What is the surface area of the cone? Express your answer in terms of π.b

Answer:

Step-by-step explanation:

3ft x 5 ft x 6 ft

15 x 6 = 90 cubic feet

Step-by-step explanation:

To get the volume, you have to do LxWxH so its 3x5x6=90

so its 90 cubic feet.

The slope of a mountain road with a 10-foot rise for a 494-foot run is found by dividing the rise by the run, resulting in a slope of approximately 0.0202 or 1/49.4, which is a dimensionless ratio.

The student's question involves finding the slope of a mountain road, which is a concept in mathematics. Slope is calculated as 'rise over run', where the 'rise' refers to the change in height and the 'run' refers to the horizontal distance covered. In this instance, the rise is 10 feet and the run is 494 feet.

To calculate the slope of the mountain road, you divide the rise by the run:

Slope = Rise ÷ Run

We substitute the given values:

Slope = 10 ft ÷ 494 ft

The slope is therefore equal to approximately 0.0202 or 1/49.4. In mathematics, slope is dimensionless; it is just the ratio of the rise to the run and does not carry any units.

Answer:

Drink=5.75

Popcorn=1.83

Percentage for drink=75.9%

Step-by-step explanation

Let the popcorn be p

the drinks be d

6p+4d=34....(1)

12p+7d=66.25...(2)

Multiply (1) by 2

12p+8d=72....(3)

Substrate (2) from (3)

d=5.75

Substitute the value for d into (1)

6p+4(5.75)=34

6p+23=34

Substrate 23 from both sides

6p=11

Divide both sides by 6

p=1.83

So for one drink=$5.75

For one popcorn=$1.83

To determine the% for drink

5.75+1.83=7.58

5.75/7.58 ×100

575/7.58

75.858~75.9%

The percentage for drink is 75.9%

Answer:

opposite side = 8.27cm

adjacent = 12.5cm

Step-by-step explanation:

to work out the other side of the triangle

give the angle = 32

using SOH CAH TOA

sineФ = opposite/ hypoteneus

sin32° = opposite/ 15cm

using cross multiplication

opposite side = sine32 x 15cm

opposite side = 0.551 x 15cm

opposite side = 8.27cm

to find the other side of the triangle using pythagoras theorem

hypotheneus ² = opposite² + adjacent²

15² = 8.27² + adjacent ²

collect the like terms

15² - 8.27² = adjacent ²

225  - 68.42 = adjacent²

156.58 = adjacent²

squaring both sides

adjacent = √ 156.58

adjacent = 12.5cm

Slope-intercept form:  y = mx + b

(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)

For lines to be perpendicular, their slopes have to be the negative reciprocal of each other. (Basically flip the sign +/- and the fraction(switch the numerator and the denominator))

For example:

Slope = 2 or [tex]\frac{2}{1}[/tex]

Perpendicular line's slope = [tex]-\frac{1}{2}[/tex]   (flip the sign from + to -, and flip the fraction)

Slope = [tex]-\frac{3}{4}[/tex]

Perpendicular line's slope = [tex]\frac{4}{3}[/tex]  (flip the sign from - to +, and flip the fraction)

y = 1/3x + 4        The slope is 1/3, so the perpendicular line's slope is [tex]-\frac{3}{1}[/tex] or -3.

Now that you know the slope, substitute/plug it into the equation:

y = mx + b

y = -3x + b       To find b, plug in the point (1, 2) into the equation, then isolate/get the variable "b" by itself

2= -3(1) + b     Add 3 on both sides to get "b" by itself

2 + 3 = -3 + 3 + b

5 = b

y = -3x + 5

The equation of the line that passes through (1,2) and is perpendicular to the line (y = 1/3x + 4) is (y = -3x + 5) and this can be determined by using the given data.

Given :

The line that passes through (1,2) and is perpendicular to the line (y = 1/3x + 4).

The following steps can be used in order to determine the equation of the line:

Step 1 - When two lines are perpendicular to each other then their slopes are:

mm' = 1

where m and m' are the slopes of the lines.

Step 2 - So, the slope of the line which is perpendicular to the line (y = 1/3x + 4) is:

[tex]\rm \dfrac{1}{3}\times m' = -1[/tex]

m' = -3

Step 3 - Now, the equation of a line that passes through the point (1,2) and has a slope -3 is:

[tex]\rm (y -2) = -3(x-1)[/tex]

Step 4 - Simplify the above equation.

y = -3x + 5

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The radius of the oblique cone is; B: 3 units

Formula for the volume of an oblique cone is;

V = ¹/₃πr²h

where;

V is volume

r is radius

h is height

We are told that diameter is equal to the height. Thus;

diameter = 2r = h

Thus;

V = ¹/₃πr²(2r)

18π = ¹/₃πr²(2r)

r = ∛(18π * 3/2π)

r = 3 units

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The radius of the cone is approximately 3 units.

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

The volume of a cone is 1/3πr²h.

We have,

We know that the height of the cone is equal to the diameter of the base, which means h = 2r.

Substituting this into the formula for the volume, we get:

V = (1/3) x π x r² x (2r) = (2/3) x π x r³

We are given that the volume of the cone is 187 cubic units, so we can set up an equation:

(2/3) x π x r³  = 187

Multiplying both sides by 3/2π, we get:

r³ = (187 x 3)/(2π)

Taking the cube root of both sides, we get:

r = (187 x 3/(2π))^(1/3) ≈ 3.00

Therefore,

The radius of the cone is approximately 3 units.

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A term in a math expression is single number or variable and are separated by a + or - or × or ÷

This expression has 4 terms

2r

1c

.5d

and 8

This expression has 4 terms 2r, 1c, 0.5d, and 8.

One mathematical expression makes up a term. It could be a single variable (a letter), a single number (positive or negative), or the number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.

Given an expression 2r+c+0.5d+8 to find the term of the given expression

A term in a math expression is a single number or variable and is separated by a + or - or × or ÷

thus this equation has four terms

that is:

2r

1c

0.5d

and 8

therefore, Given expression 2r+c+0.5d+8 has 4 terms 2r, 1c, 0.5d, and 8.

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Answer:

a parabola is a curve often resembling a U and follows a mathematical equation

Step-by-step explanation:

for example:

Answer:

In mathematics, a parabola is a plane curve

Step-by-step explanation:

Answer:

B-$ 16.89

Step-by-step explanation:

Answer:

C. 2(2x + 3)(2x - 3)

Step-by-step explanation:

[tex]8 {x}^{2} - 18 \\ = 2 \times 4 {x}^{2} - 2 \times 9 \\ = 2(4 {x}^{2} - 9) \\ = 2 \{( {2x})^{2} - ( {3)}^{2} \} \\ = 2(2x + 3)(2x - 3) \\ [/tex]

Final answer:

The expression 8x² - 18 is factored by first taking out the common factor of 2, and then applying the difference of squares formula to get the fully factored form, 2(2x + 3)(2x - 3). Option C is accurate.

Explanation:

To factor the expression 8x² - 18, we need to first take out the common factor. Here, we can see that both terms are multiples of 2. Thus, we can factor out a 2, which gives us:

2(4x² - 9)

Now, we recognize that the expression inside the parentheses is a difference of squares because 4x² is (2x)² and 9 is 32. A difference of squares can be factored into:

(a² - b²) = (a + b)(a - b)

Applying this to our expression, we get:

2((2x) + 3)((2x) - 3)

Hence, the fully factored form of the expression 8x² - 18 is:

2(2x + 3)(2x - 3) (Option C)

Answer:

The recipe makes 1/2 cup of salad dressing assuming that the salt and herbs do not make a difference.  Each serving has 1/12 of a cup.  I am not gifted in the number sentence and equation department

Step-by-step explanation:

1/3=2/6

         +

1/6=1/6

--------------

3/6=1/2

The recipe will make 1/2 cup of salad dressing. Each serving would have 1/12 cup of dressing.

To find out how many cups of salad dressing the recipe will make, we can add the quantities of olive oil and balsamic vinegar. We have 1/3 cup of olive oil and 1/6 cup of balsamic vinegar, so the total is 1/3 + 1/6 = 1/2 cup. Therefore, the recipe will make 1/2 cup of salad dressing.

To determine how much dressing there would be in one serving, we divide the total quantity of dressing (1/2 cup) by the number of servings (6). This can be represented as the number sentence: 1/2 ÷ 6 = 1/12 cup per serving.

Answer:

80°

Step-by-step explanation:

Just multiply 40° by 2 to get the arc

Answer:

80

Step-by-step explanation:

An arc's measurement is always twice the amount of its angle.

40 x 2 = 80

Answer:

1077

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

IQR is the distance between the ends of the box. The ends of the box are 15 and 21, so the IQR is 21-15, which is 6.

Answer:

B.

Step-by-step explanation:

Sorry I am late. Here's the answer for everybody else. :)

To convert 2 and 5/6 to a percent, convert the fraction to a decimal and add it to the whole number. Then multiply by 100 to find the percentage (approximately 283.3%).

In mathematics, to convert a mixed number like 25/6 to a percentage, you can first convert it to a decimal and then multiply by 100. The fraction can be converted into decimal by dividing the numerator by the denominator. In this case, 5 divided by 6 is approximately 0.8333. Since we have 2 whole and 0.8333, we can add them to get approximately 2.8333. By multiplying this by 100, we get 283.33% which we can take as an approximate value of 283.3% because it's the closest listed option in the question.

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Answer:

both are one

Answer:

det = 1 and det = 1

Step-by-step explanation:

just took the lesson on ed-genuity, these are both right :)

Answer:

36250

1450/ 1/25= 36250

72500

1450/ 1/50

Answer:

7root2/2

Step-by-step explanation:

You can solve this by multiplying by a version of 1 which will simplify but not change the expression. If you multiply this by root2/root2, you will have 7root2 in the numerator and 2 in the denominator, which is simplified. Hope this helps!

Answer:

14

Step-by-step explanation:

You fins the measure of angle C, and get 180-(118+22) = 40 degrees

You use law of sines, and get:

24/(sin40) = AC/(sin22)

Multiply both sides by sin(22)

24sin(22)/sin(40)=AC

Plug into a calculator, and get: 13.9868256738, which rounds to 14

Answer: m = 7 and b = 0

Step-by-step explanation:

y = mx + b is slope-intercept form

m = slope

b = y-intercept

You would put +0 on the end of the equation because it doesn't change anything

Let's make a table of differences

0 3 8 15 24

3  5 7  9

 2  2  2

Constant second difference means a quadratic polynomial,

f(n)=an² + bn +c

f(1)=0, f(2)=3, f(3)=8

0 = a+b+c

3 = 4a + 2b + c

8 = 9a + 3b + c

Subtracting pairs

3 = 3a+b

5 = 5a + b

Subtracting,

2 = 2a

a = 1

b = 5 - 5a = 0

c = -a-b = -1

f(n)=n² -1

Duh, shoulda noticed that at the beginning.

f(17)=17²-1 = 288

a₁ =5

aₙ = aₙ₋₁ - 7

aₙ = a₁ + d(n-1)

aₙ = 5 - 7(n-1)

a₇ = 5 - 7(6) = -37

Answer: -37

The length of line segment LN is 6 units.

To determine the length of line segment LN, we can use the segment addition postulate, which states that if you have three collinear points A, B, and C, and point B is between A and C, then AB + BC = AC.

In this case, point M is between L and N. We're given that MN = 2 and LM = 4. So, we can set up the equation:

LM + MN = LN

Substitute the given values:

4 + 2 = LN

Now, calculate the sum:

6 = LN

So, the length of line segment LN is 6 units.

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Answer:

4.5 ft³

Step-by-step explanation:

Volume = base area × height

For base area, find one angle using cosine law

18 inch = 18/12 = 1.5ft

1.5² = 2.5² + 2² - 2(2)(2.5)cos(theta)

cos(theta) = 0.8

sin(theta) = sqrt(1 - 0.8²)

sin(theta) = 0.6

Base area:

½ × 2 × 2.5 × 0.6

1.5

Volume = 1.5 × 3

= 4.5 ft³

Answer:

Step-by-step explanation:

18 inches = 18 × (1/2) ft

                = 1.5 ft

since, this is a right triangle according to the given figure then:

the area of the base (triangle) = 2 × 1.5 = 3 ft²

therefore

the volume = 1.5 × 3

                   = 4.5 ft³

Answer:

2.95 is bigger

Step-by-step explanation:

Always remember that each place after the integer in a decimal spot ends are all 0's.

This helps when we are comparing decimals.

In that case we really have:

2.9500 and 2.9490

Since 9500 is bigger than 9490, we can see that the one's digits are the same.

Since they are, 2.95 is the bigger number.

Step-by-step explanation:

Use Desmos

Answer:

See explanation

Step-by-step explanation:

You question is missing some necessary information.

However these are the mappings for the following transformation.

Rotate 180° counterclockwise about the origin. The mapping is

[tex](x,y)\to(-x,-y)[/tex]

Reflect across the line y=x.

The mapping is

[tex](x,y)\to(y,x)[/tex]

Reflect across the line y=-x

The mapping is:

[tex](x,y)\to(-y,-x)[/tex]

Rotate 270° counterclockwise about the origin. The mapping is

[tex](x,y)\to(-y,x)[/tex]

Hope this is helpful.

Please try post complete questions to get the exact answer you are looking for .

Answer:

reflect across the line y = –x (C)

Step-by-step explanation:

If you multiply the point 1,4 by the matrix you get -4, -1

it cant be 180 since that would make it -1,-4 not -4,-1.

y=x would mean its positive making it 4,1

y=-x would mean atleast -x is present and if you use other values it swaps x and y

270 would be x,-y

Answer:

Step-by-step explanation:11580

Answer:

11580 notebooks

Step-by-step explanation:

3860/4=965 notebooks per day

965x12=11580 notebooks in 12 days

Answer:

the answer is -1/3

Step-by-step explanation:

here is your step by step solution

Answer:

[tex]- \frac{1}{3} [/tex]

Step-by-step explanation:

The product of the gradients of perpendicular lines is -1.

Let the slope of the line perpendicular to line C be x.

(slope of Line C)(x)= -1

x= -1 ÷ (slope of Line C)

Let's find the slope of line C using the gradient formula.

[tex]gradient = \frac{y1 - y2}{x1 - x2} [/tex]

Gradient of Line C

[tex] = \frac{ - 6 - ( - 12)}{ - 3 - ( - 1)} \\ = \frac{ - 6 + 12}{ - 3 + 1} \\ = \frac{-6}{ - 2} \\ = 3[/tex]

Thus substituting gradient of Line C= 3,

x= -1÷ (3)

x= [tex]- \frac{1}{3} [/tex]