MATHEMATICS HIGH SCHOOL

Express the exact value of csc 60 degrees with a rational denominator?

Answers

Answer 1

Answer: $csc60^o=(1)/(sin60^o)=(1)/((\sqrt3)/(2))=(2)/(\sqrt3)=(2)/(\sqrt3)\cdot(\sqrt3)/(\sqrt3)=(2\sqrt3)/(3)$

Answer 2

Answer:

Note that the exact value of csc 60° with a rational denominator is (2√3)/3.

How to compute the above

The reciprocal identity states that csc(theta) = 1/sin(θ).

Since we know that sin 60 degrees = √3/2, we can substitute this value into the reciprocal identity -

csc 60° = 1/(√3/2).

To rationalize the denominator, we multiply the numerator and denominator by the conjugate of the denominator -

csc 60°= (1/(√3/2)) * (√3/√3).

csc 60° = √3/(√3 * (√3/2)).

= √3/(√3 * √3/2).

= √3/(√9/2).

= √3/(3/2).

To divide by a fraction, we multiply by its reciprocal -

csc 60° = √3 * (2/3).

csc 60° = (2√3)/3.

So it is correct to state that , the exact value of csc 60° with a rational denominator is (2√3)/3.

Learn more about rational denominator at:

brainly.com/question/14261303

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In a scale drawing of a house, 1 inch represents 3 feet. (a)The length of the real house is 21 feet. What is the length of the house in the scale drawing? _ inches

Answers

Answer:

7 inches

Step-by-step explanation:

divide 21 by 3

Graph the equation 5y-3x=-15

Answers

5y - 3x = - 15

isolate y for 5y - 3x = -15

y = -15 + 3x / 5

x - axis interception point of -15 + 3x / 5 ( 5,0 )

y - axis interception point of -15 + 3x / 5 ( 0, -3)

attached image.

hope this helps!

5y-3x=-15y=(-15+3x)/5
y=3/5x-3

When x = 0 y =-3
When y = 0 x = 5
When x = 10 y = 3
When x = -5 y = - 6
When x = -10 y = -9

Help with this question? I got half of it, but can't seem to get the other half. Please explain how you got your answer. Thanks!1. The equation of a plane in space is x + 3y + 2z = 6.
a.) Accurately sketch the plane on the set of axes, showing all your calculations below.
b.) The three planes of the axes and the plane you have sketched create a triangular pyramid. Find the volume of this pyramid, showing the formula you are using and all
calculations below.

My Answer:
a. I started off by finding my x-intercept. To find my x-intercept I substituted y and z with 0. So: x + 3(0) + 2(0) = 6. After multiplying and adding, I end up with x = 6. So my x-intercept is (6, 0, 0,). T find my y-intercept I substituted x and z with 0. So: 0 + 3y + 2(0) = 6. After multiplying and adding, we come up with 3y = 6. Now we divide each side by 3 to get y = 2. So my y-intercept is (0, 2, 0). To find my z-intercept, I substituted x and y with 0. So, 0 + 3(0) + 2z = 6. After multiplying and adding, I get 2z = 6. Now I divide each side by 2 to get z = 3. So my z-intercpet is (0, 0, 3). After I plotted the points and connected them, they formed a triangular pyramid.

So thats how much i got. I cant seem to figure out how to get the volume. please help.

Answers

Answer:

Volume of the pyramid = 6 cubic units

Step-by-step explanation:

The volume of a triangular pyramid is: V = (1/3)*A*H

where A is the area of the triangle base, and H is the height of the pyramid.

Taking the triangle formed in the x-y plane as the base, its area is computed as follows:

A = (1/2)*6*2 = 6 square units

where 6 and 2 are the measure of the two perpendicular sides of the triangle. This is taken from the x-intercept point (6, 0, 0) and y-intercept point (0, 2, 0).

The height of the pyramid is then the measure of the z-intercept point (0, 0, 3), that is, 3. Replacing in volume formula:

V = (1/3)*A*H

V = (1/3)*6*3

V = 6 cubic units

X - Intercept
    x + 3y + 2z = 6
x + 3(0) + 2(0) = 6
      x + 0 + 0 = 6
      x + 0 = 6
   - 0 - 0
      x = 6
X - Intercept: (6, 0, 0)

Y - Intercept
x + 3y + 2z = 6
0 + 3y + 2(0) = 6
    0 + 3y + 0 = 6
    0 + 0 + 3y = 6
      0 + 3y = 6
      - 0    - 0
      3y = 6
   3    3
      y = 2
Y - Intercept: (0, 2, 0)

Z - Intercept
x + 3y + 2z = 6
0 + 3(0) 2z = 6
0 + 0 + 2z = 6
      0 + 2z = 6
      - 0    - 0
      2z = 6
   2    2
      z = 3
Z - Intercept: (0, 0, 3)

Volume of the X - Intercept, Y - Intercept, and Z - Intercept
V = ¹/₃(¹/₂lwh)
V = ¹/₃(¹/₂(6)(2)(3))
V = ¹/₃(¹/₂(12)(3))
V = ¹/₃(¹/₂(36))
V = ¹/₃(18)
V = 6 u³

At basketball practice,charle made 52 baskets out of 80 what percent of the baskets did he make