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gayaneshka [121]
3 years ago
9

Describe the pattern. Then give the next two numbers 1,1,2,3,5,8

Mathematics
1 answer:
murzikaleks [220]3 years ago
4 0

Answer:

the next two numbers will be 13, then 21

Step-by-step explanation:

the next number is the sum of the last two numbers.

1 + 1 = 2

2 + 3 = 5

etc etc

the next two numbers will be 13, then 21

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Consider F and C below. F(x, y, z) = y2 sin(z) i + 2xy sin(z) j + xy2 cos(z) k C: r(t) = t2 i + sin(t) j + t k, 0 ≤ t ≤ π (a) Fi
Liono4ka [1.6K]

Answer:

a) f (x,y,z)= xy^2\sin(z)

b) \int_C F \cdot dr =0

Step-by-step explanation:

Recall that given a function f(x,y,z) then \nabla f = (\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z}). To find f, we will assume it exists and then we will find its form by integration.

First assume that F = \nabla f. This implies that

\frac{\partial f}{\partial x} = y^2\sin(z) if we integrate with respect to x we get that

f(x,y,z) = xy^2\sin(z) + g(y,z) for some function g(y,z). If we take the derivative of this equation with respect to y, we get

\frac{\partial f}{\partial y} = 2xy\sin(z) + \frac{\partial g}{\partial y}

This must be equal to the second component of F. Then

2xy\sin(z) + \frac{\partial g}{\partial y}=2xy\sin(z)

This implies that \frac{\partial g}{\partial y}=0, which means that g depends on z only. So f(x,y,z) = xy^2\sin(z) + g(z)

Taking the derivative with respect to z and making it equal to the third component of F, we get

xy^2\cos(z)+\frac{dg}{dz} = xy^2\cos(z)

which implies that \frac{dg}{dz}=0 which means that g(z) = K, where K is a constant. So

f (x,y,z)= xy^2\sin(z)

b) To evaluate \int_C F \cdot dr we can evaluate it by using f. We can calculate the value of f at the initial and final point of C and the subtract them as follows.

\int_C F \cdot dr = f(r(\pi))-f(r(0))

Recall that r(\pi) = (\pi^2, 0, \pi) so f(r(\pi)) = \pi^2\cdot 0 \cdot \sin(\pi) = 0

Also r(0) = (0, 0, 0) so f(r(0)) = 0^2\cdot 0 \cdot \sin(0) = 0

So \int_C F \cdot dr =0

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3 years ago
HELP ASAP:<br><br> https://auro.reeee.ee/uD3ocP
Simora [160]
I swear i just saw this on discord
8 0
3 years ago
Use the rulers to help you estimate the perimeter of this triangle. <br> 6.5 in. 3 in. 6 in. 7 in.
777dan777 [17]

Answer:

6 inches

Step-by-step explanation:

The perimeter of a triangle is a + b + c

Where, a, b, c are the length of the 3 sides of the triangle ;

Using the ruler ;

a = 1.5

b = 2

c = 2.5

Therefore,

a + b + c

1.5 + 2 + 2.5

= 6 in

6 0
3 years ago
Read 2 more answers
Help me solve for the right triangle
AleksAgata [21]

Answers:

B = 50

a = 10.9

c = 17.0

================================================

Explanation:

This is a right triangle, so the acute angles are complementary, meaning they add to 90

B+40 = 90

B+40-40 = 90-40

B = 50

Also, because this is a right triangle, we can use trig ratios to compute the missing sides

tan(angle) = opposite/adjacent

tan(40) = a/13

a = 13*tan(40)

a = 10.908

a = 10.9

cos(angle) = adjacent/hypotenuse

cos(40) = 13/c

c*cos(40) = 13

c = 13/cos(40)

c = 17.0

note: make sure your calculator is in degree mode

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3 years ago
What is the answer for this
Lady bird [3.3K]

The equation that represents this hanger is: 4w=25

The weight of one circle is: 6.25

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3 years ago
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