-9, -6, -1, 6, 15 …
What is the 8th term of the sequence?

Apply l'Hopital's rule:

[tex]\displaystyle\lim_{x\to\pi}\frac{\displaystyle\int_\pi^x (1+\tan(t))\,\mathrm dt}{\pi\sin(x)}=\lim_{x\to\pi}\frac{1+\tan(x)}{\pi\cos(x)}=\frac{1+\tan(\pi)}{\pi\cos(\pi)}=\boxed{-\frac1\pi}[/tex]

where

[tex]\displaystyle\frac{\mathrm d}{\mathrm dx}\left[\int_\pi^x(1+\tan(t))\,\mathrm dt\right]=1+\tan(x)[/tex]

follows from the fundamental theorem of calculus.

Answer:

Amelia needs to invest $989.57.

Step-by-step explanation:

The compound interest formula is given by:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

Amelia is going to invest in an account paying an interest rate of 2.3% compounded quarterly.

This means that [tex]r = 0.023, n = 4[/tex].

How much would Amelia need to invest, to the nearest hundred dollars, for the value of the account to reach $1,530 in 19 years?

We have to find P for which [tex]A(t) = 1530[/tex] when [tex]t = 19[/tex]. So

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]1530 = P(1 + \frac{0.023}{4})^{4*19}[/tex]

[tex]P = \frac{1530}{(1 + \frac{0.023}{4})^{4*19}}[/tex]

[tex]P = 989.57[/tex]

Amelia needs to invest $989.57.

Answer:

48 sec.

Step-by-step explanation:

8 devided by 10.

Answer:

48 seconds

Step-by-step explanation:

8 min / 10 laps = 0.8 mins

to convert minutes into seconds, multiply by 60

0.8*60 = 48 seconds

Answer:

C not sure though

Step-by-step explanation:

Answer:

95

Step-by-step explanation:

Ok so

so firs what we do is

1150/12 and ignore remainder

95 and remainder is 10

therefore we have 95 trucks full and 10 cars in the last truck

Answer:

use the app called msthway

Answer:

Everyone got 52/25 = 2.08 slices of pizza.

Step-by-step explanation:

1 large sized pizza = 8 slices

6.5 large sized pizzas = 52 slices

52/25 = 2.08

Hope this helps :D

Answer:

See below

Step-by-step explanation:

Q11

Triangle is 45° and therefore isosceles

Q12

Q13

Q14

Q15

Q16

Answer: i think i would be half of it

Step-by-step explanation:

Answer:

[tex]\theta = 120, 240[/tex], in degrees

Step-by-step explanation:

The secant of an angle is given by:

[tex]\sec{\theta} = \frac{1}{\cos{\theta}}[/tex]

In this question:

[tex]\sec{\theta} = -2[/tex]

So

[tex]\frac{1}{\cos{\theta}} = -2[/tex]

[tex]-2\cos{\theta} = 1[/tex]

[tex]\cos{\theta} = -\frac{1}{2}[/tex]

In the first quadrant, the angle that has cosine of 1/2 is 60º.

The cosine is negative in the second and in the third quadrant.

The equivalent angle to 60º in the second quadrant is of 180º - 60º = 120º.

The equivalent angle to 60º in the third quadrant is of 180º + 60º = 240º

So the values of [tex]\theta[/tex] in the interval are:

[tex]\theta = 120, 240[/tex], in degrees

Answer:

A

Step-by-step explanation:

a function may not have the same values of X.

Answer:

Number 1

Step-by-step explanation: Not sure just assuming I think I am right not gonna lie

Answer:

[tex]m\angle R=35^{\circ}\\m\angle T=45^{\circ}[/tex]

Step-by-step explanation:

Since both triangles in this figure are similar, their corresponding angles must be equal.

Since [tex]\angle R[/tex] corresponds with [tex]\angle U[/tex]:

[tex]m\angle U=m\angle R=\fbox{$35^{\circ}$}[/tex].

Similarly, [tex]\angle T[/tex] corresponds with [tex]\angle Q[/tex]:

[tex]m\angle Q=m\angle T=\fbox{$45^{\circ}$}[/tex].

Answers

x= -3/2

x= 3i

x= -3i

Step-by-step explanation:

f (x) = 2x3 + 3x2 + 18x + 27

Set 2x^3 + 3x^2 + 18x + 27 equal to 0.

2x^3 + 3x^2 + 18x + 27 = 0

Solve for x.

Factor the left side of the equation.

Factor out the greatest common factor from each group.

x^2 (2x + 3) + 9 (2x + 3) = 0

Factor the polynomial by factoring out the greatest common factor, 2x + 3. (2x + 3) (x^2 + 9) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

2x + 3 = 0

x^2 + 9 = 0

Set 2x + 3 equal to 0 and solve for x.

Set 2x + 3 equal to 0. 2x + 3 = 0

Solve 2x + 3 = 0 for x. Tap for more steps...  

3 x = − 2

Set x2 + 9 equal to 0 and solve for x.

Set x2 + 9 equal to 0. x2 + 9 = 0

Solve x2 + 9 = 0 for x.

x = 3i, −3i

The final solution is all the values that make (2x + 3) (x2 + 9) = 0 true.

x = − 3/2 , 3i, −3i

Answer:

450 cm

Step-by-step explanation:

25 on both sides 2x25

4 squares = 25x4

4 sides for 4 squares = 100x4

400+50

Answer: C

Step-by-step explanation:

Answer:

μy = $6.56 ; σy = 2.77

Step-by-step explanation:

Given the data :

Mean μx= $8.56

Standard Deviation σx ≈ 2.77

Profit, Y on pizza with current promo :

Price off on pizza = $2

Y = x - 2

μx = E(x) = $8.56

μy = μ(x - 2)

μy = μx - $2

μy = $8.56 - $2

μy = $6.56

For the standard deviation of y

σx ≈ 2.77

σy = σ(x - 2)

σy = σx - 2

Constants are treated as 0 for standard deviation

σy = 2.77

Answer:

B.

Step-by-step explanation:

Answer:

wait huh?

Step-by-step explanation:

cdzfv

c

c

c

c

c

Answer:

can you elaborate a little more

Answer:

your answer will be 22

Step-by-step explanation:

if you add 20 by 2 it will give you 22 use a calculator if not sure but 22 is your answer

Answer:For the first one it would be x=35

And the 2nd one would just be x=-1

Step-by-step explanation:

Answer:

j + 2

Step-by-step explanation:

1/3(3j) + 1/3(6)

1/3(3j) = j

1/3(6) = 2

Answer: j + 2

Answer:

easy do you want to get (15,20,25) from (3,4,5)and from(5,12,13)

Step-by-step explanation:

Arnav can use the fact that scaling doesn't affect the angles of a triangle, and that (3,4,5) is already stated being a Pythagorean triple.

Similar figure are zoomed in or zoomed out (or just no zoom) version of each other. They are scaled version of each other, and by scale, we mean that each of their dimension(like height, width etc linear quantities) are constant multiple of their similar figure.

So, if a side of a figure is of length L units, and that of its similar figure is of M units, then:

where 'k' will be called as scale factor.

The linear things grow linearly like length, height etc.

We're given that:

(3,4,5) is a pythagorean triple.

Let ABC be a right angled triangle possessing those sides (as the side lengths of a right angled triangle form pythagorean triple).

Scale each side of ABC by scale factor of 5, then we get:

(15, 20, 25) as a triple.

When scaling a figure, angles in it doesn't change because of angle being a relative quantity, not depending on the length of sides, but on the degree of rotation between two sides, which is unaffected because of scaling.

That means, that right angled triangle ABC, when scaled is still right angled triangle (because of its one of the angle 90 degrees still being 90 degrees in the new scaled triangle), but its sides are (15,20,25).

Now, since the triple (15,20,25) is side lengths of a right angled triangle, therefore, it is a pythagorean triple.

Thus, arnav can use the fact that scaling doesn't affect the angles of a triangle, and that (3,4,5) is already stated being a Pythagorean triple.

Learn more about scale factor here:

https://brainly.com/question/8765466

Answer:

c=5

Step-by-step explanation:

in right lower triangle

c²=a²+b²

c=√(4²+3²)=√25=5

sorry I don't understand it.which length of diagonal is needed to find.comment me.

Answer:

i think it is 12

Step-by-step explanation: