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pishuonlain [190]
3 years ago
6

Shaun plotted a point on the number line by drawing 5 equally spaced marks between 0 and 1 and placing a point in the third mark

. He claims that the point represents the fraction 3/5 because each mark represents 1/5, so the third mark represents 3/5. Explain why his reasoning is incorrect.
Mathematics
1 answer:
SIZIF [17.4K]3 years ago
4 0
If it is 5 equally spaced marks, then each mark represents 1/6

0 -- 1/6 -- 2/6 -- 3/6 -- 4/6 -- 5/6 -- 1

so the third mark would represent 3/6 which reduces to 1/2
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An airplane pilot over the Pacific sights an atoll at an angle of depression of 5 . At this time, the horizontal distance from t
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Answer:

404.98 m

Step-by-step explanation:

The angle of depression is 5°

The horizontal distance from the airplane to the atoll is 4629 meters.

We need to find the height of the plane.

If we consider a triangle. 4629 meters will be the base and angle is 5°. Let h is the height of the plane. Using trigonometry to find it :

\tan\theta=\dfrac{x}{4629 }\\\\\tan(5)=\dfrac{x}{4629 }\\\\x=\tan(5)\times 4629 \\\\x=404.98\ m

So, the height of the plane is 404.98 m.

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Answer:oh okay

Step-by-step explanation:

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Solve the radical equation. Check all purpose solutions. <br><br> Sqrt(4-3x) = x
alisha [4.7K]

Step-by-step explanation:

√(4-3x) = x

1. square both sides:

[√(4-3x)]²= (x) ²

4-3x = x²

2. shift all the terms to the right side

(minimise dealing with negative coefficient of x² terms to prevent careless mistakes)

0= x²+3x-4

no matter how you change the places of the terms, it will still be:

x²+3x-4=0

3. solve the quadratic equation, either by cross multiplication(and factorising) or the quadratic formula(if you're taught)

for me I will be using the cross multiplication table that my calculator can help me with(gives me the solution but better to show the factorised form to prevent missing out method marks)

as such:

x²+3x-4=0

(x+4)(x-1)=0

hence:

(x+4)=0 or (x-1)=0

finally:

x= -4 or x= 1

however we're not done yet as some solutions may not match with the question/ original equation provided, this we still need to check if there are any values that does not match

substitute x= -4 into the original equation:

√4-3(-4) = √4+12 = √16 = 4 > -1 , hence x= -1 is not the answer

you can substitute the values into a scientific calculator(that has the functions required) to quickly determine

then to double confirm, do the same for the other value of X that we have found:

√4-3(1) = √4-3 = √1 = 1

since the other value of x matches with the equation provided in the question, then we can now confirm that the value of x=1 is the correct value

reason for such situation to happen:

remember in step 1 when we squared both sides of the equation, that is the reason for having to check for the correct X value. let me explain further

when we square numbers, we are potentially introducing another possible answer other than the correct answer intended for us to find as well as to match with the question.

for example:

1 = 1² = (-1)²

likewise, I can even take any other number to compare, such as 100:

100=10²=(-10)²

and this scenario only happens for the even powers of x, such as x², x⁴, x⁶ so on and so forth.

hence whenever such questions come out, do remember to double check with the original question/equation

lastly, the checking portion will only apply for even powers of x in questions and/or when you happen to square them

hope this helps!

5 0
1 year ago
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