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Charra [1.4K]
3 years ago
12

10 POINTS Find the surface area of the regular pyramid. Round to the nearest tenth if necessary.

Mathematics
2 answers:
NNADVOKAT [17]3 years ago
5 0

Answer:

SA=234.8\ yd^2

Step-by-step explanation:

we know that

The surface area of the regular pyramid is equal to the area of the triangular base plus the area of its three triangular lateral faces

step 1

Find the area of the triangular base

we know that

The triangular base is an equilateral triangle

so

The area applying the law of sines is equal to

A=\frac{1}{2}(14^2)sin(60^o)

A=\frac{1}{2}(196)\frac{\sqrt{3}}{2}

A=49\sqrt{3}=84.87\ yd^2            

step 2

Find the area of its three triangular lateral faces

A=3[\frac{1}{2}bh]

we have

b=14\ yd

Find the height of triangles

Applying the Pythagorean Theorem

10^2=(14/2)^2+h^2

solve for h

100=49+h^2

h^2=100-49

h=\sqrt{51}\ yd

substitute

A=3[\frac{1}{2}(14)\sqrt{51}]      

A=149.97\ yd^2

step 3

Find the surface area

Adds the areas

SA=84.87+149.97=234.84\ yd^2

Round to the nearest tenth

SA=234.8\ yd^2

garri49 [273]3 years ago
4 0

Answer:

234.8 is correct.

Step-by-step explanation:

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Answer:

f'(x) > 0 on (-\infty ,\frac{1}{e}) and f'(x)<0 on(\frac{1}{e},\infty)

Step-by-step explanation:

1) To find and interval where any given function is increasing, the first derivative of its function must be greater than zero:

f'(x)>0

To find its decreasing interval :

f'(x)

2) Then let's find the critical point of this function:

f'(x)=\frac{\mathrm{d} }{\mathrm{d} x}[6-2^{2x}]=\frac{\mathrm{d} }{\mathrm{d}x}[6]-\frac{\mathrm{d}}{\mathrm{d}x}[2^{2x}]=0-[ln(2)*2^{2x}*\frac{\mathrm{d}}{\mathrm{d}x}[2x]=-ln(2)*2^{2x}*2=-ln2*2^{2x+1\Rightarrow }f'(x)=-ln(2)*2^{2x}*2\\-ln(2)*2^{2x+1}=-2x^{2x}(ln(x)+1)=0

2.2 Solving for x this equation, this will lead us to one critical point since x'  is not defined for Real set, and x''=\frac{1}{e}≈0.37 for e≈2.72

x^{2x}=0 \ni \mathbb{R}\\(ln(x)+1)=0\Rightarrow ln(x)=-1\Rightarrow x=e^{-1}\Rightarrow x\approx 2.72^{-1}x\approx 0.37

3) Finally, check it out the critical point, i.e. f'(x) >0 and below f'(x)<0.

8 0
3 years ago
Stephanie is a taxi driver. She rents her taxi for $300/week. She feels she can take in $120/day in fares. Let D be the number o
Lesechka [4]

Answer: a. (0, -300), (1, -180), (2, -60), (7, 540)

b. T=120D-300

c. $28080

Step-by-step explanation:

a. T=120D-300 ==> per week

D=0: T=120(0)-300

D=0: T=-300 ==> (0, -300)

D=1: T=120(1)-300

D=1: T=120-300

D=1: T=-180 ==> (1, -180)

D=2: T=120(2)-300

D=2: T=240-300

D=2: T=-60 ==> (2, -60)

D=7: T=120(7)-300

D=7: T=840-300

D=7: T=540 ==> (7, 540)

b. T=120D-300

c. T=120(7)-300

T=840-300

T=$540 per week

1 year = 52 weeks

540*52=$28080

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2 years ago
How do I find 2/3 of 12 slices of pizza eaten ​
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Multiply 12 slices by 2/3:

12 x 2/3 = (12 x 2) /3 = 24/3 = 8

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3 years ago
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What is the diameter, in meters of the circular area that gets watered by the sprinkler?
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The answer is 12 m.

Because you're not studying!

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3 years ago
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HELP ME PLSSS ITS DUE TODAY
Gnom [1K]

Answer:

<u>S': (2, 1)</u>

<u>T': (5, 3)</u>

<u>U': (1, -4)</u>

<u>S'': (1, 3)</u>

<u>T'': (4, 5)</u>

<u>U'': (0, -2)</u>

Step-by-step explanation:

Hi!

For Reflection Across the X-Axis use this :

(x, y) -> (x, - y)

So :

S': (2, 1)

T': (5, 3)

U': (1, -4)

and then the question also asks for a translation so we follow what it gave us:

S'': (1, 3)

T'': (4, 5)

U'': (0, -2)

Please ask me any questions that you still may have!

and Have a great day! :)

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