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3 years ago

Determine which set of numbers can be the measures of the sides of a triangle.

Mathematics

2 answers:

Georgia [21]3 years ago

4 0

Answer:

Option A) 13, 10, 16

Step-by-step explanation:

We are given the following information in the question:

The triangular Inequality:

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
$\text{Side 1} + \text{Side 2} > \text{Side 3}$

a) 13, 10, 16

$13 + 10 = 23 > 16$

Thus, they can be the measures of the sides of a triangle.

b) 1, 2, 3

$1 + 2 = 3 \ngtr 3$

Thus, they cannot be the measures of the sides of a triangle as they do not satisfy the triangular inequality.

c) 5.2, 11, 4.9

$5.2 + 4.9 = 10.1 \ngtr 11$

Thus, they cannot be the measures of the sides of a triangle as they do not satisfy the triangular inequality.

d) 208, 9, 219

$208 + 9 = 217 \ngtr 219$

Thus, they cannot be the measures of the sides of a triangle as they do not satisfy the triangular inequality.

klemol [59]3 years ago

3 0

Answer:

a) 13, 10, 16

Step-by-step explanation:

The usual form of the triangle inequality requires the sum of the two shortest sides exceed the longest side (a+b>c). The only choice for which this is true is ...

10 + 13 > 16 . . . . choice A

_____

Comment on the triangle inequality

Some authors also allow the sum to equal the longest side (a+b≥c). In that case, choice B (1+2=3) is also an answer. This "triangle" would look like a line segment of length 3. It has zero area.

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G find the area of the surface over the given region. use a computer algebra system to verify your results. the sphere r(u,v) =

Svetach [21]

Presumably you should be doing this using calculus methods, namely computing the surface integral along $\mathbf r(u,v)$ .

But since $\mathbf r(u,v)$ describes a sphere, we can simply recall that the surface area of a sphere of radius $a$ is $4\pi a^2$ .

In calculus terms, we would first find an expression for the surface element, which is given by

$\displaystyle\iint_S\mathrm dS=\iint_S\left\|\frac{\partial\mathbf r}{\partial u}\times\frac{\partial\mathbf r}{\partial v}\right\|\,\mathrm du\,\mathrm dv$

$\dfrac{\partial\mathbf r}{\partial u}=a\cos u\cos v\,\mathbf i+a\cos u\sin v\,\mathbf j-a\sin u\,\mathbf k$
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$\implies\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}=a^2\sin^2u\cos v\,\mathbf i+a^2\sin^2u\sin v\,\mathbf j+a^2\sin u\cos u\,\mathbf k$
$\implies\left\|\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}\right\|=a^2\sin u$

So the area of the surface is

$\displaystyle\iint_S\mathrm dS=\int_{u=0}^{u=\pi}\int_{v=0}^{v=2\pi}a^2\sin u\,\mathrm dv\,\mathrm du=2\pi a^2\int_{u=0}^{u=\pi}\sin u$
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as expected.

6 0

2 years ago

1. What is the approximate area of a circle with a diameter of 20 inches?

ad-work [718]

Answer:

1. 100 $\pi$

2. 27 $cm^{3}$

3. 30

Step-by-step explanation:

Area = $\pi$ $r^{2}$

= $\pi$ x $10x^{2}$

= 100 $\pi$

Volume = l x w x h

= 3 x 3 x 3

= 27

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2 years ago

Two percent of the customers of a store buy cigars. Half of the customers who buy cigars buy beer. 25 percent who buy beer buy c

enyata [817]

Answer:

0.95

Step-by-step explanation:

The computation of the probability that a customer neither buys beer nor buys cigars is given below;

Given that, the probabilities are

The customers who purchased cigars be 0.02

The customers who purchased cigars + beer 0.50

And, the customers who purchased beer + cigars be 0.25

Now the probabilities where the customer purchased both

= 0.05 × 0.02

= 0.10

The probability where the customer purchased beer is

= 0.01 ÷ 0.25

= 0.04

Now the probability where a customer neither buys beer nor buys cigars is

= 1 - 0.02 + 0.04 - 0.01

= 0.95

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2 years ago

1. You are standing on top of a ridge using a clinometer trying to figure out how far your dog has wandered off in

olga_2 [115]

Given:

It is given that the ridge is 360 inches tall.

Assumptions:

Assume you are 170.1 cm tall which equals 67 inches tall, the height from your eye to the floor is $360+67 = 427$ inches.

The distance from your eye level to the bottom of the ridge is 427 inches.

Assume the angle A is 60°.

To find the distance from you to your dog.

Solution:

A right-angled triangle can be formed where the angle is 60°, the distance between you and the dog is the hypotenuse of the triangle and your height from the floor is the adjacent side of the triangle.

Assume the hypotenuse of the triangle measures x inches.

To determine the length of the hypotenuse, we determine the cos of the angle.

$cos \theta = \frac{adjacent side}{hypotenuse} .$