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3 years ago

Can someone answer these correctly please!!

Mathematics

1 answer:

Pani-rosa [81]3 years ago

8 0

X= 1 is the answer as you can see values of f(x) and g(x) are same

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A ladder is leaning against a building as shown in the

JulsSmile [24]

The length of ladder is 30 ft.

<h3>How can the feet that made up the side of the building is the top of the ladder be known ?</h3>

The formula below can be used in solving the problem

Tan (∅)= $\frac{opposite}{adajacent}$

∅=70°

opposite = BC

Adjacent = 12 ft

70°= opposite/ 12

opposite= 32.96 ft

Therefore, The length of ladder is 30 ft.

NOTE; Since the actual diagram can not be found i solved another on on the same topic

Learn more about Trigonometry on:

brainly.com/question/7380655

#SPJ1

CHECK COMPLETE QUESTION BELOW:

Consider the diagram shown where a ladder is leaning against the side of a building. the base of the ladder is 12ft from the building. how long is the ladder? (to the nearest ft)

a. 25ft

b. 30ft

c. 35ft

d. 40ft

5 0

2 years ago

For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential f

Phantasy [73]

The key idea is that, if a vector field is conservative, then it has curl 0. Equivalently, if the curl is not 0, then the field is not conservative. But if we find that the curl is 0, that on its own doesn't mean the field is conservative.

$\mathrm{curl}\vec F=\dfrac{\partial(5x+10y)}{\partial x}-\dfrac{\partial(-6x+5y)}{\partial y}=5-5=0$

We want to find $f$ such that $\nabla f=\vec F$ . This means

$\dfrac{\partial f}{\partial x}=-6x+5y\implies f(x,y)=-3x^2+5xy+g(y)$

$\dfrac{\partial f}{\partial y}=5x+10y=5x+\dfrac{\mathrm dg}{\mathrm dy}\implies\dfrac{\mathrm dg}{\mathrm dy}=10y\implies g(y)=5y^2+C$

$\implies\boxed{f(x,y)=-3x^2+5xy+5y^2+C}$

so $\vec F$ is conservative.

$\mathrm{curl}\vec F=\left(\dfrac{\partial(-2y)}{\partial z}-\dfrac{\partial(1)}{\partial y}\right)\vec\imath+\left(\dfrac{\partial(-3x)}{\partial z}-\dfrac{\partial(1)}{\partial z}\right)\vec\jmath+\left(\dfrac{\partial(-2y)}{\partial x}-\dfrac{\partial(-3x)}{\partial y}\right)\vec k=\vec0$

Then

$\dfrac{\partial f}{\partial x}=-3x\implies f(x,y,z)=-\dfrac32x^2+g(y,z)$

$\dfrac{\partial f}{\partial y}=-2y=\dfrac{\partial g}{\partial y}\implies g(y,z)=-y^2+h(y)$

$\dfrac{\partial f}{\partial z}=1=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=z+C$

$\implies\boxed{f(x,y,z)=-\dfrac32x^2-y^2+z+C}$

so $\vec F$ is conservative.

$\mathrm{curl}\vec F=\dfrac{\partial(10y-3x\cos y)}{\partial x}-\dfrac{\partial(-\sin y)}{\partial y}=-3\cos y+\cos y=-2\cos y\neq0$

so $\vec F$ is not conservative.

$\mathrm{curl}\vec F=\left(\dfrac{\partial(5y^2)}{\partial z}-\dfrac{\partial(5z^2)}{\partial y}\right)\vec\imath+\left(\dfrac{\partial(-3x^2)}{\partial z}-\dfrac{\partial(5z^2)}{\partial x}\right)\vec\jmath+\left(\dfrac{\partial(5y^2)}{\partial x}-\dfrac{\partial(-3x^2)}{\partial y}\right)\vec k=\vec0$

Then

$\dfrac{\partial f}{\partial x}=-3x^2\implies f(x,y,z)=-x^3+g(y,z)$

$\dfrac{\partial f}{\partial y}=5y^2=\dfrac{\partial g}{\partial y}\implies g(y,z)=\dfrac53y^3+h(z)$

$\dfrac{\partial f}{\partial z}=5z^2=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=\dfrac53z^3+C$

$\implies\boxed{f(x,y,z)=-x^3+\dfrac53y^3+\dfrac53z^3+C}$

so $\vec F$ is conservative.

4 0

3 years ago

The function f(x) = –x2 − 2x + 15 is shown on the graph. What are the domain and range of the function?

Phantasy [73]

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

Domain: ( − ∞ , ∞ ) , { x | x ∈ R }

Range: ( − ∞ , 16 ] , { y | y ≤ 16 }

3 0

2 years ago

The sum of three consecutive even integers is -78, what are the integers ?

Digiron [165]

First, you need to analize and understand the problem, then you must choose and strategy. There is a wide variety of strategies to solve a mathematical problem, in this case, you can use the following, which is based on the information given above:
1. You have that the sum of three consecutive even integers is $-78$ , therefore, you can given the variable $x
$ to the first integer, the second even integer is $x+2$ and the third one is $x+4
$ .
2. Calculate x:
 $x+(x+2)+(x+4)=-78$ 
 $3x+6=-78$
 $x=-28
$ 
 $x+2=-28+2=-26
$ 
 $x+4=-28+4=-24
$ 
Therefore, the answer is: $-28,-26,-24
$

5 0

2 years ago

PLEASE HELP!!! I don't know how to do this... (screenshots provided)

Mrac [35]

Answer:

i really dont know how to do this and i dont think anybody here knows how to

Step-by-step explanation:

4 0

3 years ago