A cone and a sphere have the same volume. The height of the cone is 96 units.
What could be the values for the radius of the cone and the sphere? Round your answers to the nearest hundredth
as needed.
Answers
\(\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=96 \end{cases}\implies V=\cfrac{\pi r^2 (96)}{3} \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~\hspace{9em}\stackrel{\textit{since we know both Volumes are equal}}{\cfrac{4\pi r^3}{3}~~ = ~~\cfrac{\pi r^2 (96)}{3}}\)
\(4\pi r^3=\pi r^2(96)\implies 4\pi r^2\cdot r=\pi r^2(96)\implies r=\cfrac{\pi r^2(96)}{4\pi r^2}\implies \boxed{r=24} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{ \textit{\LARGE cone} }{\cfrac{\pi (24)^2(96)}{3}}\implies \stackrel{ \textit{\LARGE sphere} }{\cfrac{4\pi (24)^3}{3}}\implies18432\pi ~~ \approx ~~ \text{\LARGE 57905.84}~units^3\)
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PLEASE HELP FAST!!!! Which could be the first in solving the equation represented by the model below?
Which one?
A. Add 4 positive unit tiles to each side
B. Remove 4 unit tiles from each side
C. Add 6 positive unit tiles to each side
D. Remove 6 unit tiles from each side
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Answer:
A. add 4 positive unit tiles to each side
Step-by-step explanation:
The reason is because its easier to solve without having to worry about negatives
Solve the question using the picture attached. The question and instructions are all attached in the picture. Thank you
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Let's find the circle to find the exact value of
Sin 17pi/3:
1) Find the coterminal angle in the circle:
\(\begin{gathered} \frac{17\pi}{3}= \\ \frac{17\pi}{3}-\frac{6\pi}{3}= \\ \frac{11\pi}{3}-\frac{6\pi}{3}= \\ \frac{5\pi}{3} \end{gathered}\)2-Using the circle, the point is:
\((\frac{1}{2},\text{ }\frac{\sqrt[\square]{3}}{2})\)3) The answer is the y-coordinate, so:
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if a user enters a diameter value in the variable diameter, how would we use this to draw the correct sized circle? var circle
Answers
The user would use this to draw the proper-sized circle if they entered a diameter value in the variable diameter:
var circle = new Circle(diameter/2); circle.setPosition(100,100);add(circle);
What is the variable diameter?The unfolded limit rimless wheel and the folded rigid circular wheel are the two limited operating states for wheels with variable diameters.
These can eliminate the conflict between the lunar rover's small spacecraft volume and tractive performance.
The most important component is the variable-diameter mechanism suggested here.
If a user inputs a diameter value in the variable diameter in the example, he or she would use this to draw the appropriate-sized circle:
var circle = new Circle(diameter/2); circle.setPosition(100,100);add(circle);
Therefore, the user would use this to draw the proper-sized circle if they entered a diameter value in the variable diameter:
var circle = new Circle(diameter/2); circle.setPosition(100,100);add(circle);
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In circle K, what is the value of x? x = 30° x = 25° x = 20° x = 15º A triangle inscribed in a circle having one side as diameter, center labeled as K and two angles labeled X degrees and seventy-five degrees. The angle with x degrees is on the right side of the diameter. The 75 degree angle is on the left side of the diameter.
Answers
Answer:
The correct option is 4.
Hope this helps :D
Step-by-step explanation:
Given information: K is the center of the circle. AB is the diameter of the circle.
Angle subtended by a diameter is always a right angle. It the means the measure of that angel is 90 degree.
According to the angle sum property, the sum of interior angles of a triangle is 180 degree.
Using angle sum property in triangle ABC, we get
If A = 40° and B = 25°, calculate, correct to ONE decimal place, each of the following: cosec² B
1.1.2 tan(A - B) In the following, find, correct to One decimal place
Answers
The values are:
cosec² B ≈ 5.2
tan(A - B) ≈ 0.5
We have,
To calculate the values, we'll use the following trigonometric identities:
- Cosecant squared (cosec²) is the reciprocal of the sine squared (sin²): cosec² B = 1/sin² B
- Tangent (tan) difference formula: tan(A - B) = (tan A - tan B) / (1 + tan A * tan B)
Given:
A = 40°
B = 25°
To find cosec² B:
Find sin B using the sine function: sin B = sin(25°)
Calculate cosec² B using the reciprocal of the sine squared: cosec² B = 1/sin² B
To find tan(A - B):
Find tan A using the tangent function: tan A = tan(40°)
Find tan B using the tangent function: tan B = tan(25°)
Calculate tan(A - B) using the tangent difference formula: tan(A - B) = (tan A - tan B) / (1 + tan A * tan B)
Let's calculate the values now:
cosec² B:
sin B = sin(25°) = 0.4226 (rounded to four decimal places)
cosec² B = 1/sin² B = 1/0.4226² ≈ 5.2268 (rounded to one decimal place)
tan(A - B):
tan A = tan(40°) = 0.8391 (rounded to four decimal places)
tan B = tan(25°) = 0.4663 (rounded to four decimal places)
tan(A - B) = (tan A - tan B) / (1 + tan A x tan B)
= (0.8391 - 0.4663) / (1 + 0.8391 * 0.4663)
= 0.4662 (rounded to one decimal place)
Therefore,
The values are:
cosec² B ≈ 5.2
tan(A - B) ≈ 0.5
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What is the least positive integer by which 1922 should be divided so that the resultant integer is a
perfect square?
Answers
Answer:
1922 = 2× 31 × 31
Therefore, 1922 should be divided by 2 to get 961 which is a square of 31.
I hope this helped!
find the length and width of a rectangle whose width is 10 cm shorter than its length and whose area is 200 cm2.
Answers
Let's call the length of the rectangle "L" and the width "W". We know that the width is 10 cm shorter than the length, so we can write.
W = L - 10
We also know that the area of the rectangle is 200 cm 2, so we can write:
A = L x W
Substituting W = L - 10, we get:
A = L x (L - 10)
Expanding the brackets, we get:
A = L^2 - 10L
Now we can substitute in A = 200 and solve for L:
200 = L^2 - 10L
0 = L^2 - 10L - 200
We can use the quadratic formula to solve for L:
L = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 1, b = -10, and c = -200. Plugging in these values, we get:
L = (10 ± sqrt(10^2 - 4(1)(-200))) / 2(1)
L = (10 ± sqrt(1100)) / 2
L = (10 ± 10sqrt(11)) / 2
L ≈ 19.9 or L ≈ -9.9
We can disregard the negative solution since we're dealing with lengths, so the length of the rectangle is approximately 19.9 cm.
Now we can use W = L - 10 to find the width:
W = 19.9 - 10
W ≈ 9.9 cm
Therefore, the length of the rectangle is approximately 19.9 cm and the width is approximately 9.9 cm.
To find the length and width of a rectangle whose width is 10 cm shorter than its length and whose area is 200 cm², follow these steps:
1. Define the variables: Let the length of the rectangle be L cm, and the width be W cm.
2. Use the given information: Since the width is 10 cm shorter than the length, we can write the equation W = L - 10.
3. Use the formula for the area of a rectangle: The area of a rectangle is given by the formula A = L × W.
4. Substitute the given area and the equation from step 2: In this problem, the area is 200 cm², so we have 200 = L × (L - 10).
5. Solve the equation for L: Expand the equation to get 200 = L² - 10L. Rearrange the equation to L² - 10L - 200 = 0.
6. Factor the quadratic equation or use the quadratic formula: (L - 20)(L + 10) = 0. This gives two possible values for L: L = 20 cm or L = -10 cm.
7. Discard the negative value: Since the length of a rectangle cannot be negative, we discard the value L = -10 cm. So, the length L is 20 cm.
8. Find the width using the equation from step 2: W = L - 10 = 20 - 10 = 10 cm.
Thus, the length and width of the rectangle are 20 cm and 10 cm, respectively.
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What equations that have same solution as 2x-5=15
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Answer:
1(2x-5)=15
Step-by-step explanation: Following the steps of solving the equation, it results with the same answer.
Question 9 of 10 What is the slope of the line shown below? A. 4 B.-1/4 C.1/4 D.-4
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Answer:
c = 1/4
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Step-by-step explanation:
Carl ordered a refrigerator that weighs 192 pounds. It was shipped to him inside a box and
surrounded by packaging material. The total weight of the refrigerator, box, and packaging
material was 205 pounds.
What is the weight of the box and packaging material?
Enter your answer in the box.
pounds
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Answer:
13 pounds
Step-by-step explanation:
We know that the total weight of everything is 205 pounds, and the fridge itself is 192 pounds. So we need to calculate the weight of everything that is not a fridge, which would be:
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That means that the box and the packaging is 13 pounds. Hope this helps!
Will mark brainliest for whoever answers
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Answer:
Uh is it B, what kind of question is this
Step-by-step explanation:
Answer:
i think it is b
Step-by-step explanation:
Match the following equation to the correct situation.
4t+ t = 5t
OA. the temperature when Paige changes the thermostat by 4 degrees
ОВ.
the number of toys that Josh and Tony have when Tony has 4 times the number of toys as Josh
C. the number of text messages Susie and Kristin have when Susie has 4 more than Kristin
D.
the "talk" minutes that Tiffany has after adding 4 minutes to her phone
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Lori had $126.89 in her bank account. She deposited $21.49 into it and then wrote a check for her car repairs for $156.61.
What was the ending balance in her account?
O -$51.21
O $8.23
O $8.23
O $51.21
What is the answer?
Answers
Answer:
-8.23
Step-by-step explanation:
If Lori had $126.89 in her bank account and she deposited $21.49, she would be adding that to the amount of money in her bank account.
126.89+21.59= 148.48
Then subtract the amount of money the repairs costed.
148.48 - 156.61 = -8.23
Therefore Lori would have a balance of -$8.23.
Answer:
Lori had $126.89 in her bank account.
She deposited $21.49 into it and then wrote a check for her car repairs for $156.61
126.89+ 21.49=148.38
148.38-156.61=−8.23
the answer is -8.23
X+y+2=0 then find the value ofx^2+ y^2 +8
Answers
The calculated value of the expression x² + y² + 8 is 12 - 2xy
How to evaluate the value of the expressionFrom the question, we have the following parameters that can be used in our computation:
x + y + 2 = 0
This can be expressed as
x + y = -2
Using the sum of two squares, we have
x² + y² = (x + y)² - 2xy
So, we have
x² + y² = (-2)² - 2xy
Evaluate
x² + y² = 4 - 2xy
Add 8 to both sides
x² + y² + 8 = 12 - 2xy
Hence, the value of the expression x² + y² + 8 is 12 - 2xy
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Find the solution to the following system using substitution or elimination: y = 3x + 7 y = -2x-3 O A. (1,10) O B. (-2,1) C. (1.-4) D. (-2,-7)
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Answer:
The answer is B
Step-by-step explanation:
Because I calculated properly and check my answer 2 times
trust me this is the answer
pls mark me as brainliest
Answer:
B
Step-by-step explanation:
Pi is: (click all that are correct) *
always the same, and is 3.14 or 22/7
delicious
used to help find the circumference of a circle
always a different number pls help lol
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yes,Pi is 3.142 or 22/7
Step-by-step explanation:
22/7=3.14285714
help bounds to a degree
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The Division Law of Exponents says that if bis a nonzero number and n and
mare any numbers, then
bn/bn =bm-n
True or false
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WILL MARK YOU BRAINLIEST 1-6 show you work!!!
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Answer:
Corresponding angles; Same side interior angles ;Alternate interior angles ; Alternate exterior anglesStep-by-step explanation:
Check out the images .
I hope they help :)
The second image is a Same side interior angle
The 6-digit number 2ABCDE is multiplied by 3 and the result is the 6-digit number ABCDE2. What is the sum of the digits of this number?
Answers
We must have E = 4, since that would make a 3 • 2ABCDE end in a 2. There are no other multiples of 3n (where n is taken from {0, 1, 2, …, 9}) such that 3n ends in a 2.
So we have
3 • 2ABCD4 = ABCD42
which means 3D + 1 = 4 and so D = 1.
Then
3 • 2ABC14 = ABC142
and so 3C ends in 1. By the same reasoning as we used to determine E, we only have one possibility of C = 7, since 3 • 7 = 21 is the only multiple 3n that ends in 1.
Then
3 • 2AB714 = AB7142
which means 3B + 2 = 7 and so 3B ends in a 5. This happens if B = 5.
Then
3 • 2A5714 = A57142
which means 3A + 1 = 5 and so 3A ends in a 4. This happens if A = 8.
So we end up with
3 • 285714 = 857142
and the sum of the digits is
2 + 8 + 5 + 7 + 1 + 4 = 27
Answer:
You can also find the answer on the the Kangaroo website.
Step-by-step explanation:
sin(20) = cos(2u) = tan(24) = 3. [-/5 Points] Use the given conditions to find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas. sin(u) = -3/5, 3m/2
Answers
Using the given conditions that sin(20) = cos(2u) = tan(24) = 3, we can find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas. By substituting the known values into the formulas, we can determine the exact values of these trigonometric functions.
Given sin(20) = 3, we can use the double-angle formula for sine to find sin(2u).
The double-angle formula for sine is sin(2u) = 2sin(u)cos(u). We know that sin(u) = -3/5, so we can substitute this value into the formula to calculate sin(2u).
Therefore, sin(2u) = 2(-3/5)(cos(u)).
Given cos(2u) = 3, we can use the double-angle formula for cosine to find cos(2u).
The double-angle formula for cosine is cos(2u) = cos^2(u) - sin^2(u). Since we already know sin(u) = -3/5 and cos(u) can be calculated using the Pythagorean identity (cos^2(u) = 1 - sin^2(u)), we can substitute these values into the formula to determine cos(2u).
Finally, given tan(24) = 3, we can use the double-angle formula for tangent to find tan(2u).
The double-angle formula for tangent is tan(2u) = (2tan(u))/(1 - tan^2(u)). By substituting the known value of tan(24) = 3 into the formula, we can calculate the exact value of tan(2u).
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A ladder that is 14 feet long is placed against a building. The bottom of the ladder is 6 feet from the base of the building.
A right triangle with side length 6 feet, hypotenuse 14 feet, and side h.
In feet, how high up the side of the building is the top of the ladder? Round to the nearest tenth of a foot.
12.65
Answers
Answer:
12.6 ft
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
let h be height up the side of the building , then
h² + 6² = 14²
h² + 36 = 196 ( subtract 36 from both sides )
h² = 160 ( take the square root of both sides )
h = \(\sqrt{160}\) ≈ 12.6 ft ( to the nearest tenth )
i neeeeeeeeeeeeeeeeeeed help
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2.5* 10 ^ -3
2, 8, 14, ...
Find the 42nd term.
Answers
Solving the Question
We're given:
2, 8, 14, ...First, we must identify the pattern:
The first term is 2. Add 6 each time to get the next term.This is our written pattern statement. To convert this into an expression, we can use the following format:
\(mn+b\)
m is the number that we add each timeb is our zeroth term value, the number that comes prior the first term in the given patternn is the term numberIn this case, m is 6, and b is 2 - 6, or -4. Plug these numbers into the expression:
\(6n+(-4)\\6n-4\)
To find the 42nd term, plug in 42 as n:
\(6n-4\\6(42)-4\\248\)
AnswerThe 42nd term is 248.
a₄₂= 248.
An arithmetic progression or arithmetic sequence (AP) is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2.
If the initial term of an arithmetic progression is a and the common difference of successive members is d, then the n-th term of the sequence
This is an arithmetic sequence since there is a common difference between each term. In this case, adding
6
to the previous term in the sequence gives the next term. In other words,
aₙ= a₁+ d (n-1)
substitute in the values of a₁=2 and d=6
simplify each term
aₙ= 6n-4
substitute and calculate you will get
a₄₂= 248.
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Find the area of the composite figure.19 mm 25 mm 3 mm 6mm
Answers
The figure consists of a rectangle and 2 right triangles, as shown in the diagram below
The areas of a rectangle and a triangle are given by the following formulas
\(\begin{gathered} A_{\text{rectangle}}=lw \\ A_{\text{triangle}}=\frac{1}{2}b\cdot h \end{gathered}\)In our case,
\(\begin{gathered} A_{\text{rectangle}}=6\cdot19=114 \\ A_{\text{triangle}}=\frac{1}{2}(25-19)\cdot(3+3)=\frac{1}{2}\cdot6\cdot6=\frac{36}{2}=18 \end{gathered}\)Thus,
\(\begin{gathered} A_{\text{figure}}=A_{\text{rectangle}}+2A_{\text{triangle}}=114+36=150 \\ \Rightarrow A_{\text{figure}}=150 \end{gathered}\)The total area is 150mm^2
Will someone please help me
Answers
Answer:
see attached
Step-by-step explanation:
The relationship between time, speed, and distance is ...
distance = speed · time
Stephanie wants her first break before 65 miles, so the time until the break will satisfy the inequality ...
10t < 65 . . . break before 65 miles
t < 6.5 . . . . . divide by 10
On a graph, values less than 6.5 will appear shaded to the left of that point. Since 6.5 is not included in the solution set, the dot at that point is an open circle.
The table shows conversions of common units of length.
Unit of Length
Customary System Units
Metric System Units
1 inch
2.54 centimeters
1 foot
0.3048 meters
1 mile
1.61 kilometers
1 yard = 3 feet
1 yard = 36 inches
Which shows the best path to find the number of centimeters in 1 yard?
Answers
The number of centimetres in the 1 yard will be 9.144 cm.
What is unit conversion?Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.
Given that:-
Metric System Units
1 inch = 2.54 centimetres
1 foot = 0.3048 meters
1 mile = 1.61 kilometres
1 yard = 3 feet
1 yard = 36 inches
First, we will calculate 1 yard to feet.
1 yard = 3 feet
1 feet = 0.3048 meters
1 feet = 3.048 centimeters
1 yard = 3 x 3.048 centimeters
1 yard = 9.144 centimeters
Hence, the length of 1 yard in cm is 9.144 cm.
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