(Will give Brainliest)

For the following right triangle, find the side length x. Round your answer to the nearest hundredth.

tia_tia [17]

<h3>Answer: 6.93</h3>

Work Shown:

Use the pythagorean theorem to find x

a^2 + b^2 = c^2

x^2 + 11^2 = 13^2

x^2 + 121 = 169

x^2 = 169 - 121

x^2 = 48

x = sqrt(48)

x = 6.92820323027551

x = 6.93

5 0

3 years ago

Read 2 more answers

Find the volume of the wedge with vertices at points (0,0,0), (1,0,0), (0,1,0), (0,0,1) by integrating the area of cross-section

Angelina_Jolie [31]

Answer:

V = 1/6 cubic units

Step-by-step explanation:

Applying the concept of integrals for volume calculation:

$V = \int\limits^b_a {S(x)} \, dx$ (1)

V = volume of the solid bounded by x = a and x = b

S(x) = cross section area of the solid, perpendicular to the x axis

From the figure we have that S is the area of a triangle that has base Z and height Y

Area of the triangle = $S(x)=\frac{y(x)*z(x)}{2}$ (2)

Calculation of y(x) and z(x)

We apply the equation of the point-slope line (plane xy):

Slope = $m = \frac{y_{2} - y_{1} }{x_{2} - x_{1}}$ (3)

Equation of the line = $y - y_{1} =m(x-x_{1} )$ (4)

Replacing the points (1,0) and (0,1) in (3):

$m=\frac{1-0}{0-1} =-1$

Replacing the point (1,0) and m = -1 in (4):

$y-0=(-1)(x-1)$

y(x) = -x + 1 (Line A-B) (5)

We apply the equation of the point-slope line (plane xz):

Slope = $m = \frac{z_{2} - z_{1} }{x_{2} - x_{1}}$ (6)

Equation of the line = $z - z_{1} =m(x-x_{1} )$ (7)

Replacing the points (1,0) and (0,1) in (6):

$m=\frac{1-0}{0-1} =-1$

Replacing the point (1,0) and m = -1 in (7):

$z-0=(-1)(x-1)$

z(x) = -x + 1 (Line A-C) (8)

Replacing (5) and (8) in (2)

$S(x) = \frac{(-x + 1) * (-x + 1)}{2} =\frac{(-x + 1)^{2} }{2}$ (9)

Replacing (9) in (1) and knowing that a = 0 and b = 1:

$V = \int\limits^1_0 {\frac{(-x + 1)^{2} }{2}} \, dx = \int\limits^1_0 {\frac{x^{2}-2x+1 }{2}} \, dx$

$V =\frac{1}{2} (\frac{x^{3} }{3} -2\frac{x^{2} }{2} +x)$ evaluated from x=0 to x=1

$V= \frac{1}{2} (\frac{1}{3} -1 +1) = \frac{1}{6}$

3 0

3 years ago

What number would you add to the equation below to complete the square?x2 + 4x = 0?

julia-pushkina [17]

------------------------------------------------------------------
Equation
------------------------------------------------------------------
x² + 4x = 0

------------------------------------------------------------------
Add a constant
------------------------------------------------------------------
x² + 4x + (4/2)² - (4/2)² = 0 ← Add 2² to form perfect square

------------------------------------------------------------------
Evaluate bracket
------------------------------------------------------------------
x² + 4x + 2² - 2² = 0

------------------------------------------------------------------
Form the perfect square
------------------------------------------------------------------
(x + 2)² = 4

------------------------------------------------------------------
Square root both sides
------------------------------------------------------------------
(x+2) = $\pm$ √4

------------------------------------------------------------------
Evaluate the square root
------------------------------------------------------------------
(x+2) = $\pm$ 2

------------------------------------------------------------------
Solve x
------------------------------------------------------------------
x = 2 - 2 or x = -2 - 2

x = 0 or -4

------------------------------------------------------------------
Answer: The constant to add is 4 and the value of x = 0 or -4
------------------------------------------------------------------

7 0

3 years ago

In a call center that stays open all the time, calls arrive as a poisson process with a mean rate of 0.3 complaints per hour.(a)

DENIUS [597]

The probability the 51st call arriaves within 150hours is 0.0431, the probability the next call arrives within the next 2 hours 0.5488, the probability the sum of these 50 numbers is less than 356 is 0.4165.

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