SIMPLE CORDINATE PLOTTING! BRAINLIEST, 5 STAR, AND A LIKE ON UR ANSWER. SHOW SOME WORK.
2 answers:
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Answer:
(i) see first attached diagram
(ii) QR = 22.67 km (2 dp)
(iii) 243°
Step-by-step explanation:
A bearing is the angle in degrees measured clockwise from north.
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<u>Part (i)</u>
see first attached diagram
<u>Part (ii)</u>
The angles marked in blue on the second attached diagram are Consecutive Interior Angles. In this case they add to 180° as the North lines are parallel.
The sum of angles around a point is 360°
⇒ m∠QPR (shown in red on the second attached diagram) = 360 - 150 - (180 - 15) = 45°
To calculate the distance between Q and R (marked in red on the attached diagram), use the cosine rule.
⇒ QR² = PR² + QP² - 2(PR)(QP)cos(QPR)
⇒ QR² = 32² + 24² - 2(32)(24)cos(45)
⇒ QR² = 513.8839841...
⇒ QR = √513.8839841...
⇒ QR = 22.67 km (2 dp)
<u>Part (iii)</u>
We need to find the angle marked in green on the third attached diagram.
To do this, we need to find the angle marked in pink and the angle marked in orange, then subtract them from 360°
Pink angle = 180 - 150 = 30° (using the same consecutive angle theorem as before)
Orange angle (o) using the sine rule:
⇒ sin(o)/32 = sin(45)/QR
⇒ sin(o) = 32sin(45)/22.67
⇒ sin(o) = 0.9981652337...
⇒ o = 86.52868176...°
Therefore, the green angle = 360 - 30 - 86.52868176... = 243° (nearest degree)
In exponential form it is given as, 8⁻³ =
<u>Step-by-step explanation:</u>
We have to write the given equation in the exponential form, that is in the form of base to the power value.
Given:
log₈ ( ) = -3
Here the base is 8.
In the exponential form, it is written as,
base to the power 3 = 512
Here the reciprocal of 512 is given, so,
base to the power -3 =
So the exponential form is given as, 8⁻³ =
Answer: D
Step-by-step explanation:
To find the difference, we want to make sure both denominators are equal.
Now that the denominators are equal, we can distribute and multiply out.
With the fractions multiplied out, we can actually put it into one large fraction.
Let's subtract the top expression.
This may seem like our final answer, but we can actually factor out an 3x in the numerator and denominator.
With the 3x factored out, they cancel out because 3x/3x=1.
Our final answer is: