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Elena-2011 [213]

3 years ago

7

Find the area of a triangle with sides lengths 17, 18, and 21.4 units. Round the answer to the nearest hundredth.

1 answer:

mojhsa [17]3 years ago

8 0

To calculate for the area of the triangle given all its side, use the Heron's formula which is,

A = sqrt ((s)(s - a)(s - b)(s - c))

where A is the area. a, b, and c are the measure of the sides and s the semi - perimeter or half of the perimeter.

With the given above, s = (17 + 18 + 21.4) / 2 = 28.2

Substituting the known dimensions to the Heron's formula,

A = sqrt ((28.2)(28.2 - 17)(28.2 - 18)(28.2 - 21.4)) = 148 units^3

Thus, the area of the triangle is 148 units^3.

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What is the answer to a and b please and thank you

vagabundo [1.1K]

A.) according to the graph, Austin appears to be burning 10 calories per minute. If you look at a perfect point on the graph, which I chose (50,5) and you do x over y or calories per minute, you get a unit rate of 10 calories per minute.

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3 years ago

I know its summer and everyone done with school but someone help

Gemiola [76]

Answer:

1.55

Step-by-step explanation:

3750+900 = 4650

4650/3000 = 1.55

7 0

3 years ago

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Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:

ryzh [129]

First find the critical points of <em>f</em> :

$f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7$

$\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1$

$\dfrac{\partial f}{\partial y}=6y=0\implies y=0$

so the point (1, 0) is the only critical point, at which we have

$f(1,0)=-7$

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

$f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t$

Find the critical points of <em>g</em> :

$\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0$

$\implies\sin t=0\text{ OR }1+5\cos t=0$

$\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi$

where <em>n</em> is any integer. We get 4 critical points in the interval [0, 2π) at

$t=0\implies f(10,0)=155$

$t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299$

$t=\pi\implies f(-10,0)=235$

$t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299$

So <em>f</em> has a minimum of -7 and a maximum of 299.

4 0

3 years ago

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Likurg_2 [28]

Answer:

(15,16)

Step-by-step explanation:

C=halfway between A to B

A to B on the x axis goes across by 24

24/2 =12

3+12=15

A to B on the y axis goes up by 28

28/2 = 14

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6 0

3 years ago

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Find the average rate of change over the given interval <br> f(x) = 2^x , [3,5]

Vlada [557]

Answer:

$y=x*2^x (3,5)+y$

Step-by-step explanation:

4 0

2 years ago