to 350cm³)
£2200 is deposited in a bank paying 0.5% simple interest per annum. How much interest will have been paid after 18 years?
Answers
Answer:
The answer would be £198
principal (p) = 2200
Rate (R) = 0.5%
Time (T) = 18
Interest(I) = ?
Now,
or, Interest. = P×T×R/100
or, Interest = 2200×18×0.5/100
or, Interest = 19800/100
Hence, Interest = 198
What is 2 with an exponent of -2 equal to?
Answers
Answer:
1/4
Step-by-step explanation:
Answer:
[tex] \boxed{\frac{1}{4} } [/tex]
Step-by-step explanation:
[tex]{2}^{ - 2} = \frac{1}{ {2}^{2} } \\ \\ \: \: \: \: \: \: \: \: \: = \frac{1}{4} [/tex]
[tex] Negative \: exponent \\ \\ = > {a}^{-x} = \frac{1}{{a}^{x}} [/tex]
Simplify
4a x 6a
8a?
Answers
Answer:
[tex]=24a^2[/tex]
Step-by-step explanation:
[tex]4a\cdot \:6a=24a^2\\\mathrm{Multiply\:the\:numbers:}\:4\cdot \:6=24\\=24aa\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\\aa=\:a^{1+1}\\=24a^{1+1}\\=24a^2[/tex]
Answer:
Simply multiply across.
since they both have the same base(a),add the powers ie.(1+1)=2.
Hence 4a×6a=24a²
the square root of 7/16
Answers
Answer:
[tex] \sqrt{7} [/tex]
over 4
square the top and bottom separately and 16 squared is four but seven can't square. leave the top as seven squared and the bottom as just four
what is the slope.
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answers
Answer:
The slope is the rise over run, so...
It is 3/1 or just 3.
Step-by-step explanation:
Rise/run is slope
(2,1) is a point on the line, and so is (3,4)
Given right triangle ABC . To the nearest degree, find the measure of angle B. 20° 43° 47° 70°
Answers
Answer:
The answer is "70°"
Step-by-step explanation:
In the given question an attachment file is missing. so, the attachment file and its solution can be defined as follows:
Given:
ABC is the right triangle.
Find B=?
Solution:
[tex]\Rightarrow \sin \theta= \frac{p}{h}\\\\[/tex]
[tex]\Rightarrow \sin B^{\circ}=\frac{AB}{AC}= \frac{4.8}{5.1}\\\\[/tex]
[tex]\Rightarrow \sin B^{\circ}= .941[/tex]
[tex]\Rightarrow B^{\circ}= \sin^{-1} (0.941)\\\\\bold{\sin^{-1} (0.941) = 70.2^{\circ}}\\\\\therefore \ \ \ \ \bold{B^{\circ} = 70^{\circ}}[/tex]
Answer:
70
Step-by-step explanation:
what is the point-slope form of a line with slope -3 that contains the point 10, -1
Answers
Answer:
C. [tex] y + 1 = -3(x - 10) [/tex]
Step-by-step explanation:
The point-slope equation of a line:
[tex] y - y_1 = m(x - x_1) [/tex]
where m = slope, and the point is (x1, y1).
In this case, the point is (10, -1), so x1 = 10 and y1 = -1.
The slope is -3, so m = -3.
[tex] y - (-1) = -3(x - 10) [/tex]
[tex] y + 1 = -3(x - 10) [/tex]
Thank you for all your help I need this too ASAP pls
Answers
Answer:
A
Step-by-step explanation:
Quadratic equation
What is the product of ( x + 3) ( x - 4)?
I'm sure its x^2 - x - 12, but I wanted to double-check :D
Answers
Answer: x² - x - 12
Step-by-step explanation: When multiplying two binomials together, we can use the F.O.I.L. method.
First, Outer, Inner, Last.
We take the product of the first terms which is x² plus the product of the outer terms which is -4x plus the product of the inner terms which is 3x plus the product of the last terms which is -12.
So we have x² - 4x + 3x - 12.
Simplifying from here by combing the middle terms, we have x² - x - 12.
Pay very close attention to your positives and negatives as you F.O.I.L. because this is the area where most mistakes occur.
Which of the following could be used as an example of a mass of one kilogram?
A. a grocery sack of apples
B. 10 paperclips
C. a soda cup of water
D. a filled suitcase
Answers
Answer:
i would think C
Step-by-step explanation:
Type the integer that makes the following addition sentence true:
+ 83 = 19
Answers
Answer:
The answer is: -64
Step-by-step explanation:
To get the answer of -64, you would have to subtract. To subtract you would use this equation: 19 - 83. This would get you -64. To double check your answer, you would add -64 + 19 to make sure your answer is 83.
I would appreciate if you mark me as brainliest! :D
