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Zarrin [17]
2 years ago
10

In order to determine the slant height of several pyramids, Marjorie used the surface area formula, s= 1/2 pl+b for the slant he

ight,l . Which equation , in terms of l, represents the correct transformation of the surface area formula?
Mathematics
1 answer:
m_a_m_a [10]2 years ago
7 0

Answer:

l=\dfrac{2(S-b)}{P}

Step-by-step explanation:

The surface area formula for pyramids is given by :

S=\dfrac{1}{2}Pl+b ...(1)

We need to arrange the formula for l.

Take b to LHS,

S-b=\dfrac{1}{2}Pl\\\\2(S-b)=Pl\ [\text{cross-multiplying}]\\\\l=\dfrac{2(S-b)}{P}

So, the expression is \dfrac{2(S-b)}{P} for the slant height.

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Anyone know how to do this pleaseee?
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In 1-5, given: Two similar cylinders with heights of 8 and 5 respectively.
lana66690 [7]

Answer:

1. The ratio of their diameters is 8/5 = 8 : 5

2. The ratio of their surface area is (8/5)²

3. The ratio of their volume is (8/5)³

4.The area of the base of the larger cylinder is 128 cm²

Step-by-step explanation:

Given that the two cylinders are similar, we have;

Two cylinders are similar when the ratio of their heights is equal to the ratio of their radii

Therefore, we have;

1. The ratio of the height of the two cylinders = 8/5 = The radio of their radii = r₁/r₂

The ratio of their diameter = D₁/D₂ = 2·r₁/2·r₂ = r₁/r₂ = 8/5

The ratio of their diameters D₁/D₂ = 8/5 = 8 : 5

2. The surface area of the cylinders = 2·π·r·h + 2·π·r²

Therefore, we have;

(2·π·r₁·h₁ + 2·π·r₁²)/(2·π·r₂·h₂ + 2·π·r₂²) = (r₁·h₁ + r₁²)/(r₂·h₂ + r₂²)

h₁ = h₂ × 8/5

r₁ = r₂ × 8/5

= (8/5)²(r₂·h₂ + r₂²)/(r₂·h₂ + r₂²)  = (8/5)²

The ratio of their surface area = (8/5)²

3. The volume of the cylinder = π·r²·h

∴ The ratio of the volume = (π·r₁²·h₁)/(π·r₂²·h₂) = (8/5)³ × (π·r₂²·h₂)/(π·r₂²·h₂) = (8/5)³

The ratio of their volume = (8/5)³

4. The ratio of the area of the base of the larger cylinder to the area of the base of the smaller cylinder is (8/5)²

Therefore if the area of the base of the smaller cylinder is 50 cm², the area of the base of the larger cylinder = 50 cm² × (8/5)²  = 128 cm²

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Paha777 [63]

Answer:

The student's overall grade is 85.79%

Step-by-step explanation:

Given in the question that:

Exam = 50%; Quiz = 30%, Home work = 15% and Class participation = 5%

The total giving us 100%.

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Calculating the percentages the student had for each;

Exam total = 50*0.879 = 43.95% earned

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