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3 years ago

7

The shortest side of a triangle is 9 greater than twice the shortest side of a similar triangle. If the ratio of similitude is 7

:3 what is the length of the shortest side of each triangle?

1 answer:

chubhunter [2.5K]3 years ago

7 0

63:27 is the answer...

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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

What is the value of x

ratelena [41]

Answer:

19

Step-by-step explanation:

6 0

3 years ago

Y greater than or equal to x + 4

tatiyna

See the attached files

<h2>Explanation:</h2>

Here we have the following inequality:

$y>x+4$

In order to graph the shaded region, we have to graph the equation of the line $y=x+4$ whose slope is $m=1$ and y-intercept $b=4$ . So the graph of the line is shown in the First Figure below.

To find the shaded region we need to have a look at the symbol > that indicates that the shaded region is above the graph of the line and. Since this doesn't include the symbol =, then the line is dotted. Therefore, the resulting region is shown in the second Figure.

<h2>Learn more:</h2>

Shaded regions: brainly.com/question/9611462

#LearnWithBrainly

5 0

3 years ago

Help fast please....

IrinaVladis [17]

The second one is the answer

7 0

2 years ago

Amy tutors math. For each hour that she tutors, she earns dollars.

skelet666 [1.2K]

The equation to find Amy's earning after tutoring for 15 hours is 300 dollars.

<h3>How to find an equation?</h3>

She earn 20 dollars for each hours she tutors.

E = earnings in dollars

H = hours of tutoring

The equation relating E and H are as follows:

E = 20H

Therefore, the equation to find Amy's earning after tutoring for 15 hours is as follows;

E = 20H

E = 20 × 15

E = 300 dollars

Therefore, Amy's tutoring for 15 hours is 300 dollars.

learn more on expression here: brainly.com/question/14492671

#SPJ1

5 0

1 year ago