<span>I am assuming that this is a parametric curve.
We see that the curve intersects the x-axis when:
t - t^2 = 0 ==> t = 0 and t = 1.
Then, since x = 1 + e^t is an increasing function, the curve is being traced exactly once on the interval (0, 1).
Using the fact that the area under the curve given by the parametric equations x = f(t) and y = g(t) on (a, b) is:
A = ∫ f'(t)g(t) dt (from t=a to b),
and that f(t) = 1 + e^t ==> f'(t) = e^t, the area under the curve is:
A = ∫ e^t(t - t^2) dt (from t=0 to 1)
= e^t(-t^2 + 3t - 3) (evaluated from t=0 to 1), by integrating by parts
= e(-1 + 3 - 3) - (0 + 0 - 3)
= 3 - e. </span>
Answer:
The experimenta probability of picking a 4 is 
Step-by-step explanation:
To determine the experimental probability, we just need to divide the number of observations of the specific event by the total number of trials. In this case, we are interested in the event "picking a 4 card". This event happened 4 times. We have a total number of trials of 50. So , the experimental probability is

Answer:


Step-by-step explanation:
From the question we are told that
Sides difference 
Area difference 
Let first square be A
Let second square be B
Generally the area of a square is mathematically given by
Area of a square
Area of a square

Therefore from the equations above




Therefore
Side of the first square

Side of the second square.

Check answer

Answer:
Step-by-step explanation:
4 packs of balloons, 2 packages of plant food, flowers cost, sales tax equal to Total Amount Paid.
Now to find the cost of 2 packs of plant food,
Total Amount Paid-sales tax-4 packs of balloons-flowers cost=2 packs of plant food
Now,
2 packs of plant food/2=cost of 1 pack of plant food
Answer:
Option A.
Step-by-step explanation:
we know that
If AB is tangent to the circle
then
The triangle show in the figure must be a right triangle
Remember that
If a triangle is a right triangle, then the triangle must satisfy the Pythagorean Theorem
<u><em>Verify</em></u>
Applying the Pythagorean Theorem


-----> is not true
so
Is not a right triangle
therefore
line AB is not tangent to the circle