All categories

3 years ago

Find the 4th term in the sequence.

Mathematics

2 answers:

HACTEHA [7]3 years ago

6 0

Answer:

Step-by-step explanation:

inn [45]3 years ago

4 0

Answer:

Step-by-step explanation:

how did you put a pic up?

You might be interested in

3 times x minus 2/5 =8/5 what is x equal to

shutvik [7]

Translating this word problem into an algebraic equation, we get:

3x - 2/5 = 8/5.

Let's combine the constants: adding 2/5 to both sides of this equation yields

3x = 10/5, or 3x = 2.

Solving for x: x = 2/3

6 0

3 years ago

How many gallons of a 70% antifreeze solution must be mixed with 60 gallons of 20% antifreeze to get a mixture that is 60% a

Flura [38]

We have 60 gallons of 20% antifreeze.

How much 70% antifreeze do we add to get 60% antifreeze?

We'll make "x" the gallons of 70% we must add.

.20 * 60 + .70 x = .60 * (60 + x)

12 + .70x = 36 + .60x

.10x = 24

x = 240 gallons of 70% antifreeze.

Source

1728.com/mixture.htm (see example B)

4 0

3 years ago

Please help asap!! Will give brainlist :)

bezimeni [28]

214.2 yd? I’m not 109% percent sure

7 0

3 years ago

Read 2 more answers

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

It is known that the distance in metres through which a body falls freely varies directly as the square of the time taken. If a

erma4kov [3.2K]

Answer:

125 meters

Step-by-step explanation:

Let distance = d and time is t

Using the variation;

d = k t^2

So let’s us get k

80 = k * 4*2

16k = 80

k = 80/16 = 5

So for 5 seconds, the distance would be;

d = 5 * 5^2

d = 125 meters

4 0

3 years ago