First photo question: Given this net of a right circular cone. Find the volume and surface area of the cone.
Second photo question: Given this right circular cone. Find the volume and surface area of the cone. Make a sketch of this net of this cone including the measurements of the radii of the circle and sector and give the central angle of the sector.
Answers
Problem 1
Ignore the smaller circle for now. We'll be focusing on the portion on the right.
It's a partial circle with central angle theta = 150 degrees and radius r = 24 inches. The 24 inches also happens to be the slant height of the cone when we form the 3D figure.
Let's compute the arc length based on those inputs.
L = arc length
L = (theta/360)*2*pi*r
L = (150/360)*2*pi*24
L = 20pi
This is the distance along the green curve of this portion.
Now imagine we rolled up that partial circle on the right. We'd form the curved slanted roof of the cone. The green curve wraps around to help match up with the circular base. The 20pi calculated earlier is the circumference of this circular base. Use this to find r.
C = 2pi*r
20pi = 2pi*r
r = (20pi)/(2pi)
r = 10
-------------------------
So far we found that this cone has:
radius = r = 10slant height = s = 24Now compute the height (h) perpendicular to the base
[tex]h^2+r^2 = s^2\\\\h = \sqrt{s^2-r^2}\\\\h = \sqrt{24^2-10^2}\\\\h = \sqrt{476}[/tex]
-------------------------
We can now compute the volume
[tex]V = (1/3)*\pi*r^2*h\\\\V = (1/3)*\pi*10^2\sqrt{476}\\\\V \approx 2284.7153\\\\[/tex]
The units of which are cubic inches.
The surface area is of this cone is:
[tex]SA = \pi*r*s + \pi*r^2\\\\SA = \pi*10*24 + \pi*10^2\\\\SA \approx 1068.1415\\\\[/tex]
The units are in square inches.
For each case, I used the calculator's stored value of pi to get the most accuracy possible. Round the decimal values however you need to, or however your teacher instructs.
-------------------------
Answers:
Volume = 2284.7153 cubic inches approximatelySurface Area = 1068.1415 square inches approximately============================================================
Problem 2
Use the pythagorean theorem to find the slant height
[tex]h^2+r^2 = s^2\\\\s = \sqrt{h^2+r^2}\\\\s = \sqrt{15^2+8^2}\\\\s = \sqrt{289}\\\\s = 17\\\\[/tex]
This slant height will act as the radius of the partial circle that results when forming the net of the unrolled cone.
The process used in the previous problem was to use the slant height and central angle to find the circumference of the base.
We'll follow that process in reverse to use the circumference and slant height to find the central angle.
But first, we need to find the circumference of the base.
C = 2*pi*r
C = 2*pi*8
C = 16pi
This is the arc length similar to the green arc shown in the previous problem (the figure on the right side of that diagram)
This means we'll plug in L = 16pi and r = 17 (not to be confused with the previous radius of 8 inches) to determine theta
L = (theta/360)*2*pi*r
16pi = (theta/360)*2*pi*17
16pi = theta*(34pi/360)
theta = 16pi*(360/(34pi))
theta = 169.4118 degrees approximately
This is the central angle of the unrolled net. The diagram is basically the same as the previous drawing, where we have a circle on the left to represent the base of the cone. The other portion forms the roof of the cone.
-------------------------
Let's compute the volume (V) and surface area (SA)
[tex]V = (1/3)*\pi*r^2*h\\\\V = (1/3)*\pi*8^2*15\\\\V \approx 1005.3096\\\\[/tex]
and,
[tex]SA = \pi*r*s + \pi*r^2\\\\SA = \pi*8*17 + \pi*8^2\\\\SA \approx 628.3185[/tex]
-------------------------
Answers:
Diagram: Copy the diagram shown in problem 1. However, you'll change the "24 inches" to "17 inches". Also, the central angle is roughly 169.4118 degrees.Volume = 1005.3096 cubic inches approximatelySurface Area = 628.3185 square inches approximatelyRelated Questions
Match the tan R, cos R and sin R to the correct ratios
Answers
Sine: Opposite/Hypotenuse.
Cosine: Adjacent/Hypotenuse
Tangent: Opposite/Adjacent.
In this triangle, the adjacent side to angle R (the side touching the angle) is 12 cm, the opposite side (the side farthest away) is 5 cm, and the hypotenuse (the longest side) is 13 cm.
So, filling in the measurements with the correct SOH CAH TOA ratios results in:
tan R = 5/12
cos R = 12/13
sin R = 5/13
What is the answer to 5x+5y=0 -8x+y=36 in ordered pairs?
Answers
5(x+y)=5(0) => x+y=0
and by solving for x using elimination method
-8x+y=36
x+y=0
by subtracting both x and y we get
-9x=36 => x=-4
by inputing x into the "x+y=0" equation we get:
-4+y=0 => y=4
Jade and chet get a weekly allowance plus x dollars for each time the pair walks the dog. they plan to save 40% of their combined earnings in one week to purchase a new app for their smart tablet. their earnings in a certain week are represented in the table. earnings ($) jade 8+2x chet 4x+6 if their parents pay $2.50 each time they walk the dog, how much money will they have to purchase the app?
Answers
The amount of money Jade and chet will have to purchase the app is $11.6
How to solve equation?Jade = 8 + 2xChet = 4x + 6Where,
x = $2.50
Amount each earned:
Jade = 8 + 2x
= 8 + 2(2.50)
= 8 + 5
= $13
Chet = 4x + 6
= 4(2.50) + 6
= 10 + 6
= $16
Combined earnings = $13 + $16
= $29
Amount planned to save = 40% of combined earnings
= 40% × $29
= 0.4 × 29
= $11.6
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Kofi brought 6 books and 10 pencils from a store ama brought 3 books and 20 pencils of the same kind from the store if each of them paid $ 17000.00 from the items find the cost of each pencil each book two books and 4 pencils
Answers
Answer:
Answer by josgarithmetic(37226) (Show Source): You can put this solution on YOUR website!
system%2810b%2B6p=17000%2C3b%2B20p=17000%29
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let +a+ = the cost of 1 pencil
Let +b+ = the cost of 1 book
---------------------------
(1) +6b+%2B+10a+=+17000+
(2) +3b+%2B+22a+=+17000+
----------------------
Multiply both sides of (2) by +2+
and subtract (1) from (2)
(2) +6b+%2B+44a+=+34000+
(1) +-6b+-+10a+=+-17000+
-------------------------
+34a+=+17000+
+a+=+500+
and
(1) +6b+%2B+10a+=+17000+
(1) +3b+%2B+5a+=+8500+
(1) +3b+%2B+5%2A500+=+8500+
(1) +3b+=+8500+-+2500+
(1) +3b+=+6000+
(1) +b+=+2000+
------------------
Step-by-step explanation:
IT,LL
HELP
Can someone help me with 2. I will reward brainliest
Answers
Answer:
[tex]\tan 2 x = \dfrac{24}7[/tex]
Step by step explanation:
[tex]\textbf{2)}\\\\\text{Given that,} \\\\~~~~~\cos x = -\dfrac 45\\\\\implies \cos^2 x = \dfrac{16}{25}~~~~~~~~~~;[\text{Square both sides}]\\\\\implies 1- \sin^2 x= \dfrac{16}{25}\\\\\implies \sin^2 x = 1- \dfrac{16}{25}\\\\\implies \sin^2 x = \dfrac{9}{25}\\\\\implies \sin x =\pm\sqrt{\dfrac{9}{25}}\\\\\implies \sin x = \pm \dfrac 35\\\\[/tex]
[tex]\text{Since,}~ \pi \leq x \leq \dfrac{3\pi}{2}, ~ \text{the angle lies in the 3rd quadrant, where}~ \sin x ~ \text{is negative.}\\\\\text{So,}~ \sin x = -\dfrac 35[/tex]
[tex]\text{Now,}~\\\\\tan x = \dfrac{\sin x }{\cos x} = \dfrac{-\tfrac 35}{-\tfrac 45} = \dfrac 35 \times \dfrac 54 = \dfrac 34\\\\\\\tan 2x =\dfrac{2 \tan x }{ 1- \tan^2 x}\\\\\\~~~~~~~~~=\dfrac{2 \left( \tfrac 34 \right)}{1- \left( \tfrac 34 \right)^2}\\\\~~~~~~~~~=\dfrac{\tfrac 64}{1-\tfrac {9}{16}}\\\\\\~~~~~~~~~=\dfrac{\tfrac 32 }{\tfrac 7{16}}\\\\\\~~~~~~~~~=\dfrac 32 \times \dfrac{16}7\\\\\\~~~~~~~~~=\dfrac{24}7[/tex]
Three coins are tossed up in the air, one at a time. What is the probability that the first two will land heads up and the third will land tails up?
Answers
x-3y=4
2х-бу=Q
I’m trying to find the value of Q.
Answers
Answer:
Q=8
Step-by-step explanation:
Just multiply the entire first function by 2
therfore
(x-3y=4) * 2
therefore
=2x-6y=8
This is the same as the second function and in it, the coefficient of x is 2, therefore
Q=8
When flipping a penny, what is the theoretical probability of landing on heads? What is the theoretical probability of landing on tails?
Answers
Answer:.5 for either side
Step-by-step explanation:there are two sides, both equally likely so their probability must be equal and sun to 1. This condition is met when both probabilities are .5
Answer:
50/50 probability
Step-by-step explanation:
Answers to the questions?
Answers
Based on the relationship of special angles, the values of x are:
1. x = 34
2. x = 9
3. x = 6
What are The Relationship of Angles Formed by a Transversal and Parallel Lines?Alternate interior angles are equals and corresponding angles are also equal.
Linear pair angles are supplementary.
1. Angles j and a are linear pair angles, therefore:
3x + 15 + 2x - 5 = 180
5x + 10 = 180
5x = 180 - 10
5x = 170
x = 170/5
x = 34
2. Angles m and g are corresponding angles, therefore:
4x + 12 = 2x + 30
4x - 2x = -12 + 30
2x = 18
x = 9
3. Angles c and v are alternate interior angles, therefore:
6x + 9 = 3x + 27
6x - 3x = -9 + 27
3x = 18
x = 6
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(05.06)Keisha ran to swim practice but needed to stop by her friend Natasha’s house on the way. She stayed at Natasha’s house for 15 minutes, and together they ran the rest of the way to practice, where they stayed for 1 hour.
Which graph best represents the scenario described?
Answers
The graph third represents the provided situation first line increases and then constant then again increases and becomes constant.
What is a line graph?A line graph is a graph made up of segments of straight lines that connect the depicted data points.
We have:
Keisha ran to swim practice but needed to stop by her friend Natasha’s house on the way. She stayed at Natasha’s house for 15 minutes, and together they ran the rest of the way to practice, where they stayed for 1 hour.
Based on the information given we can say graph third represents the situation.
First Keisha ran to swim practice so the line first increases and then she but needed to stop by her friend Natasha’s house on the way. She stayed at Natasha’s house for 15 minutes which means the line should be constant.
Again they both ran so line increases.
Then they both stayed for 1 hour, so the line should be constant.
Thus, the graph third represents the provided situation first line increases and then constant then again increases and becomes constant.
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help please it says name the property
Answers
Here are four digit cards 6 5 5 7
arrange the cards to give the greatest possible answer to the calculation
Answers
Answer:
7 6 5 5
Step-by-step explanation:
the highest numbers should go in the leftmost digits place, as these are worth more
here, we put 7 in the thousands place, which is 2 thousand higher than if we put 5 in the thousands place
Which represents the polynomial written in standard form?
8x²y²-3x³y + 4x²-,7xy³
O −7xy³ + 8x²y² – 3x³y + 4x4
○ 4x² - 7xy³_ 3x³y + 8x²y²
O
2
O 4x4 + 8x²y²-3x³-7xy³
2
O-7xy³ - 3x³y + 8x²y² + 4x²
2
Answers
The polynomial written in standard from is -7xy³ - 3x³y + 8x²y² + 4x².
How to write polynomial in standard form?The standard form of a polynomial is expressed by writing the highest degree of terms first then the next degree and so on.
In other words the terms are arranged by decreasing order of degrees.
The degree of a polynomial is the exponential value of the variables.
Therefore, the polynomial written in standard from in the options is as follows:
-7xy³ - 3x³y + 8x²y² + 4x²
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Onyx surveys students at his school and finds that 80% have a pet. He wants to estimate the probability that, if he randomly selected 4 students, at least one student would NOT have a pet.
To estimate this probability, he lets the numbers 1, 2, 3, and 4 represent a student who HAS a pet and 5 represent a student who does NOT have a pet. He then has a computer randomly select 4 numbers and repeats this 20 times.
Based on this simulation, what is the estimated probability that at least one student who have NO PETS?
Represent your answer as a decimal and show your work as to how you determined the answer. pls help this one will give you 50 points
Answers
The estimated probability that at least one student who have NO PETS is 1/4.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
Onyx surveys students at his school and finds that 80% have a pet.
He wants to estimate the probability that, if he randomly selected 4 students, at least one student would NOT have a pet.
lets the numbers 1, 2, 3, and 4 represent a student who HAS a pet, and 5 represent a student who does NOT have a pet.
He then has a computer randomly select 4 numbers and repeats this 20 times.
The estimated probability that at least one student who have NO PETS
= 1/4
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Solve number 11 pls
Answers
Answer:
b. x = 123
Step-by-step explanation:
Ok, so I have a math assignment that is due on Monday (so in 2 days), but I don't understand it. Here are the instructions:
You buy a pair of jeans at a department store.
Jeans_____ $39.99
Discount___ -10.00
Subtotal____ 29.99
Sales Tax___ 31.94
I have the first two questions done for this question, and I just need help on the last one. Here it is:
The price of the jeans includes a 60% markup. After the discount, what is the percent of markup to the nearest percent?
The percent of markup is __%.
Can anyone please help me?
Thanks!
Answers
Which statement proves that quadrilateral JKLM is a kite?
Answers
The statement that proves that quadrilateral JKLM is a kite is (b) LM = JM = 3 and JK = LK = √17
The complete questionSee attachment for the complete question, the graph and the options
How to determine the true statement?The coordinates of the quadrilateral are:
J = (4,5)
K = (5,1)
L = (1,2)
M = (1,5)
Calculate the lengths of the kite using:
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]
So, we have:
[tex]JK = \sqrt{(4 -5)^2 + (5 -1)^2} = \sqrt{17[/tex]
[tex]LK = \sqrt{(1 -5)^2 + (2 -1)^2} = \sqrt{17[/tex]
[tex]LM = \sqrt{(1 -1)^2 + (5 -2)^2} = 3[/tex]
[tex]JM = \sqrt{(1 -4)^2 + (5 -5)^2} = 3[/tex]
On a kite, the adjacent sides are of equal lengths
Because LM = JM = 3 and JK = LK = √17, we can conclude that the quadrilateral JKLM is a kite
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using suitable property find 1/2*3/7-5/7*1/2+2
Answers
Answer:
13/7
Step-by-step explanation:
Method 1 :
1/2*3/7-5/7*1/2+2 = (3/14)- (5/14) + 2
= -2/14 + 2
= -2/14 + 28/14
= 26/14
= 13/7
Method 2 :
1/2*3/7-5/7*1/2+2 = (1/2) [3/7 - 5/7] + 2
= (1/2)(-2/7) + 2
= (-1/7) + 14/7
= 13/7
According to a poll conducted by the gallup corporation in march 2011, the metropolitan areas with the highest and lowest proportions of obese adults were evansville, in-ky, and boulder, co, respectively. in evansville, for every 311 people who were not obese, there were 189 who were. in boulder, for every 16 obese people, there were 109 who were not obese. at that time, the estimated populations were 358,676 for evansville and 303,482 for boulder. how many more obese people were there in evansville than in boulder
Answers
Using proportions, it is found that 96,734 more obese people were there in evansville than in boulder.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
For Evansville, the proportion of obese people is given by:
189/(311+189) = 189/500.
Hence, out of 358,676 people:
oE = 189/500 x 358676 = 135580.
For Boulder, the proportion is given by:
16/(16 + 109) = 16/125
Hence, out of 303,482 people:
oB = 16/125 x 303482 = 38846.
Hence the difference is given by:
135580 - 38846 = 96734
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Quadrilateral abcd has the vertices a(-6,4) , b(-4,5) , c(-3,3) , d(-5,1) . determine if quadrilateral abcd is a rhombus
Answers
Answer:
No
Step-by-step explanation:
The defining property of a rhombus is that it has equal side lengths.
=============================================================
Finding all side lengths :
AB
⇒ √(-4 + 6)² + (5 - 4)²
⇒ √2² + 1²
⇒ √5 units
BC
⇒ √(-3 + 4)² + (3 - 5)²
⇒ √1² + (-2)²
⇒ √5 units
CD
⇒ √(-5 + 3)² + (1 - 3)²
⇒ √(-2)² + (-2)²
⇒ √8 units
DA
⇒ √(-6 + 5)² + (4 - 1)²
⇒ √(-1)² + 3²
⇒ √10 units
As all side lengths of the quadrilateral are not equal, ABCD is not a rhombus.
What figure is graphed from the following points? Graph the figure. (6, 3) (9, 3) (9, 9)
Answers
The figure is a triangle because it has three vertices. Since the first and second points share the same y coordinate, they form a horizontal line parallel to the x-axis. The second and third coordinates also share the same x coordinate forming a vertical line parallel to the y-axis. The intersection of these two lines forms a right angle.
Answer:
RIght triangle
Step-by-step explanation:
can i have help with this
Answers
Answer:
2nd option
Step-by-step explanation:
(5x² - 4x - 1) - (- 4x² - 4)
remove first set of parenthesis and distribute second set by - 1
= 5x² - 4x - 1 + 4x² + 4 ← collect like terms
= 9x² - 4x + 3
[tex](5x^{2}-4x-1)-(-4x^{2}-4)[/tex]
=> [tex] 5x^{2}-4x-1+4x^{2}+4[/tex]
=> [tex]9x^{2}-4x+3[/tex]
hence option two is correct
Line k is parallel to y= -2x - 1 and passes through the point (4,3). What is the y intercept of line k?
A. (0,1)
B. (0,7)
C. (0,10)
D. 0,11)
Answers
Fill in the missing numbers:
Answers
Answer:
Step-by-step explanation:
2| 1 -3 -10 24
| 2 -2 -24
_______________
1 -1 -12 |0
b=2
c=-1
d=-2
What is the distance between the two points (-48,23) and (15,23)
Answers
Answer:
63 units
Step-by-step explanation:
d = √(x2-x1)^2 + (y2-y1)^2
Meaning it would look like this
d = √(15+48)^2 + (23-23)^2
we changed the subtraction sign in the first one to an addition sign because it was a double negative
hope this helped
Which expression is equivalent to the given expression? Assume the denominator does not equal zero.
14r4y6
718y2
OA 24
14
B.
7y3
12
OC. 7r4y4
OD. 2x²y³
Reset
Next
Answers
The simplification form of the provided expression is 2y⁴/x⁴ option (A) 2y⁴/x⁴ is correct after applying the integer exponent properties.
What is an integer exponent?In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
The question is incomplete.
The complete question is attached in the picture, please refer picture.
We have an expression:
[tex]= \rm \dfrac{\left(14x^4y^6\right)}{\left(7x^8y^2\right)}[/tex]
[tex]\rm =\dfrac{7\cdot \:2x^4y^6}{7x^8y^2}[/tex]
[tex]\rm =\dfrac{2x^4y^6}{x^8y^2}[/tex]
[tex]\rm =\dfrac{2y^4}{x^4}[/tex]
Thus, the simplification form of the provided expression is 2y⁴/x⁴ option (A) 2y⁴/x⁴ is correct after applying the integer exponent properties.
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Answer:
A
Step-by-step explanation:
imagine explaining
2. make sure you show all your work for full points. what is z?
Answers
Answer:
I don't understand what the means
ABC is shown on the coordinate plane below
What is the perimeter of △ABC? If necessary, round your answer to the nearest tenth.
Answers
Using the distance formula, the perimeter of triangle ABC is approximately 40.5 units.
What is the Perimeter of a Triangle?Perimeter = sum of all three sides.
Use the distance formula, [tex]d = \sqrt{(y_2 - y_1)^2 - (x_2 - x_1)^2}[/tex] to find the distance between each of the vertices of the triangle.
The given vertices are:
A = (-6, 4)B = (8, -1)C = (0, -9)AB = √[(8−(−6))² + (−1−4)²]
AB = √221
AB ≈ 14.9 units
BC = √[(8−0)² + (−1−(−9))²]
BC = √128
BC ≈ 11.3 units
AC = √[(−6−0)² + (4−(−9))²
AC = √205
AC ≈ 14.3 units
Perimeter of △ABC = 14.9 + 11.3 + 14.3
Perimeter of △ABC ≈ 40.5 units
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What is the exact value of x?
Click the keyboard icon to type your answer using the math keyboard. If needed, use "/" to create a fraction.
x
8
60°
Answers
Exact value of sin 60 = √3/2
So √3/2 x 8= 8 √3/2
Can be simplified to 4 √3
The perimeter of a square is 56cm. State the length of one of its sides.
Answers
Answer:
The length of one of the sides would be 14 cm.
Step-by-step explanation:
There are 4 sides to a square and the total perimeter is 56 cm meaning that we need to divide 56 by 4 to get the length of one side. 56 divided by 4 is equal to 14 cm, getting your answer. I hope this helps! Have a great day! :)