A storage tank will have a circular base of radius r and a height of r . The tank can be either cylindrical or hemispherical (half a sphere).

a. Write and simplify an expression for the ratio of the volume of the hemispherical tank to its surface area (including the base). For a sphere, V=4/3πr³ and SA=4πr²

Answer:

[tex]\textsf{a)} \quad x = 63^{\circ}[/tex]

[tex]\textsf{b)} \quad \boxed{\begin{minipage}{8.5 cm}\sf The angle between the tangent and the radius at a point \\on a circle is $90^{\circ}$.\end{minipage}}[/tex]

Step-by-step explanation:

The triangle inside the circle is an isosceles triangle, since two of its sides are the radius of the the circle (and therefore equal in length).

Therefore, its two base angles are 27°.

A tangent is a straight line that touches a circle at only one point.

The tangent of a circle is always perpendicular to the radius.

[tex]\implies x + 27^{\circ} = 90^{\circ}[/tex]

[tex]\implies x +27^{\circ}-27^{\circ}= 90^{\circ} - 27^{\circ}[/tex]

[tex]\implies x = 63^{\circ}[/tex]

The circle theorem that allows the calculation of angle x is:

[tex]\boxed{\begin{minipage}{8.5 cm}\sf The angle between the tangent and the radius at a point \\on a circle is $90^{\circ}$.\end{minipage}}[/tex]

The sum of three angles of a triangle is 180° . 32° is the angle at 24 when other two angles are 85° and 63°.

The sum of three angles of a triangle is 180° .

Given two angles of a triangle are 85° and 63°. We need to find the third angle at 24.

The angle at 24 be x.

By angle sum property,sum of three angles of a triangle is 180°.

The two angles are  85° and 63° and third angle is x.

85°+63°+x=180°

148°+x=180°

x=180°-148°

x=32°

Therefore the angle at 24 is 32° when other two angles are  85° and 63°.

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A good way to find patterns in data is to arrange it in tabular form, which acts as an "input-output" machine.

A pattern in mathematics is a recurring arrangement of numbers, forms, colors, and other elements. Any kind of event or object can be connected to the Pattern.

A pattern is referred to as a rule or a way in which a group of numbers is related to one another. Sometimes a pattern is also referred to as a sequence.

Putting data into a tabular format, which functions as an "input-output" computer, is a useful way to find patterns. It will process an input value, return an output value, and take another value as an input.

The table's process column will make it easier to comprehend how input and output are related.

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The expression that represents the perimeter of the triangle in centimeters is; 73[tex]w^{2}[/tex]  +  128wx  +  128[tex]x^{2}[/tex]  +  60wy +  116[tex]y^{2}[/tex]  +  64xy

We are given the measurement of each side length of the triangle, i.e.

(8w +8x) (8w+8x)

(3w + 10y) (3w+10y)

(4y + 8x) (4y+8x)

After simplifying the measurement on each side, we get;

(8w +8x) (8w+8x)= 64[tex]w^{2}[/tex] + 128wx + 64[tex]x^{2}[/tex]

(3w + 10y) (3w+10y)= 9[tex]w^{2}[/tex] +60wy +100[tex]y^{2}[/tex]

(4y + 8x) (4y+8x)= 16[tex]y^{2}[/tex] + 64xy + 64[tex]x^{2}[/tex]

To find the perimeter of the triangle, we get the addition of all side lengths

Thus, Perimeter (P) = 64[tex]w^{2}[/tex] + 128wx + 64[tex]x^{2}[/tex]   +   9[tex]w^{2}[/tex] +60wy +100[tex]y^{2}[/tex]  +   16[tex]y^{2}[/tex] + 64xy + 64[tex]x^{2}[/tex]

                           P= 73[tex]w^{2}[/tex]  +  128wx  +  128[tex]x^{2}[/tex]  +  60wy +  116[tex]y^{2}[/tex]  +  64xy

Therefore, the perimeter of the triangle is given by;   73[tex]w^{2}[/tex] + 128wx + 128[tex]x^{2}[/tex]  + 60wy + 116[tex]y^{2}[/tex] + 64xy

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The coordinates of the midpoint of a segment with the given endpoints will be (8, 9.5).

Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).

Then the coordinate of the mid-point of the line segment is given as,

(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

The endpoints are A(13, 14) and C(3, 5).

Then the coordinates of the midpoint of a segment with the given endpoints will be

(x, y) = [(13 + 3) / 2, (14 + 5) / 2]

(x, y) = (16/2, 19/2)

(x, y) = (8, 9.5)

The coordinates of the midpoint of a segment with the given endpoints will be (8, 9.5).

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Answer:

x = 6

Step-by-step explanation:

- 12x - 17 = - 89 ( add 17 to both sides )

- 12x = - 72 ( divide both sides by - 12 )

x = [tex]\frac{-72}{-12}[/tex] = 6

Answer: g(4b)=12b+7

Step-by-step explanation:

g(x)=3x+7

g(4b)=3(4b)+7

g(4b)=12b+7

Answer:

19 , 29

Step-by-step explanation:

19 + 29 = 48

mark brainiest pls

Answer: y=-0.5x-8

Step-by-step explanation:

Choose two points on the line: (0,-8) and (-6,-5)

Hence,

x₁=0   x₂=-6   y₁=-8   y₂=-5

[tex]\displaystyle\\The\ slope=\frac{y_2-y_1}{x_2-x_1}\\\\The\ slope=\frac{-5-(-8)}{-6-0} \\\\The\ slope=\frac{-5+8}{-6} \\\\The\ slope=\frac{3}{(3)(-2)}\\\\The\ slope=\frac{1}{-2} \\\\The\ slope=-\frac{1}{2}\\\\The\ slope=-0.5[/tex]

[tex]y=kx+b\\k=the\ slope=-0.5\\(0,-8) \ hence,\\-8=-0,5*0+b\\-8=0+b\\-8=b\\Thus,\\y=-0.5x-8[/tex]

Answer:

[tex] - 8 \times |2 = - 16| [/tex]

The geometric mean between pair of numbers 7 and 11 is 8.77

We know that for a sequence of numbers x1, x2,.., xn

The formula of geometric mean is,

[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]

In this question, we have been given two numbers 7 and 11

We need to find the geometric mean between pair of numbers, 7 and 11.

Using the formula for the geometric mean,

[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]

In this question, we have two numbers.

So, the value of n is 2.

[tex]\Pi=\sqrt{7\times 11}\\\\ \Pi=\sqrt{77}\\\\ \Pi=8.77[/tex]

Therefore, the geometric mean between pair of numbers 7 and 11 is 8.77

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Answer: 125.7 degrees

Step-by-step explanation:

supplementary angles add up to 180 degrees.

angle 1 + angle 2 = 180

54.3+angle 2=180.0

54.3-54.3+angle 2=180.0-54.3

angle 2=180.0-54.3

angle 2=125.7 degrees

Answer:

5y =x-15

Step-by-step explanation:

yes

The equation of the line is y = -3x/5 + 1 that passes through (5, −2), and is perpendicular to y = (5/3)x - 3.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

It is given that:

The line passes through (5, −2) and is perpendicular to y = (5/3)x - 3

The slope of the line y = (5/3)x - 3

m = 5/3

The slope of the line perpendicular to the above line:

M = -3/5

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

The equation of the line

y + 2 = (-3/5)[x - 5]

y = -3x/5 + 1

Thus, the equation of the line is y = -3x/5 + 1 that passes through (5, −2), and is perpendicular to y = (5/3)x - 3.

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Answer:

14

Step-by-step explanation:

Adding FG and GH is the answer to the wholr line. Im 90% sure thats the right answer thats whst i learnt 7 days ago.

The measure of the vertex angle is 92°

Here,

The triangle is isosceles and one base angle of an isosceles triangle has a measure of 44°

We have to find the measure of the vertex angle.

What is Isosceles triangle?

A triangle is said to be isosceles if there is any two corresponding sides are equal and there angle are equal.

Now,

The triangle is isosceles triangle.

Hence, there corresponding sides and there angles are equal.

So, Both base angles of a triangle are equal.

And, Sum of angles of a triangle are 180°

Let the measure of the vertex angle is x°

Hence,

⇒ 44° + 44° + x° = 180°

⇒ x° = 180° - 88°

⇒ x° = 92°

Therefore, The measure of the vertex angle is 92°

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The compound inequality that describes Tammy's test score x 85 < x < 92 and Tammy's test score is between 85 and 92

The given parameters are

Sam's test score is between 100 and 107

This means that

100 < Sam's score < 107

From the question, we have:

Tammy scored about 15 fewer points.

This means that

Tammy = Sam - 15

So, we have

Sam = Tammy + 15

Where

Tammy = x

This gives

Sam = x + 15

So, we have

100 < x + 15 < 107

Subtract 15 from the sides of the inequality

So, we have

85 < x < 92

This means that the compound inequality that describes Tammy's test score x 85 < x < 92

In part (a) of this solution, we have the following compound inequality

85 < x < 92

The above compound inequality means that Tammy's test score is between 85 and 92

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The given polygons that is an equilateral triangle and scalene triangle can never be similar ,as it is not possible to map equilateral triangle onto scalene triangle or vice-versa.

As given in question,

Given polygons are equilateral triangle and scalene triangle

An equilateral triangle never similar to scalene triangle.

Reason:

Therefore, the given polygons that is equilateral triangle and scalene triangle can never be similar.

The complete question is:

Determine whether the given polygons are always, sometimes, or never similar. Explain your reasoning.

An equilateral triangle and a scalene triangle

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Answer: -7/5=-9

Step-by-step explanation:

I hope it helps

Answer: - 7/5 = -9

Step-by-step explanation: Combine like terms into single fraction, multiple by 1, subtract 3, simply.

The given series is an arithmetic series and its sum is 36.4

The summation or sigma notation is used to express long summation into a single formula.

The series, given in a summation notation, is:

     [tex]\sum\limits^{10}_{n=4} {(0.8n-0.4)}[/tex]

The formula inside the sum notation represent the nth term, a(n).

Let evaluate the terms for some n, starts from n = 4 as indicated by the lower limit of the summation notation:

a(4) = 0.8 (4) - 0.4 = 2.8

a(5) = 0.8 (5) - 0.4 = 3.6

a(6) = 0.8 (6) - 0.4 = 4.4

This form a new arithmetic series, with the first term, let say f(1) =2.8 and common difference, d = 0.8.

The number of terms in this new geometric series is given by the upper and lower limit of the summation notation:

number of terms = 10 - 4 + 1 = 7

Use the sum formula for an arithmetic series,

S(n) = n/2 [2.f(1) + (n - 1) . d]

Substitute n = 7, f(1) = 2.8, and d = 0.8 into the formula:

S(7) = 7/2 [2. (2.8) + (7 - 1) . (0.8)]

S(7) = 36.4

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If the tower is located at the origin, the equation of its circular area of coverage is [tex]x^{2} +y^{2} = 225[/tex]

A circle is a closed curve that is drawn from a fixed point. This point is called the center. All points on the curve are equidistant from this center point.

The equation of a circle with center at (h, k) and radius r is given by:

[tex](x - h)^{2} + (y-k)^{2} = r^{2}[/tex]

According to the given condition,

center is origin i.e., (h, k) is (0,0)

and r = 15.

Substituting these values in the equation above,  

[tex](x - 0)^{2} + (y-0)^{2} = 15^{2}[/tex]

[tex]x^{2} + y^{2} = 225[/tex]

Thus, the equation of the tower located at origin and having coverage area of radius 15 miles is  [tex]x^{2} + y^{2} = 225[/tex].

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The highest point of this ramp will be at 30 inches.

It is given that Wheelchair ramps have at least a 12 -inch run for each rise of 1 inch and Max length for a ramp is 30 feet.

We have to find the highest point of ramp in inches.

What will be the value of 10 feet in inches ?

As we know that 1 feet = 12 inches , the value of 10 feet in inches will be ; 10 × 12 inches or 120 inches.

As per the question ;

Wheelchair ramps have at least a 12 inch run for each rise of 1 inch.

Max length for a ramp = 30 feet

or

Max length for a ramp = 30 × 12 inches

or

Max length for a ramp = 360 inches

The highest point of this ramp will be at ;

= 360 ÷ 12

= 30 inches

Thus , the highest point of this ramp will be at 30 inches.

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The value of x when y = 4 is 0. 25

From the information given, we have that;

This is expressed as;

x ∝ 1/ y²

x = y/y²

Let's substitute the value of y as 4 into the equation;

x = 4 / 4²

Find the square

x = 4 / 16

Find the ratio

x = 1/ 4

x = 0. 25

Thus, the value of x when y = 4 is 0. 25

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For the given inequality x+13<41, x is less than 28

Inequality involves two algebraic expressions linked by the signs of inequality. These signs include less than (<), greater than (>) or less than equal to (<=) and greater than equal to (>=).

Let's solve the inequality

x+13<41

Move the like terms on the same side

x< 41-13

x< 28

Therefore, x is less than 28

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The equation of line is:

y = (5/2) x - 11

Given,

Points (x₁, y₁) = (-12, -6) and (x₂, y₂) = (8, 9)

We can find the slope using the equation for slope

m = (y₂ - y₁) / (x₂ - x₁)

   = (9 -(-6)) / (8-(-12))

   = (9+6) / (8 + 12)

    = 15/20 = 3/4

We know the slope and a point, so we can use point slope form to make an equation

y-y₁ = m(x-x₁)

y - (-6) = 3/4 (x-(-12))

Distribute

y+6 = 3/4x – 3/4 × 2

y+6 = 3/4x - 3/2

Add -6 to each side

y + 6 -6 = 3/4x - (3/2)-6

y = 3/4x - (-9/2)

y = 3/4x + 9/2

This is in slope intercept form (y= mx+b)

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Answer: 2

Step-by-step explanation: There are two solutions: 2, and -8/3. 2 is the positive solution.

Answer: Functions are relations with one output for any unique input.

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

3(x + 7) + 4 = 40 ( subtract 4 from both sides )

3(x + 7) = 36 ( divide both sides by 3 )

x + 7 = 12 ( subtract 7 from both sides )

x = 5

As a check

substitute x = 5 into the left side of the equation and if the value obtained is equal to the right side (40) then it is a solution

3(5 + 7) + 4

= 3(12) + 4

= 36 + 4

= 40

left side = right side

then x = 5 is the solution to the equation

Answer: The prime factorization of 16 is 2 × 2 × 2 × 2, hence, the cube root of 16 in its lowest radical form is expressed as 2 ∛2.

Cube Root of 16.

Step-by-step explanation:

The solution for the cube root of 16 as a power of 2 is,

⇒ ∛16 = 2 ∛2

We have to given that,

To find the cube root of 16 as a power of 2.

The prime factorization of 16 are,

16 = 2 x 2 x 2 x 2

Take cube root,

⇒ ∛16 = ∛2 x 2 x 2 x 2

⇒ ∛16 = 2 ∛2

Therefore, The solution for the cube root of 16 as a power of 2 is,

⇒ ∛16 = 2 ∛2

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Answer:

14

Step-by-step explanation:

That equation, with the given constraints, is easily solved using logical reasoning.10y is a multiple of 5, and 25 is a multiple of 5; that means 7x is a multiple of 5.And we know x is a number between 10 and 20. So x has to be 14