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1 year ago

Find the surface area of a pentagon-based pyramid with slant height of 11 m.

Mathematics

1 answer:

Ronch [10]1 year ago

5 0

Answer:

108.75 square meter.

Step-by-step explanation:

<h3>Surface area of pentagon based pyramid:</h3>

$\sf \boxed{\text{\bf Surface area of pentagonal pyramid = $ \bf \dfrac{5}{2}*b*(a + s)$}}$

Here, b is the base length of the pyramid. b = 3 m

a is the apothem of the pyramid. a = 3.5 m

s is the slant height of the pyramid. s = 11 m

$\sf Surface \ area = \dfrac{5}{2}*3*(11 + 3.5)$

$\sf = \dfrac{5}{2}*3*14.5\\\\ = 108.75 \ m^2$

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Alex_Xolod [135]

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3 years ago

The equation of the graphed line is 2x – 3y = 12.

Viefleur [7K]

Answer:

Step-by-step explanation:

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3 years ago

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Kendra dives off a diving board into the water and then comes back up to the surface. Her dive can be modeled by the equation: ,

MAVERICK [17]

Answer:

1. 6 feet

2. 6.25 feet

3. 1 feet

4. 6 feet

Step-by-step explanation:

The equation is : $h(x)=x^2-7x+6$

1. The diving board is where Kendra dives off. Here, the horizontal distance, x from the diving board is 0.

So, substituting x = 0 in the equation, we get

$h(0)=0^2-7(0)+6$

$=0-0+6$

$=6$

So, the diving board is 6 feet above the surface of the water.

2. From the equation, we known that it is a parabola and the vertex is minimum.

It is the minimum height which represents the depth Kendra dives into the water.

So the $x$ coordinate of the vertex is = $\frac{-b}{2a}$

Here, a and b are the coefficients of linear term and the quadratic terms in the equation. Therefore,

a = 1 and b = -7

∴ x coordinate = $\frac{-(-7)}{2 \times 1}$

$\frac{7}{2}=3.5$

Now substituting to find f(x),

$h(3.5)=(3.5)^2-7(3.5)+6$

= -6.25

Therefore, the diver dives 6.25 feet below the water surface.

3. The horizontal distance from the board the diver enters into the water.

This is the y-intercept and it is the value of x when h(x)=0.

∴ $0=x^2-7x+6$

Factorizing, we get $(x-1)(x-6)=0$

∴ $x=1 \text{ or}\ x=6$

So there are two solutions that are the two x intercepts of the function. Here at x = 1 shows the horizontal distance from the board from where Kendra dives into the water.

4. We know that the equation given has $\text{two}$ x intercepts. These two x intercepts are the points where the parabola crosses the x-axis, which is the height $h(x)=0$ . The height is the water surface level.