What is 21/2 as a mixed number?

Mathematics

2 answers:

Daniel [21]3 years ago

3 0

Since a fraction is a form of division, you do 21/2=10 and 1/2.

aleksandrvk [35]3 years ago

3 0

To find this 21 needs to be divided by 2 without putting it in decimal form. So 2 goes into 21, 10 times and 1/2. So the answer is 10 1/2

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The mosquito population is a function of rainfall, and can be approximated by the formula N(x)=−x3+45x2+1000 where x is the numb

KiRa [710]

Answer:

Therefore the population will be maximum when x=30 inches.

Step-by-step explanation:

Given that, the mosquito population is a function of rainfall and can be approximated by the formula

$N(x)= -x^3+45x^2+1000$

where x is the number of inches of rainfall.

$N(x)= -x^3+45x^2+1000$

Differentiating with respect to x

$N'(x)= -3x^2+90x$

Again differentiating with respect to x

$N''(x)=-6x+90$

Now we set N'(x)=0

$-3x^2+90x=0$

$\Rightarrow -3x(x-30)=0$

$\Rightarrow x=0,30$

$N''(0)=-6.0+90=90>0$

$N''(30)=-6.30+90=-90$

Since at x=30, N''(x)<0, So at x=30, N(x) has maximum value.

Therefore the population will be maximum when x=30 inches.

5 0

2 years ago

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

Kitty [74]

Answer: (-2, 5) and (2, -3)

Step-by-step explanation:

Graph the line y = -2x + 1 (which is in y = mx + b format) by plotting the y-intercept (b = 1) on the y-axis and then using the slope (m = -2) to plot the second point by going down 2 and right 1 unit from the first point:

y - intercept = (0, 1) 2nd point = ( -1, 1).

Graph the parabola y = x² - 2x - 3 by first plotting the vertex and then plotting the y-intercept (or some other point):

$y = x^2-2x-3\quad \rightarrow \quad a=1,\ b=-2,\ c=-3\\\\\text{axis of symmetry:}\ x = \dfrac{-b}{2a}\ \longrightarrow \ x=\dfrac{-(-2)}{2(1)}=\dfrac{2}{2}=1\\\\\text{y-value of vertex:}\ f(1) = (1)^2-2(1)-3\quad \longrightarrow \quad y = 1 - 2 - 3=-4\\\\\text{y-intercept:}\ f(0)= (0)^2-2(0)-3\ \longrightarrow \ y=0 - 0 - 3 = -3 \\$