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1 answer:

7 0

Data:
r (radius) = 3.5 in
h (height) = 8 in
Adopt: $\pi \approx3.14$
V (volume) = ?
Ink cost per cubic inch = $0.05/in³
Total cost: ?

Calculate the volume of the paint bucket (its formed being cylindrical), we have:
 $V = \pi *r^2*h$
$V = 3.14 *3.5^2*8$
$V = 3.14*12.25*8$
$\boxed{V = 307.72\:in^3}$

What was the total cost of the paint?

price($)___measure(in³)
0.05 ---------- 1
y -------------- 307.72

It is made the rule of three: (directly proportional)

$\frac{0.05}{y} = \frac{1}{307.72}$
multiply cross
$1*y = 0.05*307.72$
$y = 15.386\:\to\:\boxed{\boxed{y\approx\$15}}\end{array}}\qquad\quad\checkmark$

Answer:
the total cost of the paint is $15

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Show that the plane and line with the given equations intersect, and then find the acute angle of intersection between them. (Gi

Reptile [31]

Answer:

angle of intersection: 5.2°

Step-by-step explanation:

The direction vector normal to the plane is ...

n = (1, 1, 3)

The direction vector of the line is ...

m = (1, -3, 1)

Then the angle θ between them can be found from the dot product:

n•m = |n|·|m|·cos(θ)

(1·1 +1(-3) +3·1) = 1 -3 +3 = 1 = √(1²+1²+3²)·√(1²+(-3)²+1²)·cos(θ)

1 = 11·cos(θ)

θ = arccos(1/11) ≈ 84.8°

This is the angle between the line and the normal to the plane, so the angle between the line and the plane will be the complement of this. Since this angle is not 90°, the line and plane must intersect.

acute angle = 90° -84.8° = 5.2°

_____

The attached graph shows the line and plane meet at a shallow angle, consistent with the above answer.