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Mademuasel [1]
3 years ago
9

If L is the line through the point (-3,5) having a slope of (2/3) complete the equation of L

Mathematics
1 answer:
Artist 52 [7]3 years ago
4 0
Y = mx + b
slope(m) = 2/3
(-3,5)...x = -3 and y = 5
now sub and find b, the y int
5 = 2/3(-3) + b
5 = -2 + b
5 + 2 = b
7 = b

so ur equation is : y = 2/3x + 7
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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]
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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
I need help, and I’m also confused.
amid [387]
There are two triangles, a big triangle and a small triangle that is inside the big triangle. Because the base of the triangles are parallel to each other( indicated by the arrow), and the small triangle is perfectly inside the bigger triangle, the sides of the triangles are proportional.

It is know that the base of the small triangle is 3.5, and the hypotenuse of the small triangle is 7cm. it is also known that the the hypotenuse of the big triangle is (7+8)=15 and the base of the big triangle is unknown.

Since the triangles are proportional,
to find the base of the big triangle

base(big)/hypotenuse(big)=base(small)/hypotenuse(small)

Plug in the numbers


x/15=3.5/7
x/15=1/2
x=15/2
x=7.5

The length of the base of the big triangle is 7.5cm
8 0
3 years ago
Convert the polar equation to rectangular form: <br><br> r = 2 / [1 + sin(theta)]
iren2701 [21]
R = 2 / (1 + sin <span>θ)

Using the following relations:

R = sqrt (x^2 + y^2)
sin </span>θ = y/R
<span>
R = 2 / (1 + y/R)
R</span>(1 + y/R<span>) = 2
</span><span>R + y = 2
R = 2 - y
sqrt(x^2 + y^2) = 2 - y

Squaring both sides:
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x^2 + y^2 = 4 - 4y + y^2

x^2 + 4y - 4 


</span>
8 0
3 years ago
What is the solution to the system of equations? Use the substitution method.
aleksandrvk [35]
{ y = 3 x - 4
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Subsititute y = 3x-4 :

[ 9 x - 3 ( 3 x-14 )=14]

Refine:

9 x  - 3 ( 3 x - 4 ) = 14

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is false , therefore the system of equations has no solution

Answer A

hope this helps! 
3 0
3 years ago
Which of the following fractions has the same value as the decimal number 0.65?
boyakko [2]

Answer:

13/20

Step-by-step explanation:

To find this, divide 13 by 20 to get .65

Hope this helped!

4 0
3 years ago
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