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2 years ago

Plz answer this I really need help

Mathematics

1 answer:

hjlf2 years ago

5 0

The firstone I guess I'm not that sure tbh

Hope it’s right
Best luck with your studying

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Find the function r that satisfies the given condition. r'(t) = (e^t, sin t, sec^2 t): r(0) = (2, 2, 2) r(t) = ()

lesantik [10]

Answer:

r(t) = (e^t +1, -cos(t) + 3, tan(t) + 2)

Step-by-step explanation:

A primitive of e^t is e^t+c, since r(0) has 2 in its first cooridnate, then

e^0+c = 2

1+c = 2

c = 1

Thus, the first coordinate of r(t) is e^t + 1.

A primitive of sin(t) is -cos(t) + c (remember that the derivate of cos(t) is -sin(t)). SInce r(0) in its second coordinate is 2, then

-cos(0)+c = 2

-1+c = 2

c = 3

Therefore, in the second coordinate r(t) is equal to -cos(t)+3.

Now, lets see the last coordinate.

A primitive of sec²(t) is tan(t)+c (you can check this by derivating tan(t) = sin(t)/cos(t) using the divition rule and the property that cos²(t)+sin²(t) = 1 for all t). Since in its third coordinate r(0) is also 2, then we have that

2 = tan(0)+c = sin(0)/cos(0) + c = 0/1 + c = 0

Thus, c = 2

As a consecuence, the third coordinate of r(t) is tan(t) + 2.

As a result, r(t) = (e^t +1, -cos(t) + 3, tan(t) + 2).

6 0

3 years ago

Find the seventh term of the sequence which has a first term of 1/2 and has a common ratio of three

prohojiy [21]

The seventh term of the sequence is 364.5

<h3>Geometric progression </h3>

From the question, we are to determine the seventh term of the sequence

Using the formula,

$a_{n} = ar^{n-1}$

Where $a_{n}$ is the nth term

a is the first term

and r is the common ratio

From the given information,

a = 1/2

r = 3

Thus,

$a_{7} = (\frac{1}{2}) 3^{7-1}$

$a_{7} = (\frac{1}{2}) 3^{6}$

$a_{7} = \frac{1}{2} \times 729$

$a_{7} = 364\frac{1}{2} \ OR \ 364.5$

Hence, the seventh term of the sequence is 364.5

Learn more on Geometric progression here: brainly.com/question/24643676

#SPJ1

3 0

2 years ago

If $x$, $y$, and $z$ are positive integers such that $6xyz+30xy+21xz+2yz+105x+10y+7z=812$, find $x+y+z$.

harina [27]

Answer:

Step-by-step explanation:

When we simplify we get $z(6xy+21x+2y+7)+30xy+105x+10y=812.$

Then we continue to factor to get: $(z+5)(6xy+21x+2y+7)&=847.$

We then see that we can factor $(6xy+21x+2y+7)$ into $(z+5)(3x+1)(2y+7)&=847.$

we then do the prime factorization of 847, which i think is, $7*11*11$ . we have to find the numbers that multiply to 847 and then plug them into z+5, 3x=1,2y+7.

It has to be a positive, non-negative integer, right?

We also see that 3x+1=11 so we see that x=10/3 (which wont work).

So 3x+1=7, so x=2.

So 11 has to be in another term. It has to be in 2y+7=11 so y=2

for the last term we get z+5=11 so z=6

2+2+6=10

Hope this helps and if you want please consider giving me brainliest. :)

8 0

3 years ago

10 pennies are flipped and arranged in a row. How many arrangements of the heads and tails are possible?

DaniilM [7]

Answer:

1000 possible arrangements

Step-by-step explanation:

6 0

3 years ago

A "thrift" is another name for a commercial bank. True or False

elixir [45]

A thrift is a kind of bank that arranges mortgages (mostly for home ownership) and sets up accounts to receive deposits.

The statement is actually false. The difference is in who they can borrow from and whether or not they are set up for profit. Thrifts are usually non profit.

4 0

2 years ago