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3 years ago

Precalc: Vector word problem:

Mathematics

1 answer:

charle [14.2K]3 years ago

8 0

Bearing in mind that $\bf \begin{cases}
x=rcos(\theta )\\\\
y=rsin(\theta )
\end{cases}$

I can make this much from that, check the picture below.

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Consider 8x2 - 48x = -104.

ki77a [65]

Answer:

$3+ 2\mathbf{i}$

$3- 2\mathbf{i}$

Step-by-step explanation:

Quadratic Equation Solving

We have the equation:

$8x^2-48x=-104$

Divide by 8:

$x^2-6x=-13$

Now complete the squares so the left side is a perfect square of a binomial:

$x^2-6x+9=-13+9=-4$

Factoring the perfect square:

$(x-3)^2=-4$

Taking the square root:

$x-3=\sqrt{-4}$

The square root of a negative number is an imaginary number:

$x-3=\pm 2\mathbf{i}$

Solving for x:

$x=3\pm 2\mathbf{i}$

The solutions are:

$3+ 2\mathbf{i}$

$3- 2\mathbf{i}$

7 0

2 years ago

Solve the equation without the use of a calculator. please Help!!! Thank you!!! 12x^3-30x=5-2x^2

nata0808 [166]

So, since we have a cubic equation with 4 terms, the first thing we should try is factoring by grouping, so:

$12x^3+2x^2-30x+5 =0 \implies \\ 2x^2(6x+1)-5(6x+1)=0 \implies \\ (2x^2-5)(6x+1) = 0$

Now that we've factored our equation, we can use ZPP and break it up:

$2x^2-5 = 0 \implies \\ 2x^2=5 \implies\\ x^2=\frac{5}{2} \implies\\ x=\pm\frac{\sqrt{5}}{\sqrt{2}}=\pm\frac{\sqrt{10}}{2} \\ \\ 6x+1 =0 \implies \\ 6x=-1 \implies\\ x=\frac{-1}{6}$

So, our solutions are:

$x\in \{\frac{\sqrt{10}}{2},-\frac{\sqrt{10}}{2},-\frac{1}{6}\}$

4 0

3 years ago

For the straight line defined by the points (2,55) and (4, 87), determine the slope (m) and y-intercept?

mamaluj [8]

Answer:

Slope(m) = 16

Y intercept (c) = 23

Step-by-step explanation:

Given:

Points : (x1, y1) = (2, 55)

(x2, y2) = (4, 87)

Using two point form to calculate slope:

$m = \frac{y2-y1}{x2-x1}$

$m = \frac{87-55}{4-2}$

m = 16

To find y intercept:

Take any one point ans slope :

Using slope point formula:

y = mx + c

87 = 16(4) + c

Solving for c:

c = 23

8 0

3 years ago

Amina has 6 ¾ L of juice that she wants to pour into ¾ L containers. What is the number of containers that she can fill?

dolphi86 [110]

Answer:

She can fill 9 containers

Step-by-step explanation:

you do 6 3/4 dived by 3/4 and you get 9

4 0

2 years ago

BRAINLIEST ASAP!!!!!!! why is it useful to factor out the gcf first when factoring

Lelu [443]

By pulling out the common factors for each pair of terms, we can rewrite the original polynomial like this:
3x(2x + 1) + 10(2x + 1)
These two terms now have a common factor of (2x + 1). Seems like we should be able to do something with that information, don't you think? In fact, we can pull out this common factor and rewrite the polynomial again:

4 0

2 years ago