Mathematics High School

The surface area of a cone is square units. the height of the cone is times greater than the radius. what is the length of the radius of the cone to the nearest foot? the radius is about feet.

Answers

Answer 1

The radius of the cone is 7 feet

How to determine the radius?

The given parameters are:

Surface Area, A = 216π

h = 8/3r

The surface area of a cone is:

[tex]A = \pi r(r + \sqrt{h^2 + r^2})[/tex]

So, we have:

[tex]216\pi = \pi r(r + \sqrt{(8/3r)^2 + r^2})[/tex]

Factor out r

[tex]216\pi = \pi r(r + r\sqrt{(8/3)^2 + 1})[/tex]

Evaluate the exponent

[tex]216\pi = \pi r(r + r * 2.85)[/tex]

Evaluate the sum

[tex]216\pi = \pi r(3.85r)[/tex]

Divide both sides by pi

[tex]216 = 3.85r^2[/tex]

Divide both sides by 3.85

[tex]56.10 = r^2[/tex]

Take the square roots of both sides

r = 7 (approximately)

Hence, the radius of the cone is 7 feet

Related Questions

A rectangle has a perimeter of 80 centimeter. its height is four times the length of its base. what is the lenght of its base?

Answers

Answer:

8 cm

Step-by-step explanation:

To find the length of the rectangle's base, form 2 equations using the given information.

Perimeter of rectangle= 2(height +base)

Let the lengths of the height and base of the rectangle be h and b cm respectively.

Perimeter= 80

2(h +b)= 80

h +b= 80 ÷2

h +b= 40 -----(1)

h= 4b -----(2)

Let's solve by substitution!

Substitute (2) into (1):

4b +b= 40

5b= 40

b= 40 ÷5

b= 8

Thus, the length of its base is 8 cm.

What are the values of the function when x=-2 and when x=4

Answers

Answer:

g(-2) = 0

g(4) = -4

Step-by-step explanation:

The outputs of each inequality are the numbers directly next to the parentheses. If an "x" value lies within a particular inequality, the values of the function are the corresponding output.

Remember, the "greater than or equal to" sign (≤) indicates that the "x" value can be equal to the number on the left. The "greater than" symbol (<) indicates that the number to the right cannot satisfy the inequality.

x = -2 lies within the inequality -2 ≤ x < 4. All "x" values that fall within this range are g(x) = 0. Therefore, g(-2) = 0.

x = 4 lies within the inequality 4 ≤ x < 10. All "x" values that fall within this range are g(x) = -4. Therefore, g(4) = -4.

HELP ASAP

Given the graph below, solve for the equation of the circle. Show your work and explain the steps you used to solve.

Answers

Answer:

(x + 3)^2 + (y - 3)^2 = 5^2

Step-by-step explanation:

They're not really much to show work. Looking at the graph we need to find the origin which is (h ,k), and the radius.

(h , k) = (-3 , 3)

The radius is r = 5 because counting it from origin to the edge.

Plug that into the formula equation: (x - h)^2 + (y - k)^2 = r^2

(x - (-3))^2 + (y - 3)^2 = 5^2

(x + 3)^2 + (y - 3)^2 = 5^2

give answer in simplest form with working out pls

Answers

Answer:

5 x 5+3/5= 25+3/5=28/5÷8/3

28/5 x8/3= 224/15 =14.93

what is an event in which the outcome does impact the probability of the next event?

Answers

Answer:

Dependent Event

Step-by-step explanation:

Dependent Events: Two events are dependent when the outcome of the first event influences the outcome of the second event. The probability of two dependent events is the product of the probability of X and the probability of Y AFTER X occurs.

6a-2y>4

Solve inequality for y

Answers

y < -2 +3a

Isolate the variable by dividing each side by factors that don't contain the variable.

combien font 3579+826

Answers

The answer is 4,405!!!

Helpppppppppp meeeeeee pleaseeeeeeeee

Answers

Answer:

If you are rounding to the nearest tens the smallest number is 45. If you are rounding to the nearest whole number, the smallest number is 49.5

Answer:

49 and 51

Hope it helps

A student made an 84% on
their Unit 1 Math Test.
What fraction is equivalent to
the score the student made on
the test?

Answers

Answer:

84/100

Step-by-step explanation:

We know that 100% is a whole, so we can use this as our denominator. If the student only got an 84, this will be our numerator. The numerator is a part of a whole, 84 is a part of 100. Therefore the answer would be 84/100.

What is the average speed of a turtle that moved 50 inches in 5 minutes? (speed = distance ÷ time)

A.
55 inches per minute

B.
10 inches per minute

C.
0.1 inches per minute

D.
250 inches per minute

Answers

B 10 inches per minute 50 divided by 5 equals 10

Answer: It would be B 10 inches per minute

Step-by-step explanation: Because if it is (Speed=distance/time) that would mean you would divide 50 into 5 which would be 10 50/5 5x10=50

how to solve x-3y=1 4x+5y=4 using elimination

Answers

Answer:

X=1, Y=0

Step-by-step explanation:

Solve for X and Y using a2 +b2 = c2

Write down the coordinates of point A.
( ……… , ………)
b) The line L is shown on the grid. Find the equation of line L in the form of y = mx + c.

..............................

Answers

The coordinates of point A is: (-2, 5)

The equation of line L, in slope-intercept form, is: y = 1/2x + 2

What is the Equation of a Line?

In slope-intercept form, the equation of a straight line is given as, y = mx + b, where:

b is the y-intercept, which is where the line cuts the y-axism is the slope = change in y / change in x.

The coordinates of point A is: (-2, 5)

Slope (m) of line L = 2/4 = 1/2.

y-intercept (b) = 2

The equation of line L will be:

y = 1/2x + 2.

Learn more about the equation of a line on:

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I really need help (i will give brainlist) Which function has a greater y-intercept ... f(x) or g(x)?

g(x)

f(x)

They are the same.

Answers

Answer:

they are exacly the same

Step-by-step explanation:

Round your answers to the nearest cent.
f(0) =
meaning the cost of buying
gallons of paint would be
in the context of the problem.
f(10)
, meaning the cost of buying
gallons of paint would be
in the context of the problem.
f(67.5)
meaning the cost of buying
gallons of paint would be
This interpretation
in the context of the problem.
Based on the observations above, it is clear that an appropriate domain for the
function is
=
This interpretation
=
This interpretation

Answers

The interpretations of the function values are: the cost of buying 0, 10 and 67.5 gallons of paint would be 0, 28.5 and 73.9, respectively

How to interpret the function values?

The equation of the function is given as:

f(x) = 9√x

When x = 0, 10 and 67.5, we have:

f(0) = 9√0 = 0

f(10) = 9√10 = 28.5

f(67.5) = 9√67.5 = 73.9

Hence, the interpretations of the function values are:

The cost of buying 0, 10 and 67.5 gallons of paint would be 0, 28.5 and 73.9, respectively

Answers

Need points, don’t use this

Answer is A

Write the following fraction as a decimal number. 4/3/100 4.003 4.03 4.33 4.34

Answers

Answer:

133.3 <-- goes on forever

I think the rest are in decimal form.

Jackie has a choice of 3 pairs of shoes, 3 pants, and 4 shirts that can make an outfit for today. Each pair of shoes has a different heel height, each pair of pants is made from a different fabric, and each shirt is a different color.

Jackie randomly picks some clothes.

What is the probability that she chooses an outfit consisting of the flat heel or spike heel shoes, the twill or the denim pants, and the white or black shirt?

Answers

Answer:

2/9

Step-by-step explanation:

i just took a test with this exact question, and the answer was 2/9

youre welcome future learners ;)

Suppose that F(x) = x² and G(x) = -1/3 (x+4)^2. Which statement best compares the graph of G(x) with the graph of F(x)?

Answers

Answer: C

Step-by-step explanation:

The graph is shifted 4 units left as seen with (x+4) so x = -4.

The graph is reflected over the x axis as seen with -a

The graph is compressed vertically because the functions a value is less than f(x) = [tex]x^2[/tex]

Answer:

Step-by-step explanation:

Changes observed :

Coefficient of x² becomes 1/3 of original, this means it is vertically compressedAlso, the coefficient has become negative, meaning it is flipped over the x-axisx² is now (x + 4)², this means it has shifted 4 units to the left.

The correct option is D.

What is the surface area of the rectangular prism below?

Answers

Answer:

the answer is A. 612

Step-by-step explanation:

SA=2(wl+hl+hw)

parenthesis() mean multiply

x means multiply

SA= 2 x width x length + height x length + height x width

A second boat passes by your port, at a distance of 1,500 feet from shore. 10 seconds later, the boat is 2,000 feet away from you. how fast was the boat going?

Answers

Speed is distance over time
So 2000-1500=500 (how far the boat went in the given time)
the time is 10 seconds
500/10=50ft/sec.

A quantity y varies inversely with the square of x. if y=8 when x=3, find y when x is 4.

Answers

I think 7/2 im not definate

I need help on this please

Answers

Answer:

Volume of a cone = (1/3) πr³

r = radius = d/2 = 2/2 = 1 ft

Volume = (1/3) * π * 1³

volume = 1.04 cubic ft

PLEASE HELP ME WITH THIS QUESTION!!!

Answers

9x²+3x-1=0

D=b²-4ac

= 3²-4×9×-1

=9+36

=45

x1= (-b+VD)/2a

= (-3+V45)/2×9

= (-3+3V5)/18

=(-1+V5)/6

x2=(-b-VD)/2a

=(-3-3V5)/18

=(-1-V5)/6

what is the measure of angle 7 ?

Answers

Answer:

97°

Step-by-step explanation:

Please see attached

Type the missing number in this sequence:
6, 8, 11, 15, 20,____,33

Answers

Answer: 26

Step-by-step explanation: the pattern is +2, +3, +4, +5. +6, +7

6+2 = 8

8+3 = 11

11+4 = 15

15+5 = 20

20+6 = 26

26+7 = 33

Answer:

Step-by-step explanation:

In this, the addition of numbers is starting from 2 and continue. Such as 6+2=8,then 8+3=11. Similarly the addition of numbers is continuing

Find the measure of the indicated angle to the nearest degree.

Answers

Answer:

62°

Step-by-step explanation:

We use the fact that the ratio of the sides of the triangle to the angles opposite them is given by the Law of Sines:

"In any triangle, the ratio of a side length to the sine of its opposite angle

is the same for all three sides"

[tex]\frac{a}{sinA} = \frac{b}{sinb} =\frac{c}{sinC}[/tex]

where A is the is the angle opposite side a, B the angle opposite to side b, C is the angle opposite to side c

For the given triangle we get
44/sin90 = 39/sin?

sin90 is 1 so we get 44/1 = 39/sin?

or cross-multiplying,

sin? = 39/44 = 0.886363..

? = sin⁻¹ (0.886363) = 62.42° ≈ 62° answer

Answer:

? ≈ 62°

Step-by-step explanation:

using the sine ratio in the right triangle

sin? = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{39}{44}[/tex] , then

? = [tex]sin^{-1}[/tex] ( [tex]\frac{39}{44}[/tex] ) ≈ 62° ( to the nearest degree )

Which number sentence is represented by this model?

Answers

Answer:

Correct answer is B. -3 • 5 = - 15

Carpet costs $8.30 per square foot. How much will it cost to carpet the room? Show your work.
The area is 812ft

Answers

Answer:

about 98 dollars to cover the whole room in carpet

Step-by-step explanation:

The Carpet costs $8.30 per square foot, so 812 ÷ 8.30 = 97 with remainder. Therefore 98 as a rounded total ✅

The two expressions below have the same value when rounded to the nearest hundredth. log subscript 5 baseline b. log subscript 9 baseline 48 what is the approximate value of log b to the nearest hundredth?

Answers

The approximate value of log b to the nearest hundredth is 1.23

Laws of logarithm

Given the following logarithmic expressions

loog(5)b and log(9)48

Determine the value of log(9) 48

log(9)48 = 1.762

Equate log(5) b to 1.762 to log(5)b to determine the value of b

log(5)b = 1.762

b = 5^1.762

b = 17.044

log b = log 17.044 = 1.232

Hence the approximate value of log b to the nearest hundredth is 1.23

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Answer:

B = 1.232

Step-by-step explanation:

Just did it

Four students each contribute $12 to buy a pizza, salad, and large soda. How much would each student pay if two more students also contributed?
E. $6.50
F. $6
G. $7
H. $8

Answers

Answer:

Step-by-step explanation:

4 students contribute 12$ Each.

So, total amount becomes 12 x 4 = 48$

If two more students contribute it makes a total of 6 students.
so we now divide the 48$ by 6
48/6=8$

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