2x+3y=20 <br> -2x+y=4 <br> Solve algebraic

The curve with equation y=e^2x/4+3e^x has one stationary point.find the exact value of the coordinates of this point

Softa [21]

$y=\dfrac{e^{2x}}{4+3e^x}$
$\implies y'=\dfrac{2e^{2x}(4+3e^x)-3e^xe^{2x}}{(4+3e^x)^2}$
$\implies y'=\dfrac{8e^{2x}+3e^{3x}}{(4+3e^x)^2}$

Stationary points occur where the derivative is zero. The denominator is positive for all $x$ , so we only need to worry about the numerator.

$8e^{2x}+3e^{3x}=e^{2x}(8+3e^x)=0$

$e^{2x}>0$ for all $x$ , so we can divide through:

$8+3e^x=0\implies e^x=-\dfrac83$

But $e^x>0$ for all $x\in\mathbb R$ , so this function has no stationary points...

I suspect there may be a typo in the question.

6 0

3 years ago

Why is a parallelogram not the same type of quadrilateral as a trapezoid?

Liula [17]

A parallelogram has two pairs of opposite sides. A trapezoid only has one pair of parallel sides.

4 0

4 years ago

I have 3 slots left and 3 answers left. Fill them in pls and u get a brainlist :)

gulaghasi [49]

Answer:

Water (one oxygen atom bonded to two hydrogen atoms)

Step-by-step explanation:

The chemical formula for water is H²O. The H is the chemical symbol for Hydrogen and O is the chemical symbol for Oxygen. The 2 is a subscript which represents how many atoms of a certain element are in a molecule. In this case, the subscript ² comes after H, indicating that there are two Hydrogen atoms inside water. There is no subscript after O, meaning there is only one Oxygen atom. Therefore, there are two Hydrogen atoms and one Oxygen atom that bond to form water. Hope this helps :))

4 0

3 years ago

Draw polygon abcdef in this coordinate plane, given its vertices a=(-2,-3), b=(0,-3), c=(0,1), d=(3,1), e=(3,3), f=(-2,3)

tiny-mole [99]

The polygon abcdef in the coordinate plane shown with area of 18 square units.

<h3>What is a regular polygon?</h3>

A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.

We have vertices for the polygon:

a=(-2,-3), b=(0,-3), c=(0,1), d=(3,1), e=(3,3), f=(-2,3)

After marking the coordinates on the coordinate plane and connecting the lines, we will get a polygon.

We can find the area of the shape:

Area of the shape = 18 square units

Thus, the polygon abcdef in the coordinate plane shown with area of 18 square units.

Learn more about the regular polygon here:

brainly.com/question/11810316

#SPJ1

7 0

2 years ago

Plsssss help I got to pass

NikAS [45]

Answer: D

Step-by-step explanation:

A. Not A because more students answered anything but none

B. Not B because 20 + 30 = 50, 50 is more than 40

C. Not C because there are 10 students above none

D. D is the answer because we have no info abt how much people are being paid

6 0

3 years ago

2x+3y=20 -2x+y=4 Solve algebraic