Horizontal tangents are such that d<em>y</em>/d<em>x</em> = 0; this happens when
(<em>y</em> - 3) / (<em>x</em> - 3) = 0 → <em>y</em> - 3 = 0 → <em>y</em> = 3
so (I) is true.
Vertical tangents are such that their slope is undefined; this happens when the denominator vanishes, or
<em>x</em> - 3 = 0 → <em>x</em> = 3
so you are right that (II) is not true.
To assess whether (III) is correct, consider what happens at different nearby points (with neither <em>x</em> = 3 nor <em>y</em> = 3) where the <em>y</em> coordinate is kept the same so that the tangent lines occur in the same row. For example,
<em>x</em> = 0, <em>y</em> = 0 → d<em>y</em>/d<em>x</em> = (-3)/(-3) = 1
<em>x</em> = 1, <em>y</em> = 0 → d<em>y</em>/d<em>x</em> = (1 - 3)/(-3) = 2/3
<em>x</em> = 2, <em>y</em> = 0 → d<em>y</em>/d<em>x</em> = (2 - 3)/(-3) = 1/3
The slopes are not the same - they have to be if these tangents are supposed to be parallel - so (III) is not true.
This makes A. (I) only the correct choice.
8x-12 = 5+15
8x-12 = 20
8x = 32 +12
x = 4 ÷8
The product of (√3x + √5)(√15x+2√30) assuming x ≥ 0 is 3√5x² + 6√10x + 5√3x + 10√6
<h3>What is the product of the expression?</h3>
It follows from the task content that the expression given whose product is to be evaluated is;
(√3x + √5)(√15x+2√30)
Hence, by multiplying the terms with each other accordingly; we have;
= (√45x² + 2√90x + √75x + 2√150)
= 3√5x² + 2√90x + √75x + 2√150
= 3√5x² + 2×3√10x + √75x + 2√150
= 3√5x² + 2×3√10x + 5√3x + 2√150
= 3√5x² + 2×3√10x + 5√3x + 10√6
= 3√5x² + 6√10x + 5√3x + 10√6
Ultimately, the product of the expression is; 3√5x² + 6√10x + 5√3x + 10√6
Learn more about product:
brainly.com/question/10090998
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Correct question is;
Factor out the GCF from the given polynomial. 10x³ + 16x² - 18x. (Type your answer in factored form.)
Answer:
GCF = 5x² + 8x - 9
Step-by-step explanation:
The given polynomial is;
10x³ + 16x² - 18x
First thing is to inspect the coefficients and see the greatest number that all three can be divided by evenly without remainder.
The greatest number is 2.
Secondly let's inspect the variables to see what we can factor out.
They all contain x. Thus, x is a factor.
Thus, we will divide each term by 2x to obtain the GCF of the polynomial.
GCF = (10x³/2x) + (16x²/2x) - (18x/2x)
GCF = 5x² + 8x - 9
