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Can 0.2 0.6 3 and 9 make 24?

saveliy_v [14]

Answer:

Yes

Step-by-step explanation:

9 x 3 - (0.6/0.2) Simplify the parentheses

9 x 3 - 3 Multiply 9 by 3

27 - 3 Subtract

24

5 0

3 years ago

<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cint%20t%5E2%2B1%20%5C%20dt" id="TexFormula1" title="\frac{d}{dx} \

Kisachek [45]

Answer:

$\displaystyle{\frac{d}{dx} \int \limits_{2x}^{x^2} t^2+1 \ \text{dt} \ = \ 2x^5-8x^2+2x-2$

Step-by-step explanation:

$\displaystyle{\frac{d}{dx} \int \limits_{2x}^{x^2} t^2+1 \ \text{dt} = \ ?$

We can use Part I of the Fundamental Theorem of Calculus:

$\displaystyle\frac{d}{dx} \int\limits^x_a \text{f(t) dt = f(x)}$

Since we have two functions as the limits of integration, we can use one of the properties of integrals; the additivity rule.

The Additivity Rule for Integrals states that:

$\displaystyle\int\limits^b_a \text{f(t) dt} + \int\limits^c_b \text{f(t) dt} = \int\limits^c_a \text{f(t) dt}$

We can use this backward and break the integral into two parts. We can use any number for "b", but I will use 0 since it tends to make calculations simpler.

$\displaystyle \frac{d}{dx} \int\limits^0_{2x} t^2+1 \text{ dt} \ + \ \frac{d}{dx} \int\limits^{x^2}_0 t^2+1 \text{ dt}$

We want the variable to be the top limit of integration, so we can use the Order of Integration Rule to rewrite this.

The Order of Integration Rule states that:

$\displaystyle\int\limits^b_a \text{f(t) dt}\ = -\int\limits^a_b \text{f(t) dt}$

We can use this rule to our advantage by flipping the limits of integration on the first integral and adding a negative sign.

$\displaystyle \frac{d}{dx} -\int\limits^{2x}_{0} t^2+1 \text{ dt} \ + \ \frac{d}{dx} \int\limits^{x^2}_0 t^2+1 \text{ dt}$

Now we can take the derivative of the integrals by using the Fundamental Theorem of Calculus.

When taking the derivative of an integral, we can follow this notation:

$\displaystyle \frac{d}{dx} \int\limits^u_a \text{f(t) dt} = \text{f(u)} \cdot \frac{d}{dx} [u]$
where u represents any function other than a variable

For the first term, replace $\text{t}$ with $2x$ , and apply the chain rule to the function. Do the same for the second term; replace

$\displaystyle-[(2x)^2+1] \cdot (2) \ + \ [(x^2)^2 + 1] \cdot (2x)$

Simplify the expression by distributing $2$ and $2x$ inside their respective parentheses.

$[-(8x^2 +2)] + (2x^5 + 2x)$
$-8x^2 -2 + 2x^5 + 2x$

Rearrange the terms to be in order from the highest degree to the lowest degree.

$\displaystyle2x^5-8x^2+2x-2$

This is the derivative of the given integral, and thus the solution to the problem.

6 0

3 years ago

The ratio of girls to boys who participated in the quiz bowl was 7:5. There were 42 girls in the competition. How many boys part

Zinaida [17]

The way i do it, is sort of like this :

Is 7 a factor of 42?
Is 5 a factor of 42?

7 is a factor of 42.
It must be in multiples of 7!

Therefore, we have 5 on the other side, which makes it 5 x 7 = 35

7 0

3 years ago

Which unit of measurement would be most appropriate to measure the distance between Atlanta, GA and Nashville, TN? A) centimeter

Helga [31]

The answer to this question should be: C. Kilometers

To answer this question, I will rearrange the option from the smallest unit into the highest unit.

Centimeter
Inch
Yards
Kilometer

Centimeter and inch are similar, they are mostly used for measure height of people or object. Yards is used for measuring a field area. Kilometer would be the biggest. It used for roads or expressing distance between city/country. So the answer should be kilometers

5 0

4 years ago

Read 2 more answers

Mr. and Mrs.jones wanted to plan a fun day with there 2 children. An adult ticket to the local amusement park is $20. A child's

Burka [1]

The total amount for the family of for to the park is 28$

4 0

2 years ago