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2 years ago

Your business is looking into three contracting firms. Based on previous research, there is a

Mathematics

1 answer:

sladkih [1.3K]2 years ago

8 0

Answer:21,000 profit

Step-by-step explanation:

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Verify the identity (tan x + 1)^2 + (tan x-1)^2= 2 sec^2 x

Elina [12.6K]

$(\tan x+1)^2+(\tan x-1)^2=2\sec^2x\\\\\text{use}\ \tan x=\dfrac{\sin x}{\cos x}\\\\L_s=\left(\dfrac{\sin x}{\cos x}+\dfrac{\cos x}{\cos x}\right)^2+\left(\dfrac{\sin x}{\cos x}-\dfrac{\cos x}{\cos x}\right)^2\\\\=\left(\dfrac{\sin x+\cos x}{\cos x}\right)^2+\left(\dfrac{\sin x-\cos x}{\cos x}\right)^2\\\\=\dfrac{(\sin x+\cos x)^2}{\cos^2x}+\dfrac{(\sin x-\cos x)^2}{\cos^2x}\\\\\text{use}\ (a\pm b)^2=a^2\pm2ab+b^2$

$=\dfrac{\sin^2x+2\sin x\cos x+\cos^2}{\cos^2x}+\dfrac{\sin^2x-2\sin x\cos x+\cos^2}{\cos^2x}\\\\=\dfrac{\sin^2x+2\sin x\cos x+\cos^2+\sin^2x-2\sin x\cos x+\cos^2}{\cos^2x}\\\\=\dfrac{2\sin^2x+2\cos^2x}{\cos^2x}=\dfrac{2(\sin^2x+\cos^2x)}{\cos^2x}\\\\\text{use}\ \sin^2x+\cos^2x=1\\\\=\dfrac{2(1)}{\cos^2x}=2\cdot\dfrac{1}{\cos^2x}=2\left(\dfrac{1}{\cos x}\right)^2\\\\\text{use}\ \sec x=\dfrac{1}{\cos x}\\\\=2(\sec^2x)=2\sec^2x=R_s\\\\L_s=R_s\Rightarrow The\ identity$

4 0

3 years ago

2. Find the number of cubical

lys-0071 [83]

Answer:number of boxes = 60

Volume of box = side × side × side.

= 3 × 3 × 3

= 27 cu. cm.

Volume of carton = length × breadth × height.

= 15 × 9 × 12

= 1620 cu. cm.

Number of boxes = Volume of carton/Volume of each box.

= 1620/27

= 60

Therefore, number of boxes = 60.

Step-by-step explanation:Volume of box = side × side × side.

= 3 × 3 × 3

= 27 cu. cm.

Volume of carton = length × breadth × height.

= 15 × 9 × 12

= 1620 cu. cm.

Number of boxes = Volume of carton/Volume of each box.

= 1620/27

= 60

Therefore, number of boxes = 60.

3 0

3 years ago

Mark all the relative minimum points in the graph

Vladimir [108]

Answer:

Step-by-step explanation:

(-6, 2) is the absolute minimum. There is no relative minimum.

7 0

3 years ago

Read 2 more answers

Find x in the figure.<br><br><br> A) x = 44<br><br> B) x = 16<br><br> C) x = 22<br><br> D) x = 66

MakcuM [25]

Answer:

Step-by-step explanation:

3x + 3x + 48 = 180

6x = 180 - 48

x = 132 / 6

x = 22

7 0

2 years ago

Read 2 more answers

X+y=-2 7x-4y=8 graph

Novay_Z [31]

Answer:

x+y=-2

7x-4y=8

Step-by-step explanation:

3 0

3 years ago