Answer:
Draw a dot at (0, 1)
Draw dot at (-1, -1)
Draw dot at (1, 3)
Connect the dots with a straight line
Step-by-step explanation:
The given equation is in slope-intercept form (y = mx + b). In this form, m is the slope and b is the y-intercept (where the line crosses through the y-axis).
The slope is 2, also written as
. This means that the line goes up 2 units for each 1 unit to the right.
9514 1404 393
Answer:
8 and 8
Step-by-step explanation:
The magnitude of a number is the positive distance it is from the origin. The number 8 is 8 units from the origin (in the + direction). The number -8 is also 8 units from the origin (in the - direction).
Both 8 and -8 have a magnitude of 8 units.
Answer:
1/4
Step-by-step explanation:
First - Convert all fraction with the Greatest Common Factor of 12
12 1/2 = 150/12
4 1/4 = 51/12
2 2/3 = 96/12
Second - Subtract the patio wood and the total
150/12 - 51/12 - 96/12 = 3/12
Third - Simplify 3/12 to 1/4
1/4 of the total wood is left to build the frame of the birdhouse.
The volume of a cone with diameter d (and hence radius d/2) and height h is
![V_{\rm cone} = \dfrac\pi3 \left(\dfrac d2\right)^2 h](https://tex.z-dn.net/?f=V_%7B%5Crm%20cone%7D%20%3D%20%5Cdfrac%5Cpi3%20%5Cleft%28%5Cdfrac%20d2%5Cright%29%5E2%20h)
so each scoop holds
![V = \dfrac\pi3 \left(\dfrac{1\,\rm in}2\right)^2 \left(2\,\mathrm{in}\right) = \dfrac\pi6 \, \mathrm{in}^3](https://tex.z-dn.net/?f=V%20%3D%20%5Cdfrac%5Cpi3%20%5Cleft%28%5Cdfrac%7B1%5C%2C%5Crm%20in%7D2%5Cright%29%5E2%20%5Cleft%282%5C%2C%5Cmathrm%7Bin%7D%5Cright%29%20%3D%20%5Cdfrac%5Cpi6%20%5C%2C%20%5Cmathrm%7Bin%7D%5E3)
of coffee.
The volume of a cylinder with base diameter d and height h is
![V_{\rm cylinder} = \pi\left(\dfrac d2\right)^2 h](https://tex.z-dn.net/?f=V_%7B%5Crm%20cylinder%7D%20%3D%20%5Cpi%5Cleft%28%5Cdfrac%20d2%5Cright%29%5E2%20h)
so the coffee can contains
![W = \pi \left(\dfrac{6 \, \rm in}2\right)^2 \left(6\dfrac14 \, \mathrm{in}\right) = 2025\pi \,\mathrm{in}^3](https://tex.z-dn.net/?f=W%20%3D%20%5Cpi%20%5Cleft%28%5Cdfrac%7B6%20%5C%2C%20%5Crm%20in%7D2%5Cright%29%5E2%20%5Cleft%286%5Cdfrac14%20%5C%2C%20%5Cmathrm%7Bin%7D%5Cright%29%20%3D%202025%5Cpi%20%5C%2C%5Cmathrm%7Bin%7D%5E3)
of coffee.
One full scoop then uses up
of the total amount of coffee in the can, so you can make 12,150 cups of coffee.
Answer:
sin 3 θ = 3 sin θ - 4 sin³θ
Step-by-step explanation:
<u><em>Step(i):</em></u>-
Given sin 3 θ
= sin ( 2θ + θ )
apply trigonometric formula
<em> sin ( A + B) = sin A cos B + cos A sin B </em>
<em> sin 2 A = 2 sin A cos B</em>
<em> Cos 2 A = 1 - 2 sin² A </em>
<em> cos ² A - sin ² A = 1</em>
<u><em>Step(ii):</em></u>-
sin 3 θ = sin ( 2θ + θ )
= sin 2θ cosθ + cos2θ sin θ
= 2 sin θ cos θ cos θ +( 1 - 2 sin² θ )sin θ
= 2 sin θ (cos² θ ) + sin θ- 2 sin³ θ
= 2 sin θ ( 1- sin²θ) + sin θ- 2 sin³ θ
= 2 sin θ - 2sin³θ + sin θ- 2 sin³ θ
= 3 sin θ - 4 sin³θ
<u><em>Final answer</em></u> :-
sin 3 θ = 3 sin θ - 4 sin³θ