The equation looks like this
y≤ -1/3x + 4
And it looks like
<h3>
Answer: D) common ratio</h3>
Explanation:
The four points on this curve are
(1, 3)
, (2, 6), (3, 12)
, (4, 24)
The equation of the curve that goes through all the points mentioned is
y = 3*2^(x-1) which is equivalent to y = 1.5*2^x
Both equations are exponential equations.
Sequences of the form
a(n) = a*(r)^(n-1)
are geometric sequences with common ratio r. In this case, r = 2.
Note how the jump from 3 to 6 is "times 2", so is from 6 to 12, and from 12 to 24. We multiply each term by 2 to get the next one.
<h2>9.</h2><h3>Given</h3>
<h3>Find</h3>
- linear approximation to the volume when the radius increases 0.4 cm
<h3>Solution</h3>
The equation for volume of a sphere is
... V = (4/3)π·r³
Differentiating gives
... dV = 4π·r²·dr
Filling in the given numbers gives
... change in volume ≈ 4π·(15 cm)²·(0.4 cm)
... = 360π cm³ ≈ 1130.97 cm³ . . . . . . volume of layer 4mm thick
<h2>11.</h2><h3>Given</h3>
- an x by x by 2x cuboid with surface area 129.6 cm²
- rate of change of x is 0.01 cm/s
<h3>Find</h3>
<h3>Solution</h3>
The area is that of two cubes of dimension x joined together. The area of each such cube is 6x², but the two joined faces don't count in the external surface area. Thus the area of the cuboid is 10x².
The volume of the cuboid is that of two cubes joined, so is 2x³. Then the rate of change of volume is
... dV/dt = (d/dt)(2x³) = 6x²·dx/dt
We know x² = A/10, where A is the area of the cuboid, so the rate of change of volume is ...
... dV/dt = (6/10)A·dx/dt = 0.6·(129.6 cm²)(0.01 cm/s)
... dV/dt = 0.7776 cm³/s
Answer:
5/9
Step-by-step explanation:
Start be letting x = 0.555...
Our original equation is:
x = 0.555...
There is only one digit repeating, the 5, so we multiply both sides of that equation by 10 and write it above the original equation.
10x = 5.555...
x = 0.555...
Now we subtract the second equation from the first equation as written above.
9x = 5
Divide both sides by 9.
x = 5/9
0.555... = 5/9
The length of the other two sides is 10 and 35 respectively.
<h3>What is a ratio?</h3>
A ratio is a quantitative relation showing the comparison between two or more numbers. It can also be written in the fractional form where the first part is the numerator and the second part is called the denominator.
From the given information:
- The sides of the triangle = 2:7:8
- The total sides of the triangle = 2+7+8 = 17
We are being told that the longest side is the triangle is equal to 40.
i.e.
x = 85
Now for the other two sides 2 and 7, their length is as follows.
Therefore, we can conclude that the length of the other two sides is 10 and 35 respectively.
Learn more about ratios here:
brainly.com/question/2328454
