Answer:
The correct answer is 218 math textbooks and 259 sociology textbooks.
Step-by-step explanation:
To solve this problem, we can make a system of equations. Let the number of sociology textbooks sold be represented by the variable "s" and the number of math textbooks sold be represented by the variable "m". Using these variables, we can make two equations:
s + m = 477
m + 41 = s
There are many ways to solve this system of equations. One approach we can take is substituting the value for s given by the second equation into the first equation. This is modeled below.
s + m = 477
(m + 41) + m = 477
Combining like terms on the left side of the equation yields:
2m + 41 = 477
Subtracting 41 from both sides of the equation gives us:
2m = 436
Finally, dividing both sides of the equation by 2 gives us:
m = 218
To solve for the number of sociology textbooks, we can substitute into either of our original equations.
m + 41 = s
(218) + 41 = s
s = 259
Therefore, your answer is m = 218 and s = 259, or 218 math textbooks and 259 sociology textbooks were sold.
Hope this helps!
Answer:
- r(0) = <0, 100> . . . . . . . .meters
- r'(0) = <7.071, 7.071> . . . . meters per second
Step-by-step explanation:
<u>Initial Position</u>
The problem statement tells us we're measuring position from the ground at the base of the building where the projectile was launched. The initial horizontal position is presumed to be zero. The initial vertical position is said to be 100 meters from the ground, so (in meters) ...
r(0) = <0, 100>
<u>Initial Velocity</u>
The velocity vector resolves into components in the horizontal direction and the vertical direction. For angle α from the horizontal, the horizontal component of velocity is v₁·cos(α), and the vertical component is v₁·sin(α). For v₁ = 10 m/s and α = π/4, the initial velocity vector (in m/s) is ...
r'(0) = <10·cos(π/4), 10·sin(π/4)>
r'(0) ≈ <7.071, 7.071>
18.5•40=740
40•1.5=60
60•5.5=330
740+330=1070
A: $1070
Answer:
Ight...
Step-by-step explanation:
Hi
Answer:
The area of the sector is 26.69
Step-by-step explanation:
First of all we need to calculate the area
To solve this problem we need to use the area formula of a circle:
a = area
r = radius = 3
π = 3.14
a = π * r²
we replace with the known values
a = 3.14 * (3)²
a = 3.14 * 9
a = 28.26
The area of the circle is 28.26
A complete circle has 2pi radians
We divide 17/9 pi by 2pi and obtain the fraction of the total circle
(17pi/9) / 2pi = 17/18
we multiply this fraction with the area of the circle and obtain the area of the sector
28.26 * 17/18 = 12.43cm
The area of the sector is 26.69