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3 years ago

(5k − 1 + 2k3) − (6k3 − 3k2 − 8) + (8k3 − 2k2 − 7k)

Mathematics

2 answers:

Sedaia [141]3 years ago

4 0

It is 45/79k I beileve so

Vera_Pavlovna [14]3 years ago

3 0

Answer:

4k^3 + k^2 - 2k + 7

Step-by-step explanation:

Hope this helps, and good luck

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Find dy/dx by implicit differentiation. y cos x = 5x2 + 3y2

lbvjy [14]

Step 1:
Start by putting $\frac{d}{dx}$ in front of each term

$\frac{d}{dx}[y cos x]= \frac{d}{dx}[5x^2]+ \frac{d}{dx}[ 3y^2]$
-----------------------------------------------------------------------------------------------------------------
Step 2:

Deal with the terms in 'x' and the constant terms
$\frac{d}{dx}[ycosx]= 10x+ \frac{d}{dx} [3y^2]$
----------------------------------------------------------------------------------------------------------------
Step 3:

Use the chain rule for the terms in 'y'
$\frac{d}{dx}[ycosx]=10x+6y \frac{dy}{dx}$
--------------------------------------------------------------------------------------------------------------
Step 4:

Use the product rule on the term in 'x' and 'y'
$(y) \frac{d}{dx} cos x+(cos x) \frac{d}{dx}y =10x+6y \frac{dy}{dx}
$
$y(-siny)+(cosx) \frac{dy}{dx} =10x+6y \frac{dy}{dx}$
--------------------------------------------------------------------------------------------------------------

Step 5:

Rearrange to make $\frac{dy}{dx}$ the subject
$-y sin(y)+cos(x) \frac{dy}{dx} =10x+6y \frac{dy}{dx}$
$cos(x) \frac{dy}{dx}-6y \frac{dy}{dx}=10x+y sin(y)$
$[cos(x) - 6y] \frac{dy}{dx}=10x + y sin(y)$
$\frac{dy}{dx}= \frac{10x+ysin(y)}{cos(x)-6y}$ ⇒ Final Answer

5 0

4 years ago

Any help would be greatly appreciated thank you

maria [59]

Answer:

Option D. Strong positive correlation

Step-by-step explanation:

Like the r-value of 0.987 is positive (0.987>0) and close to 1, the correlation of the graph is a strong positive correlation

6 0

4 years ago

What is the equation of a vertical ellipse with a major axis= 20 and a minor axis = 14?

Sunny_sXe [5.5K]

$\bold{\text{Answer: b.}\quad \dfrac{y^2}{100}+\dfrac{x^2}{49}=1}$

<u>Step-by-step explanation:</u>

The ellipse is vertical so y has the biggest radius.

Major axis (y) = 20 so the y-radius is 20/2 = 10

Minor axis (x) = 14 so the x-radius is 14/2 = 7

The equation of an ellipse is: $\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1$ where

(h, k) is the center of the ellipse
a is the x-radius
b is the y-radius

Given: a = 7, b = 10

Assume: (h, k) = (0, 0)

$\dfrac{(x-0)^2}{7^2}+\dfrac{(y-0)^2}{10^2}=1\\\\\\\dfrac{x^2}{49}+\dfrac{y^2}{100}=1\\\\\\\longrightarrow \dfrac{y^2}{100}+\dfrac{x^2}{49}=1$

6 0

3 years ago

A delivery truck weighs 5.5 tons before it is loaded with packages. Once the delivery truck is full of x packages it weighs 6.1

KIM [24]

Answer:

80 packages

Step-by-step explanation:

0.0075*80= 0.6 5.5 + 0.6= 6.1

4 0

2 years ago

Solve for n -3n-5=16

Nezavi [6.7K]

Answer:

n = -7

Step-by-step explanation:

Solve for n:

-3 n - 5 = 16

Hint: | Isolate terms with n to the left-hand side.

Add 5 to both sides:

(5 - 5) - 3 n = 5 + 16

Hint: | Look for the difference of two identical terms.

5 - 5 = 0:

-3 n = 16 + 5

Hint: | Evaluate 16 + 5.

16 + 5 = 21:

-3 n = 21

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of -3 n = 21 by -3:

(-3 n)/(-3) = 21/(-3)

Hint: | Any nonzero number divided by itself is one.

(-3)/(-3) = 1:

n = 21/(-3)

Hint: | Reduce 21/(-3) to lowest terms. Start by finding the GCD of 21 and -3.

The gcd of 21 and -3 is 3, so 21/(-3) = (3×7)/(3 (-1)) = 3/3×7/(-1) = 7/(-1):

n = 7/(-1)

Hint: | Simplify the sign of 7/(-1).

Multiply numerator and denominator of 7/(-1) by -1:

Answer: n = -7

7 0

3 years ago

Read 2 more answers