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3 years ago

What is the inradius of a triangle with side lengths 9, 40, and 41?

Mathematics

1 answer:

Mars2501 [29]3 years ago

6 0

Answer: 20.5

Step-by-step explanation:

From the measure of the length of the sides of the triangle, 9, 40 and 41 we can infer that the triangle is a right angled triangle. 9-40-41 is a Pythagorean triplet.

In a right angled triangle, the circumradius is half the hypotenuse.

In the given triangle, the hypotenuse = 41.

Therefore, the circumradius is 41÷2= 20.5 units.

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Find the derivative of the function at P 0 in the direction of A. f(x,y,z) = 3 e^x cos(yz), P0 (0, 0, 0), A = - i + 2 j + 3k

Alik [6]

The derivative of $f(x,y,z)$ at a point $p_0=(x_0,y_0,z_0)$ in the direction of a vector $\vec a=a_x\,\vec\imath+a_y\,\vec\jmath+a_z\,\vec k$ is

$\nabla f(x_0,y_0,z_0)\cdot\dfrac{\vec a}{\|\vec a\|}$

We have

$f(x,y,z)=3e^x\cos(yz)\implies\nabla f(x,y,z)=3e^x\cos(yz)\,\vec\imath-3ze^x\sin(yz)\,\vec\jmath-3ye^x\sin(yz)\,\vec k$

and

$\vec a=-\vec\imath+2\,\vec\jmath+3\,\vec k\implies\|\vec a\|=\sqrt{(-1)^2+2^2+3^2}=\sqrt{14}$

Then the derivative at $p_0$ in the direction of $\vec a$ is

$3\,\vec\imath\cdot\dfrac{-\vec\imath+2\,\vec\jmath+3\,\vec k}{\sqrt{14}}=-\dfrac3{\sqrt{14}}$

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3 years ago

A car license plate is made up of 7 letters or numbers, where the numbers are whole numbers 0 through 9.

Simora [160]

Answer:

0.28

Step-by-step explanation:

To know the probability we first need to know the total number of choices for each character in the license plate. Since there are a total of 10 possible numbers (0-9) and 26 letters in the English Alphabet. Then this means that each character has a total of 36 possible choices. Out of these 36 only 10 are numbers, therefore the probability of the first character being a number is

$\frac{10}{36}$ or 0.2777

If we rounded the decimal to the nearest hundredth it would be 0.28

4 0

2 years ago

Heather is 5 feet 7 inches tall. There are

lisabon 2012 [21]

Heather is about 167.5 cm

5’7” is equal to 67 inches
when you multiply 67 inches by 2.5 cm (which is around 1 inch) you get 167.5cm

5 0

3 years ago

Read 2 more answers

Braden about three adult tickets and one child ticket at the movie theater and paid $32. Karen bought seven adult tickets and tw

Rama09 [41]

The cost of one adult ticket is $8 and cost of one child ticket is $8.

Step-by-step explanation:

Let,

Cost of one adult ticket = x

Cost of one child ticket = y

According to given statement;

3x+y=32 Eqn 1

7x+2y=72 Eqn 2

Multiplying Eqn 1 by 2

$2(3x+y=32)\\6x+2y=64\ \ \ Eqn\ 3$

Subtracting Eqn 3 from Eqn 2

$(7x+2y)-(6x+2y)=72-64\\7x+2y-6x-2y=8\\x=8$

Putting x=8 in Eqn 1

$3(8)+y=32\\24+y=32\\y=32-24\\y=8$

The cost of one adult ticket is $8 and cost of one child ticket is $8.

Keywords: linear equation, elimination method

Learn more about linear equations at:

#LearnwithBrainly

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3 years ago

Below is the graph of f(x)=In(x). how would you describe the graph of g(x)=1/3In(x)

svet-max [94.6K]

The graph of g(x) would look the same as the given graph, EXCEPT that it'd be compressed by a factor of 1/3. Try graphing both f(x) and g(x) on your calculator and then comparing the 2 graphs.

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3 years ago

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