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2 years ago

Find the 50ty term if the nth term is 5n-3

Mathematics

1 answer:

masha68 [24]2 years ago

4 0

Answer:

247

Step-by-step explanation:

From the question given above, the following data were obtained:

nth term (Tₙ) = 5n – 3

Number of term (n) = 50

50th term (T₅₀) =?

The 50th term can be obtained as follow:

Tₙ = 5n – 3

T₅₀ = 5(50) – 3

T₅₀ = 250 – 3

T₅₀ = 247

Therefore, the 50th term is 247.

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2 years ago

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3 years ago

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Please solve with working much appreciated

mojhsa [17]

Answer:

x°= 55°

Step-by-step explanation:

First, find the degrees of the larger triangle.

Since every triangle equals 180° degrees, make an equation.

60°+90°+a°= 180°

Now, add the degrees together.

120°+a°= 180°

Then subtract from both sides.

120°+a°= 180°

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Now that you know the sum of all the angles, subtract 25° from 60°(which is the measure of a).

60°-25°= 35°

Now that we have the measurement of the angle from the smaller triangle inside the larger one, make an equation.

35°+90°+x°= 180°

Then, add the degrees.

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6 0

2 years ago

Write the expression: The quotient of the sum 3y and 5, and y squared.

lesya692 [45]

Answer:

(3y + 5) / (y^2)

Step-by-step explanation:

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6 0

2 years ago

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).

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2 years ago