Simplify the expression 2.5(8.7 + 4.6 )

What is the volume of a right circular cone that has a height of 11.7meters and a base with a circumference of 9 meters? Round t

nekit [7.7K]

Answer:

25.1 cubic meters

Step-by-step explanation:

The volume is given by ...

V = (1/3)Bh

where B is the area of the base.

B = πr² = π(C/(2π))² = C²/(4π)

Then the volume is ...

V = (1/3)(C²/(4π))h = C²h/(12π)

V = (9 m)²(11.7 m)/(12·3.14159) ≈ 25.1 m³

The volume of the cone is about 25.1 cubic meters.

7 0

2 years ago

A hook in an office storage closet can hold no more than 6 pounds. An order of jumbo paperclips weighs 2 pounds and an order of

Kruka [31]

Answer:

It would be A, or the first graph

Step-by-step explanation:

So we’ve now created an equation

2x + 3y ≤ 6

From here, we can convert this into something easier to read

y ≤ -2/3x + 2

Now, we know that the y-intercept is 2 so either A or B

We also know the shaded area should be below the line (because the smallest part of the “≤” is facing the y).

Therefore, the answer is A

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2 years ago

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The base of an aquarium with given volume V is made of slate and the sides are made of glass. If the slate costs seven times as

lubasha [3.4K]

Answer:

$l = \sqrt[3]{\frac{2V}{7}}$ $b = \sqrt[3]{\frac{2V}{7}}$ $h = \sqrt[3]{\frac{49V}{4}}$

Step-by-step explanation:

Represent the volume of the box with V and the dimensions with l, b and h.

The volume (V) is:

$V = l * b * h$

Make h the subject of the formula

$h = \frac{V}{lb}$

The surface area (S) of the aquarium is:

$S = lb + 2(lh + bh)$

Where lb represents the area of the base (i.e. slate):

The cost (C) of the surface area is:

$C = 7 * lb + 1 * 2(lh + bh)$

$C = 7lb + 2(lh + bh)$

$C = 7lb + 2h(l + b)$

Substitute $\frac{V}{lb}$ for h in the above equation

$C = 7lb + 2*\frac{V}{lb}(l + b)$

$C = 7lb + \frac{2V}{lb}(l + b)$

$C = 7lb + \frac{2V}{b} + \frac{2V}{l}$

Differentiate with respect to l and with respect to b

$C_l=7b - \frac{2V}{l^2}$ $=0$

$C_b=7l - \frac{2V}{b^2}$ $=0$

To solve for b and l, we equate both equations and set l to b (to minimize the cost)

$7b - \frac{2V}{l^2}=7l - \frac{2V}{b^2}$

$7l - \frac{2V}{l^2}=7b - \frac{2V}{b^2}$

By comparison:

$l =b$

$C_l=7b - \frac{2V}{l^2}$ $=0$ becomes

$7l - \frac{2V}{l^2}=0$

$7l = \frac{2V}{l^2}$

Cross Multiply

$7l^3 = 2V$

Solve for l

$l^3 = \frac{2V}{7}$

$l = \sqrt[3]{\frac{2V}{7}}$

Recall that: $l =b$

$b = \sqrt[3]{\frac{2V}{7}}$

Also recall that:

$h = \frac{V}{lb}$

$h = \frac{V}{\sqrt[3]{\frac{2V}{7}}*\sqrt[3]{\frac{2V}{7}}}$

$h = \frac{V}{\sqrt[3]{\frac{4V^2}{49}}}$

Apply law of indices

$h = \sqrt[3]{\frac{49V^3}{4V^2}}$

$h = \sqrt[3]{\frac{49V}{4}}$

The dimension that minimizes the cost of material of the aquarium is:

$l = \sqrt[3]{\frac{2V}{7}}$ $b = \sqrt[3]{\frac{2V}{7}}$ $h = \sqrt[3]{\frac{49V}{4}}$

8 0

2 years ago

In triangle FGH, FG = 12.3 cm, GH = 10.6 cm, Measure of angle G = 80 degrees, and Measure of angle H = 55 degrees. If Triangle A

aalyn [17]

Question:

In triangle FGH, FG = 12.3 cm, GH = 10.6 cm, m angle G=80 degrees, and m angle H=55 degrees. If triangle ABC GHF, which statement is true?

(A) AB = 12.3 cm

(B) AB = 10.6 cm

(C) m∠C = 55°

(D) m∠C = 80°

Answer:

Option B:

AB = 10.6 cm

Solution:

The image of the triangle is attached below.

In ΔFGH,

FG = 12.3 cm, GH = 10.6 cm, m∠G = 80° and m∠H = 55°

Option A: AB = 12.3 cm

Given ΔGHF $\sim$ ΔABC.

Corresponding parts of congruence triangles are congruent.

GH = AB = 10.6 cm

So, option A is not true.

Option B: AB = 10.6 cm

Already proved in option A that AB = 10.6 cm

So, option B is true.

Option C: m∠C = 55°

ΔGHF $\sim$ ΔABC

Corresponding parts of congruence triangles are congruent.

m∠G = m∠A = 80°

m∠H = m∠B = 55°

Sum of the angles of a triangle = 180°

⇒ m∠A + m∠B + m∠C = 180°

⇒ 80° + 55° + m∠C = 180°

⇒ m∠C = 180° – 80° – 55°

⇒ m∠C = 45°

So, option C is not true.

Option D: m∠C = 80°

Already proved in option C that m∠C = 45°.

So, option D is not true.

Hence option B is the true statement that AB = 10.6 cm.

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2 years ago

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Naledi climbed up a mountain. Her initial altitude was 40 meters above sea level, and it increased by 10 meters each hour.Let )g

Goshia [24]

Answer:

$U_{n} = (40) + (n - 1)(10)$

Step-by-step explanation:

The constant increase every hour indicates a linear correlation, which can be represented by an arithmetic sequence.

The nth term formula is a formula for any specific term you wish to find.

The formula is:

$U_{n} = a + (n - 1)d$

a = starting value of the sequence

d = the common difference (i.e. the difference between any two consecutive terms of the sequence)

n = the value corresponding to the position of the desired term in the sequence (i.e. 1 is the first term, 2 is the second, etc.)

Un = the actual vaue of the the term

In this case:

a = 40

d = 10

And so, the nth term formula is:

$U_{n} = (40) + (n - 1)(10)$

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2 years ago

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