Four times a number is greater than 48. What are the possible values for the
number?

Answer:

Hence, the Area is [tex]\frac{24}{5} \;\text {and the Volume of the bounded region is } \frac{24\pi}{5}[/tex]

Step-by-step explanation:

Concept :

Area of the region bounded by two curve :

[tex]\int_a^b(R^2-r^2)dx[/tex]

volume of the solid generated by revolving the region about the x-axis is :

 [tex]\int_a^b\pi(R^2-r^2)dx[/tex]   where [tex]R[/tex] is long radius of bounded region from x-axis and [tex]r[/tex] is short radius of bounded region from x-axis.

Given :

[tex]y=6x[/tex] and [tex]y=6x^2[/tex]

To find :

Area of the region bounded by [tex]y=6x[/tex] and [tex]y=6x^2[/tex] and volume of the solid generated by revolving the region about the x-axis.

Explanation :

[tex]\because y=6x\;\text{and}\;y=6x^2[/tex]

[tex]\therefore 6x=6x^2\\\Rightarrow x=1[/tex]

Area of the region bounded by [tex]y=6x[/tex] and [tex]y=6x^2[/tex] is :

     [tex]\int_a^b(R^2-r^2)dx=\int_0^1((6x)^2-(6x^2)^2)dx\\[/tex]

[tex]\Rightarrow \int_0^1((6x)^2-(6x^2)^2)dx=\int_0^1(36x^2-36x^4)dx\\\Rightarrow \int_0^1((6x)^2-(6x^2)^2)dx=36\int_0^1(x^2-x^4)dx\\\Rightarrow \int_0^1((6x)^2-(6x^2)^2)dx=36\left(\frac{x^3}{3}-\frac{x^5}{5}\right)_0^1\\\Rightarrow \int_0^1((6x)^2-(6x^2)^2)dx=36\left(\frac{1}{3}-\frac{1}{5}\right)\\\Rightarrow \int_0^1((6x)^2-(6x^2)^2)dx=36\times\frac{2}{15}\\\Rightarrow \int_0^1((6x)^2-(6x^2)^2)dx=\frac{24}{5}[/tex]

Volume of the solid generated by revolving the region about the x-axis.

      [tex]\int_0^1\pi((6x)^2-(6x^2)^2)dx=\int_0^1\pi(36x^2-36x^4)dx[/tex]

[tex]\Rightarrow \int_0^1\pi((6x)^2-(6x^2)^2)dx=36\pi\int_0^1(x^2-x^4)dx\\\Rightarrow \int_0^1\pi((6x)^2-(6x^2)^2)dx=36\pi\left(\frac{x^3}{3}-\frac{x^5}{5}\right)_0^1\\\Rightarrow \int_0^1\pi((6x)^2-(6x^2)^2)dx=36\pi\left(\frac{1}{3}-\frac{1}{5}\right)\\\Rightarrow \int_0^1\pi((6x)^2-(6x^2)^2)dx=36\pi\times\frac{2}{15}\\\Rightarrow \int_0^1\pi((6x)^2-(6x^2)^2)dx=\frac{24\pi}{5}[/tex]  

Answer:

106°

Step-by-step explanation:

isosceles triangle has two sides equal meaning two sides measure 37 so

37+37=74

180-74=106

(total measurement of a triangle is 180)

Answer:

(46,56)

Step-by-step explanation:

Answer and Step-by-step explanation:

Assuming the room is a type of rectangle, we need to divide the area by the width to get the length.

So, do 400 divided by 20 to get the length, as length times width equals the area.

400 divided by 20 = 20.

The length of the room is 20 ft. (meaning the room is a perfect square.

#teamtrees #PAW (Plant And Water)

Answer:

where is the question?

Step-by-step explanation:

the picture is all black.

Answer:

4840 yards squared!

Answer:

1

Step-by-step explanation:

C is the point on the ground where the person is standing and which is making the angle of elevation of 60° AB (Height) = ? Example 2 :Height of tree is 8.65m, the angle of elevation of the top of tree is 60° find the distance at which the person is standing away from tree ? Solution : Let AB is the tree. B is the foot and A is the top of tree.

2 ft above

Now

Angle be x

Apply Pythagorean theorem

[tex]\\ \rm\Rrightarrow tanx=\dfrac{10}{400}[/tex]

[tex]\\ \rm\Rrightarrow tanX=\dfrac{1}{40}[/tex]

[tex]\\ \rm\Rrightarrow tanX= 0.025[/tex]

[tex]\\ \rm\Rrightarrow X=tan^{-1}(0.025)[/tex]

[tex]\\ \rm\Rrightarrow X=1.432°[/tex]

Answer:

Step-by-step explanation:So for this question, you need to find side KI and you can find it with the pythagorean theorem

[tex]5^2+\sqrt{21}^2 = c^2[/tex]

25+21=c^2

46=c^2

c=sqrt46

c=6.78

sin(opposite/hypotnuse)

sin(sqrt21/ sqrt46) =.0117

Answer:

The correct options are:

Option b) (1, 3 + 1/2)

Option d) (2,3)

Step-by-step explanation:

Suppose that we have a function:

y = f(x)

A ordered pair (a, b) satisfies this function if:

b = f(a).

In this case, the function is:

y = -(1/2)*x + 4

Let's try with each one of the options:

a) (-1, 3 + 1/2)

Replacing these values we get:

3 + 1/2 = -(1/2)*-1 + 4

3 + 1/2 = 1/2 + 4

3 + 1/2 = 4 + 1/2

This is false, then the point (-1, 3 + 1/2) does not satisfy the function.

b) (1, 3 + 1/2)

Replacing these values we get:

3 + 1/2 = -(1/2)*1 + 4

3 + 1/2 = 4 - 1/2 = (3 + 1) - 1/2 = 3 + (1 - 1/2) = 3 + 1/2

3 + 1/2 = 3 + 1/2

This ordered pair satisfies the function.

c) (2&1/2, 3)

Replacing these values we get:

3 = (-1/2)*(2 + 1/2) + 4

3 = -(1/2)*2 - (1/2)*(1/2) + 4

3 = -1 - 1/4 + 4

3 = 3 - 1/4

This is false, then the point (2 + 1/2, 3) does not satisfy the function.

d) (2, 3)

Replacing these values in the function we get:

3 = -(1/2)*2 + 4

3 = - 1 + 4

3 = 3

This is true, then (2, 3) satisfies the function.

Answer:

2x18=36

im not sure if that's what you meant but i can answer again if you want

Step-by-step explanation:

Answer:

sin ( 330 )

 csc  ( 60 )

cos  ( 390 )

Step-by-step explanation:

Answer:

x = 19

Step-by-step explanation:

123°+3x = 180°

3x = 180°-123°

3x = 57

x = 57/3

x = 19

The reason why we use 123° + 3x = 180° because both are adjacent angles. Adjacent angles add up to 180°

Answer:

50

Step-by-step explanation:

10% of 100 is 10 so times it by 5

Answer:

The line equation is x=3 because the line covers all of the possible y values within the coordinate x=3.

Answer:

5 is D

6 is C

Step-by-step explanation:

Define:

Equilateral - All sides and angles are congruent

Isosceles: Two congruent sides and two congruent angles

Scalene: No congruent sides or angles

Right triangle: A triangle with a right angle ( note that a right angle has a measure of 90 degrees )

obtuse triangle: A triangle with an obtuse angle ( obtuse angles have a measure of more than 90 degrees. )

Acute triangle : A triangle with an acute angle ( an acute angle has a measure of less than 90 degrees )

Answer:

the triangle shown in # 5 has a right angle and 2 congruent sides and angles

Therefore the triangle in #5 is a right isosceles

The triangle shown in #6 has an angle with a measure that is more than 90 degrees and have no congruent sides or angles therefore the triangle in #6 is an obtuse scalene.

Answer:

87.2%

Step-by-step explanation:

move the decimal point 2 places to the right

Answer:

C.0

Step-by-step explanation:

THINK PEMDAS

1*6 multiply first. 1*6 is 6

2*-3 is -6

then when you add them, they cancel out

6-6=0

Answer:

A. 846 cm²

Step-by-step explanation:

1539 ÷ 19 = 81

√81 = 9

9 · 9 · 81 = 1539

A = 2(wl + hl + hw)

A = 2(19 · 9 + 9 · 9 + 9 · 19)

846 cm²

Answer:

7.57363849

Step-by-step explanation: square root of 57.36 = 7.57363849

Answer:

1434/25 is 57.36 the square root of 57.36 is 7.57

Answer:

Step-by-step explanation:

TAX CALCULATION: 260 x .06 = $15.6

Next, add the tax to the original price.

260 + 15.6 = $275.6

$275.6 is the final price including tax.

Answer:

D.

Step-by-step explanation:

Answer:

Step-by-step explanation:

D

[tex]adjacnt {}^{2} = opposite {}^{2} + hypotenuse {}^{2} \\ adjacent {}^{2} = 8 {}^{2} + 12 {}^{2} \\ adj {}^{2} = 64 + 144 \\ adj {}^{2} = 208 \\ adjacent = \sqrt{208} \\ adjacent = 4 \sqrt{13} [/tex]

Answer:

let the length of GE be x,

[tex] \frac{9}{3} = \frac{x}{2} [/tex]

being similar triangle.

9×2=x×3

18 = 3x

x = 18/3

x = 6 cm

Answer:

16 will be your answer

Step-by-step explanation:

hope it helps..

Thanks again for the points bro!!

Answer:

This length is greater than the 12 cm side of the rectangle, so it confirms our initial guess, the longest line segment is 12.89 cm long.

Answer:

24 muffins

240 muffins

2 boxes

Step-by-step explanation:

here is the complete question

Amy is baking muffins. Each baking tray can hold 6 muffins.

a. If Amy bakes 4 trays of muffins, how many muffins will she have in all?

b. The corner bakery produced 10 times as many muffins as Amy baked. How many muffins did the bakery produce?

If the Corner Bakery packages the muffins in the boxes of a 100 how many boxes of a 100 could they make

Number of muffins Amy has = number of trays x capacity of each tray

6 x 4 = 24 muffins

b. Muffins the bakery produces = 10 x 24 = 240 muffins

c. Number of boxes = 240 / 100 = 2. 4

that is 2 boxes of 100