Given:
The circumference of the base of a cone is 10π cm.
The circumference of the base of a second similar cone is 20π.
To find:
The ratio of the surface area of the first cone to that of the second cone.
Solution:
Let the radii of base of two cones are [tex]r_1[/tex] and [tex]r_2[/tex] respectively.
Circumference of the circular base is [tex]2\pi r[/tex], where, r is radius.
We have,
[tex]2\pi r_1=10\pi\text{ cm}[/tex]
[tex]r_1=\dfrac{10\pi}{2\pi}\text{ cm}[/tex]
[tex]r_1=5\text{ cm}[/tex]
And,
[tex]2\pi r_2=20\pi\text{ cm}[/tex]
[tex]r_2=\dfrac{20\pi}{2\pi}\text{ cm}[/tex]
[tex]r_2=10\text{ cm}[/tex]
It two cons are similar, then ratio of there areas is equal to square of the ratio of there corresponding dimensions, i.e., radius or heights.
[tex]\dfrac{A_1}{A_2}=\left(\dfrac{r_1}{r_2}\right)^2[/tex]
[tex]\dfrac{A_1}{A_2}=\left(\dfrac{5}{10}\right)^2[/tex]
[tex]\dfrac{A_1}{A_2}=\left(\dfrac{1}{2}\right)^2[/tex]
[tex]\dfrac{A_1}{A_2}=\dfrac{1}{4}[/tex]
The ratio form is
[tex]V_1:V_2=1:4[/tex]
Therefore, the ratio of the surface area of the first cone to that of the second cone is 1:4.
The ratio of the surface area of first cone to that of the second cone is; 1:4
Surface AreaFormula for the circumference of the base of a cone is;
C = 2πr
Where;
C is circumference
r is radius
Thus;
For the first cone;10π = 2πr
r = 10π/2π
r = 5
For the second cone;20π = 2πr
r = 20π/π
r = 10
Now, formula for surface area of the base is;
A = πr²
Thus, ratio of both area of first cone to second cone is;
A1/A2 = 5²/10²
A1/A2 = 25/100
A1/A2 = 1/4
Thus, ratio of first cone to that of the second cone is; 1:4
Read more on surface area of cone at; https://brainly.com/question/6613758
help i’ll give brainiest thing !
Answer:
Yes, it is enough
[tex]y = -3x + 16[/tex]
Step-by-step explanation:
Given
[tex]Point = (6, -2)[/tex]
[tex]m = -3[/tex]
Required
Is the given info enough to find the equation?
Yes, it is enough and the proof is as follows:
And equation is solved using:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex](x_1,y_1) = (6,-2)[/tex]
[tex]m = -3[/tex]
Substitute these values in [tex]y - y_1 = m(x - x_1)[/tex]
[tex]y - (-2) = -3(x - 6)[/tex]
[tex]y +2 = -3(x - 6)[/tex]
Open bracket
[tex]y +2 = -3x + 18[/tex]
Make y the subject
[tex]y = -3x + 18-2[/tex]
[tex]y = -3x + 16[/tex]
From the above, one can see that the given info is enough
Mai earns $7 per hour mowing her neighbor’s lawns. She also earned $14 for hauling away bags of recyclables for some neighbors. Priya babysits her neighbor’s children. She earns $8.40 per hour. Priya and Mai have agreed to go to the movies the weekend after they have earned the same amount of money for the same number of hours. How many hours do they have to work before they can go to the movies? How much will they have earned.
Answer:
5 hours for priya 4 of yard mowing and 1 bag moving and they will both earn 42 dollars
Step-by-step explanation:
Line g is dilated by a scale factor of 3 from the origin to create line g'. Where are points E' and F' located after dilation, and how are lines g and g' related? coordinate plane with point E at negative 4 comma 0 and point F at 0 comma 2, line g intersects points E and F The locations of E' and F' are E' (−4, 0) and F' (0, 2), and lines g and g' are the same line. The locations of E' and F' are E' (−2, 0) and F' (0, 1), and lines g and g' intersect at point F. The locations of E' and F' are E' (−1, 0) and F' (0, 0), and lines g and g' are not related. The locations of E' and F' are E' (−12, 0) and F' (0, 6), and lines g and g' are parallel.
Dilation involves changing the size of a shape.
The true statement is that the locations of E' and F' are E' (−12, 0) and F' (0, 6), and lines g and g' are parallel.
The given parameters are:
[tex]k =3[/tex] --- the scale factor
[tex]E = (-4,0)[/tex]
[tex]F =(0,2)[/tex]
Multiply the coordinates of point E and F by the scale factor (k), to determine the new coordinates of E and F.
[tex]E' = E \times k[/tex]
[tex]E' = (-4,0) \times 3[/tex]
[tex]E' = (-12,0)[/tex]
[tex]F' = F \times k[/tex]
[tex]F' = (0,2) \times 3[/tex]
[tex]F' = (0,6)[/tex]
Given that line g is represented by points E and F; line g' would be represented by points E' and F'
So, both lines would be parallel.
Hence, the true option is (d)
Read more about dilation at:
https://brainly.com/question/3457976
Answer:
The locations of E' and F' are E' (−12, 0) and F' (0, 6), and lines g and g' are parallel.
Step-by-step explanation:
What is the slop of the line that contains the points (0,1)and(-2,-9).write your answer as a friction in simplest from (hint:2/1 should be simplified to 2
Answer:
5
Step-by-step explanation:
To find the slope we will use the slope formula:
[tex]slope = \frac{y2 - y1}{x2 - x1}[/tex]
They give us the points of (0,1) and (-2,-9) in the equation. Let's label each thing to fit the equation:
y2 = -9
y1 = 1
x2 = -2
x1 = 0
Now, plug it all in to the equation:
[tex]\frac{-9-1}{-2-0} = \frac{-10}{-2} = 5[/tex]
Therefore, the slope is 5.
I hope this helps!!
- Kay :)
Tell whether (12, 43) is a solution of y = 3x + 7.
yes
no
Answer:
yes
Step-by-step explanation:
Help plsssssssssss number 3
Answer:
a
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Think of a car. when you are going 15 miles an hour that means that every hour, you are crossing 15 miles. In this situation the dolphin is going 25 km for every hour. one hour would be 25, two hours would be 50 and so on.
PLEASE OPEN THE PHOTO AND ANSWER ILL GUVE BRAINLIEST (SORRY FOR SPELLINGing)
Answer:
Honestly im confused by this but i think its the second one
Step-by-step explanation:
The music teacher asked his class to vote for their favorite instrument and created a pie chart to display the results.
There are 20 students in his class. Which statements are true? Check all that apply.
THE ANSWER IS B,D,E,F!!!!
Answer:
bdef
Step-by-step explanation:
Answer:
b= brains b= dad e= end f= fun
Step-by-step explanation:
Bob and Kathy want to save a total of $500,000 for retirement. How much should they deposit monthly into an account that pays 3.9% interest,
compounded monthly, to meet their goal in 24 years?
$1,051.17
$2,102.34
$950.41
$4,446.41
Answer:
it would 4,446.41
Step-by-step explanation:
Name a point on this line.
y + 2 = 3(x – 4)
Question 3 options:
(4,-2)
(-2,4)
(2,-4)
(-4,2)
is 12,43 a solution of y =3x+7
Answer:
Yes it is
Step-by-step explanation:
Georgia goes shopping with $80 to spend on food for a party. She buys 9 pizzas that all cost the same price, $20 worth of soda and $15 worth of ice cream. If she spent all of her money, what was the cost of each pizza?
Answer:
$5
Step-by-step explanation:
20+15=35
80-35=45
45 divided by 9 = 5
Round to the nearest thousand 5.2182
Answer:
5.218
Step-by-step explanation:
5 or more, you add one. Four or less, you change it to zero.
plzz i need fasssssst
Answer: 1. a) 0 b) -4 2. a) 3 b) -9 3. a) -80 b) -339 c) -14 4. a) 110 b) -87
Step-by-step explanation: This took forever
please. i’m begging you
find the value of this expression if x=1 and y=4
xy^2/7
Answer:
2 2/7
Step-by-step explanation:
What we know:
x = 1, and y = 4
The equation is xy^2/7
1(4)^2/7
4^2/7
16/7 = 2 2/7
i need help with this badddddddddd
Answer:
She forgot to add the zero when she multiplied 27 x 50
Step-by-step explanation:
If you need one ask me I can try my best to explain
Name a point on this line.
y - 8 = -7(x + 1)
Question 4 options:
(-1, 8)
(-8, 1)
(8, -1)
(1, -8)
Answer: y - 8 = -7(x + y - 8 = -7(x + y - 8 = -7(x + y - 8 = -7(x + y - 8 = -7(x + y - 8 = -7(x + y - 8 = -7(x + y - 8 = -7(x + y - 8 = -7(x + y - 8 = -7(x + y - 8 = -7(x + y - 8 = -7(x + y - 8 = -7(x + y - 8 = -7(x + y - 8 = -7(x + y - 8 = -7(x + y - 8 = -7(x + y - 8 = -7(x + y - 8 = -7(x +
Step-by-step explanation: 8, -1)
HEYYYY HELP ME OUT WILL GIBE BRAINLIST
Answer:
c no is correct answer ☺️
A hotel rents 240 240 rooms at a rate of $ 40 $40 per day. For each $ 2 $2 increase in the rate, four fewer rooms are rented. Find the room rate that maximizes daily revenue. The rate that maximizes revenue is $
Answer:
The daily rate that maximizes the revenue is $40 and the maximum revenue is $9600
Step-by-step explanation:
Given
[tex]Rooms = 240[/tex]
[tex]Price= \$40[/tex]
[tex]Increment = \$2[/tex]
First, we calculate the revenue.
[tex]Revenue (r) = Price (p) * Number\ of\ Rooms(n)[/tex]
[tex]r = p*n[/tex]
Let x be the change in rate.
i.e.
For every 2x increment in price (p) i.e. p + 2x
There will be 4 fewer rooms (n) i.e. n - 4x
So, the revenue is updated as:
[tex]r = (p + 2x) * (n - 4x)[/tex]
[tex]Price = 40[/tex]
So:
[tex]r = (40 + 2x) * (n - 4x)[/tex]
[tex]Rooms = 240[/tex]
So:
[tex]r = (40 + 2x) * (240 - 4x)[/tex]
Expand
[tex]r = 40 * 240 - 40 * 4x + 2x * 240 - 2x*4x[/tex]
[tex]r = 9600 - 160x + 480x - 8x^2[/tex]
Reorder
[tex]r = -8x^2 - 160x + 480x + 9600[/tex]
[tex]r = -8x^2 +320x + 9600[/tex]
The maximum of a function is calculated as:
[tex]Max = -\frac{b}{2a}[/tex]
In: [tex]r = -8x^2 +320x + 9600[/tex]
[tex]a = -8[/tex] [tex]b = 320[/tex] [tex]c = 9600[/tex]
So:
[tex]Max = -\frac{b}{2a}[/tex]
[tex]Max = -\frac{320}{-8}[/tex]
[tex]Max = \frac{320}{8}[/tex]
[tex]Max = 40[/tex]
To get the maximum revenue;
Substitute 40 for x in [tex]r = -8x^2 +320x + 9600[/tex]
[tex]r = -8(40)^2 + 320 * 40 + 9600[/tex]
[tex]r = 9600[/tex]
The daily rate that maximizes the revenue is $40 and the maximum revenue is $9600
THIS ONE PLEASE IM STUMPED
-3 3/4+ 1/2 please help
Answer:
-3.25 or -3 1/4
Step-by-step explanation:
-3.75
+ .5
_______
line has the equation y=6x +b. What must be the value of b for the line to model a directly proportional relationship
The value of y varies directly with x. When y=2 2/5,x=3/5 what is the value of y when x is 4/5
A 1 1/5
B 3 3/5
C 3 1/5
D 5 1/5
Answer:
the correct ans should be 88/15
Step-by-step explanation:
since, y is directly proportional to x then,
y=kx where k=proportionality constant
when y=22/5 and x=3/5
or,22/5=k*3/5
or,22/5*5/3=k
•°•k=22/3
now, when x=4/5
we know,
y=kx
or,y=22/3*4/5
•°•y=88/15
Plz help me with this?!?! I will mark you brainliest!!!
Answer: 2/5 liters
Step-by-step explanation: This is because you need to add 1/10 and 3/10. The answer is 4/10, which can be simplified to 2/5.
Samuel pays $59.99 plus $0.25 for each minute over 450 minutes for his cell phone plan. Monica
pays $64.99 plus $0.10 for each minute over 450 minutes for her cell phone plan. Which system
of equations represents this situation? Letx represent the number of minutes over 450
Answer:
D
Step-by-step explanation:
Samuel pays 59.99 for the 450 minutes but when he goes over he pays 0.25 for each minute he goes over. The same thing for Monica
The correct option is D
Given that,
Samuel pays $59.99 plus $0.25 for each minute over 450 minutes for his cell phone plan. Monica pays $64.99 plus $0.10 for each minute over 450 minutes for her cell phone plan.Based on the above information, the equation is as follows:
y = 59.99 + 0.25x
y = 64.99 + 0.10x
Learn more: https://brainly.com/question/1152162?referrer=searchResults
2/9 divided by 4????
Answer:
2/36 or simplfyed is 1/18
Step-by-step explanation:
Answer:
2/9 ÷ 4 = 2/36
Step-by-step explanation:
2/9 & 4
2/9÷4=?
2/9×1/4
=2/36
So 2/36 is equivalent fraction for 2/9 divided by 4
I don't know these some one help?
Answer:
I hope that's help you.
m = -7
t = 2
n = 10
The radar system in an airport determines the location of inbound and outbound planes once they are within range. The range, based on the signal from the tower, is represented by the polar equation r = 10cos(θ). Which graph represents the signal range of the airport’s radar system?
Answer:The one with the circle on the right.
Step-by-step explanation:
It was A for me but its D for you that's why I'm saying the one with the circle on the Right
Answer: A
Step-by-step explanation:
pls help i give brainliest if u answer early and good
Answer:
1 - BC = 5
2 - 174 (I think, im pretty sure tho)
3- 107
Step-by-step explanation:
Lets be real chief, you aren't here to learn. Ur taking test
Also, I got those numbers based on the images. The pic was kind of blurry