Let the required equation be y = mx + c; where y = 1, m = f'(0), x = 0
f(a) = sec(a)
f'(a) = sec(a)tan(a)
f'(0) = sec(0)tan(0) = 0
y = mx + c
1 = 0(0) + c
c = 1
Therefore, required equation is
y = 1.
Answer:
27 and 153 degrees
Step-by-step explanation:
Delta math
Answer:
Total volume in the two glasses is 740 mL.
Step-by-step explanation:
Given:
Ratio of the volume of soda in glass A to the volume of glass B = 8/3 : 7/2
Volume of soda in glass A = 320mL
To Find :
The total volume in the two glasses = ?
Solution:
Let the volume of soda in glass B be x
then
Substituting the values ,
x = 420
Now total volume of soda in the two glasses
=> volume of soda in glass A + volume of soda in glass B
=> 320 + 420
=>740mL
Let us say that:
x = cost of shorts
y = cost of slacks
z = cost of sports coat
From the given statements, we can create the following
equations:
eqtn 1: 3 x + y =
10.96
eqtn 2: 7 x + 2 y +
z = 30.40
eqtn 3: 4 x + z =
14.45
Rewrite eqtn 1 explicit to y:
y = 10.96 – 3 x -->
eqtn 4
Rewrite eqtn 3 explicit to z:
z = 14.45 – 4x -->
eqtn 5
Plug in the values of y (eqtn 4) and z (eqtn 5) to eqtn
2:
7 x + 2 (10.96 – 3 x) + 14.45 – 4 x = 30.40
7 x + 21.92 – 6 x + 14.45 – 4 x = 30.40
- 3 x + 36.37 = 30.40
- 3 x = - 5.97
x = 1.99
Eqtn 4:
y = 10.96 – 3 x
y = 10.96 – 3 (1.99)
y = 4.99
Eqtn 5:
z = 14.45 – 4x
z = 14.45 – 4 (1.99)
z = 6.49
Therefore each shirt cost $1.99, each slacks cost $4.99,
and each sports coat cost $6.49.
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Answer:
Vertex is (-1, -9)
Step-by-step explanation:
To find the x-value of the vertex, we use the formula
x
=
−
b
2
a
(This is considered the axis of symmetry).
a
=
1
and
b
=
2
with
c
=
−
8
(These are the numbers in order)
By substituting we get
x
=
−
(
2
)
2
⋅
1
, which simplifies to
x
=
−
1
.
Once you find x, substitute back into the equation to find y.
y
=
(
−
1
)
2
+
2
(
−
1
)
−
8
y
=
1
−
2
−
8
y
=
−
9
Putting the two numbers together you get the coordinates
(
−
1
,
−
9
)
.
