An automobile engineer is redesigning a conical chamber that was originally specified to be 12 inches long with a circular base of diameter 5.7 inches. In the new design, the chamber is scaled by a factor of 1.5. The volume of the original chamber is a.)102.02 b.)248.04 c.)306.06 d.)412.08 cubic inches. This is a.)242.47 b.)344.49 c.)432.16 d.)448.21 cubic inches less than the volume of the new chamber.

Answers

Answer 1

Answer: The answers are:
a.)102.02
a.)242.47

The volume of the cone can be expressed as:
$V = (1)/(3) \pi r^(2) h$
where:
V - the volume of the cone,
r - the radius of the cone,
h - the height of the cone.

It is given:
h = 12 in
R = 2r = 5.7 in ⇒ r = 5.7 in ÷ 2 = 2.85 in
π = 3.14

Therefore, the volume of the original conical chamber (V₁)
$V = (1)/(3) *3.14*(2.85) ^(2) *12 = 3.14*8.1225*4 = 102.02 in^(3)$

Further, the new chamber is scaled by a factor of 1.5. That means that radius and height of the original chamber are increased 1.5 times:
r₁ = r · 1.5 = 2.85 in · 1.5 = 4.275 in
h₁ = h · 1.5 = 12 in · 1.5 = 18 in

The volume of the new chamber is:
$V_1= (1)/(3) *3.14*(4.275) ^(2) *18 = 3.14*18.28*6=344.49 in ^(3)$

The difference between two chambers is:
V₁ - V = 344.49 - 102.02 = 242.47

Answer 2

Answer:

Answer:

a and a

Step-by-step explanation:

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Identify the solution set of the inequality using the given replacement set x < –2; {–5, –2.6, –2, –0.8, 1, 1.5}. A. {–5, –2.6} B. {–5, –2.6, –2} C. { –2, –0.8, 1, 1.5} D. {–0.8, 1, 1.5}

Answers

If x < - 2 and x ∈ { - 5, - 2.6, - 2, - 0.8, 1, 1.5 }
- 5 < - 2 and - 2.6 < - 2
The solution set is:
A ) { - 5 , - 2.6 }

If x < - 2 and x ∈ { - 5, - 2.6, - 2, - 0.8, 1, 1.5 }

- 5 < - 2 and - 2.6 < - 2

The solution set is:

A ) { - 5 , - 2.6 }

Please help me answer this I'm so confused

Answers

Hi Akeka,

So in the image, it's a little hard to see some of the bits, but I hope I am getting this right.

One of the options is Rotation, r (180° (lambda) (5,0)).

Now, if I'm remembering high school correctly, this means that Δ ABC needs to be rotated 180°, on the point (5,0) in order to get Δ DBE.

Looking back at the image, we can see that both triangles share the point B, which is at (5,0). Now, to visually check, we can see that points C and E are exactly 180° apart from each other (think of the angle), and points D and A are exactly 180° apart.

We can see that Δ DBE is Δ ABC, rotated 180° on the point (5,0).

-Hope this helps and I hope I did this right!

What is the solution to the equation?4 x squared − 3 equals 77
Choose all answers that are correct.

A.
5 square root of 2

B.
2 square root of 5

C.
− 2 square root of 5

D.
− 5 square root of 2

Answers

The answers are B. 2 square root of 5 and C. − 2 square root of 5.

$4 x^(2) -3=77$
$4 x^(2) =77+3$
$4 x^(2) =80$
$x^(2) =80:4$
$x^(2) =20$
$x= √(20)$
$x= √(4*5)$
$x= √(4)* √(5)$

Since √4 could be either -2 or +2, the solutions are:
$x=2 √(5)$ or $x=-2 √(5)$

What is the answer to this question? (Geometry)