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3 years ago

You purchase 13 pumpkins for $80.50. Small pumpkins cost $3.50. Large pumpkins cost $7. How many of each did you buy?

Mathematics

1 answer:

svet-max [94.6K]3 years ago

7 0

You bought 3 small pumpkins and 10 large pumpkins

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“encontrar la integral indefinida y verificar el resultado mediante derivación”

Oliga [24]

$I=\displaystyle\int\frac x{(1-x^2)^3}\,\mathrm dx$

Haz la sustitución:

$y=1-x^2\implies\mathrm dy=-2x\,\mathrm dx$

$\implies I=\displaystyle-\frac12\int\frac{\mathrm dy}{y^3}=\frac1{4y^2}+C=\frac1{4(1-x^2)^2}+C$

Para confirmar el resultado:

$\dfrac{\mathrm dI}{\mathrm dx}=\dfrac14\left(-\dfrac{2(-2x)}{(1-x^2)^3}\right)=\dfrac x{(1-x^2)^3}$

$I=\displaystyle\int\frac{x^2}{(1+x^3)^2}\,\mathrm dx$

Sustituye:

$y=1+x^3\implies\mathrm dy=3x^2\,\mathrm dx$

$\implies I=\displaystyle\frac13\int\frac{\mathrm dy}{y^2}=-\frac1{3y}+C=-\frac1{3(1+x^3)}+C$

(Te dejaré confirmar por ti mismo.)

$I=\displaystyle\int\frac x{\sqrt{1-x^2}}\,\mathrm dx$

Sustituye:

$y=1-x^2\implies\mathrm dy=-2x\,\mathrm dx$

$\implies I=\displaystyle-\frac12\int\frac{\mathrm dy}{\sqrt y}=-\frac12(2\sqrt y)+C=-\sqrt{1-x^2}+C$

$I=\displaystyle\int\left(1+\frac1t\right)^3\frac{\mathrm dt}{t^2}$

Sustituye:

$u=1+\dfrac1t\implies\mathrm du=-\dfrac{\mathrm dt}{t^2}$

$\implies I=-\displaystyle\int u^3\,\mathrm du=-\frac{u^4}4+C=-\frac{\left(1+\frac1t\right)^4}4+C$

Podemos hacer que esto se vea un poco mejor:

$\left(1+\dfrac1t\right)^4=\left(\dfrac{t+1}t\right)^4=\dfrac{(t+1)^4}{t^4}$

$\implies I=-\dfrac{(t+1)^4}{4t^4}+C$

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3 years ago

SOLVE x + 3y = -1 y = x - 7 Write the solution below.

ki77a [65]

Answer:

x= 5 ........................ .......

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2 years ago

Linda commutes a total of 54 miles to and from work every day. She needs a new car, and good gas mileage is important to her. Sh

joja [24]

Answer:

she would save 1.1 extra gallons

Step-by-step explanation:

54 miles to work

30 miles a gallon so 1.8 gallons to get to work

27 miles a gallon so 2 gallons to get to work

30 miles car saves 5.4 miles more each day she drives to work

5.4 X 5 = 27 extra miles so 1.1 gallons she would be saving each work week

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3 years ago

What is 7/10 in simplest form

andrey2020 [161]

You can not simplify 7/10 because 7 os only on 1 and 7s times table.

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3 years ago

Read 2 more answers

PLS HELP WITH THE QUESTION IN THE PICTURE!!!

Ksivusya [100]

Answer:

Step-by-step explanation:

Interesting question. The wording is a bit awkward. I think you have to assume the base is a square and each succeeding base is also a square.

So the first thing to do is to add the bases together.

30*30 + 23*23 + 16*16 + 9*9

Don't add these -- not yet.

Now take the height into consideration

6 *(30*30 + 23*23 + 16*16 + 9*9)

The point is that you only have to multiply by 6 once.

6*(900 + 529 + 256 + 81)

6*(1766)

10596 cubic inches

The answer is D

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3 years ago