Answer:
Total time spent by Tiwa to set up the computer and install software = 6 hours
Step-by-step explanation:
Given:
Time spent by Tiwa to set up her computer = ![1\frac{1}{2}\ hours](https://tex.z-dn.net/?f=1%5Cfrac%7B1%7D%7B2%7D%5C%20hours)
Time spent to install the software is 3 times the time she took to set up the computer.
To find the total time Tiwa took to set up her computer and install the software.
Solution:
Time spent by Tiwa to install the software can be given as:
⇒ ![3\times 1\frac{1}{2} \ hours](https://tex.z-dn.net/?f=3%5Ctimes%201%5Cfrac%7B1%7D%7B2%7D%20%5C%20hours)
<em>In order to multiply mixed numbers we first change them to fractions.</em>
We multiply the denominator to the whole number and add the numerator to it. Then we write the number as numerator of a fraction with the same denominator.
So, ![1\frac{1}{2}=\frac{3}{2}](https://tex.z-dn.net/?f=1%5Cfrac%7B1%7D%7B2%7D%3D%5Cfrac%7B3%7D%7B2%7D)
So, we have:
⇒ ![3\times \frac{3}{2}\ hours](https://tex.z-dn.net/?f=3%5Ctimes%20%5Cfrac%7B3%7D%7B2%7D%5C%20hours)
⇒ ![\frac{9}{2}\ hours](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B2%7D%5C%20hours)
Total time spent by Tiwa to set up the computer and install software can be given as:
⇒ ![\frac{3}{2}\ hours+\frac{9}{2}\ hours](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7D%5C%20hours%2B%5Cfrac%7B9%7D%7B2%7D%5C%20hours)
Since denominators are same, so we simply add the numerators.
⇒ ![\frac{3+9}{2}\ hours](https://tex.z-dn.net/?f=%5Cfrac%7B3%2B9%7D%7B2%7D%5C%20hours)
⇒ ![\frac{12}{2}\ hours](https://tex.z-dn.net/?f=%5Cfrac%7B12%7D%7B2%7D%5C%20hours)
⇒ ![6\ hours](https://tex.z-dn.net/?f=6%5C%20hours)
Answer:
Step-by-step explanation:
1.
cot x sec⁴ x = cot x+2 tan x +tan³x
L.H.S = cot x sec⁴x
=cot x (sec²x)²
=cot x (1+tan²x)² [ ∵ sec²x=1+tan²x]
= cot x(1+ 2 tan²x +tan⁴x)
=cot x+ 2 cot x tan²x+cot x tan⁴x
=cot x +2 tan x + tan³x [ ∵cot x tan x
=1]
=R.H.S
2.
(sin x)(tan x cos x - cot x cos x)=1-2 cos²x
L.H.S =(sin x)(tan x cos x - cot x cos x)
= sin x tan x cos x - sin x cot x cos x
![=\textrm{sin x cos x }\times\frac{\textrm{sin x}}{\textrm{cos x} } - \textrm{sinx}\times\frac{\textrm{cos x}}{\textrm{sin x}}\times \textrm{cos x}](https://tex.z-dn.net/?f=%3D%5Ctextrm%7Bsin%20x%20cos%20x%20%7D%5Ctimes%5Cfrac%7B%5Ctextrm%7Bsin%20x%7D%7D%7B%5Ctextrm%7Bcos%20x%7D%20%7D%20-%20%5Ctextrm%7Bsinx%7D%5Ctimes%5Cfrac%7B%5Ctextrm%7Bcos%20x%7D%7D%7B%5Ctextrm%7Bsin%20x%7D%7D%5Ctimes%20%5Ctextrm%7Bcos%20x%7D)
= sin²x -cos²x
=1-cos²x-cos²x
=1-2 cos²x
=R.H.S
3.
1+ sec²x sin²x =sec²x
L.H.S =1+ sec²x sin²x
=
[
]
=1+tan²x ![[\frac{\textrm{sin x}}{\textrm{cos x}} = \textrm{tan x}]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B%5Ctextrm%7Bsin%20x%7D%7D%7B%5Ctextrm%7Bcos%20x%7D%7D%20%3D%20%5Ctextrm%7Btan%20x%7D%5D)
=sec²x
=R.H.S
4.
![\frac{\textrm{sinx}}{\textrm{1-cos x}} +\frac{\textrm{sinx}}{\textrm{1+cos x}} = \textrm{2 csc x}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctextrm%7Bsinx%7D%7D%7B%5Ctextrm%7B1-cos%20x%7D%7D%20%2B%5Cfrac%7B%5Ctextrm%7Bsinx%7D%7D%7B%5Ctextrm%7B1%2Bcos%20x%7D%7D%20%3D%20%5Ctextrm%7B2%20csc%20x%7D)
L.H.S=![\frac{\textrm{sinx}}{\textrm{1-cos x}} +\frac{\textrm{sinx}}{\textrm{1+cos x}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctextrm%7Bsinx%7D%7D%7B%5Ctextrm%7B1-cos%20x%7D%7D%20%2B%5Cfrac%7B%5Ctextrm%7Bsinx%7D%7D%7B%5Ctextrm%7B1%2Bcos%20x%7D%7D)
![=\frac{\textrm{sinx(1+cos x)+{\textrm{sinx(1-cos x)}}}}{\textrm{(1-cos x)\textrm{(1+cos x})}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Ctextrm%7Bsinx%281%2Bcos%20x%29%2B%7B%5Ctextrm%7Bsinx%281-cos%20x%29%7D%7D%7D%7D%7B%5Ctextrm%7B%281-cos%20x%29%5Ctextrm%7B%281%2Bcos%20x%7D%29%7D%7D)
![=\frac{\textrm{sinx+sin xcos x+{\textrm{sinx-sin xcos x}}}}{{(1-cos ^2x)}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Ctextrm%7Bsinx%2Bsin%20xcos%20x%2B%7B%5Ctextrm%7Bsinx-sin%20xcos%20x%7D%7D%7D%7D%7B%7B%281-cos%20%5E2x%29%7D%7D)
![=\frac{\textrm{2sin x}}{sin^2 x}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Ctextrm%7B2sin%20x%7D%7D%7Bsin%5E2%20x%7D)
= 2 csc x
= R.H.S
5.
-tan²x + sec²x=1
L.H.S=-tan²x + sec²x
= sec²x-tan²x
=![\frac{1}{cos^2x} -\frac{sin^2x}{cos^2x}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bcos%5E2x%7D%20-%5Cfrac%7Bsin%5E2x%7D%7Bcos%5E2x%7D)
![=\frac{1- sin^2x}{cos^2x}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1-%20sin%5E2x%7D%7Bcos%5E2x%7D)
![=\frac{cos^2x}{cos^2x}](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bcos%5E2x%7D%7Bcos%5E2x%7D)
=1
Answer:
one tenth of a sandwich
Step-by-step explanation:
3 should be added to the tiles
Heres a tip---- if it has a square its 90 degrees if it doesnt its 180 and if its in an x shape theyre equal