Answer:
) See annex
b) See annex
x = 0,5 ft
y = 2 ft and
V = 2 ft³
Step-by-step explanation: See annex
c) V = y*y*x
d-1) y = 3 - 2x
d-2) V = (3-2x)* ( 3-2x)* x ⇒ V = (3-2x)²*x
V(x) =( 9 + 4x² - 12x )*x ⇒ V(x) = 9x + 4x³ - 12x²
Taking derivatives
V¨(x) = 9 + 12x² - 24x
V¨(x) = 0 ⇒ 12x² -24x +9 = 0 ⇒ 4x² - 8x + 3 = 0
Solving for x (second degree equation)
x =[ -b ± √b²- 4ac ] / 2a
we get x₁ = 1,5 and x₂ = 0,5
We look at y = 3 - 2x and see that the value x₂ is the only valid root
then
x = 0,5 ft
y = 2 ft and
V = 0,5*2*2
V = 2 ft³
We can conclude that the value of x is (∠MNP + 66)/8 and angle m∠RNM = ∠RNQ - ∠MNP + 78.
<h3>
What are angles?</h3>
- An angle is a figure in Euclidean geometry formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle.
- Angles formed by two rays are located in the plane containing the rays.
- Angles are also formed when two planes intersect.
- These are known as dihedral angles.
So,
- ∠MNQ = ∠MNP + ∠PNQ
- 8x + 12 = ∠MNP + 78
- 8x + 12 - 78 = ∠MNP
- 8x - 66 = ∠MNP
- 8x = ∠MNP + 66
- x = (∠MNP + 66)/8
Now, substitute 'x = (∠MNP + 66)/8' in 8x + 12:
- ∠MNQ = 8x + 12
- ∠MNQ = 8 ×(∠MNP + 66)/8 + 12
- ∠MNQ = ∠MNP + 66 + 12
- ∠MNQ = ∠MNP + 78
Hence, m∠RNM = ∠RNQ - ∠MNP + 78
Therefore, in the given question value of x is (∠MNP + 66)/8 and angle m∠RNM = ∠RNQ - ∠MNP + 78.
Know more about angles here:
brainly.com/question/25716982
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The answer is Option B 
Step-by-step explanation:
Step 1: Group the given cubic polynomial into two sections.
So polynomial can be grouped as
Step 2:Find what's the common in each section.
In section 
the come term is 
In section (8x + 48) the come term is 8
Step 3:Factor the commonalities out of the two terms.
Factoring out from the first section , we get 
Factoring out 8 from the second section(8x + 48) , we will get 8(x + 6).
Step 4: Combine the factors together for terms contains the same factor,
Combining we get,
X = 47 + 9y
xy = 1860
y(47 + 9y) = 1860
47y + 9y² = 1860
9y² + 47y - 1860 = 0
> using a quadratic equation solver on a calculator but you can also use the quadratic equation = [-b+/- √(b²-4ac)]/(2a)
> only integer solution is x = 12
12y = 1860
y = 155
integers are 12 and 155
Answer:
I think is 18
Step-by-step explanation:
because is the same of the L
