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2 years ago

Replace ∗ with a monomial so that the result is an identity:(5x + ∗)(5x − ∗) = 25x2–0.16y4

Mathematics

1 answer:

Eddi Din [679]2 years ago

5 0

Answer:

0.4y²

Step-by-step explanation:

25x² - 0.16y⁴

(5x)² - (0.4y²)²

(5x - 0.4y²)(5x + 0.4y²)

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The length of a side of a triangle is 26 in. A line, parallel to the given side ,divides the triangle into 2 parts of equal area

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Answer:

13 $\sqrt{2}$

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2 years ago

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4) A window is in the form of a rectangle surmounted by a semicircle. The rectangle is of clear glass, whereas the semicircle is

lisov135 [29]

Answer:

l=0.1401P\\

w =0.2801P

where P = perimeter

Step-by-step explanation:

Given that a window is in the form of a rectangle surmounted by a semicircle.

Perimeter of window =2l+\pid/2+w

$P= 2l+3.14 (w/2)+w$

Or $P = 2l+2.57w\\l = \frac{P-2.57w}{2}$

To allow maximum light we must have maximum area

Area = area of rectangle + area of semi circle where rectangle width = diameter of semi circle

$A=lw +\pi \frac{w^2}{8}$

$A=lw +\pi \frac{w^2}{8}\\A=w*\frac{P-2.57w}{2}+0.3925w^2\\2A= Pw-2.57w^2+(0.785w^2)\\2A' = P-5.14w+1.57 w\\2A" =-5.14+1.57$

Hence we get maximum area when i derivative is 0

i.e. $P-5.14w+1.57 w=0\\3.57w =P\\w = \frac{P}{3.57} =0.2801P$

$l = \frac{P-2.57w}{2}\\l = 0.1401P$

Dimensions can be

$l=0.1401P\\w =0.2801P$

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2 years ago

Dan divide a pie into eighths.how many equal parts are their

cluponka [151]

There are 8 equal parts. Each part is 1/8 of the whole 8/8

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3 years ago

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An object is launched at 19.6 m/s from a height of 58.8 m. The equation for the height (h) in terms of time (t) is given by h(t)

beks73 [17]

H(t) = Ho +Vot - gt^2/2

Vo = 19.6 m/s
Ho = 58.8 m
g = 9.8 m/s^2

H(t) = 58.8 + 19.6t -9.8t^2/2 = 58.8 + 19.6t - 4.9t^2

Maximun height is at the vertex of the parabole

To find the vertex, first find the roots.

58.8 + 19.6t - 4.9t^2 = 0

Divide by 4.9

12 + 4t - t^2 = 0

Change sign and reorder

t^2 - 4t -12 = 0

Factor

(t - 6)(t + 2) =0 ==> t = 6 and t = -2.

The vertex is in the mid point between both roots

Find H(t) for: t = [6 - 2]/2 =4/2 = 2

Find H(t) for t = 2

H(6) = 58.8 + 19.6(2) - 4.9(2)^2 = 78.4

Answer: the maximum height is 78.4 m

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2 years ago

Find the slope of the line 7x-4y=10

Harman [31]

Answer:

The slope is $m=(7/4)$