Answer:
The length of hypotenuse is 12.5
Step-by-step explanation:
First 7.5 x 7.5 = 56.25
Then 10 x 10 = 100
Add them together 56.25 + 100 = 156.25
Then square root 156.25 and you get 12.5
Slope of line = tan(120) = -tan(60) = - √3
Distance from origin = 8
Let equation be Ax+By+C=0
then -A/B=-√3, or
B=A/√3.
Equation becomes
Ax+(A/√3)y+C=0
Knowing that line is 8 units from origin, apply distance formula
8=abs((Ax+(A/√3)y+C)/sqrt(A^2+(A/√3)^2))
Substitute coordinates of origin (x,y)=(0,0) =>
8=abs(C/sqrt(A^2+A^2/3))
Let A=1 (or any other arbitrary finite value)
solve for positive solution of C
8=C/√(4/3) => C=8*2/√3 = (16/3)√3
Therefore one solution is
x+(1/√3)+(16/3)√3=0
or equivalently
√3 x + y + 16 = 0
Check:
slope = -1/√3 .....ok
distance from origin
= (√3 * 0 + 0 + 16)/(sqrt(√3)^2+1^2)
=16/2
=8 ok.
Similarly C=-16 will satisfy the given conditions.
Answer The required equations are
√3 x + y = ± 16
in standard form.
You can conveniently convert to point-slope form if you wish.
Step-by-step explanation:
remember, tan = sin/cos.
of course, one solution is x = 0. sin(0) = 0, tan(0)=0).
for the general solution we look at x <> 0.
3×sin(x) = 2×tan(x) = 2×sin(x)/cos(x)
3 = 2/cos(x)
3×cos(x) = 2
cos(x) = 2/3
x = 48.1896851...°
Answer:
Step-by-step explanation:
Stephen uses 
kilograms of tofu in each serving of his dish.
He has 
kilograms of tofu.
We want to determine how many servings Stephen can make.
To do this, we divide the total weight of tofu by the weight per serving.
Stephen can make .
