Generate Quiz 6A54A7DA15C0D

Starting from the positive x-axis, you rotate counterclockwise by the specified angle to determine the terminal side.

The equivalent angle for −1710∘ can be found by expressing it as a multiple of 360∘:

−1710∘ = −5 × 360∘ + 90∘

Since four complete counterclockwise rotations is equal to no rotation at all, the terminal side of −1710∘ is the same as the terminal side of 90∘.

Thus, −1710∘’s terminal side points downward along the positive y-axis.

sin(90-a)=cos(a)….. Angle is in 1st quadrant

The right response is c) – cos 2x.

Applying the trigonometric formula:

Cos^2x + sin^2x = 1.

and (sin x – cos x) = -cos 2x

Consequently, c) – cos 2x is the right response.

The expression that is provided is:

(c – a) / (c + a)

The Law of Tangents can be used to express this in terms of trigonometric functions:

tan((γ + α) / 2) / tan((γ – α) / 2) = (c + a) / (c – a)

where:

The angles opposite the sides of lengths c and an are denoted by γ and α, respectively.
Thus, (c) tan((γ+α)/tan((γ-α)/2) is the right choice.

Solution: The discriminant is equal to zero D=0 since the roots are equal and distinct.

The equation states that 5×2-Px+1=0, where a=5 b=-P c=1.

D=b2-4ac=0

(-P)2-4(5)(1)=0

P2-20=0

P2 = 20

P = 20 = ±25

Since P has a negative sign, it cannot equal -25, and it cannot equal 25 because it would be greater than zero. Therefore, the correct option is -25<P<25.

THE RIGHT ANSWER (C)

An impossible event has a probability of 00 in probability theory. This is due to the fact that the ratio of favorable outcomes to all outcomes in the sample space is the definition of the probability of an event. An impossible event has a probability of 00 since there are no favorable outcomes.

Therefore, P(A)=0 if event A is not possible.

A plane is divided into upper and lower planes by a horizontal line, also known as the x-axis.

The right response is (b) 243.

Answer:

The following formula can be used to find the sum of a geometric series’ first n terms:

a_1 (1 – r^n) / (1 – r) = S_n

where:

The sum of the first n terms is S_n.

The first term is a_1.

R is the standard ratio.

The number of terms is n.

We must determine the sum of the first six terms (n = 6) given that the first term (a_1) is 3. Any term can be divided by the preceding term to find the common ratio (r). The common ratio in this instance is 3, as each term is multiplied by three to obtain the subsequent term.

The values can now be entered into the formula:

3 (1 – 3^6) / (1 – 3) = S_6

3 (-728) / (-2) = S_6

S_6 equals 2184.

Justification:

The values in the answer choices are near 2184. But rather than asking for the sum of all the terms (infinite series), the question asks for the sum of the first six terms. As the number of terms tends to infinity, the series diverges (goes to positive or negative infinity) because the common ratio (3) is greater than 1.

Note: It is critical to determine how many terms (n) are being summed and to apply the appropriate formula. Additionally, when working with infinite geometric series, remember to take the series’ convergence into account.

The following formula can be used to find the sum of a geometric series’ first n terms:

S_n = a(1 – r^n) / (1 – r)

where:

The sum of the first n terms is S_n.

The first term is a.

R is the standard ratio.

The number of terms is n.

Since each term is multiplied by 32 to obtain the subsequent term, the common ratio (r) in this instance is 32, and the first term (a) is 2. The sum of the first n terms (Sn) is what we are asked for.

Answer: (b) a(1 – r^n) **

To determine the sum of the first n terms, we can enter the values of a, r, and n into the formula:

S_n = 2. (1 – (\frac{2}{3})^n) / (1 – \frac{2}{3})

The sum of the geometric series’ first n terms is expressed in this condensed form.