Answer:
z is equal to -0.88235294117
Step-by-step explanation:
so you first need to do is z minus 16z which is -17z.
you now have -17z is 15
you need to divide each side by -17z
so -17z divided by -17 is 1 z
and 15 divided by -17 is -0.88235294117
so z is equal to -0.88235294117
check the picture below. So the parabola looks more or less like so.
bearing in mind that the distance "p" is the same from the vertex to the directrix or the focus point, so the vertex is therefore half-way between those two fellows, now, from 3,4 up to y = 8, there are 4 units, and the vertex is half-way, thus is at y = 6, and x = 3, (3, 6) as you see there in the picture.
the parabola is vertical, meaning the squared variable is the "x", and is opening downwards, meaning the "p" distance is negative, so since "p" is 2 units, then p = -2.
![\bf \textit{parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=3\\ k=6\\ p=-2 \end{cases}\implies 4(-2)(y-6)=(x-3)^2\implies -8(y-6)=(x-3)^2 \\\\\\ y-6=\cfrac{(x-3)^2}{-8}\implies \blacktriangleright y=-\cfrac{1}{8}(x-3)^2+6 \blacktriangleleft](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bparabola%20vertex%20form%20with%20focus%20point%20distance%7D%0A%5C%5C%5C%5C%0A4p%28y-%20k%29%3D%28x-%20h%29%5E2%0A%5Cqquad%0A%5Cbegin%7Barray%7D%7Bllll%7D%0Avertex%5C%20%28%20h%2C%20k%29%5C%5C%5C%5C%20p%3D%5Ctextit%7Bdistance%20from%20vertex%20to%20%7D%5C%5C%0A%5Cqquad%20%5Ctextit%7B%20focus%20or%20directrix%7D%0A%5Cend%7Barray%7D%0A%5C%5C%5C%5C%5B-0.35em%5D%0A%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%0A%5Cbegin%7Bcases%7D%0Ah%3D3%5C%5C%0Ak%3D6%5C%5C%0Ap%3D-2%0A%5Cend%7Bcases%7D%5Cimplies%204%28-2%29%28y-6%29%3D%28x-3%29%5E2%5Cimplies%20-8%28y-6%29%3D%28x-3%29%5E2%0A%5C%5C%5C%5C%5C%5C%0Ay-6%3D%5Ccfrac%7B%28x-3%29%5E2%7D%7B-8%7D%5Cimplies%20%5Cblacktriangleright%20y%3D-%5Ccfrac%7B1%7D%7B8%7D%28x-3%29%5E2%2B6%20%5Cblacktriangleleft)
The wide of the model should be approximately 5.194 inches
Step-by-step explanation:
You are building a scale model of a fishing boat
- The boat is 62 ft long
- The boat is 23 ft wide
- The model will be 14 in long
We need to find how wide should it be
∵ The boat is 62 feet long
∵ The model of the boat is 14 inches long
- That means 14 inches represents 62 feet
By using the ratio method
→ Actual (ft) : Model (in)
→ 62 : 14
→ 23 : x
By using cross multiplication
∵ 62 × x = 23 × 14
∴ 62 x = 322
- Divide both sides by 62 to find x
∴ x ≅ 5.194
∵ x represents the wide of the model
∴ The wide of the model is approximately 5.194 inches
The wide of the model should be approximately 5.194 inches
Learn more:
You can learn more about the scale drawing in brainly.com/question/570757
#LearnwithBrainly
Answer:
below
Step-by-step explanation:
10ˣ = 5
applying log to both sides
xlog 10 = log5
x = 0•699
