The equation y=19x relates proportional quantities x and y. What is the value of x when y is 4? Enter your answer in the box

Mathematics

2 answers:

Igoryamba3 years ago

8 0

$\frac{4}{19}$

eimsori [14]3 years ago

6 0

Answer: 4=1/9x

Step-by-step explanation:

4*9/1=36

x=36

You might be interested in

A month ago, the ratio of nurses to doctors on a hospital staff was 3:5. Since that time, two additional nurses joined the staff

bija089 [108]

Answer:

Step-by-step explanation:

The ratio of nurses to docters a month ago was 3:5. Now, it's 4:5. You can tell that there aren't 4 nurses because 3 => 4 is only one nurse. If you duplicate both ratios (multiply both sides by 2), you get 6:10 (for a month ago) and 8:10 (now). This is correct because 6+2=8. Hope it helps!

6 0

3 years ago

A hiker is hiking in a valley. The height of the valley is h(x,y)=4x2+y2 where x and y are the east-west and north-south distanc

Ainat [17]

Answer:

A. $\frac{\partial{h}}{\partial{t}}=0$

Step-by-step explanation:

A. The problems asked for 2 ways to solve it, expanding the equation with the substitution x(t)=2 cos(t) and y(t)=4 sin(t) to differentiate it . The other way is by chain rule.

Expanding and differentiating:

We start by substituting x(t)=2 cos(t) and y(t)=4 sin(t) in h(x,y)=4x2+y2:

$h(x,y)=4x^{2}+y^{2}= 4(2cos(t))^{2}+(4sin(t))^{2}\\h(x,y)=4(4cos^{2}(t))+(16sen^{2}(t))\\h(x,y)=16cos^{2}(t)+16sen^{2}(t)=16(sen^{2}(t)+cos^{2}(t))\\h(x,y)=16$

So, in the path that the hiker chose:

$\frac{\partial{h}}{\partial{t}}=0$

Chain rule:

We start differentiating h(x,y) using chain rule as follows:

$\frac{\partial{h}}{\partial{t}}= \frac{\partial{h}}{\partial{x}}\frac{\partial{x}}{\partial{t}}+\frac{\partial{h}}{\partial{y}}\frac{\partial{y}}{\partial{t}}$

Now, it´s easy to find all these derivatives:

$\frac{\partial{h}}{\partial{x}}=8x\\\frac{\partial{x}}{\partial{t}}=-2sin(t)\\\frac{\partial{h}}{\partial{y}}=2y\\\frac{\partial{y}}{\partial{t}}=4cos(t)$