Explanation:
The parabola is a 'mountain'-type (because the coefficient of
x
2
is negative. Also, it is symmetrical in respect to the
y
-axis, because there is no
x
-term.
We can now simplify the problem to finding a rectangle with vertices at
(
0
,
0
)
,
(
x
,
0
)
,
(
0
,
y
)
and
(
x
,
y
)
and then double the
x
-values.
The area will then be
A
=
x
⋅
y
If we substitute the equation of the parabola for
y
:
A
=
x
⋅
(
49
−
x
2
)
=
49
x
−
x
3
To find the extremes (max of min) we need the derivative and set it to zero:
A
'
=
49
−
3
x
2
=
0
→
x
2
=
49
3
→
x
=
√
49
3
≈
4.04
...
(remember we will have to double that)
Use this in the original function:
y
=
49
−
x
2
=
49
−
49
3
=
98
3
≈
32.67
Answer :
Dimensions will be
8.08
x
32.67
graph{49-x^2 [-65.4, 66.33, -13.54, 52.3]}
Answer: F is 11m.
Step-by-step explanation: Because H,I,G are all increasing their numbers like plus 3, plus 2, and the last one has to be plus 1.
Answer:
5.7
Step-by-step explanation:
The altitude divides right triangle ABC into similar right triangles ADB and BDC. The ratios of short leg to long leg will be proportional in these similar triangles, so you have ...
AD/BD = BD/CD
Cross multiplying gives ...
AD·CD = BD²
(x+3)(2x+3) = 5²
2x² +9x = 16 . . . . . perform the multiplication, subtract 9
2(x² +4.5x) = 16
2(x² +4.5x +2.25²) = 16 +2(2.25²) . . . . . add 2(2.25²) to complete the square
2(x +2.25)² = 26.125 . . . . . write as a square
x +2.25 = √13.0625 . . . . . .divide by 2, take the positive square root
x = -2.25 +√13.0625 . . . . subtract 2.25 to find x
We want the value of CD, so ...
CD = 2x +3 = 2(-2.25 +√13.0625) +3
CD = -1.5 +2√13.0625 ≈ 5.7284
The length of CD is about 5.7 units.
Answer:
The sum of 15 and a number is
85 - 15 = 70
Answer: D
Step-by-step explanation:
Formula= 2piRh +2piR^2
2pi*7*11 + 2pi*49 = 791.68 or 792
