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3 years ago

7

Help me with this question

1 answer:

timama [110]3 years ago

5 0

Answer:

15 square units

Step-by-step explanation:

5*3=15

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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 <em>f</em>, 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 <em>x</em> :

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

Differentiate both sides with respect to <em>y</em> :

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

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

Integrate both sides with respect to <em>y</em> :

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

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

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

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

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

Integrate both sides with respect to <em>z</em> :

$h(z)=C$

So we end up with

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

7 0

3 years ago

In the right triangle the measure of C is 90

liq [111]

The measure of a right angle is 90 degrees

6 0

3 years ago

Find, leave your answers in terms of pie,

Yuri [45]

Area of square = 10x10
= 100
area of circle = pi(r)^2
= pi (5)^2
=25pi

area of shaded = 100 -25pi

circumference of circle = 2pi (r)
= 2pi(5)
= 10pi

perimeters of shaded = 10pi + 10 + 10
= 10pi +20

8 0

2 years ago

Who can help me?<br>please<br>Thank you

4vir4ik [10]

The sum of the interior triangles in a triangle is 180, so if we add all the angle measures together, we should get 180. Therefore, we can make an equation like this,

$110-2x+x+50+5x-40=180$

Simplify this.

$4x+120=180$

$4x=60$

$x=15$

Now we can find each angle measure.

$110-2x$

$110-2(15)$

$110-30$

$80$

$x+50$

$15+50$

$65$

$5x-40$

$5(15)-40$

$75-40$

$35$

So the angle labeled $110-2x$ is the largest angle in the triangle.

7 0

3 years ago

Read 2 more answers

Elizabeth is a manager at a nursery and is in charge of displaying potted trees in a row Elizabeth has 150 citrus trees and 180

vampirchik [111]

Answer: the greatest number of trees that ElizaBeth can have in a row is 30

Step-by-step explanation:

given data:

citrus trees = 150

palm trees = 180

As we have to find the greatest number of trees that Elizabeth can have in a row, we will find the GCF or greatest common factor.

150 = 2 x 3 x 5 x 5

180 = 2 x 2 x 3 x 3 x 5

Greatest common factor is = 2 x 3 x 5 = 30

Therefore, the largest number of trees that ElizaBeth can have in a row is 30.

4 0

3 years ago