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3 years ago

Given f(x) = 5x^6 what is the domain?

Mathematics

1 answer:

zheka24 [161]3 years ago

8 0

Answer:

The domain is all real numbers

Step-by-step explanation:

The domain of a function is the values that the input can take.

The input has no restrictions, so x can be any value

The domain is all real numbers

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Right △ABC has its right angle at C, BC=4 , and AC=8 .

PolarNik [594]

Answer:

Part A) $sin(A)=\frac{\sqrt{5}}{5}$

Part B) $tan(B)=2$

Part C) $sec(A)=\frac{\sqrt{5}}{2}$

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the length side AB (hypotenuse of the right triangle)

Applying the Pythagorean Theorem

$AB^2=BC^2+AC^2$

substitute the given values

$AB^2=4^2+8^2$

$AB^2=80$

$AB=\sqrt{80}\ units$

simplify

$AB=4\sqrt{5}\ units$

step 2

Find sin(A)

we know that

In the right triangle ABC

$sin(A)=\frac{BC}{AB}$ ----> by SOH (opposite side divided by the hypotenuse)

substitute the given values

$sin(A)=\frac{4}{4\sqrt{5}}=\frac{\sqrt{5}}{5}$

step 3

Find tan(B)

we know that

$tan(B)=\frac{AC}{BC}$ ----> by TOA (opposite side divided by adjacent side)

substitute the values

$tan(B)=\frac{8}{4}=2$

step 4

Find sec(A)

we know that

$sec(A)=\frac{1}{cos(A)}$

$cos(A)=\frac{AC}{AB}$ ----> by CAH

$sec(A)=\frac{AB}{AC}$

substitute the values

$sec(A)=\frac{4\sqrt{5}}{8}$

simplify

$sec(A)=\frac{\sqrt{5}}{2}$

3 0

4 years ago

Which of the following is a trinomial?

Alekssandra [29.7K]

A trinomial consists of 3 variables. Hence the answer will be A. C2 + C + 6

7 0

3 years ago

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Evaluate:25 divided by 5+2 multiplied by 3

dolphi86 [110]

Answer:

Step-by-step explanation:

25 than you divided 5 + 2 than you multiply 3 and you get

8 0

2 years ago

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Find the 2 critical points of the given function and then determine whether it is a local maximum, local minimum, or saddle poin

grandymaker [24]

Answer:

Step-by-step explanation:

Given is a function f in two variables as

$f(x, y) = (x − y)(xy − 9)$

To find critical points of the given function and also to find max, min or saddle point.

Find the partial derivatives

$f(x,y) = x^2y-xy^2-9x+9y$

$f_x=2xy-y^2-9\\f_y =x^2-2xy+9\\f_{xy} =2x-2y = f_{yx}$

$f_{xx}=2y\\ f_{yy}=-2x$

Equate first derivatives to 0

Adding fx and fy we get

$x^2-y^2 =0\\$

x=±y

Only real roots are (x,y) =(3,3) and (-3,-3)

$D(3,3)=f_{xx}(3,3) f_{yy}(3,3)-f_{xy}^2(3,3) \\=-36-0$

(3,3) is a saddle point

$D(-3,-3) = -36$

(-3,-3) is also a saddle point.

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3 years ago

The variables y and x have a proportional relationship, and y = 12 when x = 5.

Sergio [31]

Y= (12x8) / 5
Y= 19.2

6 0

1 year ago

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