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2 years ago

Using the unit circle, determine the value of sin 450°

Mathematics

1 answer:

ch4aika [34]2 years ago

7 0

Answer:

To find the value of sin 450 degrees using the unit circle, represent 450° in the form (1 × 360°) + 90° [∵ 450°>360°] ∵ sine is a periodic function, sin 450° = sin 90°.

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3.Write the product as a trinomial. (2r – 5)(r + 10)

Maurinko [17]

B is the correct answer

5 0

3 years ago

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Evaluate f(x) = x2 – 12 when x = 5

Ede4ka [16]

Answer:

f(5) = 13

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Function notation and substitution

Step-by-step explanation:

Step 1: Define

f(x) = x² - 12

x = 5

Step 2: Evaluate

Substitute: f(5) = 5² - 12
Exponents: f(5) = 25 - 12
Subtract: f(5) = 13

4 0

3 years ago

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Find the work done by F= (x^2+y)i + (y^2+x)j +(ze^z)k over the following path from (4,0,0) to (4,0,4)

babunello [35]

$\vec F(x,y,z)=(x^2+y)\,\vec\imath+(y^2+x)\,\vec\jmath+ze^z\,\vec k$

We want to find $f(x,y,z)$ such that $\nabla f=\vec F$ . This means

$\dfrac{\partial f}{\partial x}=x^2+y$

$\dfrac{\partial f}{\partial y}=y^2+x$

$\dfrac{\partial f}{\partial z}=ze^z$

Integrating both sides of the latter equation with respect to $z$ tells us

$f(x,y,z)=e^z(z-1)+g(x,y)$

and differentiating with respect to $x$ gives

$x^2+y=\dfrac{\partial g}{\partial x}$

Integrating both sides with respect to $x$ gives

$g(x,y)=\dfrac{x^3}3+xy+h(y)$

Then

$f(x,y,z)=e^z(z-1)+\dfrac{x^3}3+xy+h(y)$

and differentiating both sides with respect to $y$ gives

$y^2+x=x+\dfrac{\mathrm dh}{\mathrm dy}\implies\dfrac{\mathrm dh}{\mathrm dy}=y^2\implies h(y)=\dfrac{y^3}3+C$

So the scalar potential function is

$\boxed{f(x,y,z)=e^z(z-1)+\dfrac{x^3}3+xy+\dfrac{y^3}3+C}$

By the fundamental theorem of calculus, the work done by $\vec F$ along any path depends only on the endpoints of that path. In particular, the work done over the line segment (call it $L$ ) in part (a) is

$\displaystyle\int_L\vec F\cdot\mathrm d\vec r=f(4,0,4)-f(4,0,0)=\boxed{1+3e^4}$

and $\vec F$ does the same amount of work over both of the other paths.

In part (b), I don't know what is meant by "df/dt for F"...

In part (c), you're asked to find the work over the 2 parts (call them $L_1$ and $L_2$ ) of the given path. Using the fundamental theorem makes this trivial:

$\displaystyle\int_{L_1}\vec F\cdot\mathrm d\vec r=f(0,0,0)-f(4,0,0)=-\frac{64}3$

$\displaystyle\int_{L_2}\vec F\cdot\mathrm d\vec r=f(4,0,4)-f(0,0,0)=\frac{67}3+3e^4$

8 0

3 years ago

122333444455555666666777777788888888 what is the patern

Lelechka [254]

Answer:

each number it being counted that number of times

hope this helps

have a good day :)

Step-by-step explanation:

3 0

3 years ago

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Whats the cost of each vegetable if 5 squash and 2 zucchini is $1.32

alex41 [277]

Answer:

Step-by-step explanation:

We first need to define a couple of variables. Let s = the cost of 1 squash and z = the cost of 1 zucchini.

Now lets translate the words into algebra:

"The cost of 5 squash and 2 zucchini is $1.32" ===> 5s + 2z = 1.32

"Three squash and 1 zucchini cost $0.75" ===> 3s + z = 0.75

There are several ways to solve systems of equations. Let's use substitution. We can find what z equals in terms of s by manipulating the second equation:

3s + z = 0.75

-3s -3s

------------ -------------

z = -3s +0.75

Now lets substitute (-3s + 0.75) into the first equation for z, then solve for s:

5s + 2(-3s + 0.75) = 1.32

Can you handle it from here?

(Hint: Once you have solved for s, you can substitute that value back into either of the equations and solve for z.)

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3 years ago