What is the tan M, sin M and Cos M?

Find the probability of rolling a prime number on the first die and even number on the second

Zinaida [17]

Answer:

0.25

Step-by-step explanation:

Prime outcomes on a die: 2,3,5

P(prime) = 3/6 = 1/2

Even outcom: 2,4,6

P(even) = 3/6 = 1/2

P(prime & even)

= P(prime) × P(even)

= ½ × ½

= ¼ or 0.25

4 0

3 years ago

If two sides of a triangle are 9cm and 15cm in length, which COULD be the measure of the third side?

MArishka [77]

The lemght could be 15 because a triangle has two long sides and one short one and the two are equivalent

5 0

3 years ago

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

4 years ago

Identify the maximum and minimum values of the function y = 8 cos x in the interval [-2π, 2π]. Use your understanding of transfo

Lina20 [59]

Pls. see attachment for the answer.

5 0

3 years ago

What is the least possible degree of the polynomial graphed above?

Degger [83]

Considering it's critical points, it is found that the least possible degree of the polynomial graphed above is of 4.

<h3>What are the critical points of a function?</h3>

The critical points of a function are the values of x for which:

$f^{\prime}(x) = 0$

In a graph, they are the turning points, and if a function has n critical points, the least possible degree is of n + 1.

In this problem, the function has 3 turning points, at x = -3, between x = -3 and x = 3, and at x = 3, hence the least possible degree of the polynomial graphed above is of 4.

More can be learned about the critical points of a function at brainly.com/question/2256078

5 0

2 years ago