Write 2.75 as a mixed number and as an improper fraction.<br> Write your answers in simplest form.

The volume of a triangular prism is 84 cubic inches. What is the volume of a similar prism that is smaller by a scale 1/2

wariber [46]

I'm not entirely sure but since the proportions are halved, the volume may be (84/2) = 42

3 0

3 years ago

780000 is the successor of what

slavikrds [6]

Answer:

790000 is the successor of 780000

Step-by-step explanation:

please mark as brainliest plzzzzzzzzzz.

6 0

3 years ago

2x-3y=6 whats the slope and y-intercept?

VARVARA [1.3K]

Answer:

The slope is 2/3 and the y-intercept is -2

Step-by-step explanation:

2x - 3y = 6

-2x -2x Subtract 2x from both sides

-3y = -2x + 6

y = 2/3x - 2 Divide both sides by -3 to get y by itself

The slope is 2/3 and the y-intercept is -2

7 0

3 years ago

Find the absolute maximum and absolute minimum of the function f(x,y)=2x3+y4f(x,y)=2x3+y4 on the region {(x,y)|x2+y2≤64}{(x,y)|x

ddd [48]

Check where the first-order partial derivatives vanish to find any critical points within the given region:

$f(x,y)=2x^3+y^4\implies\begin{cases}f_x=6x^2=0\\f_y=4y^3=0\end{cases}\implies(x,y)=(0,0)$

The Hessian for this function is

$\mathbf H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}12x&0\\0&12y^2\end{bmatrix}$

with $\det\mathbf H(0,0)=0$ , so unfortunately the second partial derivative test fails. However, if we take $x=0$ we see that $f(x,y)>0$ for different values of $y$ ; if we take $y=0$ we see $f(x,y)$ takes on both positive and negative values. This indicates (0, 0) is neither the site of an extremum nor a saddle point.

Now check for points along the boundary. We can parameterize the boundary by

$(x,y)=(8\cos t,8\sin t)$

with $0\le t\le2\pi$ . This turns $f(x,y)$ into a univariate function $F(t)$ :

$F(t)=f(8\cos t,8\sin t)=2^{10}\cos^3t+2^{12}\sin^4t$

$\implies F'(t)=3\cdot2^{10}\cos^2t(-\sin t)+2^{14}\sin^3t\cos t=2^{10}\sin t\cos t(16\sin^2t-3\cos t)$

$F'(t)=0\implies\begin{matrix}\sin t=0\implies t=0,\,t=\pi\\\\\cos t=0\implies t=\dfrac\pi2,\,t=\dfrac{3\pi}2\\\\16\sin^2t-3\cos t=0\implies t=2\tan^{-1}\sqrt{\dfrac{\sqrt{1033}-32}3},\,t=2\pi-2\tan^{-1}\sqrt{\dfrac{\sqrt{1033}-32}3}\end{matrix}$