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nika2105 [10]
3 years ago
14

Plzzz Help ASAP! This image shows a square pyramid what is the surface area of this square pyramid?

Mathematics
1 answer:
padilas [110]3 years ago
7 0

Answer:

72\ ft^{2}

Step-by-step explanation:

we know that

The surface area of the square pyramid is equal to the area of the square base plus the area of its four lateral triangular faces

so

SA=b^{2}+4[\frac{1}{2}bh]

where

b is the length side of the square base

h is the height of the triangular face

Remember that

Each lateral triangular face is a triangle 45°-90°-45°

so

h=b/2

we have

b=6\ ft

so

h=6/2=3\ ft

substitute in the formula

SA=6^{2}+4[\frac{1}{2}(6)(3)]=72\ ft^{2}

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Calculus piecewise function. ​
Kipish [7]

Part A

The notation \lim_{x \to 2^{+}}f(x) means that we're approaching x = 2 from the right hand side (aka positive side). This is known as a right hand limit.

So we could start at say x = 2.5 and get closer to 2 by getting to x = 2.4 then to x = 2.3 then 2.2, 2.1, 2.01, 2.001, etc

We don't actually arrive at x = 2 itself. We simply move closer and closer.

Since we're on the positive or right hand side of 2, this means we go with the rule involving x > 2

Therefore f(x) = (x/2) + 1

Plug in x = 2 to find that...

f(x) = (x/2) + 1

f(2) = (2/2) + 1

f(2) = 2

This shows \lim_{x \to 2^{+}}f(x) = 2

Then for the left hand limit \lim_{x \to 2^{-}}f(x), we'll involve x < 2 and we go for the first piece. So,

f(x) = 3-x

f(2) = 3-2

f(2) = 1

Therefore, \lim_{x \to 2^{-}}f(x) = 1

===============================================================

Part B

Because \lim_{x \to 2^{+}}f(x) \ne \lim_{x \to 2^{-}}f(x) this means that the limit \lim_{x \to 2}f(x) does not exist.

If you are a visual learner, check out the graph below of the piecewise function. Notice the gap or disconnect at x = 2. This can be thought of as two roads that are disconnected. There's no way for a car to go from one road to the other. Because of this disconnect, the limit doesn't exist at x = 2.

===============================================================

Part C

You'll follow the same type of steps shown in part A.

However, keep in mind that x = 4 is above x = 2, so we'll deal with x > 2 only.

So you'd only involve the second piece f(x) = (x/2) + 1

You should find that f(4) = 3, and that both left and right hand limits equal this value. The left and right hand limits approach the same y value. The limit does exist here. There are no gaps to worry about when x = 4.

===============================================================

Part D

As mentioned earlier, since \lim_{x \to 4^{+}}f(x) = \lim_{x \to 4^{-}}f(x) = 3, this means the limit \lim_{x \to 4}f(x) does exist and it's equal to 3.

As x gets closer and closer to 4, the y values are approaching 3. This applies to both directions.

4 0
1 year ago
Which number(s) below belong to the solution set of the inequality? Check all that apply.x + 16 &lt; 51.
natta225 [31]
If you subtract 16 on both sides... x will be alone. Therefore 51-16=35
x=35 (B)
5 0
2 years ago
Ng the Percent of a Number<br> 1. What is 5% of 60 ?
Igoryamba
The answer is 3. Hope this helps and pls give thanks!
7 0
2 years ago
Read 2 more answers
X 5 X6 7 8 A garden table and a bench cost $659 combined. The garden table costs $91 less than the bench. What is the cost of th
Greeley [361]

Answer:

The bench was $375 and the garden table was $284.

Step-by-step explanation:

Let x be the value of the bench, if the table is 91 less than the value of the bench then the equation can be:

x + x-91 = 659

2x -91 = 659

Add 91 to both sides of the equation to isolate the 2x:

2x - 91 + 91 = 659 + 91

2x = 750

Divide both sides by 2 to get 1x:

2x ÷ 2 = 750 ÷ 2

x = 375

This means the bench was $375 and the garden table was $284.

Hope this helps!

8 0
3 years ago
Need help with 25 &amp; 27 PLEASE!!!
Mumz [18]

Answer:

1

Step-by-step explanation:

easy

6 0
2 years ago
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