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2 years ago

In triangle ABC, AC = 4, BC = 5, and 1 < AB < 9. Let D, E and F be the

Mathematics

2 answers:

QveST [7]2 years ago

8 0

The answer will be C.4

Charra [1.4K]2 years ago

4 0

The answer would be 4

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Simplify (4s5t−7−2s−2t4)3. Write your answer using only positive exponents. Evaluate any numerical powers.

schepotkina [342]

Answer:

−21

Step-by-step explanation:

=12s5t−6t4−6s−21

5 0

3 years ago

EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a functi

Valentin [98]

If there is such a scalar function f, then

$\dfrac{\partial f}{\partial x}=4y^2$

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}$

$\dfrac{\partial f}{\partial z}=16ye^{4z}$

Integrate both sides of the first equation with respect to x :

$f(x,y,z)=4xy^2+g(y,z)$

Differentiate both sides with respect to y :

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}$

$\implies\dfrac{\partial g}{\partial y}=4e^{4z}$

Integrate both sides with respect to y :

$g(y,z)=4ye^{4z}+h(z)$

Plug this into the equation above with f , then differentiate both sides with respect to z :

$f(x,y,z)=4xy^2+4ye^{4z}+h(z)$

$\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}$

$\implies\dfrac{\mathrm dh}{\mathrm dz}=0$

Integrate both sides with respect to z :

$h(z)=C$

So we end up with

$\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}$

7 0

2 years ago

The actual depth of a lake is 15.8 meters.

Anna35 [415]

Answer:

0.2 meters

Step-by-step explanation:

16-15.8 is 0.2 haha

8 0

2 years ago

3x−1−(x+3)=1 PLEASE HELP IDK HOW TO DO IT

torisob [31]

Answer:

x = 5/2

x = 2 1/2

x = 2.5

Step-by-step explanation:

3x - 1 - (x + 3) = 1

3x - 1 - x - 3 = 1

2x - 1 - 3 = 1

2x - 4 = 1

2x = 1 + 4

2x + 5

2x = 5

x = 5/2 → 2 1/2 → 2.5 ( can be written in any of these forms depending on what you need to do)

Hope this helped! :)

7 0

2 years ago

Read 2 more answers

Two sides of a triangle measure 8 cm and 15 cm. Whi[:h could be the length of the third side?

lutik1710 [3]

18 cm is correct .

Step-by-step explanation:

The sum of two smaller sides is greater that the largest side.

It is given that the two sides of a triangle measure 8 cm and 15 cm.

Case 1: Let 8 cm and 15 cm. are smaller side. So,

Third side < 8 + 15

Third side < 23

It means 3rd side must be less than 23

Case 2: Let 15 cm is the largest side.

15 < Third side + 8

15 - 8 < Third side

7 < Third side

It means 3rd side must be greater than 7.

Since only 18 is less than 23 and greater than 7, therefore the possible length of third sides is 18 cm and option 2 is correct.

8 0

2 years ago