The line y = x + 3 has slope 1, so we look for points on the curve where the tangent line, whose slope is dy/dx, is equal to 1.
y² = x
Take the derivative of both sides with respect to x, assuming y = y(x) :
2y dy/dx = 1
dy/dx = 1/(2y)
Solve for y when dy/dx = 1 :
1 = 1/(2y)
2y = 1
y = 1/2
When y = 1/2, we have x = y² = (1/2)² = 1/4. However, for the given line, when y = 1/2, we have x = y - 3 = 1/2 - 3 = -5/2.
This means the line y = x + 3 is not a tangent to the curve y² = x. In fact, the line never even touches y² = x :
x = y² ⇒ y = y² + 3 ⇒ y² - y + 3 = 0
has no real solution for y.
Answer:
49
Step-by-step explanation:
To complete the square we use the formula:
So we can plug in 14 for b to find c.
Now this equation can be factored into:
The numbers after the decimal place are represented as 10ths, hundredths, thousandths, and so on. 0.6 is said as "Zero point six tenths." Or "Zero and six tenths."
0.06 is said as "Zero point zero six hundredths." Or "Zero and six hundredths."
Answer:
The answer is 1,550
Step-by-step explanation:
First you find the area of the rectangle 1
Area = ab
=(21 in) (17in)
=357 sq in.
this will be the same for rectangle 3 = 357 sq. in.
next find the area of rectangle 2
area=ac
=(21 in) (11 in)
=231 sq in.
this will be the same for rectangle 4 = 231 sq. in.
next find the area of rectangle 5
area = bc
=(17 in) (11 in.)
=187 sq. in
this will be the same for rectangle 6 = 187 sq. in.
Next add all areas together
Total surface area = 2(ac) + 2(ab) + 2(bc)
= 2(231) sq in. + 2(357) sq in. + 2(187) sq. in
= 462 + 174+ 374
= 1550 sq. in
