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3 years ago

There are 68 calories in 1 serving of cereal. If a bowl holds 7 servings, how many calories are in the bowl?

Mathematics

1 answer:

maria [59]3 years ago

6 0

Answer:

476

Step-by-step explanation:

$68 \times 7 = 476$

because there are 68calories per serving and there are 7 servings

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Find the extreme values of f subject to both constraints f(x,y) = 2x^2+3y^2-4x-5, x^2 + y^2 <=16

Softa [21]

$f(x,y)=2x^2+3y^2-4x-5$
$f_x=4x-4=0\implies x=1$
$f_y=6y=0\implies y=0$

$f(x,y)$ has only one critical point at $(x,y)=(1,0)$ . The function has Hessian

$\mathbf H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}4&0\\0&6\end{bmatrix}$

which is positive definite for all $(x,y)$ , which means $f(x,y)$ attains a minimum at the critical point with a value of $f(1,0)=-7$ .

To find the extrema (if any) along the boundary, parameterize it by $x=4\cos t$ and $y=4\sin t$ , with $0\le t$ . On the boundary, we have

$f(x(t),y(t))=F(t)=2(4\cos t)^2+3(4\sin t)^2-4(4\cos t)-5=32\cos^2t+48\sin^2t-16\cos t-5$
$F(t)=35-16\cos t-8\cos2t$

Find the critical points along the boundary:

$F'(t)=16\sin t+16\sin2t=16\sin t+32\sin t\cos t=16\sin t(1+2\cos t)=0$
$\implies t=0,\dfrac{2\pi}3,\pi,\dfrac{4\pi}3$

Respectively, plugging these values into $F(t)$ gives 11, 47, 43, and 47. We omit the first and third, as we can see the absolute extrema occur when $F(t)=47$ .

Now, solve for $x,y$ for both cases:

$t=\dfrac{2\pi}3\implies\begin{cases}x=4\cos t=-2\\y=4\sin t=2\sqrt3\end{cases}$

$t=\dfrac{4\pi}3\implies\begin{cases}x=4\cos t=-2\\y=4\sin t=-2\sqrt3\end{cases}$

so $f(x,y)$ has two absolute maxima at $(x,y)=(-2,\pm2\sqrt3)$ with the same value of 47.

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3 years ago

I need help with this can you?

Reptile [31]

Answer:

A and D

Step-by-step explanation:

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3 years ago

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Hi guys can you help me evaluating expressions <br><br> Please

EastWind [94]

26.) 3(2)² - 8(-3)²

= 3*4 - 8 + 9

= 12 - 8 + 9 = 13

27.) I 7 - 4(2) I

7 - 8 = -1, but since this is absolute value, which is a number's distance from zero, your answer for 27 would be a positive one.

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= 4 + 2(-3)

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3 years ago

Consider the equation 1+n+6/n+1=4/n-2

Inga [223]

A. The LCD is (n+1)(n-2)

B. n = -1, n = 2

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I’ve add a picture of the answers at the bottom in case I wasn’t clear on question C.

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4 years ago

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Calcule (1/2)-² POR FAVOR RESPONDEM

dolphi86 [110]

Answer:

I think it's 1/4 or .25

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3 years ago

There are 68 calories in 1 serving of cereal. If a bowl holds 7 ​servings, how many calories are in the​ bowl?

There are 68 calories in 1 serving of cereal. If a bowl holds 7 servings, how many calories are in the bowl?