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3 years ago

In Exercise, find the derivative of the function. y = ex - 4

Mathematics

1 answer:

Marianna [84]3 years ago

8 0

Answer: The required derivative would be $\dfrac{dy}{dx}=e^x$

Step-by-step explanation:

Since we have given that

$y=e^x-4$

We need to find the derivative of the above function:

As we know that

$\dfrac{d}{dx}e^x=e^x$

and

derivative of constant term = 0

So, the derivative w.r.t. x would be

$\dfrac{dy}{dx}=e^x-0=e^x$

Hence, the required derivative would be $\dfrac{dy}{dx}=e^x$

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Write an expression for the area of the shaded region in its simplest form. Show all of your steps.

netineya [11]

The area of the shaded region is going to be the area of the rectangle minus the area of the square.

Area of a rectangle is L * W.
A = L * W
A = (x + 10)(2x + 5)
A = x(2x + 5) + 10(2x + 5)
A = 2x^2 + 5x + 20x + 50
A = 2x^2 + 25x + 50 .....this is the area of the rectangle

area of a square is : A = a^2...where a is one side
A = (x + 1)^2
A = (x + 1)(x + 1)
A = x(x + 1) + 1(x + 1)
A = x^2 + x + x + 1
A = x^2 + 2x + 1

now we subtract the area of the square from the area of the rectangle to get the area of the shaded region.

2x^2 + 25x + 50 - (x^2 + 2x + 1) =
2x^2 + 25x + 50 - x^2 - 2x - 1 =
x^2 + 23x + 49 <== the area of the shaded region

6 0

3 years ago

What is the equation of a circle that has a center at (-4, 10) and a radius of 8?

mars1129 [50]

Answer:

The equation of the circle is $(x + 4)^2 + (y - 10)^2 = 64$ , third option is correct.

Step-by-step explanation:

Equation of a circle:

The equation of a circle with center $(x_0,y_0)$ and radius r is given by:

$(x - x_0)^2 + (y - y_0)^2 = r^2$

Center at (-4, 10)

This means that $x_0 = -4, y_0 = 10$ .

Radius of 8:

This means that $r = 8$ . So

$(x - x_0)^2 + (y - y_0)^2 = r^2$

$(x - (-4))^2 + (y - 10)^2 = 8^2$

$(x + 4)^2 + (y - 10)^2 = 64$

The equation of the circle is $(x + 4)^2 + (y - 10)^2 = 64$ , third option is correct.

3 0

3 years ago

Can you help me find the volume base area latera area and total area please to this problem

krek1111 [17]

Answer:

BA = 25π,

LA = 25√2π,

TA = 25π + 25√2π,

V = 41 and 2 / 3π

Step-by-step explanation:

We need to determine the height here, as it is not given, and is quite important to us. The height is a perpendicular line segment to the radius, hence forming a 45 - 45 - 90 degree triangle as you can see. Therefore, by " Converse to Base Angles Theorem " the height should be equal in length to the radius,

( Height = 5 inches = Radius

______

Now knowing the height, let's begin by calculating the base area. By it's name, we have to find the area of the base. As it is a circle, let us apply the formula " πr^2 "

$\pi r^2\\= \pi ( 5 )^2\\= 25\pi$ - Base Area = 25π

______

The lateral area is simply the surface area excluding the base area, the surface area having a formula of " πr^2 + πrl. " Thus, the lateral area can be calculated through the formula " πrl, " but as we are not given the slant height ( l ) we have to use another formula, $l= \sqrt{r^2+h^2}$ -