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3 years ago

Whats the difference between a subset and a proper subset? {5,8} {2,5,8} Is {5,8} a subset of {2,5,8}.

Mathematics

1 answer:

valina [46]3 years ago

8 0

Answer:

$\{5,8\}$ is a subset of $\{2,5,8\}$

Step-by-step explanation:

Required

Difference between subset and proper subset

To answer this question, I will use the following illustration.

$A = \{1,2,3\}$

$B = \{2,3\}$

$C = \{1,2,3\}$

In the above sets, set B is a proper subset of set A because all elements of B can be found in A, but not element of A can be found in B.

Set C is a subset of A because $A = C$

Using the above illustration, we have:

$\{5,8\}$ and $\{2,5,8\}$

$\{5,8\}$ is a subset of $\{2,5,8\}$ , because 5 and 8 are in $\{2,5,8\}$ but 2 which ca be found in $\{2,5,8\}$ is not in $\{5,8\}$

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Jim is building a model of a square pyramid for a class project. The side length of the square base is 20 inches and the slant h

Brums [2.3K]

Answer:

$SA = 920 inches^{2}$

Step-by-step explanation:

Given Data:

Slant height of square pyramid = l = 13 inches

Base edge of square pyramid = s = 20 inches

To Find Out:

Surface area of square pyramid = SA = ?

Formula:

$SA = s^{2} + 2 * s * l$

Solution:

$SA = s^{2} + 2 * s * l$

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3 years ago

Find the general expression for the slope of a line tangent to the curve of y=2x^2+4x at the point P(x,y) . Then find the slopes

ArbitrLikvidat [17]

Complete Question

Find the general expression for the slope of a line tangent to the curve of y=2x^2+4x at the point P(x,y) . Then find the slopes for $x = 3$ and x=0.5. Sketch the curve and the tangent lines. What is the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) ?

Answer:

The generally expression for the slope of $y = 2x^2 + 4x$ is $y' = 4x +4$

The graph is shown on the first uploaded image

The generally expression for the slope of $y=2x^2+4$ is $y' = 4x$

Step-by-step explanation:

From the question we are told that

The equation of the curve is $y = 2x^2 + 4x$

First we differentiate the equation

$y' = 4x +4$

Therefore the generally expression for the slope tangent to the curve $y=2x^2+4x$ is $y' = 4x +4$

The next step is to substitute for x = 3 and x = 0.5

So for $x_1 = 3$

$y' = 4(3) +4$

$y' =m_1= 16$

And for $x_2 = 0.5$

$y' = 4(0.5) +4$

$y' =m_2= 6$

Here m_1 and m_2 are slops of the curve

Next we obtain the coordinates of the tangent lines

So at $x_1 = 3$

$y_1 = 2(3)^2 + 4(3)$

$y_1 = 21$

So the coordinate for the first tangent line is

$(x_1 , y_1 ) = (3 , 21)$

At $x_2 = 0.5$

$y_2 = 2(0.5)^2 + 4(0.5)$

=> $y_2 = 2.5$

So the coordinate for the second tangent line is

$(x_2 , y_2 ) = (0.5 , 2.5)$

Next we obtain the equation for the tangent lines

So generally the slope is mathematically represented as

$m = \frac{y - y_1 }{x-x_1}$

For $(x_1 , y_1 ) = (-3 , 21)$ and $y' =m_1= 16$

$16 = \frac{y -21 }{x-3)}$

=> $y = 16x - 27$

For $(x_2 , y_2 ) = (0.5 , 2.5)$ and $y' =m_2= 6$

$6 = \frac{y -2.5 }{x-0.5}$

$y = 6x -0.5$

Generally the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) is mathematically evaluated by differentiating y=2x^2+4 as follows

$y' = 4x$

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