Answer:
[tex]54\pi\ cm^2[/tex]
Step-by-step explanation:
1. Approach
In order to solve this problem, one needs to find the height of the cone. This can be done using the Pythagorean theorem. After finding the height of the cone, one can use the formula to find the surface area of a cone, to find the surface area of this particular cone.
2. Find the height of the cone
The Pythagorean theorem is a property that relates the sides of a right triangle. The radius (distance from the center to circumference (outer edge)) of the base, the height of the cone, and the slant of the cone forms a right triangle. Thus, one can use the Pythagorean theorem to solve for the height. The Pythagorean states the following:
[tex]a^2+b^2=c^2[/tex]
Please note that (a) and (b) represent the sides adjacent (next to) the right angle, (c) represents the hypotenuse (the side opposite the right angle). In this case (a) is the height, and (b) is the radius of the base. (c) is the diagonal of the cone. Substitute the given values in and solve for the height,
[tex]a^2+b^2=c^2[/tex]
[tex]a^2+3^3=15^2[/tex]
Simplify,
[tex]a^2+3^3=15^2[/tex]
[tex]a^2+9=225[/tex]
Inverse operations,
[tex]a^2+9=225[/tex]
[tex]a^2=216[/tex]
[tex]a=\sqrt{216}[/tex]
3. Find the surface area of the cone
The following formula can be used to find the surface area of a cone,
[tex]A_s=\pi r(r+\sqrt{h^2+r^2})[/tex]
Where (h) is the height of the cone, (r) is the radius of the base of the cone, and ([tex]\pi[/tex]) represents the value (3.1415...). Substitute the given values into the formula and solve for the surface area,
[tex]A_s=\pi r(r+\sqrt{h^2+r^2})[/tex]
[tex]A_s=\pi(3)(3}+\sqrt{\sqrt{216}^2+3^2}[/tex]
Simplify,
[tex]A_s=\pi(3)(3}+\sqrt{\sqrt{216}^2+3^2}[/tex]
[tex]A_s=\pi(3)(3}+\sqrt{216+9})[/tex]
[tex]A_s=\pi(3)(3}+\sqrt{225})[/tex]
[tex]A_s=\pi(3)(3}+15)[/tex]
[tex]A_s=\pi(3)(18)[/tex]
[tex]A_s=\pi(54)[/tex]
if 5 hockey balls and 3 sticks cost $230.00 and 5 balls and 2 sticks cost $200 how much does one hockey ball cost?
step by step explanation:
Answer:
$28.
Step-by-step explanation:
We have the system of equations
5b + 3s = 230 (b = cost of 1 ball and s = cost of 1 stick).
5b + 2s = 200
Subtract the above from the first equation:
s = 30
So, substituting in equation 1:-
5b + 3(30) = 230
5b = 230 - 3(30) = 140
b = 28.
Checking in equation 2:-
5(28) + 2(30)
= 10 + 60
= 200.
- this checks out OK.
The cost of one hockey ball will be $28.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The system of equations from the given data are:-
5b + 3s = 230 (b = cost of 1 ball and s = cost of 1 stick).
5b + 2s = 200
Subtract the above from the first equation:
s = 30
So, substituting in equation 1:-
5b + 3(30) = 230
5b = 230 - 3(30) = 140
b = 28.
Therefore, the cost of one hockey ball will be $28.
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The circumference of a circle is 6π m. What is the area, in square meters? Express your answer in terms of
π
π.
Answer:
9π meters
Step-by-step explanation:
SInce 6π is the circumference of the circle, 6π would be the diameter.
We need to then convert 6π into the radius which we can do by dividing 6π by 2 to get 3π.
The formula for the area of a circle is πr^2. Plug in the previous result for the radius to get the following:
π3^2
9π
Answer:
Area=9π m²
Step-by-step explanation:
Hi there!
We are given that the circumference of a circle is 6π meters, and we want to find the area of the circle
The formula to find the circumference of a circle is 2πr, where r is the radius
The formula to find the area of a circle is πr², where r is the radius
So we need to find the radius
As 6π and 2πr both equal the circumference of the circle, 6π is equal to 2πr. This is possible by a property known as transitivity (if a=b and b=c, then a=c) .
As an equation, the result is:
6π=2πr
Divide both sides by 2π
3=r
So the radius is 3 meters
Now, substitute 3 as the radius in πr² to find the area
A=πr²
A=π(3)²
Raise 3 to the second power, which is the same as multiplying it by itself
A=π*9
A=9π m²
Hope this helps!
hello pls help it has to do with shapes and volume. thank u :D
Hi there!
[tex]\large\boxed{r\approx 10.6 cm}[/tex]
Solve for the radius using the pythagorean theorem:
a² + b² = c²
We know the lengths of the hypotenuse and one leg, so:
a = 12
b = ?
c = 16
Plug these into the equation:
12² + b² = 16²
Simplify:
144 + b² = 256
Subtract both sides by 144:
b² = 112
Take the square root:
b ≈ 10.6
Thus the radius is about 10.6 cm.
The curved part of this figure is a semicircle.
What is the best approximation for the area of this figure?
18+24.25π units²
18+12.125π units²
36+24.25π units²
36+12.125π units²
Answer:
carna estralia con frema es 36+12.125tt ernits es answeana
Step-by-step explanation:
Answer:
18+12.125π units²
Sarah has 27
27 feet of wire to make bead necklaces. If each necklace
requires 12 feet of wire, how many necklaces can she make?
1
Answer:
= 2 R 3
= 2 3/12
= 2 1/4
Step-by-step explanation:
0 2
1 2 2 7
− 0
2 7
− 2 4
3
Need help ! Help needed very much !
Answer:
x/2 > 5
Step-by-step explanation:
Quotient means division
x/2
is more than means greater
x/2 > 5
match the property to its correct name
A} additive inverse property
B} multiplicative inverse property
C} commutative property of multiplication
D} multiplicative identity
E} commutative property of complement
F} ascending property of multiplication
G} distributive property
H} associative property of multiplication
I} additive identification property
J} zero property
{1} x+(y-z)=(x+y)+z
2} (pq) * 1 = pq
3} (5x)y-5(xy)
4} a+5b = 5b + a
5} a+0=a
6} gh - hg
7} 8 + (-8)=0
8} x * 0 = 0
9} 5 * (1/5)=1
10} 2(a+h)=2a * 2b
Additive inverse and multiplicative inverse are mathematics function which creates net impact of an equation as zero.
The correct names are matched with their respective properties.
A. 7. 8 + [-8] = 0
B. 9. 5 * [1/5] = 0
C. 4. a + 5b = 5b + a
D. 2. [pq] * 1 = pq
E. 6. gh - hg
F. 3. [5x] y-5 [xy]
G. 10. 2 [a + b] = 2a * 2b
I. 5. a + 0 = a
J. 8. x* 0 = 0
Additive inverse property is when the net result from addition is zero.
Multiplicative inverse property is the equation which gives answer zero when two variables are multiplied.
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Find the value of x.
r h==ptgggggggggggggggggggggggggggggggggggggggggggggggggggtnnnnnnn
Can SOMEONE PLEASE HELP ME? I really need to get this work done by tonight. PLEASE
suppose the function g(x) doubles the square of the input and then subtracts 13. what is g(3)?
Given:
The function [tex]g(x)[/tex] doubles the square of the input and then subtracts 13.
To find:
The value of [tex]g(3)[/tex].
Solution:
Let [tex]x[/tex] be the input value.
The square of the input is [tex]x^2[/tex].
Doubles the square of the input [tex]2x^2[/tex].
Doubles the square of the input and then subtracts 13, i.e., [tex]2x^2-13[/tex].
So, the function is:
[tex]g(x)=2x^2-13[/tex]
Putting [tex]x=3[/tex] in the above function, we get
[tex]g(3)=2(3)^2-13[/tex]
[tex]g(3)=2(9)-13[/tex]
[tex]g(3)=18-13[/tex]
[tex]g(3)=5[/tex]
Therefore, the value of [tex]g(3)[/tex] is 5.
Two cards are drawn from a deck of 52 playing cards. The first card is NOT replaced into the deck before the 2nd card is drawn What is the probability of drawing a King and then another King?
Answer:
probability that 2 cards drawn from a deck of 52 cards are both kings.
is probability that first card is a king times probability that second card is a king
with replacement 4/52*4/52 =0.592%
without replacement 4/52*3/51=0.452%
Step-by-step explanation:
I am a 4 digit number all my digits are different they add up to 20 the hundred's digit is double than the one's digit
Answer:
- 2864
Step-by-step explanation:
Given that,
The number is of 4 digits
All are different
The sum of the 4 digits = 20
Hundred's digit is twice than one's digit
A.T.Q.
Let the unit digit be 4. So, the hundred's digit would be 4 * 2 = 8
Now, we have
_8_4
We know that the sum of four digits is 20. Thus,
_ + 8 + _ + 4 = 20
∵ _ + _ = 20 - 12 = 8
The possible numbers must make a sum of 8. Thus, one possibility can be 2 and 6.
Therefore, the number can be
2864
( 2 + 8 + 6 + 4 = 20)
Mrs. Helton is making gift bags as prizes for her math classes. She has 30 little bags of Hershey Kisses and 15 Blow Pops. What is the greatest number of gift bags she can make if all gift bags are the same, and she does not want any left over?
Answer:
3
Step-by-step explanation:
I LOVE CANDY hope it helps 45/3 is hte gretaets factor the answer is 3.. i think
Answer:
45 gift bags.
Step-by-step explanation:
take 30 and divide it by 15. your answer is 2. 2 hk bags and 1 blow pop is equal to 3. so you would multiply 3 by 15 to get your conclusion
A ladder that is 17 feet long is 8 feet from the base of a wall. How far up the wall does the ladder reach?
Using Pythagoras theorem
[tex]\\ \Large\sf\longmapsto P^2=H^2-B^2[/tex]
[tex]\\ \Large\sf\longmapsto P^2=17^2-8^2[/tex]
[tex]\\ \Large\sf\longmapsto P^2=289-64[/tex]
[tex]\\ \Large\sf\longmapsto P^2=225[/tex]
[tex]\\ \Large\sf\longmapsto P=\sqrt{225}[/tex]
[tex]\\ \Large\sf\longmapsto P=15ft[/tex]
Answer:
Applying the Pythagorean theorem we have :wall length is : a²-b²=c²⇒17²-8²=c²⇒c=15(c>=0)Step-by-step explanation:
we have : the length of the ladder is the hypotenuse of the triangle ; the length of the ladder, which is far from the wall, is the right angle side of the triangle (draw your own illustration)
Solve the equation step by step
Let x be the amount of salt in the solution.
At day's end, the concentration of salt in the beaker is
x / (4 L) = 0.08 = 8%
Solve for x to get
x = 0.08 (4 L) = 0.32 L
So at the beginning, the concentration of salt in the beaker was
(0.32 L) / (5 L) = 0.064 = 6.4%
If the fourth term in a geometric sequence is –1 and the common ratio is –1, find the explicit formula of the sequence.
A)
an = (1) ⋅ (–1)n – 1 for n ≥ 1
B)
an = (– 1) ⋅ (1)n – 1 for n ≥ 1
C)
an = (–1) ⋅ (–1)n – 1 for n < 1
D)
an = (1) ⋅ (1)n – 1 for n ≥ 2
Answer:
Hello,
Answer A
Step-by-step explanation:
[tex]a_4=-1\\q=-1\ common\ ratio\\\\a_4=a_1*q^3\ -1=a_1*(-1)^3 \Longrightarrow\ a_1=1\\\\\\\boxed{a_n=1*(-1)^{n-1}}\\\\\\Since \ all \ formula\ are\ so\ bad\ written,\ I\ suppose\ that\ the\ answer \ is \ A\\[/tex]
Answer:
an = (1) ⋅ (–1)n – 1 for n ≥ 1
Step-by-step explanation:
took the test and got it right
hope this helps
If the distance between the points (2, -2) and (-1, x) is 5, one of the values of x is
We know
[tex]\boxed{\sf Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}[/tex]
ATQ
[tex]\\ \sf\longmapsto \sqrt{(-1-2)^2+(x+2)^2}=5[/tex]
[tex]\\ \sf\longmapsto \sqrt{(-3)^2+x^2+4x+4}=5[/tex]
[tex]\\ \sf\longmapsto \sqrt{9+x^2+4x+4}=5[/tex]
[tex]\\ \sf\longmapsto \sqrt{x^2+4x+13}=5[/tex]
[tex]\\ \sf\longmapsto x^2+4x+13=5^2=25[/tex]
[tex]\\ \sf\longmapsto x^2+4x+13-25=0[/tex]
[tex]\\ \sf\longmapsto x^2+4x-12=0[/tex]
[tex]\\ \sf\longmapsto x^2+6x-2x-12=0[/tex]
[tex]\\ \sf\longmapsto x(x+6)-2(x+6)=0[/tex]
[tex]\\ \sf\longmapsto (x-2)(x+6)=0[/tex]
[tex]\\ \sf\longmapsto x=2\:or\:x=-6[/tex]
There is a bag filled with 5 blue, 4 red and 3 green marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 different colours?
Answer:
66%
bcz out of 3 stuff in 100% is 66%
please help me please i will give brainliest
Answer:
I think It would be A
Step-by-step explanation:
Answer:
i think its A
Step-by-step explanation:
(if its not im sorry :( )
A rectangular hockey field is 50m long and 35m wide calculate the length of it's diagonal
Answer:
length=50m
width=35m
diagonal=?
using Pythagoras theorem
where c=diagonal,a=length(50m),b=width(35)
c² =a² + b²
c² =(50)² + (35)²
c² =2500+1225=3725
Taking square root on both sides
c=61m
Therefore the diagonal is 61m
Plz help me ASAP TwT
Answer:
Angle CBA
Step-by-step explanation:
It would be CBA because Angle 1 is between those 3 points. Angle 1 is where B is so B would have to go in the middle.
Hope this helps :)
1-2. Roel earns P 8,000 per month as basic salary. In addition, he earned P 5,725.50 as commission and P 852.50 as overtime pay in January. How much did he earn that month?
3-4. A biscuit factory originally packaged 0.65kg of crackers. To increase profitability, the company reduced the weight by 0.035 kg with a more affordable price. What is the new weight per pack of crackers?
Answer:
a. he earn 14578.00 in that month.
a microwave oven has a capacity of 1.59ft³. the interior of the microwave of the is 14 in wide and 14 in deep. what is the height of the interior of the microwave, to the nearest tenth of a foot
Step-by-step explanation:
The easiest way to do this is to imagine the microwave as a box. Ignore the turntables, whether or not something will spin if it touches an edge, and anything else that would make the fact that we're talking about a microwave confusing. This is a box now. :)
The capacity of our box is 1.59 ft^3, which means it can hold that much of "things" inside it. Instead of a capacity, we'll think of it as the box's total area. A tricky thing to note, is the area is given in ft, where the interior values are given as inches. So we'll need to turn the inches into feet.
To get the area of a box, we do length x width x height.
We're already given the length, 14 (inches), and the width, 14 (inches), so all we need to find now is the height (feet). To turn the lengths into feet, we'll divide them by 12, because there are 12 inches in 1 foot, or Feet = Inches / 12.
To finally turn it into math:
Area (A) = length (L) * width (W) * height (H)
[tex]A = L * W * H[/tex]
Insert known values.
[tex]1.59 = \frac{14}{12} * \frac{14}{12} * H[/tex]
Multiply.
[tex]1.59 = \frac{196H}{144}[/tex]
Simplify.
[tex]1.59 = \frac{49H}{36}[/tex]
Multiply both sides by 36.
[tex]1.59*36 = \frac{49H}{36}*36[/tex]
Simplify.
[tex]57.24 = 49H[/tex]
Divide both sides by 49.
[tex]\frac{57.24}{49} = \frac{49H}{49}[/tex]
Simplify.
[tex]1.16816326... = H[/tex]
To turn make this the nearest Tenth, we round up to the first decimal place.
Answer:
H = 1.2 ft
Full working out for this question please.
Answer:
B. 3.2
Step-by-step explanation:
5 companies have 0 computers.
10 companies have 1 computer.
10 companies have 2 computers.
30 companies have 3 computers.
25 companies have 4 computers.
20 companies have 5 computers.
To find mean:
0 x 5 = 0
10 x 1 = 10
10 x 2 = 20
30 x 3 = 90
25 x 4 = 100
20 x 5 = 100
100 + 100 + 90 + 20 + 10 + 0 = 320
20 + 25 + 30 + 10 + 10 + 5 = 100
100 companies were surveyed.
100 companies use 320 computers in total.
320 / 100 = 3.2
SHOW YOUR STEPS PLEASE. SOMEONE PLEASE HELP ME I NEED THE ANSWER ASAP!!!
The cost, c(x), in dollars per hour of running a certain steamboat is modelled by the function c(x)=1.7x^2-13.6+166.4, where x is the speed in kilometres per hour. At what approximate speed should the boat travel to achieve minimum cost? what is the minimum cost?
Answer:
x = 4
139.2
Step-by-step explanation:
Given the Cost function :
C(x) = 1.7x² - 13.6x + 166.4
To achieve minimum cost ;
dc/dx = 0
dc/dx = 2(1.7)x - 13.6
3.4x - 13.6 = 0
3.4x = 13.6
x = 13.6 / 3.4
x = 4
To achieve minimum cost, speed = 4 ;
Minimum cost will be :
C(x) = 1.7x² - 13.6x + 166.4
Put x = 4
C(4) = 1.7(4)² - 13.6(4) + 166.4
C(4) = 27.2 - 54.4 + 166.4 = 139.2
Minimum cost = 139.2
What is the value of x in the figure below? In this diagram, AABD ~ ACAD.
15
B
х
20
Answer:
E
Step-by-step explanation:
(leg of big triangle)² = (part of hypotenuse below it) × (whole hypotenuse)
15² = x × 20
225 = 20x ( divide both sides by 20 )
[tex]\frac{225}{20}[/tex] = x , that is
x = [tex]\frac{45}{4}[/tex] → E
The value of the x in the given triangle is 45/4.
What are similar triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.
Given is right triangle ABC, divided into two more right triangles, ADC and ADB, also, triangle ABD ~ triangle CAD.
Therefore, according to the definition of similar triangles, the corresponding sides are in proportion.
we have,
CA / CB = CD / CA
15/20 = x/15
x = 15²/20
x = 225/20
x = 45/4
Hence, the value of the x in the given triangle is 45/4.
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Is (3,8) a solution to the inequality 14x + 12y = 12?
1. Find the ratio of of 25cm and 1m .
2. Find the product of (a + 4)(a − 4).
Answer:
1..
solution....
here given
25cm
1m=100cm
now,
25/100=1/4
1:4
2....
(a+4)(a-4)
a^2-4^2
a^2-16
Step-by-step explanation:
hope it will help you
Can someone help please
Answer:
[tex]10^{-3}[/tex]
Step-by-step explanation:
Answer:
https://tex.z-dn.net/?f=10%5E%7B-3%7D
Step-by-step explanation:
trigonometric identities
With 180° < θ < 270°, we know that both cos(θ) < 0 and sin(θ) < 0.
Then from the Pythagorean identity, it follows that
sin²(θ) + cos²(θ) = 1 ==> sin(θ) = -√(1 - cos²(θ))
and so
sin(θ) = -√(1 - (-8/13)²) = -√105/13
Recall the double angle identity for sine:
sin(2θ) = 2 sin(θ) cos(θ) = 2 (-√105/13) (-8/13) = 16√105/169
