We are given two points: (4, -8) and (8, 5)
General equation of a line: y = mx + c
First find m (the gradient). There is a formula for this: (change in y)/(change in x) = gradient
(5 - -8) / (8 - 4) = (13) / (4) = 3.25 = m
y = 3.25x + c
Now we need to find c (the y-intercept; the value of y when x=0).
Substitute in any one of the coordinates - let's use (8, 5)
(5) = 3.25(8) + c
(5) = 26 + c
c = -21
The equation of the line: y = 3.25x - 21
I think that this answer is correct - sorry if it seems rushed.
Hope this answer helps :)
Answer:
The volume of the solid is 243
Step-by-step explanation:
From the information given:
BY applying sphere coordinates:
0 ≤ x² + y² + z² ≤ 81
0 ≤ ρ² ≤ 81
0 ≤ ρ ≤ 9
The intersection that takes place in the sphere and the cone is:
Thus; the region bounded is: 0 ≤ θ ≤ 2π
This implies that:
ρcosФ = ρsinФ
tanФ = 1
Ф = π/4
Similarly; in the X-Y plane;
z = 0
ρcosФ = 0
cosФ = 0
Ф = π/2
So here; 
Thus, volume: 
![V = \bigg [-cos \phi \bigg]^{\pi/2}_{\pi/4} \bigg [\theta \bigg]^{2 \pi}_{0} \bigg [\dfrac{\rho^3}{3} \bigg ]^{9}_{0}](https://tex.z-dn.net/?f=V%20%3D%20%5Cbigg%20%5B-cos%20%5Cphi%20%20%5Cbigg%5D%5E%7B%5Cpi%2F2%7D_%7B%5Cpi%2F4%7D%20%20%5Cbigg%20%5B%5Ctheta%20%20%5Cbigg%5D%5E%7B2%20%5Cpi%7D_%7B0%7D%20%5Cbigg%20%5B%5Cdfrac%7B%5Crho%5E3%7D%7B3%7D%20%20%5Cbigg%20%5D%5E%7B9%7D_%7B0%7D)
![V = [ -0+ \dfrac{1}{\sqrt{2}}][2 \pi -0] [\dfrac{9^3}{3}- 0 ]](https://tex.z-dn.net/?f=V%20%3D%20%5B%20-0%2B%20%5Cdfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%5D%5B2%20%5Cpi%20-0%5D%20%5B%5Cdfrac%7B9%5E3%7D%7B3%7D-%200%20%5D)
V = 243
Answer:
=-5x
Step-by-step explanation:
Remove parentheses (-a)=-a
= -5x.3
hoped i helped :) can i get brainiest
Answer:
P=$254
Step-by-step explanation:
let Hot N' Spicy be x
and Mild Mannered be y
the objective function is
38x+35y=P
the constraints are
1. tomato sauce
2x+3y=18--------1
2. hot peppers
2x+y=10--------2
solving 1 and 2 we have
using substitution method
2x+y=10--------2
y=10-2x
put y=10-2x in eqn 1
2x+3(10-2x)=18
2x+30-6x=18
2x-6x=18-30
-4x=-12
x=12/4
x=3
put x=3 in eqn 2 we have
2(3)+y=10
6+y=10
y=10-6
y=4
He should make 3 gallons of Hot N' Spicy
and 4 gallons Mild Mannered
38(3)+35(4)=P
114+140=P
254=P
P=$254
