Answer:
F(2, 11/2)
Step-by-step explanation:
The expression:
(x-2)² = 10(y - 3)
can be rewritten in the vertex form as follows:
(x-2)² = 10y - 30
(x-2)² + 30 = 10y
1/10(x-2)² + 3 = y
General vertex form is:
y = a(x-h)² + k
then, the vertex is locate at (h, k). In this case the vertes is (2, 3), and <em>a </em>= 1/10
The focus of a parabola is located ar F(h, k+p), where <em>p</em> = 1/(4a). Replacing into these equations:
p = 1/(4*1/10) = 5/2
F(2, 3+5/2) = F(2, 11/2)
Do you recognize that the hypotenuse here has the length 22 and that the opposite side is the unknown (x)? The angle is 21 degrees.
This is a perfect application of the tangent function:
tan 21 deg = opp / adj = opp / 22 = x / 22
tan 21 deg = 0.384 so x would be 22 tan 21 deg, or
x = 22*(0.384)
= 8.45 (answer)
Answer:
k = 10
Explanation:
The initial polynomial is:
If f(-2) = 0, then when we replace x by -2, the result will be 0. It means that we can write the following equation:
Therefore, we can solve for k as follows:
So, the value of k is 10
I'm not quite sure how I'd attach a picture of my working so I'll explain the method.
16) I multiplied both 3.5 and 40 by ten so that I could divide them to find the number of servings. 35 divided by 400 is 11 remainder 15. If you then divide the remainder by 10 you get 11 servings and 1.5 ounces left over.
17) if you add up 26, 17, and 37 inches you get 80 inches, or just over 6 feet. Hence, he should buy an 8 foot length rod in order to have as little waste as possible.
18) 12.25 pounds is 196 ounces. Hence, the shipping rate at $0.26/ounce would end up being $50.96. From this we can see that the flat-rate box at $25 is less expensive.
