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4 years ago

I dO nOt coMprEheNd PLEASE HELPPP

1 answer:

3 0

Lines y=-x+2 and y=3x+1 intersect the y=axis. If you plot them out on a graph using the equation y=mx+b, then they are parallel and are set on the y-axis.

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A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of t

dusya [7]

1. Check the picture. Let the radius of the semicircle be R, so the width of the rectangle is 2R, and let the height of the rectangle be H.

2. The perimeter of the semicircle is $\frac{1}{2}*circumference = \frac{1}{2}*2 \pi R=\pi R$

the total perimeter is $\pi R+2H+2R=2H+( \pi +2)R$

We can write H in terms of R, in order to decrease the number of variables:

$2H+( \pi +2)R=22$

$2H=22-( \pi +2)R$

$H= \frac{22-( \pi +2)R}{2} =11- \frac{( \pi +2)R}{2}$

3. The total area as a function of R is the area of the semicircle + the area of the rectangle:

$A(R)= \pi R^2+2R*H=\pi R^2+2R*(11- \frac{( \pi +2)R}{2})=$

$\pi R^2+22R-( \pi +2)R^2=\pi R^2+22R- \pi R^2 -2R^2=22R-2R^2$

so $A(R)=22R-2R^2$ is clearly a quadratic function, with its graph a parabola which opens downward (since the coefficient of R^2 is negative)

The maximal value of A(R) is the maximal value the parabola can reach, that is its vertex.

4. $A(R)=22R-2R^2=2R(11-R)$ means the roots are at R=0 and R=11, so the axis of symmetry passes through R=11/2

thus the vertex point is (11/2, A(11/2))=(11, 2*(11/2)(11-11/2))=(11, 11*11/2)=(11,121/2)
=(11, 60.5)

5. Answer: Largest possible area is 60.5 feet squared

8 0

3 years ago

Find f · dr c for the given f and

ruslelena [56]

Parameterize the path $\mathcal C$ by

$\mathbf r(t)=x(t)\,\mathbf i+y(t)\,\mathbf j$

with

$x(t)=3\cos t$
$y(t)=3\sin t$

and $0\le t\le\pi$ . Then

$\displaystyle\int_{\mathcal C}\mathbf f(x,y)\cdot\mathrm d\mathbf r=\int_{t=0}^{t=\pi}\mathbf f(x(t),y(t))\cdot\dfrac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt$
$=\displaystyle\int_0^\pi(9\cos^2t\,\mathbf i+9\sin^2t\,\mathbf j)\cdot(-3\sin t\,\mathbf i+3\cos t\,\mathbf j)\,\mathrm dt$
$=27\displaystyle\int_0^\pi(\cos t\sin^2t-\sin t\cos^2t)\,\mathrm dt=-18$

5 0

3 years ago

An empty 5-gal water jug weighs 0.75 lb. With 3 c of water inside, the jug weighs 2.25 lb. Which equation models the jug’s weigh

s344n2d4d5 [400]

Answer:

y=.75 x=.75 for one cup of water

Step-by-step explanation:

3 0

3 years ago

Plzzz help me im trustin yall

lys-0071 [83]

Answer:

Step-by-step explanation:

(8x + 8)(x + 3) = $8x^{2} +24x+8x+24$ = $8x^{2} +32x+24$ .

3 0

3 years ago

Read 2 more answers

What is the simplified value of the expression below? 8.5+(12+4)x2-7

Lilit [14]

B. 33.5 is your answer
First you want to add 12+4 because it is in parentheses
8.5+16x2-7
Then you multiply 16 by 2
8.5+32-7
Then you add 8.5 to 32
40.5-7
Then you subtract 7 from 40.5 giving you your answer
33.5

7 0

4 years ago

Read 2 more answers