Answer:
C, A
Step-by-step explanation:
If you would like me to explain, I could but this would be difficult. Trust me.
Answer:
c = 29
Step-by-step explanation:
Law of sines is given as: ![\frac{a}{sin(A)} = \frac{b}{sin(B)} = \frac{c}{sin(C)}](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba%7D%7Bsin%28A%29%7D%20%3D%20%5Cfrac%7Bb%7D%7Bsin%28B%29%7D%20%3D%20%5Cfrac%7Bc%7D%7Bsin%28C%29%7D%20)
B = 180 - (57 + 44) = 79°
b = 41
C = 44°
c = ?
Thus:
![\frac{b}{sin(B)} = \frac{c}{sin(C)}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bb%7D%7Bsin%28B%29%7D%20%3D%20%5Cfrac%7Bc%7D%7Bsin%28C%29%7D%20)
Substitute
![\frac{41}{sin(79)} = \frac{c}{sin(44)}](https://tex.z-dn.net/?f=%20%5Cfrac%7B41%7D%7Bsin%2879%29%7D%20%3D%20%5Cfrac%7Bc%7D%7Bsin%2844%29%7D%20)
Multiply both sides by sin 44
![\frac{41}{sin(79)}*sin(44) = \frac{c}{sin(44)}*sin(44)](https://tex.z-dn.net/?f=%20%5Cfrac%7B41%7D%7Bsin%2879%29%7D%2Asin%2844%29%20%3D%20%5Cfrac%7Bc%7D%7Bsin%2844%29%7D%2Asin%2844%29%20)
![\frac{41*sin(44)}{sin(79)}*sin(44) = c](https://tex.z-dn.net/?f=%20%5Cfrac%7B41%2Asin%2844%29%7D%7Bsin%2879%29%7D%2Asin%2844%29%20%3D%20c%20)
c = 29.0140633 ≈ 29
Answer:
Area = 370 m²
Cost to paint = £105
Step-by-step explanation:
Area of the wall of a cinema hall = Area of a trapezoid (1)+ Area of a rectangle (2) + Area of a trapezoid (3)
Area of a trapezoid =
where
and
are the parallel sides and h is the distance between these sides.
Area of trapezoid (1) = ![\frac{1}{2}(11+12)\times 6](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%2811%2B12%29%5Ctimes%206)
= 69 m²
Area of the rectangle (2) = Length × Width
= 12 × 15
= 180 m²
Area of the trapezoid (3) = ![\frac{1}{2}(12+10)\times 11](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%2812%2B10%29%5Ctimes%2011)
= 121 m²
Now area of the wall = 69 + 180 + 121
= 370 m²
One tin covers the area = 25 m²
Number of tins required to paint the wall = ![\frac{\text{Total area}}{\text{Area covered by one tin}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BTotal%20area%7D%7D%7B%5Ctext%7BArea%20covered%20by%20one%20tin%7D%7D)
= ![\frac{370}{25}](https://tex.z-dn.net/?f=%5Cfrac%7B370%7D%7B25%7D)
= 14.8
Therefore, number of tins to be purchased = 15
Cost to paint the complete wall = 15 × £7
= £105
Answer:
34 minutes
Step-by-step explanation:
Given:
Ratio of time for which Pepperoni pizza and cheese pizza should be baked is given as:
![P = 3C - 2](https://tex.z-dn.net/?f=P%20%3D%203C%20-%202)
Where
is the time for which pepperoni pizza should be baked and
is the time for which Cheese pizza should be baked.
Also, it is given that a small Cheese pizza should be baked for 12 minutes.
In other words, we are given that: ![C=12\ min](https://tex.z-dn.net/?f=C%3D12%5C%20min)
To find:
For how long small pepperoni pizza should be baked ?
In other words,
![P=?](https://tex.z-dn.net/?f=P%3D%3F)
Solution:
Let us put the value of
in the equation of the model.
![P = 3C - 2](https://tex.z-dn.net/?f=P%20%3D%203C%20-%202)
![\Rightarrow P = 3\times 12 - 2\\\Rightarrow P = 36 - 2\\\Rightarrow P = \bold{34\ min}](https://tex.z-dn.net/?f=%5CRightarrow%20P%20%3D%203%5Ctimes%2012%20-%202%5C%5C%5CRightarrow%20P%20%3D%2036%20-%202%5C%5C%5CRightarrow%20P%20%3D%20%5Cbold%7B34%5C%20min%7D)
Therefore, a small pepperoni pizza should be baked for <em>34 minutes</em>.
Answer:
sin (- 135°)= – sin 135°= – sin (1 × 90°+ 45°) = – cos 45° = – 1√2
cos (- 135°)= cos 135°= cos (1 × 90°+ 45°) = – sin 45°= – 1√2
tan (- 135°) = – tan 135° = – tan ( 1 × 90° + 45°) = – (- cot 45°) = 1
csc (- 135°)= – csc 135°= – csc (1 × 90°+ 45°)= – sec 45° = – √2
sec (- 135°)= sec 135°= sec (1 × 90°+ 45°)= – csc 45°= – √2
cot (- 135°) = – cot 135° = – cot ( 1 × 90° + 45°) = – (-tan 45°) = 1
Step-by-step explanation:
hope this helps