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3 years ago

F(x) = x^-1, x=.9. Use linear approximation to estimate answer

1 answer:

8 0

L(x) = f'(a)(x - a)
f(x) = x^(-1), f'(x) = -x^(-2)
Let a = 1, f'(a) = -(1)^(-2) = -1
L(0.9) = f'(1)(0.9 - 1) = -1(-0.1) = 0.1

Therefore, linear approximation of f(x) = x^(-1) for x = 0.9 is 0.1

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Use the given information to find the exact value of the trigonometric function

eimsori [14]

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Half Angle Formula

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Answer:

$\cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}$

Checking:

$\begin{gathered} \frac{\theta}{2}=\cos ^{-1}(-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}) \\ \frac{\theta}{2}=118.22^{\circ} \\ \theta=236.44^{\circ}\text{ (3rd quadrant)} \end{gathered}$

Also,

$\csc \theta=\frac{1}{\sin\theta}=\frac{1}{\sin (236.44)}=-\frac{6}{5}\text{ QED}$

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3 years ago

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ludmilkaskok [199]

32.3 is a decimal number in which 3 is the digit at the tenth place.

Mixed number contains a whole number and a fraction part.

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$\frac{3}{10}$ is the fraction in the simplest form.

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dezoksy [38]

Answer:

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3 years ago

Triangle ABC is an isosceles right triangle inscribed in a circle. The center of the circle is point D and the diameter of the c

Paha777 [63]

Answer:

* AD is congruent to DC and BD true

* m∠B = 90° true

* The measure of arc AC is equal to the measure of arc AB not be true ( The right answer )

* The measure of arc AB is equal to measure of arc BC true

Step-by-step explanation:

∵ D is the center of the circle and A , B and C are points on the circle

∴ AD , DB and DC are radii on the circle D

∴ AD ≡ DC ≡ DB

∵ AC passing through point D which is the center of the circle

∴ AC is the diameter of the circle D

∵ ∠B is opposite to the diameter of the circle and vertex B lies on the circle

∵ ∠B is an inscribed angle and ∠ADC is a central angle subtended by the same arc AC

∴m∠B = half m∠ADC

∵ m∠ADC = 180°

∴ m∠B = 90°

∵ The measure of arc AC = 180°

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∴ m∠BAC = m∠BCA = (180° - 90°) ÷ 2 = 45°

∵ ∠ACB is an inscribed angle subtended by arc AB

∴ m∠ACB = half measure of arc AB

∵ The measure of arc AB = 45° × 2 = 90°

∴ The measure of arc AC ≠ the measure of arc AB

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∴ AB = BC

∵ AB subtended by arc AB

∵ BC subtended by arc BC

∴ The length of arc AB = the length of arc BC

∵ If two arcs are equal in length, then they will be equal in measure

∴ The measure of arc AB is equal to the measure of arc BC

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