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3 years ago

Finding the surface area

Mathematics

1 answer:

mars1129 [50]3 years ago

7 0

So hmm notice the picture below

the triangular prism, is really just 3 rectangles and 2 triangles, stacked up to each other at the edges

now, just get the area of the triangles and the rectangles, and add them up, and that's the surface area of the triangular prism

now, what's the length "x"? well $\bf x^2=5^2+7^2\implies x=\sqrt{25+49}\implies x=\sqrt{74}$

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Warren picked 3/4 of a pound of strawberries. That afternoon, Warren's

Crazy boy [7]

Answer: 2

Step-by-step explanation:

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3 years ago

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How many extraneous solutions exist for the logarithmic equation below if it is solved in the most efficient way possible?log_(2

Nadusha1986 [10]

Answer:

No extraneous solution

Step-by-step explanation:

We have the logarithmic equation given by,

$\log_{2}[\log_{2}(\sqrt{4x})]=1$

i.e. $\log_{2}(\sqrt{4x})=2^{1}$

i.e. $\sqrt{4x}=2^{2}$

i.e. $\sqrt{4x}=4$

i.e. $4x=4^{2}$

i.e. $4x=16$

i.e. $x=4$

So, the solution of the given equation is x=4.

Now, as we domain of square root function is x > 0 and also, the domain of logarithmic function is $( 0,\infty )$ .

Therefore, the domain of the given function is x > 0.

We know that the extraneous solution is the solution which does not belong to the domain.

But as x=4 belongs to the domain x > 0.

Thus, x = 4 is not an extraneous solution.

Hence, this equation does not have any extraneous solution.

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3 years ago

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The vertices of a square CDEF are C(1,1), D(3,1), E(3,-1) and F(1,-1). What formulas prove that the diagonals are congruent perp

Oxana [17]

To prove that the diagonals are congruent, you need to formula to compute the distance between two points:

$d(A,B) = \sqrt{(A_x-B_x)^2 + (A_y-B_y)^2}$

Using that formula, you may prove that $d(C,E) = d(D,F)$ , which means that the two diagonals have the same length.

To prove that they are perpendicular, you need the formula to compute the slope of a segment. The slope, knowing the enpoints, is given by

$m = \cfrac{\Delta y}{\Delta x} = \cfrac{A_y-B_y}{A_x-B_x}$

You can use this formula to prove that

$m_{CE} = -\cfrac{1}{m_{DF}}$

In fact, if one slope is the opposite of the reciprocal of the other, the two segments are perpendicular.

Finally, to prove that they bisect each other, you first need to find the point where they meet. First of all, you need to find the line the segments lie on: the formula is

$y-y_0 = m(x-x_0)$

where $(x_0,y_0)$ is one of the points belonging to the line, and you already know how to find the slope. Then, you find the point of intersection, say A, by solving the system involving the two lines: