slope = - 
calculate the slope m using the gradient formula
m= (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (- 3, 6)
m = 
= 
= -
Answer:
lim(x---->0) = -5
Step-by-step explanation:
first: sin(x-π/2)= -cosx
so the equation will be :
lim(x---->0) = [-6cos(ax)-1}/cosx
solve :
lim(x---->0) = [-(6cos(a(0))-1}/cos(0)
cos0=1
lim(x---->0)=(-(6(1)-1)/1
lim(x---->0)=-6+1/1
lim(x---->0)=-5
log(x) + log(3) = log(18)
log(x) + 0.477121 = 1.255273
Add -0.477121 to both sides.
log(x) + 0.477121 + −0.477121 = 1.255273 + −0.477121
log(x)+0 = 0.778152
Divide both sides by 1.
log(x)+0/1 = 0.778152/1
log(x)=0.778152
Solve Logarithm
log(x) = 0.778152
10log(x) = 100.778152
x = 100.778152
x = 6.00001
Answer:
- dimensions: 12 ft by 5 ft
- area: 60 ft²
Step-by-step explanation:
Let x represent the shorter dimension in feet. Then the longer one is x+7 and the Pythagorean theorem tells us the relation of these to the diagonal is ...
x² + (x+7)² = 13²
2x² +14x + 49 = 169 . . . . eliminate parentheses
x² +7x -60 = 0 . . . . . subtract 169 and divide by 2
(x +12)(x -5) = 0 . . . . factor the equation
x = -12 or +5 . . . . . . . only the positive value of x is useful here.
The short dimension is 5 ft, so the long dimension is 12 ft. The area is their product, 60 ft².
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<em>Comment on finding the area</em>
The quadratic equation above can be rearranged and factored as ...
x(x +7) = 60
Since the dimensions of the garden are x and (x+7), this product is the garden's area. This equation tells us the area is 60. We don't actually have to find the dimensions.
