Which number has a terminating decimal expansion? А. 12 / B. 12 C. D. 11

At what point on the graph of y=1/4x^4 is the tangent line parallel to the line 24x -3y=8

Rama09 [41]

Answer:

a) dy/dx = 4/(2y+1)^2.

(b) y = 4/9 x - 14/9

(c) d2y/dx2 = -64/243

Step-by-step explanation:

You have the following equation

(1)

(a) You first derivative implicitly the equation (1) respect to x:

next, you solve the last result for dy/dx:

(2)

(b) The equation for the tangent line is given by:

(3)

with yo = -2 and xo = -1

To find the slope m you use the result of the equation (2), because dy/dx evaluated in (-1,-2) is the slope at such point:

m =

Hence, by replacing in the equation (3) you obtain:

hence, the equation for the tangent line is y = 4/9 x - 14/9

(c) To find d2y/dx2 you derivative the result obtain in the equation (2):

(4)

the second derivative for the point (-1,-2) is obtained by replacing y=-2 and dy/dx=m=4/9 in the equation (4):

hence, d2y/dx2 evaluated in (-1,-2) is -64/243

Step-by-step explanation:

3 0

3 years ago

A farmer sells 8.9 kilograms of apples and pears at the farmer's market. 3 /4 of this weight is apples, and the rest is pears. H

aleksandrvk [35]

Answer: 2.225 kg

Step-by-step explanation:

You know that:

- The total weight the farmer sold was 8.9 kilograms.

- 3/4 of this weight is apples, and the rest is pears.

Therefore, to calculate the amount of kilograms of pears she sold at the farmer's market (which you can call x), you need to apply the following proccedure.

Thefore, you obtain the following result:

$x=8.9kg-(8.9kg*\frac{3}{4})\\x=2.225kg$

4 0

3 years ago

Read 2 more answers

A(n) _____ is any side of a polygon that shares a side with only one angle of a pair of angles.

erastovalidia [21]

Answer:

non-included

Step-by-step explanation:

A non included side of a polygon shares a side with only one angle of a pair of angles.

4 0

3 years ago

Read 2 more answers

Find the volume of this sphere.<br> Use 3 for TT.<br> V [?]in3<br> V = Tr3<br> 8 in

frutty [35]

Answer:

The volume of the sphere is 2048 in³.

Step-by-step explanation:

The volume of a sphere is given by:

$V = \frac{4}{3}\pi r^{3}$

Where:

r: is the radius = 8 in

Having the radius and by using 3 for π, the volume is:

$V = \frac{4}{3}*3 (8 in)^{3} = 2048 in^{3}$

Therefore, the volume of the sphere is 2048 in³.

I hope it helps you!

4 0

3 years ago

Log10 (2x + 1) - logio(3x - 2) = 1

Pavlova-9 [17]

Answer: x=3/4

Step-by-step explanation:

To solve, first express the left side as one logarithm. To do so, apply the quotient rule which is log_bM/N=log_bM-log_bN .

log((2x+1)/(3x-2))=1

Then, express the equation to its equivalent exponential form to eliminate the logarithm.

Note that the exponential form of log_b M=a is M=b^a .

Since the base of the logarithm in the given equation is not written, it indicates that its base is 10.

So re-writing the equation, it becomes:

log_10((2x+1)/(3x-2))=1

And its exponential form is:

(2x+1)/(3x-2)=10^1

(2x+1)/(3x-2)=10

Now that the equation has no more logarithm, the next step is to remove the x in the denominator.

To do so, multiply both sides by 3x-2.

(3x-2)*(2x+1)/(3x-2)=10*(3x-2)

2x+1=30x-20

Next, combine like terms.

To combine 30x and 2x, bring them together on one side of the equation. So, move 2x to the right side by subtracting both sides by 2x.

2x-2x+1=30x-2x-20

1=28x-20

To combine 20 and 1, bring them together on the side opposite the term with x. So, add both sides by 20.

1+20=28x-20+20

21=28x

And, divide both sides by 28 to have x only at the right side.

21/28=(28x)/28

3/4=x

Hence, the solution to the given equation is x=3/4 .

3 0

3 years ago

Which number has a terminating decimal expansion? А. 12 / B. 12 C. D. 11​

Which number has a terminating decimal expansion? А. 12 / B. 12 C. D. 11