All categories

3 years ago

Find the equation of the tangent line to the graph of f(a) = sec(a) at the point (0, 1).

1 answer:

5 0

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.

You might be interested in

Answer both with STEPS

Amanda [17]

Answer:

7 )

x = $\frac{3\sqrt{2} }{2}$

$y= 3$

8 )

$x=6\sqrt{6}$

$y= 9\sqrt{2}$

Step-by-step explanation:

7 ) 8)

In Δ ABC In Δ XYZ

∠ C = 45° ∠ X = 60°

∠ A = 90° ∠ Y = 90°

$AC= \frac{3\sqrt{2} }{2}$ $XY= 3\sqrt{6}$

To Find :

x = ?

y = ?

Solution:

We Know

In Δ ABC

∠ C = 45°

∠ A = 90°

∴ ∠ B = 45° ......Angle sum property of a triangle i.e 180°

∴ Δ ABC is an Isosceles Triangle

∴ AC = AB = x = $\frac{3\sqrt{2} }{2}$

Now appplying Trignometry identity we get

$\sin C = \frac{\textrm{side opposite to angle C}}{Hypotenuse}\\\\\sin 45 = \frac{AC}{BC}\\\\\frac{1}{\sqrt{2} } =\frac{\frac{3\sqrt{2} }{2}}{y}\\\\y=\frac{3\times \sqrt{2}\times \sqrt{2} }{2}\\\\y= 3$

Now In Δ XYZ

∠ X = 60°

∠ Y = 90°

∴∠ Z = 30° . .....Angle sum property of a triangle i.e 180°

Now appplying Trignometry identity we get

$\tan X = \frac{\textrm{side opposite to angle X}}{\textrm{side adjacent to angle X}}$

$\tan 60 = \frac{YZ}{XY}\\\\\sqrt{3} =\frac{y}{3\sqrt{6} }\\ y= 3\sqrt{3} \sqrt{6} \\y= 9\sqrt{2}$

Now,

$\sin X = \frac{\textrm{side opposite to angle C}}{Hypotenuse}\\\\\\\sin 60 = \frac{YZ}{XZ}\\ \\\frac{\sqrt{3} }{2} =\frac{9\sqrt{2} }{x} \\\\x=\frac{18\sqrt{2} }{\sqrt{3} } \\\textrm{after fationalizing the denominator root 3 we get}\\\\x=6\sqrt{6}$

8 0

2 years ago

What is the prime factorization of 210

Kazeer [188]

Answer:

= 2*3 * 5 * 7

Step-by-step explanation:

210 = 21* 10

= 3*7 * 5*2

= 2*3 * 5 * 7

8 0

2 years ago

Read 2 more answers

(01.07 MC) Lines BC and ED are parallel. They are intersected by transversal AE, in which point B lies between points and E. The

Brrunno [24]

Answer:

m∠ABC = m∠BED; Corresponding Angles Theorem

Step-by-step explanation:

<u>Given:</u> line BC is parallel to line ED m∠ABC = 70° m∠CED = 30°

<u>Prove:</u> m∠BEC = 40°

Statement Justification

1. line BC is parallel to line ED - Given

2. m∠ABC = 70° - Given

3. m∠CED = 30° - Given

4. m∠BEC + m∠CED = m∠BED - Angle Addition Postulate

5. m∠ABC = m∠BED - Corresponding Angles Theorem

6. m∠BEC + 30° = 70° - Substitution Property of Equality

7. m∠BEC = 40° Subtraction Property of Equality

6 0

2 years ago

Read 2 more answers

In the first quadrant you start at 2,4 and move 5 units right

NikAS [45]

Answer:

Thanks for asking!

Step-by-step explanation:

(2,9)

5 0

3 years ago

Which statement is true about the graph of two lines y=-6 and x=1/6

Gelneren [198K]

The graph of the line y = -6 is a horizontal line which passes through the y axis at -6. On the other hand, the graph of the equation, x = 1/6 is a vertical line that passes through the x-axis at 1/6. The intersection of these lines is at a point that is expressed as (1/6, -6).

7 0

2 years ago