What is the solution to the inequality below?

x² > 81

A.

B.

C.

D.​

The question is incomplete. The complete question is :

The volume of a right circular cone with radius r and height h is V = pir^2h/3. a. Approximate the change in the volume of the cone when the radius changes from r = 5.9 to r = 6.8 and the height changes from h = 4.00 to h = 3.96.

b. Approximate the change in the volume of the cone when the radius changes from r = 6.47 to r = 6.45 and the height changes from h = 10.0 to h = 9.92.

a. The approximate change in volume is dV = _______. (Type an integer or decimal rounded to two decimal places as needed.)

b. The approximate change in volume is dV = ___________ (Type an integer or decimal rounded to two decimal places as needed.)

Solution :

Given :

The volume of the right circular cone with a radius r and height h is

[tex]$V=\frac{1}{3} \pi r^2 h$[/tex]

[tex]$dV = d\left(\frac{1}{3} \pi r^2 h\right)$[/tex]

[tex]$dV = \frac{1}{3} \pi h \times d(r^2)+\frac{1}{3} \pi r^2 dh$[/tex]

[tex]$dV = \frac{2}{3} \pi r h (dr)+\frac{1}{3} \pi r^2 dh$[/tex]

a). The radius is changed from r = 5.9 to r = 6.8 and the height is changed from h = 4 to h = 3.96

So, r = 5.9  and dr = 6.8 - 5.9 = 0.9

     h = 4  and dh = 3.96 - 4 = -0.04

Now, [tex]$dV = \frac{2}{3} \pi r h (dr)+\frac{1}{3} \pi r^2 dh$[/tex]

[tex]$dV = \frac{2}{3} \pi (5.9)(4)(0.9)+\frac{1}{3} \pi (5.9)^2 (-0.04)$[/tex]

[tex]$dV=44.484951 - 1.458117$[/tex]

[tex]$dV=43.03$[/tex]

Therefore, the approximate change in volume is dV = 43.03 cubic units.

b).  The radius is changed from r = 6.47 to r = 6.45 and the height is changed from h = 10 to h = 9.92

So, r = 6.47  and dr = 6.45 - 6.47 = -0.02

     h = 10  and dh = 9.92 - 10 = -0.08

Now, [tex]$dV = \frac{2}{3} \pi r h (dr)+\frac{1}{3} \pi r^2 dh$[/tex]

[tex]$dV = \frac{2}{3} \pi (6.47)(10)(-0.02)+\frac{1}{3} \pi (6.47)^2 (-0.08)$[/tex]

[tex]$dV=-2.710147-3.506930$[/tex]

[tex]$dV= -6.22$[/tex]

Hence, the approximate change in volume is dV = -6.22 cubic units

Answer:

45.3 miles/h

Step-by-step explanation:

let 'x' be the speed of the car.

60 × 2/3 = 120/3 = 40  

30 × 1/5 = 151/5  

151/5 /40 = x / 60  

151 / 200 = x / 60

=> x = (151×60) / 200

=> x = 45.3

(hope this helps can i plz have brainlist :D hehe)

Answer:

220/221

Step-by-step explanation:

cos math

Answer:

60.5m^2

Step-by-step explanation:

the area of the square

=11m×11m

=121m^2

the area of triangle

=11m×11m÷2

=121m^2÷2

=60.5m^2

the area of the shaded region

=121m^2-60.5m^2

=60.5m^2

the answer is not very sure,

if it is wrong, i am sorry for it.

The area of the garden be  after he doubles the length and width is 160 square feet.

Given that,

Based on the above information, the calculation is as follows:

We know that

Area = (length) (width)

Now if the area is doubled

So,

= (2) (length)  (2) (width)

= 4(length) (width)

= 4 (40)

= 160

Therefore, we can conclude that option b is correct.

Learn more: brainly.com/question/24169758

Step-by-step explanation:

sorry po hindi ko po alam sagot

You need to find the area of the hexagon, and the area of the triangle.

The formula for the area of a triangle is

[tex]a = \frac{bh}{2} [/tex]

I hope this helps you a little.

Answer:

93.5 units^2

Step-by-step explanation:

a^2+b^2=c^2

a=3

b=?

c=6

b=√6^2-3^2

b=3√3=5.196

5.196×3=15.5884

15.5884×6

Answer:

17.25

Step-by-step explanation:

Answer:

230.56%

Step-by-step explanation:

maybe

Answer:

No lol that seems very confusing but was it 26.6?

Answer:  26.6

Step-by-step explanation:

7 times 1/5= 7/5

7/5 times 19= 26.6

I hope ti helps and may God bless you! have a nice day, bye!

Answer:

37.3 ft

Step-by-step explanation:

x/56 = 32/48

cross multiply:

56x32 = 1792

48x

1792/48 = 37.3

Answer:

D

Step-by-step explanation:

first multiply both sides by 12

collect like terms

x/12×12+3×12<=7×12

x+36<=84

x<=84-36

x<=48

Answer:

Design and implement a plan that collects data.

Step-by-step explanation:

Answer:

Design and implement a plan that collects data.

Step-by-step explanation:

Looking at the answer choices, we can use the process of elimination:

1) Form a question that can be answered by data.

2) Design and implement a plan that collects data.

3) Analyze the data using graphical and numerical methods.

4) Interpret and compare the data.

1) The question is most likely already formed, as a survey cannot be conducted without a question or objective. Not 1.

2) A survey collects data.

3) This happens after the collection of data, or the survey. Not 3.

4) This also happens after the collection of data, or the survey. Not 4.

Answer:

the length of the opposite side (x), is 27.2

Step-by-step explanation:

For the given right triangle problem;

the opposite side of the given angle, opp. = 22

the hypothenuse side,  hypo. = x

given angle of the triangle, θ = 54⁰

The length of the opposite side (x), is calculated as follows;

[tex]sin \ \theta = \frac{opp.}{hypo.} \\\\sin (54) = \frac{22}{x} \\\\x = \frac{22}{sin(54)} \\\\x = 27.2[/tex]

Therefore, the length of the opposite side (x), is 27.2

Answer:

cash price:

10% = 250

2500 - 250 = $2,250

hire purchase:

2500 + 500 + 150(18) = $5,700

a) 5,700 - 2,250 = $3,450

Answer:

[tex]Median= 20[/tex]

Step-by-step explanation:

Given

The attached box plot

Required

The median

The median is represented by the vertical line inside the rectangle on the box plot.

Using the description above to read the median from the given box plot.

[tex]Median = 20[/tex]

It is also the same as the second quartile

Answer:

sin(75°) = [tex]\frac{\sqrt{2}+\sqrt{6} }{4}[/tex]

Step-by-step explanation:

Given: sin(75°)

Rewrite: sin(30° + 45°)

Use sum and difference identity:

sin(α + β) = sinαcosβ + cosαsinβ

sin(30°+45°) = sin(30°)cos(45°) + cos(30°)sin(45°)

sin(30°+45°) = (1/2)(√2 / 2) + (√3 / 2)(√2 / 2)

sin(30°+45°) = (√2 / 4) + (√6 / 4)

sin(30°+45°) = [(√2 + √6) / 4]

sin(75°) = [(√2 + √6) / 4]

Answer:

=0.1428571428751

I hope it's helps you

Answer:

C) 14/4

Step-by-step explanation:

Multiply the amount of land per month by the number of months.

(2/4)(7) = 14/4 acres

Option C is correct, 14/4  acres of land does the business plant with trees after the 7 months

A fraction represents a part of a whole.

A business plants trees on 2/4 acre of land each month for 7 months.

We have to find the number of acres of land does the business plant with trees after the 7 months

To find this we have to multiply seven with two by four

7×2/4

14/4

Hence, 14/4  acres of land does the business plant with trees after the 7 months

To learn more on Fractions click:

https://brainly.com/question/10354322

#SPJ2

Answer:

Gradient = 2

Step-by-step explanation:

Gradient of a line = Slope of the line

Since, slope of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,

Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Given line in the graph passes through two points (1, 0) and (2, 2)

Therefore, slope or gradient of the line = [tex]\frac{2-0}{2-1}[/tex]

                                                                  = 2

Gradient = 2 will be the answer.

Answer:

opposite = 5√2

adjacent 5√2

Step-by-step explanation:

the opposite leg can be determined using

Sin = opposite / hypotenuse

√2 / 2= opposite / 10

opposite = 5√2

the adjacent leg can be determined using

cos = adjacent / hypotenuse

√2 / 2= adjacent / 10

adjacent = 5√2

Answer:

I thing they both are........

well when thinking of gravity you have to think of the size and mass of the object so,

The sun (largest and most mass)

Earth

Earth's moon

Discover satellite (cause it's tiny and light compared to the sun!)

Answer:

6

Step-by-step explanation:

Factorize of the above numbers :

30 = 2 • 3 • 5

66 = 2 • 3 • 11

84 = 22 • 3 • 7

Build a prime factors table

Number of times each prime factor

appears in the factorization of :

Prime

Factor Number

30 Number

66 Number

84 G.C.F

(min)

2 1 1 2 1

3 1 1 1 1

5 1 0 0 0

7 0 0 1 0

11 0 1 0 0

GCF = 2 • 3

Greatest Common Factor is :

6

Answer:

Move the corners of the triangle up the axis by two blocks.

A = (-7,-3)

B = (-2,6)

C=  (6,-3)

Answer:

isn't it just 4?

Step-by-step explanation:

according to the table it's just asking you to name what is with x of f(x). I might be wrong though

Answer:

When two lines are crossed by another line (called the Transversal): Alternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.