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Alex Ar [27]
2 years ago
9

Use the net to find the lateral area of the prism.

Mathematics
1 answer:
salantis [7]2 years ago
6 0
The lateral area is represented in the diagram by a rectangle 11 cm wide and
(8 + 15 + 17) cm = 40 cm long.

The lateral area is 
   (11 cm)*(40 cm) = 440 cm²
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Prove that :( 1 + 1/<img src="https://tex.z-dn.net/?f=tan%5E%7B2%7DA" id="TexFormula1" title="tan^{2}A" alt="tan^{2}A" align="ab
Aliun [14]

Answer:

See explanation

Step-by-step explanation:

Simplify left and right parts separately.

<u>Left part:</u>

\left(1+\dfrac{1}{\tan^2A}\right)\left(1+\dfrac{1}{\cot ^2A}\right)\\ \\=\left(1+\dfrac{1}{\frac{\sin^2A}{\cos^2A}}\right)\left(1+\dfrac{1}{\frac{\cos^2A}{\sin^2A}}\right)\\ \\=\left(1+\dfrac{\cos^2A}{\sin^2A}\right)\left(1+\dfrac{\sin^2A}{\cos^2A}\right)\\ \\=\dfrac{\sin^2A+\cos^2A}{\sin^2A}\cdot \dfrac{\cos^2A+\sin^A}{\cos^2A}\\ \\=\dfrac{1}{\sin^2A}\cdot \dfrac{1}{\cos^2A}\\ \\=\dfrac{1}{\sin^2A\cos^2A}

<u>Right part:</u>

\dfrac{1}{\sin^2A-\sin^4A}\\ \\=\dfrac{1}{\sin^2A(1-\sin^2A)}\\ \\=\dfrac{1}{\sin^2A\cos^2A}

Since simplified left and right parts are the same, then the equality is true.

3 0
3 years ago
What is the measurement of BC to the nearest centimeter?
77julia77 [94]

Answer:

a   8

Step-by-step explanation:

You are given two sides and the included angle. Since you don't have any side and the opposite angle, you must use the law of cosines.

a^2 = b^2 + c^2 - 2bc\cos A

a^2 = 5^2 + 11^2 - 2(5)(11)\cos 39^\circ

a^2 = 25 + 121 - 110\cos 39^\circ

a^2 = 60.51

a = 7.779

Answer: a = 8 cm

7 0
3 years ago
Carla and rob left a 20% tip after having lunch at a restaurant the amount of the tip was $6 Carla's lunch cost $15 which equati
siniylev [52]
This question is a little tricky.  Carla had a bill of $15, which we will add to the cost of Rob's lunch.  They left a 20% tip on the TOTAL cost of both their lunches, which should equal $6.  20% is equivalent to 0.2.  So, the equation is 6=0.2(x+15).  In other words, 20% of the sum of Carla and Rob's lunches is 6 dollars.

Answer: 6=0.2(x+15)
6 0
3 years ago
Solve for b. -11b+7 = 40−11b+7=40
Oksana_A [137]

Answer:

This equation is false

Step-by-step explanation:

Well,

-11b + 7 = 4 - 11b + 7 = 40

combine like terms

-11b + 7 = -11b + 3 = 40

Communicative property

-3 to both sides

-11b + 4 = -11b = 40

-4 to both sides

-11b = -11b = 36

+11b to both sides

0 = 36

0 is not equal to 36 meaning that this equation is false.

<em>Thus,</em>

<em>the equation given is false.</em>

<em />

<em>Hope this helps :)</em>

6 0
3 years ago
What is the exact value of cos 45° ?
Georgia [21]
Let the two sides of a right triangle be equal to one, which means that the hypotenuse is √2

Since cosa=adjacent side / hypotenuse

cos45=1/√2

We can rationalize the denominator by multiplying numerator and denominator by √2

√(2)/2

or if you prefer:  √(1/2)
3 0
3 years ago
Read 2 more answers
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