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3 years ago

The line y = 2x – 3 touches the curve y = x^2 + kx + 6. Find the possible values of k.

Mathematics

1 answer:

Ugo [173]3 years ago

8 0

The value of "k" will be a value greater than 4 or less than -8

If the line y = 2x – 3 touches the curve y = x^2 + kx + 6, this means that both equations will be equal as shown:

$2x - 3 = x^2 + kx + 6$

Rewrite in the form $ax^2+bx+c=0$

$2x - 3 = x^2 + kx + 6\\x^2+kx-2x+6+3 =0\\x^2+(k-2)x+9=0\\$

The roots has a distinct solution if b² - 4ac > 0

From the equation

a = 1

b = k-2

c = 9

Substitute into the formula:

$(k-2)^2-4(1)(9) > 0\\k^2-4k+4-36>0\\k^2-4k-32>0$

Factorize

$k^2+8k-4k-32 >0\\k(k+8)-4(k+8)>0\\(k-4)(k+8)>0\\k>4 and k>-8$

Hence the value of "k" will be value greater than 4 or less than -8

Learn more here: brainly.com/question/24896483

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How do you write 31% as a fraction in simplest from

Illusion [34]

The fraction is 31/100, the decimal is 0.31 which means your simplest form is 31/100

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3 years ago

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Find the equation of the linear function represented by the table below in slope-intercept form. x y 1 -3 2 -9 3 -15 4 -21

aleksley [76]

Answer:

The numbers:

1, -3, 2, -9, 3, -15, 4, -21,

are not linear.

Step-by-step explanation:

If it was linear:

4, 3, 2, 1, -3, -9, -15, -21

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3 years ago

If <img src="https://tex.z-dn.net/?f=%20300cm%5E%7B2%7D%20" id="TexFormula1" title=" 300cm^{2} " alt=" 300cm^{2} " align="absmid

Artist 52 [7]

Check the picture below. Recall, is an open-top box, so, the top is not part of the surface area, of the 300 cm². Also, recall, the base is a square, thus, length = width = x.

$\bf \textit{volume of a rectangular prism}\\\\
V=lwh\quad 
\begin{cases}
l = length\\
w=width\\
h=height\\
-----\\
w=l=x
\end{cases}\implies V=xxh\implies \boxed{V=x^2h}\\\\
-------------------------------\\\\
\textit{surface area}\\\\
S=4xh+x^2\implies 300=4xh+x^2\implies \cfrac{300-x^2}{4x}=h
\\\\\\
\boxed{\cfrac{75}{x}-\cfrac{x}{4}=h}\\\\
-------------------------------\\\\
V=x^2\left( \cfrac{75}{x}-\cfrac{x}{4} \right)\implies V(x)=75x-\cfrac{1}{4}x^3$

so.. that'd be the V(x) for such box, now, where is the maximum point at?

$\bf V(x)=75x-\cfrac{1}{4}x^3\implies \cfrac{dV}{dx}=75-\cfrac{3}{4}x^2\implies 0=75-\cfrac{3}{4}x^2
\\\\\\
\cfrac{3}{4}x^2=75\implies 3x^2=300\implies x^2=\cfrac{300}{3}\implies x^2=100
\\\\\\
x=\pm10\impliedby \textit{is a length unit, so we can dismiss -10}\qquad \boxed{x=10}$

now, let's check if it's a maximum point at 10, by doing a first-derivative test on it. Check the second picture below.

so, the volume will then be at $\bf V(10)=75(10)-\cfrac{1}{4}(10)^3\implies V(10)=500 \ cm^3$

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3 years ago

NEED HELP ASAP ILL GIVE YOU BRAINLIST

lesya [120]

Answer is D You'll do the diameter squared then you multiply by π

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3 years ago

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ANSWER ASAP GIVING BRAINLIEST AND STUFF!

kupik [55]

Answer:

Nope

The absolute value of a number or an expression is always positive or zero. It cannot be negative. With absolute value, we are only interested in how far a number is from zero, not the direction.

Step-by-step explanation:

The absolute value of a number means the distance from 0. ... You cannot have negative distance, so it has to be positive.

How can you use absolute value to represent a negative number?

EX:

Subtract one number from the other and give the result the sign of the number that has the greater absolute value. 2 – 9 = -7 because the difference between 9 and 2 is 7 and the -9 has the larger absolute value making the result negative.

(SORRY) IF THIS IS WRONG THIS IS WHAT THE INTERNET GAVE TO ME <3 anyways i hope this kinda help you understand

3 0

3 years ago