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1 year ago

Condense the expression into a

Mathematics

1 answer:

liberstina [14]1 year ago

7 0

$2(\log 18-\log 3)+\dfrac 12 \log \dfrac{1}{16}=2 \log \dfrac{18}{3}+\log \sqrt{\dfrac{1}{16}}\\=2 \log 6+\log \dfrac{1}{4}=\log 6^2+\log \dfrac{1}{4}=\log 36+\log \dfrac{1}{4}\\=\log \dfrac{36}{4}=\log 9$

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Solve the equation X³+2X²-5X -6

Natali [406]

Answer: x = {-1, -3, 2}

Step-by-step explanation:

x³ + 2x² - 5x - 6 = 0

Use the rational root theorem to find the possible roots: ±1, ±2, ±3, ±6

Use Long division, Synthetic division, or plug them into the equation to see which root(s) work (result in a remainder of zero).

I will use Synthetic division. Let's try x = 1

1 | 1 2 -5 -6

| ↓ 1 3 -2

1 3 -2 -8 ← remainder ≠ 0 so x = 1 is NOT a root

Let's try x = -1

- 1 | 1 2 -5 -6

| ↓ -1 -1 6

1 1 -6 0 ← remainder = 0 so x = -1 is a root!

The coefficients of the reduced polynomial are: 1, 1, -6 --> x² + x - 6

Factor: x² + x - 6

(x + 3)(x - 2)

Set those factors equal to zero to solve for x:

x + 3 = 0 --> x = -3

x - 2 = 0 --> x = 2

Using Synthetic Division and Factoring the reduced polynomial, we found

x = -1, -3, and 2

6 0

2 years ago

48 POINTS ANSWER ASAP

SVETLANKA909090 [29]

Rewrite 5% as a decimal and then multiply by 60.

X = 0.05 x 60

8 0

3 years ago

Read 2 more answers

17. Each person on a Ferris wheel pays $6.50

patriot [66]

Answer:

$468

Step-by-step explanation:

6.5x72 passengers= $468

6 0

2 years ago

a man wanted to paint a cylinder gas tank. What amount of surface area will need to be covered if it had a radius of 14 inches a

Over [174]

Answer:

224

Step-by-step explanation:

in a cylinder the only sides that would actually count is the top and bottom
you would multiply the top and bottom.
14 x 16 = 224
if I'm wrong let me know

5 0

3 years ago

Find the cross product of <img src="https://tex.z-dn.net/?f=-%20%5Cfrac%7B3%7D%7B4%7Dv" id="TexFormula1" title="- \frac{3}{4}v"

dsp73

For any scalars $c_1,c_2$ , we have

$c_1\mathbf v\times c_2\mathbf w=c_1c_2\mathbf v\times\mathbf w$

So

$\left(-\dfrac34\mathbf v\right)\times\left(-\dfrac12\mathbf w\right)=\dfrac38\mathbf v\times\mathbf w$

We have

$\mathbf v\times\mathbf w=\begin{vmatrix}\mathbf i&\mathbf j&\mathbf k\\-2&12&-3\\-7&4&-6\end{vmatrix}$
$=\begin{vmatrix}12&-3\\4&-6\end{vmatrix}\mathbf i-\begin{vmatrix}-2&-3\\-7&-6\end{vmatrix}\mathbf j+\begin{vmatrix}-2&12\\-7&4\end{vmatrix}\mathbf k$
$=-60\,\mathbf i-(-9)\,\mathbf j+76\,\mathbf k$
$=\begin{bmatrix}-60\\9\\76\end{bmatrix}$

which makes

$\left(-\dfrac34\mathbf v\right)\times\left(-\dfrac12\mathbf w\right)=\dfrac38\begin{bmatrix}-60\\9\\76\end{bmatrix}=\begin{bmatrix}-\frac{45}2\\\\\frac{27}8\\\\\frac{57}2\end{bmatrix}$

4 0

3 years ago