Let x=height. then base is x+4. plug what we know into the formula for the area of a triangle
A=½bh
16=½*(x+4)*(x)
32=x²+4x
x²+4x-32=0
(x+8)(x-4)=0
so x can be-8 our 4. when we plug-8 in for x we get a negative height. since a triangle cannot have a negative side length we discard-8 and try 4. height=4 and base=8
At point of intersection the two equations are equal,
hence, 6x³ =6x²
6x³-6x²=0
6x²(x-1)=0 , the values of x are 0 and 1
The points of intersection are therefore, (0,0) and (1,6)
To find the slopes of the tangents at the points of intersection we find dy/dx
for curve 1, dy/dx=12x, and the other curve dy/dx=18x²
At x=0, dy/dx=12x =0, dy/dx=18x² = 0, hence the angle between the tangents is 0, because the tangents to the two curves have the same slope which is 0 and pass the same point (0,0) origin.
At x=1, dy/dx =12x = 12, dy/dx= 18x² =18, Hence the angle between the two tangents will be given by arctan 18 -arctan 12
= 86.8202 - 85.2364 ≈ 1.5838, because the slope of the lines is equal to tan α where α is the angle of inclination of the line.
Answer:
-y=-x
The problem:
y=x then -y=?
Step-by-step explanation:
If y=x, then -y=-x.
Just like if u=9, then -u=-9.
Or, if -m=8, then m=-8.
Answer:
248
Step-by-step explanation:
Solution for What is 400 percent of 62:
400 percent *62 =
(400:100)*62 =
(400*62):100 =
24800:100 = 248
Now we have: 400 percent of 62 = 248
Question: What is 400 percent of 62?
Percentage solution with steps:
Step 1: Our output value is 62.
Step 2: We represent the unknown value with $x$.
Step 3: From step 1 above,$62=100\%.
Step 4: Similarly, x=400\%.
Step 5: This results in a pair of simple equations:
62=100\%(1).
x=400\%(2).
Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both
equations have the same unit (%); we have
\frac{62}{x}=\frac{100\%}{400\%}
Step 7: Again, the reciprocal of both sides gives
\frac{x}{62}=\frac{400}{100}
\Rightarrow x=248
Therefore, 400 of 62 is 248
Answer:
2x+20 + x+40 = 180
Step-by-step explanation:
The angles are supplementary so they add to 180
2x+20 + x+40 = 180
