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A student is given that point P(a, b) lies on the terminal ray of angle Theta, which is between StartFraction 3 pi Over 2 EndFra

Harman [31]

Answer:

A.

The student made an error in step 3 because a is positive in Quadrant IV; therefore,

$cos\theta = \frac{a\sqrt{a^2 + b^2}}{a^2 + b^2}$

Step-by-step explanation:

Given

$P\ (a,b)$

$r = \± \sqrt{(a)^2 + (b)^2}$

$cos\theta = \frac{-a}{\sqrt{a^2 + b^2}} = -\frac{\sqrt{a^2 + b^2}}{a^2 + b^2}$

Required

Where and which error did the student make

Given that the angle is in the 4th quadrant;

The value of r is positive, a is positive but b is negative;

Hence;

$r = \sqrt{(a)^2 + (b)^2}$

Since a belongs to the x axis and b belongs to the y axis;

$cos\theta$ is calculated as thus

$cos\theta = \frac{a}{r}$

Substitute $r = \sqrt{(a)^2 + (b)^2}$

$cos\theta = \frac{a}{\sqrt{(a)^2 + (b)^2}}$

$cos\theta = \frac{a}{\sqrt{a^2 + b^2}}$

Rationalize the denominator

$cos\theta = \frac{a}{\sqrt{a^2 + b^2}} * \frac{\sqrt{a^2 + b^2}}{\sqrt{a^2 + b^2}}$

$cos\theta = \frac{a\sqrt{a^2 + b^2}}{a^2 + b^2}$

So, from the list of given options;

The student's mistake is that a is positive in quadrant iv and his error is in step 3

3 0

3 years ago

Help me please quickly.

Vikki [24]

Answer:

M

Step-by-step explanation:

5 comes from point M

I hope this is good enough for you:

7 0

3 years ago

A teacher is making a history test composed of the same number of multiple-choice questions as short-answer questions. She estim

STALIN [3.7K]

Answer:

The inequality is $5.5n \leq 45$

Step-by-step explanation:

Total time:

The total time to complete the test is the sum of the number of multiple-choice questions multiplied by the time it takes to solve each and the number of short-answer questions multiply by the time it takes to solve each.

In this question:

Same number(n) of both.

Multiple-choice takes 2 minutes, short-answer takes 3.5 minutes. The total time is given by:

$T = 2n + 3.5n = 5.5n$

Write an inequality to determine how many questions, n, the teacher can include if the test must take students less than 45 minutes to complete.?

This means that:

$T \leq 45$

So

$5.5n \leq 45$

The inequality is $5.5n \leq 45$

5 0

3 years ago

Factor completely 2w^5-10w^3

Kryger [21]

$2w^5-10w^3=2w^3(w^2-5)$

8 0

3 years ago

To buy a car, Ahmed borrowed $15000 for 3 years at an annual simple interest rate of 9%. how much interest will he pay if he pay

allochka39001 [22]

4,050$ and 19,050 that is your answer

3 0

2 years ago