The Volume of largest Right Circular Cylinder that can be inscribed in Sphere of radius 3 cm is 65.3 cm³ .
Let the half height of of the cylinder be = h ;
we use h instead of [tex]\frac{h}{2}[/tex] for easier simplification ,
In order to find the Volume of cylinder , we multiply the area of top with the total height of cylinder .
So , Volume = [tex]\pi \times (Radius Of Cylinder)^{2}\times (Height Of Cylinder)[/tex]
Volume = [tex]\pi \times (\sqrt{r^{2} -h^{2} } )^{2}\times (2h)[/tex];
Volume [tex]= 2\pi h(r^{2} -h^{2} )[/tex]
Now , we need the derivative of volume function and equate to 0. If we move the h inside parenthesis, we only need to use power rule to get derivative.
So , we get , V = [tex]2\pi (r^{2} h-h^{3} )[/tex] ,
On simplifying further ,
we have ,
Volume of Largest Right Circular Cylinder ⇒ [tex]\frac{4\sqrt{3} \pi r^{3} }{9}[/tex] ;
it is given that radius of sphere is = 3 cm ,
Substituting value of radius in Volume formula ,
we get ,
V = [tex]\frac{4\sqrt{3} \times 3.14\times 3^{3} }{9}[/tex] ;
V = 65.2636 cm³
V ≈ 65.3 cm³.
Therefore , the volume of the largest right circular cylinder is 65.3 cm³.
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For a project in his Geometry class, Elijah uses a mirror on the ground to measure the height of his school building. He walks a distance of 8. 25 meters from the school, then places a mirror on flat on the ground, marked with an X at the center. He then steps 0. 8 meters to the other side of the mirror, until he can see the top of the school clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1. 45 meters. How tall is the school? Round your answer to the nearest hundredth of a meter
The school is 24.63 meters tall.
To calculate the height of the school, Elijah can use the concept of similar triangles. Since the mirror is on the ground and parallel to it, the angle between the ground and the line from his eyes to the mirror is 90 degrees. The angle between the ground and the line from his eyes to the top of the school is also 90 degrees. The triangle formed by these lines and the line from his eyes to the top of the school is similar to the triangle formed by these lines and the line from his eyes to the mirror.
Using the similar triangles, the ratio of the height of the school to the distance from Elijah's eyes to the mirror is equal to the ratio of the distance from Elijah's eyes to the ground to the distance from the mirror to the school.
Therefore
(Height of school) / (Distance from eyes to mirror) = (Distance from eyes to ground) / (Distance from mirror to school)
Plug in the given values:
(Height of school) / 0.8 = 1.45 / (8.25 - 0.8)
Solving for the height of the school:
Height of school = (0.8 * 1.45) / (8.25 - 0.8)
= 1.16 / 7.45
= 0.1562
= 24.63 meters
The school is 24.63 meters tall.
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please help, if you get it right i'll mark you brainliest!!!!!
Answer:
Step-by-step explanation:
Back
Area = L * W
L = 20
W = 8
Area = 20 * 8
Area = 160
2 Triangles
Area = 1/2 one smaller leg*other smaller leg
one smaller leg = 8
The other one = 15
Area = 1/2 8 * 15 = 60
But there are 2 of them 2 * 60 = 120
Base
L = 20
W = 15
Area = L * W
Area = 20*15 = 300
Front (slanted) Face
L = 20
W = 17
Area = L * W
Area = 20*17 340
Total 920
PLS HELP DO TOMORROW!!!
Answer: 3 grams
Step-by-step explanation:
I just looked up the answer lol- I tried though, (Also I can't guarantee if it's right... But it probably is).
Assuming that birthdays are distributed equally throughout the week, what is the probability that two people that have never met passing each other on the street were both born on a Friday is
1/7 2/7 1/49 2/49 4/49
Probability of Two people was born on Friday = 1/49
What is the definition of probability?
Possibility of happening an event is called probability. It is given by the ratio of favorable outcome to the total possible outcome. Probability is different kinds such as independent probability, dependent probability, conditional probability and so on.
What is the probability that two people were born on a Friday?
Assume that birthdays are equally distributed throughout the week.
probability of one people having birthday on Friday = 1/ 7
probability of another people has birthday on Friday = 1/7
probability of two people was born on Friday = 1/7× 1/7 = 1/ 49
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The value of x is -1/4 Order these expressions from least to greatest:
X
1-x
x-1
-1÷x
Answer:
Step-by-step explanation:
-1 divided by x
1 - x
X - 1
*PLEASE HELP ASAP!!!*
Therefore Because of this, the square root is 2 is "irrational" (cannot be written as a fraction) since, if it were, the result would be absurd.
What is the square root?A mathematical concept known as a square root is indeed a factor of a number that, when multiplied on its own, equal the original value. For instance, 3 and -3 are the cube roots of 9. Starting in the second millennium BC, the Babylonians created effective methods for approximating square roots.
Here,
In this case, The square root of 2 is "irrational" (cannot be expressed in a fraction) because, if It Could,
You Would Have the Nonsensical Situation That The Fraction Would Have Even Integer value
At Both The Top And Bottom And Could Therefore Always Be Simplified.
.
Therefore Because of this, the square root is 2 is "irrational" (cannot be written as a fraction) since, if it were, the result would be absurd.
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Please help me! Will mark brainliest if you show steps
Amahl does computer repairs in his home. He charges a set fee to analyze the problem, plus an hourly rate for his labor. The table below shows C, the total charge to his customer, based on H, the number of hours of labor required.
Which equation could amahl use to determine his customer's total charge?
A. C = 9h + 21
B. C = 12h + 15
C. C = 15h + 9
D. C + 24h + 15
Answer:
definitely equation B
steps:
multiply 12 by the hours, and add 15. for each part, it will equal the total charge. 12*2+15 and so on. hope this helps
How do you solve for 4=2+W over 2
Need to know immediately
Solving for W in the equation 4 = (2 + W) / 2 gives W = 6
How to solve for WUsing the equation 4 = (2 + W) / 2, W is solved by making it the subject of the formula and this is means placing W alone at the left hand side of the equation'
This is achieved by the following procedure
clearing the fraction
4 = (2 + W) / 2,
8 = 2 + W
rearranging the equation
W + 2 = 8
subtracting 2 from both sides of the equation
W + 2 - 2 = 8 - 2
since 2 - 2 = 0 we have
W = 6
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Copy and complete each of the Diamond Problems below.
The pattern used in the Diamond Problems is shown at right.
b.
a.
0.32
12
"1
J
c.
9
2
d.
234
31
Core Connections, C
"
J
The provided schematic must be followed in order to answer these diamond problems. You must multiply the values on the left (x) and right (y) cells in order to find the value that belongs in the top cell.
we have,
For Diamond Problems a
x+y=1.2
xy=.32
so value of x= .8 and y = .4.
for Diamond Problems b
x= 11
x+y=25.
so y= 14 and xy=11*14=154.
for Diamond Problems c
x=-7
y=-9
so x+y=-16 and xy= 63.
for Diamond Problems d
x+y=31
xy=234
x=13 and y=18
Is figuring out puzzles a skill?Because puzzles engage both the left and right sides of your brain, solving them aids in the development of your problem-solving abilities. Solving puzzles with others is a terrific method to improve your communication and cooperation skills in addition to your problem-solving and critical thinking abilities.
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A swimming pool is a shape of a rectangular prism. The pool is 10 feet deep. It length is 3 times it's width. The volume of the pool is 27000 cubic feet. Find the length and the width of the pool.
Answer:
Step-by-step explanation:
V = l * w * h
27000ft3 = (2w) * w * 10ft
27000ft3 = 2w^2 * 10ft
2700 = 2w^2
1350 = w^2
W = 36.74
Winton wants to find the volume of a cube. He uses the formula for volume of a cube V = s to the power of 3 where s is the length of one side of the cube. if s = 0.5 centimeter, what is the volume of the cube?
Answer:
Answer: 0.125 cm^3
Is an isosceles triangle always 60 degrees?
No, an isosceles triangle is not always 60 degrees. The angles of an isosceles triangle must be equal, but the overall measure of the angles can be any value greater than 0 degrees.
A triangle having two equal sides and two equal angles is known as an isosceles triangle.. The equal sides create two equal angles that are opposite each other. The two equal angles are the only two angles that define an isosceles triangle. There is no specific measure for the angles of an isosceles triangle, so the angles do not necessarily have to be 60 degrees and The angles can be any value greater than 0 degrees. The two equal angles, however, must be equal in measure to make the triangle an isosceles triangle. Therefore, an isosceles triangle is not always 60 degrees.
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What is the name of 3 side?
The three sides of a triangle are referred to as the base, the height, and the hypotenuse.
The base and height of a triangle can be used to calculate the area of the triangle using the formula:
Area = (Base x Height) / 2
To calculate the hypotenuse of a triangle, the Pythagorean Theorem is used. The theorem states that the sum of the squares of the lengths of the two sides of a right triangle is equal to the square of the length of the hypotenuse.
The formula for the Pythagorean Theorem is:
a2 + b2 = c2
where a and b are the two sides of the triangle and c is the hypotenuse.
To calculate the hypotenuse of a triangle, the following steps are taken:
1. Measure the length of each side of the triangle.
2. Square the length of each side (multiply the length by itself).
3. Add the two values together.
4. Find the square root of the sum. This is the length of the hypotenuse.
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If i add (2x-3y=10) and (5x+3y=-4) what is the result
Answer:
7x = 6
Step-by-step explanation:
2x - 3y = 10
+ 5x + 3y = -4
------------------------
7x = 6
In a certain school district, students from grade 6 through grade 12 can participate in a school-sponsored community service activity. The following bar chart shows the relative frequencies of students from each grade who participate in the community service activity.
According to the given bar chart options A, B and C are the correct.
How do you find relative frequency?Relative frequency can be defined as the number of times an event occurs divided by the total number of events occurring in a given scenario.
Given that, the bar chart shows the relative frequencies of students from grades 6 to 12 who participate in the community service activity.
Relative Frequency = Subgroup frequency/ Total frequency.
Relative Frequency = f/ n.
From the given bar chart we can see that
The maximum number of participating students was in grade 9.
The number of participating students in grade 6 was equal to the number of participating students in grade 7.
The relative frequency of all participating students in grades 6 and 7 combined was 0.60.
Therefore, options A, B and C are the correct answers.
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Complete question is in attachment:
What are the 3 ways to find x-intercept?
The three ways of finding the x-intercept are:
Using a Graph of a Line.Using the Equation of the Line.Using the Quadratic Formula.By looking at the equation, we may determine the y-intercept when the equation is expressed in the slope-intercept form (y=mx+b). The y-intercept is the value of b. This is due to the fact that the y-intercept occurs when the x value is 0. Y = B when x = 0, since mx = 0 at this point.
We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.
The formula for the x-intercept is y = 0: The x-intercept(s) can be determined by factoring or by employing the quadratic formula because ax2 + bx + c=0.
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5. Katie has 15/20 of a dollar in her pocket. Lisa has the same amount of money in
her pocket. What fraction of a dollar does Lisa have in her pocket?
A. 5/10 B. 3/4
C. 4/5 D. 2/10
Answer:
Step-by-step explanation:
it B.
just put in the calculator and it gives you the reduced fraction
Answer:
B. 3/4
Step-by-step explanation:
Find the GCD (or HCF) of the numerator and denominator
GCD of 15 and 20 is 5
Next, divide both the numerator and denominator by the GCD
15 ÷ 5 = 3
20 ÷ 5 = 4
Finally, put them back into a fraction
[tex]\frac{3}{4}[/tex]
Therefore, 15/20 simplified to the lowest terms is 3/4.
Sabrina rode on a Ferris wheel at the state fair. The radius of the Ferris wheel was 106 feet. What is the approximate distance Sabrina traveled in one revolution of the Ferris wheel? (Use 3.14 for T.)
9514 1404 393
Answer:
666 ft
Step-by-step explanation:
The circumference of the wheel is given by the formula ...
C = 2πr
For a radius of 106 ft, the circumference is ...
C = 2(3.14)(106 ft) = 665.68 ft
Sabrina traveled about 666 feet in one revolution.
Another one (last one!) it’s a test! Please no likes or something other than an answer!
Answer:
2, 6
Step-by-step explanation:
x always go first
please help me find the answer
Answer:
use calculator
Step-by-step explanation:
Answer:
-21 i think
Step-by-step explanation:
Between -10 and -16 has to be -13, because -13 is three apart from -10, and three apart from -16. That means that the numbers decrease by 3. So, the number line would be:
-10
-13
-16
-19
-21
Hope this helps!
ILL BRAINLIEST YOU AND GIVE YOU 10 extra points
Answer:
A
Step-by-step explanation:
Side A which is 4 is an angle of 41.40
Side B which is 5 is an angle of 55.7
Side C which is 6 is an angle of 82.8
Reduce 22/154
to its lowest form.
Answer: 1/7
Step-by-step explanation: Find the GCD (Greatest Common Denominator) of the numerator and denominator. The GCD of 22 and 154 is 22. Divide both the numerator and denominator by the GCD = 22 ÷ 22; 154 ÷ 22. Reduced fraction: 1/7. Therefore, 22/154 simplified to lowest terms is 1/7.
Use the table to work out the values of a, b, c, and d.
2
y = 2x – 2
-3
a
-2
-6
-1
b
0
-2.
1
a
d
Answer:
aaaaaaaaa x=3-2y
HELP ME PLEASE!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
No he's going to have to try this one again.
The y intercept is found by making x = 0
The original equation becomes
2y - 120 = 0 Add 120 to both sides
2y = 120 Divide by 2
y = 120/2
y = 60
The y intercept is 60
Cornelio creates a tree diagram to show all possibilities for flipping a coin four times.How many possibilities are in the sample space at the end of the tree diagram
A 4
B 5
C 8
D 16
Option D is correct, there are 16 possibilities are in the sample space at the end of the tree diagram
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that Cornelio creates a tree diagram to show all possibilities for flipping a coin four times
We need to find the number of possibilities are in the sample space at the end of the tree diagram
The number of times coin is flipped=4
We can use 2ⁿ to figure out the number of possible outcomes where n is the number of tosses.
Now n=4, so the number of possibilities are 2⁴
2×2×2×2
16
Hence, option D is correct, there are 16 possibilities are in the sample space at the end of the tree diagram
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Can u please help...................
Answer:
(-2, 2)
Step-by-step explanation:
You want the circumcenter of the triangle with vertices A(2, -3), B(2, 7), and C(-6, -3).
CircumcenterThe circumcenter is the center of the circle that circumscribes the triangle. Here, the triangle is a right triangle, so the circumcenter is the midpoint of the hypotenuse.
MidpointThe midpoint of segment BC is the average of the coordinates of B and C:
X = (B +C)/2 = ((2, 7) +(-6, -3))/2 = (2 -6, 7 -3)/2 = (-4, 4)/2
X = (-2, 2)
The circumcenter is (-2, 2).
__
Additional comment
The right angle subtends an arc of twice its measure, 180°, so the circumscribed triangle occupies a semicircle, and the hypotenuse is a diameter. That puts the center of the circle at the midpoint of the hypotenuse.
How do I solve x-5(x-1=x-(2 x-3)
Answer:
x = 2/3
Step-by-step explanation:
x - 5(x - 1) = x - (2x - 3)
x - 5x + 5 = x - 2x + 3
-5x + 5 = -2x + 3
-3x = -2
x = 2/3
Write the equation of the perpendicular bisector’s of the line AB given: A(1,3) & B(-3,5)
Answer:
y = 2x + 1
Step-by-step explanation:
[tex]\frac{5-3}{-3-1}[/tex] = [tex]\frac{2}{-4}[/tex] = [tex]\frac{1}{-2}[/tex]
Perpendicular slopes are the opposite reciprocals . So the slope of the line will be 2
slope (m) = 2
y = 3 You could use either point given. I chose (1,3)
x = 1 From the point given (1,3)
y = mx + b substitute in what you know and solve for b
3 = (2)(1) + b
3 = 2 + b Subtract 2 from both sides
1 = b
The y-intercept is 1.
y = mx + b
y = 2x + 1
Line g has an equation of y= 1/3x–1. Parallel to line g is line h, which passes through the point (10,2). What is the equation of line h?
The Garcia family bought 400 yards of fencing to enclose a circular wildflower garden. They will use all of the fencing whats the area
The area of the windflower garden that is enclosed by a circular fence of 400 yards length is equal to 12732.39 square yards.
What is circumference of a circle?The measurement of the circle's perimeter, also known as its circumference, is called the circle's border. It is the length around the border of the circular object or the circle itself.
What is the formula for calculating the perimeter of a circle?The formula for calculating the perimeter of a circle is ,
Perimeter/ Circumference of a circle = 2 * pi * r, where pi = 3.14 and r is the radius of the circle.
Taking the given information in the question, i.e circumference of the circular fencing wire , i.e C = 400 yards
or , 2 * pi * r = 400
or , r = 400/(2* 3.14)
r = 63.66 yards
Now the area of the circular fence is given by,
Area = pi * r^2
Area = 3.14 * 63.66^2
Area = 12732.39 square yards
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