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3 years ago

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Mathematics

1 answer:

Leto [7]3 years ago

7 0

The area of the rectangle in terms of length (l) is $l^{2}-7l$ , if the width of the rectangle is 7 feet less than its length.

Step-by-step explanation:

The given is,

Width of the rectangle is 7 feet less than its length

Length is l

Step:1

Formula for area of rectangle,

Area, $a = lb$

Where,

l - Length of the rectangle

b - Width of the rectangle

Step:2

From the given values,

w = $l$ - 7 ( ∵ from given)

The equation becomes

= $l$ × ( $l$ -7 )

= $l^{2}$ - 7 $l$

Area, a = $l^{2}$ - 7 $l$ square feet

Result:

The area of the rectangle in terms of length (l) is $l^{2}-7l$ , if the width of the rectangle is 7 feet less than its length.

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Factor the expression below 36a2-25b2 which binomial is factor of the expression

Serhud [2]

Answer: (6a + 5b) • (6a - 5b)

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "b2" was replaced by "b^2". 1 more similar replacement(s).

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(36 • (a2)) - 52b2

Step 2 :

Equation at the end of step 2 :

(22•32a2) - 52b2

Step 3 :

Trying to factor as a Difference of Squares :

3.1 Factoring: 36a2-25b2

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 36 is the square of 6

Check : 25 is the square of 5

Check : a2 is the square of a1

Check : b2 is the square of b1

Factorization is : (6a + 5b) • (6a - 5b)

Final result :

(6a + 5b) • (6a - 5b)

brainly would epic!

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3 years ago

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In the diagram, point D is the center of the medium-sized circle that passes through C and E, and it is also the center of the l

mestny [16]

9514 1404 393

Answer:

5/8

Step-by-step explanation:

The area of the smaller circles is proportional to the square of the ratio of their diameters. The two smallest circles have diameters equal to 1/4 the diameter of the largest circle. Hence their areas are (1/4)^2 = 1/16 of that of the largest circle.

Similarly, the medium circle has a diameter half that of the largest circle, so its area is (1/2)^2 = 1/4 of the are of the largest circle.

The smaller circles subtract 2×1/16 +1/4 = 3/8 of the area of the largest circle. Then the shading is 1-3/8 = 5/8 of the area of the largest circle.

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3 years ago

Differentiate with respect to X <br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B%20%5Cfrac%7Bcos2x%7D%7B1%20%2Bsin2x%20%7D%20

Mice21 [21]

Power and chain rule (where the power rule kicks in because $\sqrt x=x^{1/2}$ ):

$\left(\sqrt{\dfrac{\cos(2x)}{1+\sin(2x)}}\right)'=\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'$

Simplify the leading term as

$\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}$

Quotient rule:

$\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'=\dfrac{(1+\sin(2x))(\cos(2x))'-\cos(2x)(1+\sin(2x))'}{(1+\sin(2x))^2}$

Chain rule:

$(\cos(2x))'=-\sin(2x)(2x)'=-2\sin(2x)$

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Put everything together and simplify:

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$=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2}{(1+\sin(2x))^2}$

$=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac{\sin(2x)+1}{(1+\sin(2x))^2}$

$=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac1{1+\sin(2x)}$

$=-\dfrac1{\sqrt{\cos(2x)}}\dfrac1{\sqrt{1+\sin(2x)}}$

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Answer:

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katen-ka-za [31]

N=d-2
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