Note that
![\displaystyle{ \sin30^{\circ}= \frac{1}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%20%5Csin30%5E%7B%5Ccirc%7D%3D%20%5Cfrac%7B1%7D%7B2%7D%20)
and
![\displaystyle{ \cos30^{\circ}= \frac{ \sqrt{3}}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%20%5Ccos30%5E%7B%5Ccirc%7D%3D%20%5Cfrac%7B%20%5Csqrt%7B3%7D%7D%7B2%7D%20)
.
From the unit circle, we can check that
![\sin30^{\circ}](https://tex.z-dn.net/?f=%5Csin30%5E%7B%5Ccirc%7D)
and
![\sin(-30)^{\circ}](https://tex.z-dn.net/?f=%5Csin%28-30%29%5E%7B%5Ccirc%7D)
have the same value, but opposite signs, that is:
![\sin(-30)^{\circ}=-\sin(30)^{\circ}=-\frac{1}{2}](https://tex.z-dn.net/?f=%5Csin%28-30%29%5E%7B%5Ccirc%7D%3D-%5Csin%2830%29%5E%7B%5Ccirc%7D%3D-%5Cfrac%7B1%7D%7B2%7D)
.
Thus,
![\displaystyle{ \cos(x-y)= \cos(-30^{\circ}-60^{\circ})=cos(-90^{\circ})](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%20%5Ccos%28x-y%29%3D%20%5Ccos%28-30%5E%7B%5Ccirc%7D-60%5E%7B%5Ccirc%7D%29%3Dcos%28-90%5E%7B%5Ccirc%7D%29)
.
Note that
![cos(-90^{\circ})](https://tex.z-dn.net/?f=cos%28-90%5E%7B%5Ccirc%7D%29)
is the x-coordinate of the lowest point on the unit circle, that is (0, -1). Thus
![cos(-90^{\circ})=0](https://tex.z-dn.net/?f=cos%28-90%5E%7B%5Ccirc%7D%29%3D0)
Answer: 0
Width -
x ft.
Length -
(x+6)ft.
x(x+6)=315
x²+6x-315=0
a=1, b=6, c=-315
D=b²-4ac=36+4*1*315=1296, √D=√1296=36
![x = \frac{-b+/- \sqrt{D} }{2a} \\ \\ x= \frac{-6+/-36}{2} \\ \\ x=15, x=-21](https://tex.z-dn.net/?f=%20%20x%20%3D%20%20%20%5Cfrac%7B-b%2B%2F-%20%5Csqrt%7BD%7D%20%7D%7B2a%7D%20%0A%5C%5C%20%5C%5C%20x%3D%20%5Cfrac%7B-6%2B%2F-36%7D%7B2%7D%20%0A%5C%5C%20%5C%5C%20x%3D15%2C%20x%3D-21)
For the width we can use only positive number.
The width =
15 ft.
The length =15+6=
21 ft.
Check :
Area =15*21=315 ft²
We have to draw the model for 5 divide 1/7 . In order to draw the model we use below steps.
Draw 1/7 boxes to represent 1/7 groups.
Assume 5 as the number which represents the total of these 1/7 groups.
Put a question mark at the first box.
Attached is the model to represents 5 divide 1/ 7 .
5/(1/7)
5*7
35
In the question mark we should put 35.
learn more of model here
brainly.com/question/11016284
#SPJ9
Since lines PS and QR are parallel, then the coefficient of x are the same when the line is equated in the form y = mx + c, where m is the gradient
So, for line QR, the gradient is 1/2
For PS, the equation is
3y = kx + 12
(divide both sides by 3)
y = (k/3)x + 4
Since the gradients are equal, k/3 = 1/2
(multiply both sides by 3)
k = 3/2
Answer:
45
Step-by-step explanation:
9 x 5 = 45
45 / 9 = 5
45 is the answer!