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2 years ago

Yun was trying to factor 7x^2-14x7x

Mathematics

2 answers:

disa [49]2 years ago

8 0

the width of Yun's area model is 7x units or ( x-2 )units .

<u>Step-by-step explanation:</u>

Here we have , Yun was trying to factor 7x^2-14x. He found that the greatest common factor of these terms was 7x and made an area model: What is the width of Yun's area model. Let's find out:

We know that area of rectangle :

⇒ $Area = length(width)$ .........(1)

Now , According to question we have

⇒ $Area = 7x^2-14x$

⇒ $Area = 7x(x-2)$

Comparing this equation to equation (1) we get that :

⇒ $width = 7x$ or , $width =x -2$

Therefore , the width of Yun's area model is 7x units or ( x-2 )units .

ANEK [815]2 years ago

8 0

49x

Step-by-step explanation:

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Alison wants to distribute the carnations and roses equally among the 6 flower shops. Factor the expression from Part A using 6

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2 years ago

Kayson mixes 300300300 milliliters (\text{mL})(mL)left parenthesis, start text, m, L, end text, right parenthesis of spinach, 20

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Answer:

Total, T = (300s+200b+42d) mg

Step-by-step explanation:

Given that,

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2 years ago

Prove that sinA-sin3A+sin5A-sin7A/cosA-cos3A-cos5A+cos7A= cot2A

MAVERICK [17]

Write the left side of the given expression as N/D, where
N = sinA - sin3A + sin5A - sin7A
D = cosA - cos3A - cos5A + cos7A
Therefore we want to show that N/D = cot2A.

We shall use these identities:
sin x - sin y = 2cos((x+y)/2)*sin((x-y)/2)
cos x - cos y = -2sin((x+y)/2)*sin((x-y)2)

N = -(sin7A - sinA) + sin5A - sin3A
= -2cos4A*sin3A + 2cos4A*sinA
= 2cos4A(sinA - sin3A)
= 2cos4A*2cos(2A)sin(-A)
= -4cos4A*cos2A*sinA

D = cos7A + cosA - (cos5A + cos3A)
= 2cos4A*cos3A - 2cos4A*cosA
= 2cos4A(cos3A - cosA)
= 2cos4A*(-2)sin2A*sinA
= -4cos4A*sin2A*sinA

Therefore
N/D = [-4cos4A*cos2A*sinA]/[-4cos4A*sin2A*sinA]
= cos2A/sin2A
= cot2A

This verifies the identity.

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2 years ago

The most economical proportion for a right circular cone is to have its height three times long as its base diameter. What later

defon

9514 1404 393

Answer:

∛(2500π)√37 m² ≈ 120.911 m²

Step-by-step explanation:

If the height is 3 times the diameter, it is 6 times the radius. Then the volume is ...

V = 1/3πr²h

V = 1/3πr²(6r) = 2πr³

For a volume of 100 m³, the radius is ...

100 m³ = 2πr³

r = ∛(50/π) m

The lateral area of the cone is computed from the slant height. For this cone, the slant height is found using the Pythagorean theorem:

s² = r² +(6r)² = 37r²

s = r√37

Then the lateral area is ...

LA = πrs

LA = π(∛(50/π) m)(∛(50/π) m)√37

LA = ∛(2500π)√37 m² ≈ 120.911 m²

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