F(x) = -2x^3+6x-4, g(x) = -1/2f(x)

Mathematics

1 answer:

m_a_m_a [10]3 years ago

6 0

That’s good because I can’t be motivated

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In the diagram of O, m∠JOK = 60° and OJ = 6 in. What is the exact area of the shaded region?

Sophie [7]

Answer: 6π

<u>Step-by-step explanation:</u>

Area of a circle is π r².

Area of a section of a circle is π r² × the section of the circle.

$A=\pi r^2\bigg(\dfrac{\theta}{360^o}\bigg)$

Given: r = 6, Ф = 60°

$A=\pi (6)^2\bigg(\dfrac{60^o}{360^o}\bigg)\\\\\\.\quad =\pi (6)^2\bigg(\dfrac{1}{6}\bigg)\\\\\\.\quad =6\pi$

3 0

3 years ago

The amount of $180.00 is what percent greater than $135.00

olga nikolaevna [1]

Percent change = ((new value) - (old value))/(old value) × 100%
= (180 -135)/135 × 100%
= 33 1/3%

180 is about 33% greater than 135.

8 0

4 years ago

Find two unit vectors orthogonal to both given vectors. i j k, 4i k

Maurinko [17]

The cross product of two vectors gives a third vector $\mathbf v$ that is orthogonal to the first two.

$\mathbf v=(\vec i+\vec j+\vec k)\times(4\,\vec i+\vec k)=\begin{vmatrix}\vec i&\vec j&\vec k\\1&1&1\\4&0&1\end{vmatrix}=\vec i+3\,\vec j-4\,\vec k$

Normalize this vector by dividing it by its norm:

$\dfrac{\mathbf v}{\|\mathbf v\|}=\dfrac{\vec i+3\,\vec j-4\,\vec k}{\sqrt{1^2+3^2+(-4)^2}}=\dfrac1{\sqrt{26}}(\vec i+3\,\vec j-4\vec k)$

To get another vector orthogonal to the first two, you can just change the sign and use $-\mathbf v$ .

6 0

3 years ago

A grain silo has a circular base with an area of 260 square feet and is 21 feet tall What is the total volume?

Leya [2.2K]

The correct answer is 5460 cubic feet or 5460 $ft^{3}$

Explanation:

The silo has a cylindrical shape, in this context, the volume of the silo or any other cylinder can be calculated by using the formula $Volume =\pi r^{2} h$ . In this formula the symbol $\pi$ refers to the number 3.1415..., the letter $r$ refers to the radius of the base and the letter $h$ refers to the height.

Moreover, in this case, it is known the heigh (21 feet) and the area of the base (260 square feet). Additionally, this area of the base is the result of the formula $Area = \pi r^{2}$ , which is exactly the first section of the formula to find the volume. This implies that by multiplying the area of the base by the height the volume is known. Here is the process: