All categories

3 years ago

Please help me simplify these expressions

Mathematics

1 answer:

Fantom [35]3 years ago

7 0

Answer:

1. -18x¹¹

2. 3n⁷

Step-by-step explanation:

For these problems, there are two things you need to worry about: negative signs and exponents.

1. Let's look at the signs first. There is only one value with a negative sign, meaning that the negative sign will stay.

When multiplying with exponents, you have to add up the exponents. Don't forget the numerical coefficients.

-3x² · 3x · 2x³ · x⁵ = -18x¹¹

2. There are two negative signs in this probem, meaning that they will cancel out. Multiply the rest like we did in the first problem.

3n² · -n² · -n³ = 3n⁷

You might be interested in

PLEASE HELP I NEED THIS TO BE DONE

yanalaym [24]

To find the mean you add all the #'s and divide by how many there are. 4+5+6+7 +8= 30 /5 is 6. Tara is right.

5 0

3 years ago

Chec<br> Match each data relationship with a type of correlation.

AleksandrR [38]

I've attached an image showing the data relationship.

Answer:

1) y does not change based on changes in x: no-correlation

2) y tends to increase as x increases: positive correlation

3) y tends to decrease as x increases: negative correlation

Step-by-step explanation:

1) y does not change based on changes in x: This means that there is no correlation between y and x since change in x doesn't affect y.

2) y tends to increase as x increases: This implies positive correlation because the output increases with increase in input.

3) y tends to decrease as x increases: This implies negative correlation because the output decreases with increase in input values.

5 0

3 years ago

Read 2 more answers

Solve the initial value problem

tigry1 [53]

$9(t+1)\dfrac{\mathrm dy}{\mathrm dt}-7y=14t\implies\dfrac{\mathrm dy}{\mathrm dt}-\dfrac7{9(t+1)}y=\dfrac{14t}{9(t+1)}$

Look for an integrating factor $\mu(t)$ :

$\ln\mu=\displaystyle-\frac79\int\frac{\mathrm dt}{t+1}=-\frac79\ln(t+1)\implies\mu=(t+1)^{-7/9}$

Multiply both sides by $\mu$ :

$(t+1)^{-7/9}\dfrac{\mathrm dy}{\mathrm dt}-\dfrac79(t+1)^{-16/9}y=\dfrac{14}9t(t+1)^{-16/9}$

Condense the left side as the derivative of a product:

$\dfrac{\mathrm d}{\mathrm dt}\left[(t+1)^{-7/9}y\right]=\dfrac{14}9t(t+1)^{-16/9}$

Integrate both sides:

$(t+1)^{-7/9}y=\displaystyle\frac{14}9\int t(t+1)^{-16/9}\,\mathrm dt$

For the integral on the right, substitute

$u=t+1\implies t=u-1\implies\mathrm dt=\mathrm du$

$\displaystyle\int t(t+1)^{-16/9}\,\mathrm dt=\int(u-1)u^{-16/9}\,\mathrm du$

$\displaystyle=\int\left(u^{-7/9}-u^{-16/9}\right)\,\mathrm du=\frac92u^{2/9}+\frac97u^{-7/9}+C$

$\implies(t+1)^{-7/9}y=\dfrac{14}9\left(\dfrac92(t+1)^{2/9}+\dfrac97(t+1)^{-7/9}+C\right)$

$\implies(t+1)^{-7/9}y=7(t+1)^{2/9}+2(t+1)^{-7/9}+C$

$\implies y=7(t+1)+2+C(t+1)^{7/9}=7t+9+C(t+1)^{7/9}$

Given that $y(0)=12$ , we get

$12=9+C\implies C=3$

$\implies\boxed{y(t)=7t+9+3(t+1)^{7/9}}$

6 0

3 years ago

Solving radical equation

Darya [45]

$\bf \sqrt{k-9}-\sqrt{k}=-1\implies \sqrt{k-9}=\sqrt{k}-1\impliedby \textit{squaring both sides}
\\\\\\
(\sqrt{k-9})^2=(\sqrt{k}-1)^2\implies k-9=(\sqrt{k}-1)(\sqrt{k}-1)\impliedby \textit{FOIL}
\\\\\\
k-9=k-2\sqrt{k}+1\implies -10=-2\sqrt{k}\implies \cfrac{-10}{-2}=\sqrt{k}
\\\\\\
\sqrt{\cfrac{-10}{-2}}=k$