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2 years ago

which side lengths form a right triangle

Mathematics

2 answers:

katrin [286]2 years ago

4 0

Answer:

I think b

Step-by-step explanation:

m_a_m_a [10]2 years ago

3 0

Answer:

Step-by-step explanation:

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Find the exact length of the curve. x=et+e−t, y=5−2t, 0≤t≤2 For a curve given by parametric equations x=f(t) and y=g(t), arc len

Rama09 [41]

The length of a curve C parameterized by a vector function r(t) = x(t) i + y(t) j over an interval a ≤ t ≤ b is

$\displaystyle\int_C\mathrm ds = \int_a^b \sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2} \,\mathrm dt$

In this case, we have

x(t) = exp(t ) + exp(-t ) ==> dx/dt = exp(t ) - exp(-t )

y(t) = 5 - 2t ==> dy/dt = -2

and [a, b] = [0, 2]. The length of the curve is then

$\displaystyle\int_0^2 \sqrt{\left(e^t-e^{-t}\right)^2+(-2)^2} \,\mathrm dt = \int_0^2 \sqrt{e^{2t}-2+e^{-2t}+4}\,\mathrm dt$

$=\displaystyle\int_0^2 \sqrt{e^{2t}+2+e^{-2t}} \,\mathrm dt$

$=\displaystyle\int_0^2\sqrt{\left(e^t+e^{-t}\right)^2} \,\mathrm dt$

$=\displaystyle\int_0^2\left(e^t+e^{-t}\right)\,\mathrm dt$

$=\left(e^t-e^{-t}\right)\bigg|_0^2 = \left(e^2-e^{-2}\right)-\left(e^0-e^{-0}\right) = \boxed{e^2-\frac1{e^2}}$

5 0

2 years ago

Complete the table of ordered pairs for the linear y=2x-8

ExtremeBDS [4]

Given:

Consider the below figure attached with this question.

The linear equation is:

$y=2x-8$

To find:

The values to complete the table of ordered pairs for the given linear equation.

Solution:

We have,

$y=2x-8$

Substituting $x=0$ in the given equation, we get

$y=2(0)-8$

$y=0-8$

$y=-8$

So, the value for first blank is -8.

Substituting $y=-2$ in the given equation, we get

$-2=2x-8$

$-2+8=2x$

$\dfrac{6}{2}=x$

$3=x$

So, the value for second blank is 3.

Substituting $x=2$ in the given equation, we get

$y=2(2)-8$

$y=4-8$

$y=-4$

So, the value for third blank is -4.

Therefore, the required complete table is:

x y

0 -8

3 -2

2 -4

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2 years ago

How does the position of the decimal point in a quotient as you divide by increasing powers of 10

Digiron [165]

The value decimal point is changing going to the right as you divide a number by 10. For example => 2000.3 / 10 notice the decimal point => 200.013, the value of decimal numbers increases as the value of whole number decreases.Let’s divide again => 200.013 / 10 => 20.0013 , now we already have 4 digits in our decimals. So, simply as we divide the given number by 10, the decimal point moves to the left making the value of whole number decreases and making the number of digits of decimal increase.

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3 years ago

Determine the intervals on which the function is increasing, decreasing and constant

viva [34]

Answer:

increasing: (-∞, 0)
decreasing: (0, ∞)

Step-by-step explanation:

The function goes up to the right until it gets to the vertex at x=0. Then it goes down to the right. That is, it is ...

increasing from -∞ to 0 (not including 0)

decreasing from 0 to +∞ (not including 0)

_____

At x=0, the function is neither increasing nor decreasing, so x=0 is not part of either interval.

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3 years ago

Explain how to find surface area of a rectangular prism. Be specific and use examples.

Leya [2.2K]

As you can see in the picture above, there are six faces of a rectangular prism; two are formed with dimensions width and height, two are formed by the dimensions length and width, and two are formed by the dimensions length and height. So, if you know the length, width, and height of the rectangular prism, then the formula for the surface area is

=(2⋅ℎ⋅ℎ)+(2⋅ℎ⋅ℎℎ)+(2⋅ℎ⋅ℎℎ)

4 0

3 years ago

￼ which side lengths form a right triangle￼

which side lengths form a right triangle