Given the following equation of an exponential function determine the decay rate.

(Pls do solution or take picture)In the figure, ACEF is a rectangle and BC = CD DE The area of rectangle ACEF is 80 cm. Find the

poizon [28]

Answer:

28 cm²

Step-by-step explanation:

The area of Δ BDF is the area of the rectangle subtract the area of the 3 white triangles.

Since the area of the rectangle = 80 cm² and

area = length × breadth, then

breadth = 80 ÷ 10 = 8 cm

Thus CE = EF = 8 cm and CD = DE = BC = 4 cm

Area of Δ DEF = 0.5 × 10 × 4 = 20 cm²

Area of Δ ABF = 0.5 × 8 × (10 - 4) = 0.5 × 8 × 6 = 24 cm²

Area of Δ BCD = 0.5 × 4 × 4 = 8 cm²

Thus

area of Δ BDF = 80 - (20 + 24 + 8) = 80 - 52 = 28 cm²

6 0

4 years ago

What is the distance between the points (1, 25) and (4, 21)

Elena-2011 [213]

Hello!

To find the distance between the points (1, 25) and (4, 21), you need to use the distance formula.

The distance formula is: $d =\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$ . With the distance formula, you have to assign the ordered pairs before substituting them into the formula, which is also used to to find the slope of functions.

$d =\sqrt{(21-25)^{2}+(4-1)^{2}}$

$d =\sqrt{(-4)^{2}+(3)^{2}}$

$d=\sqrt{25}$

$d=5$

Therefore, the distance between the two points is 5 units.

4 0

3 years ago

Find the absolute maximum and absolute minimum values of f on the given interval.

anyanavicka [17]

The question is missing parts. Here is the complete question.

Find the absolute maximum and absolute minimum values of f on the given interval.

$f(x)=xe^{-\frac{x^{2}}{32} }$ , [ -2,8]

Answer: Absolute maximum: f(4) = 2.42;

Absolute minimum: f(-2) = -1.76;

Step-by-step explanation: Some functions have absolute extrema: maxima and/or minima.

Absolute maximum is a point where the function has its greatest possible value.

Absolute minimum is a point where the function has its least possible value.

The method for finding absolute extrema points is

1) Derivate the function;

2) Find the values of x that makes f'(x) = 0;

3) Using the interval boundary values and the x found above, determine the function value of each of those points;

4) The highest value is maximum, while the lowest value is minimum;

For the function given, absolute maximum and minimum points are:

$f(x)=xe^{-\frac{x^{2}}{32} }$

Using the product rule, first derivative will be:

$f'(x)=e^{-\frac{x^{2}}{32} }(1-\frac{x^{2}}{16} )$

$f'(x)=e^{-\frac{x^{2}}{32} }(1-\frac{x^{2}}{16} )$ = 0

$1-\frac{x^{2}}{16}=0$

$\frac{x^{2}}{16}=1$

$x^{2}=16$

x = ±4

x can't be -4 because it is not in the interval [-2,8].

$f(-2)=-2e^{-\frac{(-2)^{2}}{32} }=-1.76$

$f(4)=4e^{-\frac{4^{2}}{32} }=2.42$

$f(8)=8e^{-\frac{8^{2}}{32} }=1.08$

Analysing each f(x), we noted when x = -2, f(-2) is minimum and when x = 4, f(4) is maximum.

Therefore, absolute maximum is f(4) = 2.42 and

absolute minimum is f(-2) = -1.76

8 0

3 years ago

1/3 divided by 5/6a what is the answer please I don’t get it;(

Aleksandr [31]

Answer:to divide you have to have the same number for the bottom number so you will divide 2\6 by 5\6a and you will probably get a answer with a graphing calculator i hope this helps

Step-by-step explanation:

3 0

3 years ago

The radius of a circle is 6 inches. What is the area of a sector bounded by a 90° arc?

hjlf

Answer:

[1] Let's make the problem easier to start. Imagine that they had said to find the area of a sector bounded by a 360* arc (the whole circle). Could we have found the area then?

Sure we could! We know that A = pi*r^2, so that would just be:

A = pi*(6)^2 = 36*pi sq. miles.

Easy. But of course, we weren't so lucky... they want 135*... drat!

[2] Well, let's get a little closer, could we find the area if the angle was 180*? Sure! That's just half the circle. After all:

180*/360* = 1/2.

We know the whole circle is 36*pi sq. miles. So, the area bounded by a 180* arc would just be half of this: 18*pi sq. miles.

"But that's not the question," you scream!! Alright, alright, calm down... let's bring it all together.

[3] We know the area of the whole circle [1]. We also know that if we can figure out the fraction of the circle the problem is easy [2]. So, what fraction of a circle would match an arc of 135*?

Well, we can see that

135*/360* = 0.375 or 3/8

So the area is just 0.375 of the whole circle:

0.375* 36*pi sq. miles = 13.5*pi sq. miles

Read more on Brainly.com - brainly.com/question/2978439#readmore

7 0

3 years ago