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3 years ago

What is the simplified form of 2 times 10 squared to the second power in standard notation?

Mathematics

2 answers:

Semmy [17]3 years ago

4 0

2 times 10 squared to the second power in standard notation

2 x(10^2)^2
=2x10^4
=20000

pav-90 [236]3 years ago

4 0

Original Form: (2*√10)^2

Standard Notation Form: 6.32455532034^2 = 40

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Ple help me whats the slope?

mestny [16]

Answer:

-4/3

Step-by-step explanation:

that is the answer...no explanation needed

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3 years ago

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Which explanation can be used to informally derive the formula for the volume of a cone? A. A cone consists of a circle as a bas

TEA [102]

Answer:

D. A cylinder is exactly 3 times bigger than a cone with the same height and radius. Therefore, the formula for the volume of a cone is 1/3 of the volume of a cylinder with the same height and radius.

Step-by-step explanation:

A cylinder and a cone with the same radius will have different volumes. This is because the cone comes to a point whereas the cylinder does not.

A filled cone will hold 1/3 of the amount of a cylinder with the same radius. This means that we can derive the formula for a cone by multiplying the formula for the volume of a cylinder by 1/3.

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4 years ago

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a farmer has 100m for fence avaibiable, with which he intends to build a pen for his sheep. he intends to create a rectangular p

Reika [66]

The perimeter of the area of the pen the farmer intends to build for his

ship includes the length of the permanent stone wall.

Response:

i) The length and width of the rectangular pen are; x, and $\dfrac{100 - x}{2}$ , therefore;

The area is; $A = \dfrac{1}{2} \cdot x \cdot (100 - x)$

$ii) \hspace{0.5 cm}\dfrac{dA}{dx} = 50 - x$

$\dfrac{d^2A}{dx^2} = -1$

iii) The value of x that makes the area as large as possible is x = 50

<h3>How is the function for the area and the maximum area obtained?</h3>

Given:

The length of fencing the farmer has = 100 m

Part of the area of the pen is a permanent stone wall.

Let x represent the length of the stone wall, we have;

2 × Width = 100 m - x

Therefore;

Width, w, of the rectangular pen, $w = \mathbf{\dfrac{100 - x}{2}}$

Area of a rectangle = Length × Width

Area of the rectangular pen, is therefore;

$A = x \times \dfrac{100 - x}{2} = \underline{\dfrac{1}{2} \cdot x \cdot (100 - x)}$

$ii) \hspace{0.5 cm} \mathbf{\dfrac{dA}{dx}}$ , and $\mathbf{\dfrac{d^2A}{dx^2} }$ are found as follows;

$\dfrac{dA}{dx} = \mathbf{\dfrac{d}{dx} \left( \dfrac{1}{2} \cdot x \cdot (100 - x) \right)} = \underline{50 - x}$

$\dfrac{d^2A}{dx^2} = \mathbf{ \dfrac{d}{dx} \left( 50 - x\right)} = \underline{-1}$

iii) The value of x that makes the area as large as possible is given as follows;

Given that the second derivative, $\dfrac{d^2A}{dx^2} =-1$ , is negative, we have;

At the maximum area, $\dfrac{dA}{dx} = \mathbf{0}$ , which gives;

$\dfrac{dA}{dx} = 50 - x = 0$

x = 50

The value of x that makes the area as large as possible is x = 50

Learn more about the maximum value of a function here:

brainly.com/question/19021959

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2 years ago

Find the equation of the line using the point-slope formula. Write the final equation using slope-intercept form. Perpendicular

polet [3.4K]

Answer:

Slope-intercept form: y = -5x - 8

Point-slope form: y - 2 = -5(x + 2)

Step-by-step explanation:

Given the equation, 5y = x - 4, which passes through point (-2, 2):

Transform the given equation into its slope-intercept form, y = mx + b.

In order to do so, divide both sides by 5 to isolate y:

5y = x - 4

$\displaystyle\mathsf{\frac{5y}{5}\:=\:\frac{1x\:-\:4}{5}}$

$\displaystyle\mathsf{y\:=\:\frac{1}{5}x\:-\:\frac{4}{5}}$ ⇒ This is the slope-intercept form of 5y = x - 4.

Next, we must determine the equation of the line that is perpendicular to $\displaystyle\mathsf{y\:=\:\frac{1}{5}x\:-\:\frac{4}{5}}$ .

<h2>Definition of Perpendicular Lines:</h2>

Perpendicular lines have negative reciprocal slopes. This means that if we multiply the slopes of two lines, their product will equal to -1.

In other words, if the slope of the given equation is m₁, and the slope of the other line perpendicular to the given linear equation is m₂, then: m₁ × m₂ = -1.

Slope of the given equation: m₁ = ⅕

$\displaystyle\mathsf{Slope\:of\:other\:line\:(m_2 )\:=\:-5\:or\:-\frac{5}{1}}$

If we multiply these two slopes:

m₁ × m₂ = -1

$\displaystyle\mathsf{m_1\:\times\\\:m_2\:=\:\frac{1}{5}\times\\-\frac{5}{1}\:=\:-1}$

Now that we have identified the slope of the other line that is perpendicular to 5y = x - 4, we must determine the y-intercept of the other line.

The y-intercept is the point on the graph where it crosses the y-axis, for which it is the value of "y" when its corresponding x-coordinate equals to zero (0).
Thus, the standard coordinates of the y-intercept is (0, b), for which its y-coordinate is the value of "b" in the slope-intercept form, y = mx + b.

Using the slope of the other line, m₂ = -5, and the given point, (-2, 2), substitute these values into the slope-intercept form to find the value of the y-intercept, b:

y = mx + b

2 = -5(-2) + b

2 = 10 + b

Subtract 10 from both sides to isolate b:

2 - 10 = 10 - 10 + b

-8 = b

The equation of the other line that is perpendicular to 5y = x - 4 is:

Linear Equation that is perpendicular to 5y = x - 4 in slope-intercept form:

<h2>Rewrite the Equation in Point-slope Form:</h2>

The point-slope form is: y - y₁ = m(x - x₁)

In order to rewrite y = -5x - 8 in its point-slope form, we must substitute the value of the given point, (-2, 2) into the point-slope form:

y - y₁ = m(x - x₁)

y - 2 = -5[x - (-2)]

y - 2 = -5(x + 2) ⇒ This is the point-slope form of the line that is perpendicular to 5y = x - 4.

6 0

3 years ago

Translate each equation into slope-intercept form. Then, state the slope and y-intercept . 4y=2x+20

likoan [24]

Answer:

The slope-intercept form of the equation: y = 0.5x + 5

The slope: m = 0.5

The y-intercept: b = 5

Step-by-step explanation:

Slope-intercept form is y = mx + b, where m is the slope and b is y-intecept

4y = 2x + 20 {divide both sides by 4}

y = 0.5x + 5 ⇒ m = 0.5 and b = 5

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3 years ago