What is this expression in scientific notation

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

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

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

Use the chain rule for the terms in 'y'
$\frac{d}{dx}[ycosx]=10x+6y \frac{dy}{dx}$
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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}
$
$y(-siny)+(cosx) \frac{dy}{dx} =10x+6y \frac{dy}{dx}$
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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

3 years ago

Helppppppp pleaseeeeeee

pshichka [43]

Answer:

(2a, 2b)

Step-by-step explanation:

(0, 2b)

(2a, 0)

(2a, 2b)

I racked my brain for that.

4 0

3 years ago

I dont quite understand this.. Check the picture and help

wariber [46]

5) 74.925

6) 470

i think this is correct but i'm not completely sure

6 0

2 years ago

Ten pictures, each measuring 4 inches by 6 inches, are mounted on a piece of green poster board so that there is no overlap. The

alexandr1967 [171]

Answer:

100 square inches

Step-by-step explanation:

Dimension of each of the ten pictures= 4 inches by 6 inches

Area of one of the pictures=4*6=24 Square Inch.

Total Area of the 10 pictures=24*10=240 Square Inches.

Dimension of the Poster Board=20 inches by 17 inches.

Area of the Poster Board=20*17=340 Square Inches.

Area not covered by the pictures=340-240=100 Square Inches

Therefore, 100 square inches of the green background will show after the pictures are mounted.

3 0

2 years ago

(3/5)^2+4X3-2 what is the value of the expression

Sliva [168]

Answer:

10.36

Step-by-step explanation:

So your solution would be:

$(\frac{3}{5})^{2} + 4 \times 3 - 2$

$=(\frac{3}{5})^{2} + 4 \times 3 - 2$

$=\dfrac{3^{2}}{5^{2}} + 4 \times 3 - 2$

$=\dfrac{9}{25} + 4 \times 3 - 2$

$=0.36 + 4 \times 3 - 2$

$=0.36 + 12 - 2$

$=12.36 - 2$

$=10.36$

Just try to remember PEMDAS.

Parenthesis, Exponent, Multiplication/Division, Addition/Subtraction.

This is the order we follow when going about expressions with many operations.

Let's start with the parenthesis part. Notice that there is an exponent beside the parenthesis enclosing the fraction. Here we use the quotient to a power rule. We distribute the exponent to the numerator and the denominator.

$=(\frac{3}{5})^{2} + 4 \times 3 - 2\\$

$=\dfrac{3^{2}}{5^{2}} + 4 \times 3 - 2$

$=\dfrac{9}{25} + 4 \times 3 - 2$

Now that we got the parenthesis and exponent out of the way, let's move on to the next. Multiplication/Division. Whichever comes first, you do it first.

We have a fraction so we do that first. Then we do the multiplication after.

$=0.36 + 4 \times 3 - 2$

$=0.36 + 12 - 2$

Next we do the addition/subtraction. Again, whichever comes first.

$=12.36 - 2$

$=10.36$

7 0

3 years ago