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3 years ago

Need help trigonometry

Mathematics

1 answer:

pochemuha3 years ago

3 0

Answer:

The measure of angle F is 67.6°

Step-by-step explanation:

In the right triangle DEF

∵ ∠E is the right angle

∵ Side DF is opposite to ∠E

∴ DF is the hypotenuse of the triangle DEF

∵ Side EF is the adjacent side of ∠F

∵ The cosine ratio = $\frac{Adjacent}{Hypotenuse}$

∴ cos∠F = $\frac{EF}{DF}$

∵ EF = 8 units

∵ DF = 21 units

→ Substitute them in the cosine ratio above

∴ cos∠F = $\frac{8}{21}$

→ Use $cos^{-1}$ to find the measure of angle F

∵ m∠F = $cos^{-1}(\frac{8}{21})$

∴ m∠F = 67.60731219 degrees

→ Round it the nearest tenth of a degree

∴ m∠F = 67.6°

∴ The measure of angle F is 67.6°

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ICE Princess25 [194]

Using derivatives, it is found that the x-values in which the slope belong to the interval (-1,1) are in the following interval:

(-15,-10).

<h3>What is the slope of the tangent line to a function f(x) at point x = x0?</h3>

It is given by the derivative at x = x0, that is:

$m = f^{\prime}(x_0)$ .

In this problem, the function is:

$f(x) = 0.2x^2 + 5x - 12$

Hence the derivative is:

$f^{\prime}(x) = 0.4x + 5$

For a slope of -1, we have that:

0.4x + 5 = -1

0.4x = -6

x = -15.

For a slope of 1, we have that:

0.4x + 5 = 1.

0.4x = -4

x = -10

Hence the interval is:

(-15,-10).

More can be learned about derivatives and tangent lines at brainly.com/question/8174665

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Given: ∠A and ∠B are complementary angles.

Eddi Din [679]

Answer:

- For the statement $-3x=24$ , the reason is: <em>Subtraction property of Equality</em>

- For the statement $x=-8$ , the reason is: <em>Division property of Equality.</em>

- For the statement $m\angle B=-6(-8)-39$ , the reason is: <em>Substitution property of Equality.</em>

Step-by-step explanation:

The missing pictures are attached.

We must remember that:

- The Subtraction property of Equality states that:

$If\ a=b,\ then\ a+c=b+c$

- The Division property of Equality states that:

$If\ a=b,\ then\ \frac{a}{c}=\frac{b}{c}$

- The Substitution property of Equality states that:

$If\ a=b,\ then\ b\ can\ replace\ a$

Knowing this properties we can identify the missing reasons that correctly complete the proof.

- For the statement $-3x=24$ , the reason is:

Subtraction property of Equality

(Because it is obtained by subtracting 66 from both sides of $-3x+66=90$ )

- For the statement $x=-8$ , the reason is:

Division property of Equality

(Because it is obtained by dividing both sides of $-3x=24$ by -3)

- For the statement $m\angle B=-6(-8)-39$ , the reason is:

Substitution property of Equality

(Because it is obtained by substituting the value of "x" into $m\angle B=-6x-39$ )

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3 years ago

Need help trigonometry​

Need help trigonometry