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nordsb [41]
2 years ago
9

Pinning as branliest for best explained answer ::

Mathematics
1 answer:
Anika [276]2 years ago
7 0

Answer:

sol:x=(5y+53)/11

value of x in 4x+3y=0

4×(5y+53)/11+3y=0

(20y+212+33y)/11=0

53y+212=0/11

y=-212/53

y=-4

now

value of x

4x+3y=0

4x+3×-4=0

4x=12

x=12/4

x=4

by solving both we get,

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3. The curve C with equation y=f(x) is such that, dy/dx = 3x^2 + 4x +k
Andreas93 [3]

a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have

\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt

Evaluate the integral to solve for y :

\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt

\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x

\displaystyle y = x^3+2x^2+kx - 2

Use the other known value, f(2) = 18, to solve for k :

18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}

Then the curve C has equation

\boxed{y = x^3 + 2x^2 + 2x - 2}

b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:

\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2

The slope of the given tangent line y=x-2 is 1. Solve for a :

3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1

so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).

Decide which of these points is correct:

x - 2 = x^3 + 2x^2 + 2x - 2 \implies x^3 + 2x^2 + x = x(x+1)^2=0 \implies x=0 \text{ or } x = -1

So, the point of contact between the tangent line and C is (-1, -3).

7 0
2 years ago
PLEASE HELP ANSWER !!!
geniusboy [140]

Answer:

the answer is 81

Step-by-step explanation:

1. find 75

2. add 75 + 24

3. subtract from 180 to find x

3 0
3 years ago
Please helpp geometry (click for picture)
NeTakaya

Answer:

20 degrees

Step-by-step explanation:

Since angle B and angle A are both inscribed angles to the same arc, they must be equal. Therefore:

7x-8=5x

Subtract 5x from both sides:

2x-8=0

Add 8 to both sides:

2x=8

Divide both sides by 2:

x=4

Now, you can plug this back into the equation for angle B:

B=7(4)-8

B=28-8

B=20

Hope this helps!

3 0
3 years ago
What is the nth term rule of the quadratic sequence below?<br> -5, -3,3, 13, 27, 45, 67, ...
Svetllana [295]

Answer:

the pattern is +2, +6, +10, +14, +18 etc

so its in increment of 4

the rest is trivial

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Check picture to see question<br><br> no guessing
GaryK [48]
Y= 40 x is the answer, hope this helped.
6 0
3 years ago
Read 2 more answers
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