5(-42/-7) + (-15)

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

The largest county in the state of Texas is 6064 square miles larger than the smallest county in the same state. The size of the

Ann [662]

The smallest county is 129 square miles large.

Step-by-step explanation:

Let,

Smallest county = x

Largest county = y

According to given statement;

The largest county in the state of Texas is 6064 square miles larger than the smallest county in the same state.

y = x+6064 Eqn 1

The size of the largest county is 48 times the size of the smallest county plus one square mile.

y = 48x+1 Eqn 2

As Eqn 1 and Eqn 2 are both equal to y, therefore,

Eqn 1 = Eqn 2

$x+6064=48x+1\\6064-1=48x-x\\6063=47x\\47x=6063$

Dividing both sides by 47

$\frac{47x}{47}=\frac{6063}{47}\\x=129\ square \ miles$

The smallest county is 129 square miles large.

Keywords: linear equation, substitution method

Learn more about substitution method at:

#LearnwithBrainly

7 0

3 years ago

Lenny rolls two number cubes. What is the probability that the sum of the numbers Lenny rolls is either 4 or 7?

Mashutka [201]

Probability of an event =

(number of ways the event can happen) / (total number of possible outcomes) .

Well, the total number of possible outcomes is easy. It's

(6 possibilities for the first cube) x (6 possibilities for the 2nd cube)

= 36 total possible ways for two cubes to roll.

Now, how many of those possibilities show either 4 or 7 ?

Well, here's how a 4 can come up:

1 . . . 3

2 . . . 2

3 . . . 1

and here's how a 7 can come up:

1 . . . 6

2 . . . 5

3 . . . 4

4 . . . 3

5 . . . 2

6 . . . 1 .

So there are 9 ways all together for Lenny to be successful.

The probability is (9/36) .

That's 1/4 , or 25% .

7 0

3 years ago

Read 2 more answers

Luanda wants to buy a box of cereal. Which box has the lowest cost per ounce? Group of answer choices 20-oz box for $3.20 10-oz

marin [14]

Answer: 15-oz for 2.25

3.20÷20= 0.16

1.70÷10= 0.17

2.25÷15= 0.15

2.72÷16= 0.17

I hope this helps:

3 0

2 years ago

Joseph completes the paintings shown in 129 minutes. If he took the same amount of time to complete each painting, how much time

olga55 [171]

Depending on how many paintings there were you would divide that number by 129 to figure out how long it took to complete one painting. Hope this helps.

6 0

3 years ago

5(-42/-7) + (-15) - (-3)​

5(-42/-7) + (-15) - (-3)