Answer:
f(n) = - 0.5n + 6
Step-by-step explanation:
Because Vince cuts down his television watching at a steady pace, his situation models a linear function. As such, we can use slope-intercept form to write and predict his hours watching tv in n weeks.
Slope-intercept form is y=mx+b. In this case, we are choosing to use f(n) instead of y to show the number of hours he is watching tv. We are also choosing to use n weeks instead of x. So we have the form f(n)=mn+b.
We know that Vince starts out at watching 6 hours a week. This is our initial value known as the y-intercept and represented by b. As each week passes, he will decrease from the previous week by 30 minutes or -0.5 hours since 30 out of 60 minutes is 0.5. And since he is decreasing it should be a negative rate of -0.5 and is represented by m.
We substitute b=6 and m=0.5 into our form to get f(n)=-0.5n+6. Let's test week 1. After 1 week he should be down from 6 hours to 5.5 hours or 5 hours and 30 minutes. Let's substitute n=1.
f(n)=-0.5(1)+6=-0.5+6=5.5
We can substitute for any n week and find the amount.
Answer:
15/32
Step-by-step explanation:
5/8 ÷ 1 1/3
Change to an improper fraction
5/8 ÷ ( 3*1+1)/3
5/8 ÷ 4/3
Copy dot flip
5/8 * 3/4
15/32
Answer:
3.27 meters
Step-by-step explanation:
The given equation gives a y(0) = 0, for the deflection of 3 cm. Then for a deflection of 2.5 cm, we want y(x) = 0.005, half a centimeter above the low point on the beam. Using this value, we can solve for x:
0.005 = 3/6400x^2
32/3 = x^2
4√(2/3) = x ≈ 3.26599 ≈ 3.27 . . . . meters
The deflection of the beam is 2.5 cm at a distance of 3.27 meters from center.
We are asked in the problem to solve for x in the expression tan(x+π)+2sin(x+π) = 0. tan theta is equal to sin theta over cos theta. Hence, the expression results to tan (x+π) = sin (x+π) / cos (x+π) = -2sin (x+π). Thus, 1/cos (x+π) = -2. cos (x+π) = -1/2, cosine becomes negative in the third and fourth quadrants. cosine is 1/2 when the terminal angle is pi/3. x is equal to pi/3 then and 5 pi/6.
