The slope is the factor in front of x, so slope is 9.
The y intercept is 7 (that's the point of cross the y axis, where x=0)
There are multiple definitions of "standard form" for lines, so here are the two i can think of:
9x - y = -7 (the implicit function form)
or
y-7 = 9*(x-0) (the point-slope form)
Lmk if you have questions.
Answer:
x= 15/7
Step-by-step explanation:
Set up the equation in long division form with x-5 outside of the box. Then you want to input the values as you go. Let me know if you want me to clarify my steps.
Answer:
45 degrees
Step-by-step explanation:
Here, we want to get the value of the acute angle
From the question, we have it that the sin of the acute angle equals its cosine
Recall;
cos A = sin (90-A)
Hence, if A is 45, then Cos A and Sine A will be the same
This means the value of theta which is the acute angle is 45 degrees
<h3>Given</h3>
- a cone of height 0.4 m and diameter 0.3 m
- filling at the rate 0.004 m³/s
- fill height of 0.2 m at the time of interest
<h3>Find</h3>
- the rate of change of fill height at the time of interest
<h3>Solution</h3>
The cone is filled to half its depth at the time of interest, so the surface area of the filled portion will be (1/2)² times the surface area of the top of the cone. The filled portion has an area of
... A = (1/4)(π/4)d² = (π/16)(0.3 m)² = 0.09π/16 m²
This area multiplied by the rate of change of fill height (dh/dt) will give the rate of change of volume.
... (0.09π/16 m²)×dh/dt = dV/dt = 0.004 m³/s
Dividing by the coefficient of dh/dt, we get
... dh/dt = 0.004·16/(0.09π) m/s
... dh/dt = 32/(45π) m/s ≈ 0.22635 m/s
_____
You can also write an equation for the filled volume in terms of the filled height, then differentiate and solve for dh/dt. When you do, you find the relation between rates of change of height and area are as described above. We have taken a "shortcut" based on the knowledge gained from solving it this way. (No arithmetic operations are saved. We only avoid the process of taking the derivative.)
Note that the cone dimensions mean the radius is 3/8 of the height.
V = (1/3)πr²h = (1/3)π(3/8·h)²·h = 3π/64·h³
dV/dt = 9π/64·h²·dh/dt
.004 = 9π/64·0.2²·dh/dt . . . substitute the given values
dh/dt = .004·64/(.04·9·π) = 32/(45π)
