Answer:dhfkasdlasuyf984r98yt4ewiuhkjsdehfkjldashfkjnklsdgdfbgjudfigjsoaifsdgfljgdfrkjsgldhsagkjdsahfldskjaghkjldhfsagkdjaslhdsafkljhdsakhfdsfhdkjasfdksjhfdskfdshfdskjfkjsdhfkljdsf
Step-by-step explanation:sdfhdskaaaaahlfkjsdhafdkjshfdkjsahfdsjkl;;lewqjrewrmnlfkjdssssssssscjo;lsdq'/d;nfdoljshasfjldksnfdkljscdslfndsofndsjkndsanfkldsaofkljdnasfokjidhasfkdh;.asfkjdsahf;ad.shjifadjsfkldsajfhdsajfkdsjnfdasjfcdslaaa
Answer:
a) Vertex is at (-3, -1)
b) y-intercept is at (0,8)
c) x intercept is at (-4,0) and (-2,0)
d) x=-3
Step-by-step explanation:
The vertex of a parabola is the lowest or highest point, implying that all points are reflected across it. It's the only y value that doesn't have a corresponding pair.
For example, -1 and 1, -3 and 3, and so on.
The vertex is at (-3,-1) because it is the sole point without a corresponding y value (-3,-1)
The y-intercept is where the parabola meets the y axis or when the x value equals 0. To determine the y-intercept, simply find when x = 0.
intercept y: (0,8)
The x-intercepts are the same as the y-intercepts; you must determine where the parabola crosses the x-axis or when y = 0.
x intercept 1:(-4,0)
x intercept 2: (-2,0)
The axis of symmetry is also the x coordinate of the vertex which is 3 so
x = 3
U mean y = 0.9^x ...?
.
its exponential decay...
.
because.. y = (1/e)^x is exponential decay...
.
(1/e) < 1
Answer:
- Base Length of 68cm
- Height of 34 cm.
Step-by-step explanation:
Given a box with a square base and an open top which must have a volume of 157216 cubic centimetre. We want to minimize the amount of material used.
Step 1:
Let the side length of the base =x
Let the height of the box =h
Since the box has a square base
Volume 
Surface Area of the box = Base Area + Area of 4 sides
Step 2: Find the derivative of A(x)
Step 3: Set A'(x)=0 and solve for x
![A'(x)=\dfrac{2x^3-628864}{x^2}=0\\2x^3-628864=0\\2x^3=628864\\x^3=314432\\x=\sqrt[3]{314432}\\ x=68](https://tex.z-dn.net/?f=A%27%28x%29%3D%5Cdfrac%7B2x%5E3-628864%7D%7Bx%5E2%7D%3D0%5C%5C2x%5E3-628864%3D0%5C%5C2x%5E3%3D628864%5C%5Cx%5E3%3D314432%5C%5Cx%3D%5Csqrt%5B3%5D%7B314432%7D%5C%5C%20x%3D68)
Step 4: Verify that x=68 is a minimum value
We use the second derivative test
Since the second derivative is positive at x=68, then it is a minimum point.
Recall:
Therefore, the dimensions that minimizes the box surface area are:
- Base Length of 68cm
- Height of 34 cm.
