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Ghella [55]
3 years ago
10

The budget for Ohio is 69.1 billion with a population of 11.69 million residents. Round all scientific answers with two decimals

with no spaces. Example: 1.23x10^4 or 1.23E4 Write the budget in scientific notation. 1 point Debt: Write the population in scientific notation. 1 point Population: Calculate the Budget Per Capita and write your answer in standard notation. Round to a whole number. 2 points Use the budget per capita in a sentence explaining what this value means. 4 points
Mathematics
1 answer:
e-lub [12.9K]3 years ago
6 0

Answer:

Step-by-step explanation:

Hello,

This question requires us to convert numbers from standard form to scientific form. This can easily be done using a calculator or just writing the number down then put a decimal point after the first digit and count the rest which would be raised to the power of that number.

Budget = 69.1 billion

Converting this to scientific form = 6.91×10¹⁰

Population = 11.67 million

Converting this to scientific form = 1.167×10⁷

Budget per capita refers to budget allocated to each individual in the population.

Budget per capita is used to compare economic indices or indicators of various countries with different population sizes.

Budget per capita = budget / total population

Budget per capita = 6.91×10¹⁰ / 1.169×⁷

Budget per capita = 5911.03

What this implies is that for each individual living in the state of Ohio, the amount budgeted for that particular period (mostly in a given year) is 5911.03

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Find dy/dx by implicit differentiation for ysin(y) = xcos(x)
tatyana61 [14]

Answer:

\frac{dy}{dx}=\frac{\cos(x)-x\sin(x)}{\sin(y)+y\cos(y)}

Step-by-step explanation:

So we have:

y\sin(y)=x\cos(x)

And we want to find dy/dx.

So, let's take the derivative of both sides with respect to x:

\frac{d}{dx}[y\sin(y)]=\frac{d}{dx}[x\cos(x)]

Let's do each side individually.

Left Side:

We have:

\frac{d}{dx}[y\sin(y)]

We can use the product rule:

(uv)'=u'v+uv'

So, our derivative is:

=\frac{d}{dx}[y]\sin(y)+y\frac{d}{dx}[\sin(y)]

We must implicitly differentiate for y. This gives us:

=\frac{dy}{dx}\sin(y)+y\frac{d}{dx}[\sin(y)]

For the sin(y), we need to use the chain rule:

u(v(x))'=u'(v(x))\cdot v'(x)

Our u(x) is sin(x) and our v(x) is y. So, u'(x) is cos(x) and v'(x) is dy/dx.

So, our derivative is:

=\frac{dy}{dx}\sin(y)+y(\cos(y)\cdot\frac{dy}{dx}})

Simplify:

=\frac{dy}{dx}\sin(y)+y\cos(y)\cdot\frac{dy}{dx}}

And we are done for the right.

Right Side:

We have:

\frac{d}{dx}[x\cos(x)]

This will be significantly easier since it's just x like normal.

Again, let's use the product rule:

=\frac{d}{dx}[x]\cos(x)+x\frac{d}{dx}[\cos(x)]

Differentiate:

=\cos(x)-x\sin(x)

So, our entire equation is:

=\frac{dy}{dx}\sin(y)+y\cos(y)\cdot\frac{dy}{dx}}=\cos(x)-x\sin(x)

To find our derivative, we need to solve for dy/dx. So, let's factor out a dy/dx from the left. This yields:

\frac{dy}{dx}(\sin(y)+y\cos(y))=\cos(x)-x\sin(x)

Finally, divide everything by the expression inside the parentheses to obtain our derivative:

\frac{dy}{dx}=\frac{\cos(x)-x\sin(x)}{\sin(y)+y\cos(y)}

And we're done!

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2 years ago
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3 years ago
Sidney skated for 1 1/10 hours last month and 8 7/10 hours this month. How many
olganol [36]

Answer:

the number of hours does sidney skate in all is 9.8 hours

Step-by-step explanation:

The computation of the number of hours does sidney skate in all is as follows:

= Last month + this month

= 1 \frac{1}{10} + 8 \frac{7}{10}\\\\= \frac{11}{10} + \frac{87}{10}\\\\= \frac{98}{10}

= 9.8 hours

Hence, the number of hours does sidney skate in all is 9.8 hours

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Answer:

angle B=120º

Step-by-step explanation:

15+45=60

We know that all triangles have angle measures that equal 180

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angle B=120º

7 0
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