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3 years ago

Ten students enter a math contest. In how many ways can 1st, 2nd, and 3rd place trophies be awarded?

1 answer:

4 0

After one of them is chosen for 1st, there are only 9 choices for 2nd, and then there are only 8 choices for 3rd... and so on. There are 720 different ways to pick 1st, 2nd, and 3rd place from among 10 original students

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How do you know 7.031 is greater than 7.03

slavikrds [6]

We know because they are both 7, but 7.031 has 031. 7.03 only has .03, if that makes sense

3 0

3 years ago

Consider the following vector function. R(t) = 9 2 t, e9t, e−9t (a) find the unit tangent and unit normal vectors t(t) and n(t)

garik1379 [7]

The unit tangent vector is T(u) and the unit normal vector is N(t) if the vector function. R(t) is equal to 9 2 t, e9t, e−9t.

<h3>What is vector?</h3>

It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.

We have vectored function:

$\rm R(t) = (9\sqrt{2t}, e^{9t}, e^{-9t})$

Find its derivative:

$\rm R'(t) = (9\sqrt{2}, 9e^{9t}, -9e^{-9t})$

Now its magnitude:

$\rm |R'(t) |= \sqrt{(9\sqrt{2})^2+ (9e^{9t})^2+ (-9e^{-9t})^2}$

After simplifying:

$\rm R'(t) = 9 \dfrac{e^{18t}+1}{e^{9t}}$

Now the unit tangent is:

$\rm T(u) = \dfrac{R'(t)}{|R'(t)|}$

After dividing and simplifying, we get:

$\rm T(u) = \dfrac{1}{e^{18t}+1} (\sqrt{2}e^{9t}, e^{18t}, -1)$

Now, finding the derivative of T(u), we get:

$\rm T'(u) = \dfrac{1}{(e^{18t}+1)^2} (9\sqrt{2}e^{9t}(1-e^{18t}), 18e^{18t}, 18e^{18t})$

Now finding its magnitude:

$\rm |T'(u) |= \dfrac{1}{(e^{18t}+1)^2} (9\sqrt{2}e^{9t}(1-e^{18t})^2+ (18e^{18t})^2+( 18e^{18t})^2)$

After simplifying, we get:

$\rm |T'(u)|= \dfrac{9\sqrt{2}e^{9t}}{e^{18t}+1}$

Now for the normal vector:

Divide T'(u) and |T'(u)|

We get:

$\rm N(t) = \dfrac{1}{e^{18t}+1} ( 1-e^{18t}, \sqrt{2}e^{9t}, \sqrt{2}e^{9t})$

Thus, the unit tangent vector is T(u) and the unit normal vector is N(t) if the vector function. R(t) is equal to 9 2 t, e9t, e−9t.

Learn more about the vector here:

brainly.com/question/8607618

#SPJ4

3 0

2 years ago

4x + y s8<br> yz - 4x - 1

aleksandrvk [35]

Answer:

the first one the expression is not factorable with ration numbers

the second one is the same thing

Step-by-step explanation:

8 0

3 years ago

Help me plz answer if know don’t answer for points

Mashutka [201]

Download an app called Socratic and scan this problem it may help and give an answer if no one answers to this

5 0

3 years ago

The length of a rectangle is 12 feet more than twice the width. If the area is 320 square feet, what is the length? What is the

Softa [21]

Answer:

Length of rectangle is 32 feet and width is 10 feet

Step-by-step explanation:

Given,

The length of a rectangle is 12 feet more than twice the width and area is 320 square feet

Let's assume, width of rectangle x feet and length of the Rectangle be 12 + 2x respectively. To Calculate the length and width of rectangle we'll use the formula of area of rectangle:

$\\ \star \: { \underline{ \boxed { \pmb{ \sf{ \purple{Area _{(rectangle)}= Length \times width}}}}}} \\ \\$