Answer:
30 degrees
Step-by-step explanation:
u dot v=1*4+1*4+1*4+0*4=4+4+4+0=12
|u|=sqrt(1^2+1^2+1^2+0^2)=sqrt(3)
|v|=sqrt(4^2+4^2+4^2+4^2)=sqrt(4*4^2)=2*4=8
cos(theta)=u dot v/(|u||v|)
cos(theta)=12/(sqrt(3)*8)
cos(theta)=3/(sqrt(3)*2)
cos(theta)=sqrt(3)/2
theta=30 degrees
X^2+15^2=25^2
X^2+225=625
Isolate X
X^2=400
Take the square root on both sides
X=positive and negative 20 but in this case the negative is thrown out because you can't have a negative side
Answer: 20
One way to look at this is to make 2 equations and treat it as a set of equations. We will make the cost of a donut equal to x, and the cost of a coffee equal to y.
Harold's order:
4x + 2y = 4.08
Melinda's order:
2x + 3y = 3.92
To combine these equations, we need to cancel out either x or y:
4x + 2y = 4.08
<span>2x + 3y = 3.92
</span>
4x + 2y = 4.08
<span>4x + 6y = 7.84
</span>
4x + 2y = 4.08
<span>-4x - 6y = -7.84
</span>
We can now combine these equations:
4x + 2y = 4.08
<span>-4x - 6y = -7.84
</span>
-4y = -3.76
y = 0.94
Therefore the cost of a large coffee is $0.94. We can plug this into either original equation to find the cost of a donut.
<span>4x + 2y = 4.08
</span>4x + 2(0.94) = 4.08
4x + 1.88 = 4.08
4x = 2.20
x = 0.55
The cost of a donut is $0.55, and the cost of a large coffee is $0.94.
