X²/9 + y²/16 = 1
The general for mula of an ellipse is:
(x-h)²/a² + (y-k)²/b² = 1. Since h = k = 0, this ellipse
x²/9 + y²/16 = 1
passes by the center O. (Note that a = 3 and b = 4)
Moreover sin b>a so the majore axis is (on the y-axis) and a the minor axis (on the x-axis) [Its shape is as a vertical egg].
On a system of perpendicular axis that intercept in O., take on the x-axis 2 points A & B with respective coordinate A(3.0) and B(-3,0)
On the y-axis your report A'(0,+4) and B'(0,-4). So you have the vertex of the ellipse, then it's easy to draw it
Newton's Law of Cooling
Tf=Ts+(Ti-Ts)e^(-kt) where Tf is temp at time t, Ts is temp of surroundings, Ti is temp of object/fluid. So we need to find k first.
200=68+(210-68)e^(-10k)
132=142e^(-10k)
132/142=e^(-10k)
ln(132/142)=-10k
k=-ln(132/142)/10
k≈0.0073 so
T(t)=68+142e^(-0.0073t) so how long until it reaches 180°?
180=68+142e^(-0.0073t)
112=142e^(-0.0073t)
112/142=e^(-0.0073t)
ln(112/142)=-0.0073t
t= -ln(112/142)/(0.0073)
t≈32.51 minutes
The x- intercept is where y = 0 on the graph and the y- intercept is where x= 0 on the graph. When X=0, all the terms, except for the constant are equal to zero, thus the y- intercept is the constant. y=10 when x=0. Use the quadratic formula to find the x value where y=0.
x= (-b +or- sqrt(b^2 -4ac))/2a
y=ax^2 +bx +c
The answer for the x- int is imaginary. This happens because 10 is the parabola's minimum value and it never touches the x- axis. y-int is 10
Answer: 5.37
Step-by-step explanation:
Let x = ACT scores.
Given: ACT scores have a mean of 20.8 and 9 percent of the scores are above 28. The scores have a distribution that is approximately normal.
i.e. P(X>28)=0.09 (i)
Now,
![P(X>28)=P(\dfrac{X-\mu}{\sigma}>\dfrac{28-20.8}{\sigma})\\\\= P(z>\dfrac{7.2}{\sigma})\ \ \ \ [z=\dfrac{X-\mu}{\sigma}]](https://tex.z-dn.net/?f=P%28X%3E28%29%3DP%28%5Cdfrac%7BX-%5Cmu%7D%7B%5Csigma%7D%3E%5Cdfrac%7B28-20.8%7D%7B%5Csigma%7D%29%5C%5C%5C%5C%3D%20P%28z%3E%5Cdfrac%7B7.2%7D%7B%5Csigma%7D%29%5C%20%5C%20%5C%20%5C%20%5Bz%3D%5Cdfrac%7BX-%5Cmu%7D%7B%5Csigma%7D%5D)
(ii)
One -tailed z value for p-value of 0.09 =1.3408 [By z-table]
From (i) and (ii)
Hence, the standard deviation = 5.37
To answer this item, we assume that the topic is in similar polygons such that the ratio of the corresponding sides should be equal. In this item,
BY/YC = AX/XC
Substituting the known values,
6/10 = 18/XC
The value of XC from the equation is 30. The answer is letter C.
