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3 years ago

Which expression represents”9 less than the product of 5 and a number n”?

Mathematics

2 answers:

Alika [10]3 years ago

6 0

9 less means subtract

the product of 5 and the number n mea multiply 5 and n

D. 5n-9

vampirchik [111]3 years ago

3 0

5n-9 because less than means subtract and product means multiply

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Find the absolute maximum and minimum values of f(x,y)=xy−4x in the region bounded by the x-axis and the parabola y=16−x2.

skad [1K]

Answer:

The absolute maximum and minimum is $20\; \text{and} -20.$

Step-by-step explanation:

We first check the critical points on the interior of the domain using the

first derivative test.

$f_x=y-4=0$

$f_y=x=0$

The only solution to this system of equations is the point (0, 4), which lies in the domain.

$f_{xx}=0, \;f_{yy}=0\; \text{and}\; f_{xy}=-1$

$\Rightarrow f_{xx}f_{yy}-f_{xy}=o-1=-1$

$\therefore (0,4)$ is a saddle point.

Boundary points - $(4,0), (-4,0), (0,16)$

Along boundary $y=16-x^2$

$f=x(16-x^2)-4x$

$=16x-x^3-4x$

$\Rightarrow f^'=16-3x^2-4=0$

$\Rightarrow 3x^2=12$

$\Rightarrow x=\pm2,\;\;y=14$

Values of f(x) at these points.

$\begin{array}{}(4,0)=-16\\(-4,0)=16\\(0,16)=0\\(2,14)=20\\(-2,14)=-20\end{array}$

Therefore, the absolute maximum and minimum is $20\; \text{and} -20.$

6 0

3 years ago

Write the slope intercept form of the equation of the line through the given point with the given slope

aleksandrvk [35]

Given that,

Point = (-5,3)

Slope, m = -3/5

To find,

The slope intercept form of the equation of the line.

Solution,

The general form of equation is :

y = mx +b

We have, x = -5, y = 3

So,

$3=\dfrac{-3}{5}(-5)+b\\\\3=-3+b\\\\b = 6$

The equation is :

$y=\dfrac{-3}{5}x+6$

Hence, the required equation is $y=\dfrac{-3}{5}x+6$ .

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3 years ago

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Delvig [45]

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3 years ago

Pls help, its multiple choice btw

ryzh [129]

Answer:

the answer is c

Step-by-step explanation:

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