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2 years ago

I need help question number 7 homework

Mathematics

1 answer:

s2008m [1.1K]2 years ago

3 0

What is the question?

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Evaluate the integral. (sec2(t) i t(t2 1)8 j t7 ln(t) k) dt

polet [3.4K]

If you're just integrating a vector-valued function, you just integrate each component:

$\displaystyle\int(\sec^2t\,\hat\imath+t(t^2-1)^8\,\hat\jmath+t^7\ln t\,\hat k)\,\mathrm dt$

$=\displaystyle\left(\int\sec^2t\,\mathrm dt\right)\hat\imath+\left(\int t(t^2-1)^8\,\mathrm dt\right)\hat\jmath+\left(\int t^7\ln t\,\mathrm dt\right)\hat k$

The first integral is trivial since $(\tan t)'=\sec^2t$ .

The second can be done by substituting $u=t^2-1$ :

$u=t^2-1\implies\mathrm du=2t\,\mathrm dt\implies\displaystyle\frac12\int u^8\,\mathrm du=\frac1{18}(t^2-1)^9+C$

The third can be found by integrating by parts:

$u=\ln t\implies\mathrm du=\dfrac{\mathrm dt}t$

$\mathrm dv=t^7\,\mathrm dt\implies v=\dfrac18t^8$

$\displaystyle\int t^7\ln t\,\mathrm dt=\frac18t^8\ln t-\frac18\int t^7\,\mathrm dt=\frac18t^8\ln t-\frac1{64}t^8+C$

8 0

3 years ago

A restaurant sells a refillable coffee mug for $7.75. Each refill costs $3.25. Last month Keith

coldgirl [10]

82.75 minus the cost of the mug
Which equals 75 dollars and 75 divided by the cost of the refills which is 3.25 equals 24 refills

8 0

2 years ago

Protozoa are single-celled organisms. Paramecium aurelia is one type of protozoan. The number of paramecium aurelia doubles ever

Sphinxa [80]

Answer:

16 days

Step-by-step explanation:

Given that:

Number of paramecium Aurelia doubles every 1.25days

5 days ago ; number of paramecium Aurelia = 1

How many are there now?

Using the relation :

Multiplier^(total number of days / time it takes to multiply)

Multiplier = doubles = 2

Total number rof days =. 5

Time it takes to. Multiply = 1.25

The formula becomes :

Number(n) of ptotozoan in 5days is given by 2^(5/1.25)

n = 2^(5/1.25)

n = 2^4

n = 2 * 2 * 2 * 2 =. 16

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2 years ago

The large square below has a side length of 8 inches, and the smaller white square inside the large square has a side length of

Helga [31]

Does anybody know this answer to this question

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3 years ago

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SOMEONE PLEASE HELP I WILL GIVE YOU 100 POINT

Naddik [55]

The asymptote for f(x) is y = 0

Notice the asymptote for g(x) is y = -1, which shift f(x) down 1

apply this to f(x)'s rule: $3^{x}-1$

Notice the graph of f(x) is shifted right 2 units...this horizontal movement must be applied to the x in f(x)'s rule: $3^{x-2} -1$

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2 years ago

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I need help question number 7 homework​

I need help question number 7 homework