What is the smaller of the numbers 1 and -10/3

I need help with this one.

Mandarinka [93]

Answer:

$T_{n}$ = $\frac{1}{5}$ $T_{n-1}$ with T₁ = 5000

Step-by-step explanation:

There is a common ratio r between consecutive terms in the sequence, that is

r = $\frac{1000}{5000}$ = $\frac{200}{1000}$ = $\frac{40}{200}$ = $\frac{1}{5}$

This indicates the sequence is geometric with recursive rule

$T_{n}$ = r $T_{n-1}$

Here tr = $\frac{1}{5}$ , thus

$T_{n}$ = $\frac{1}{5}$ $T_{n-1}$ , T₁ = 5000

3 0

3 years ago

Katie wants to buy some popcorn for her family at the theater. Each small tub of popcorn costs $3 and each large tub of popcorn

Molodets [167]

For this case we propose a system of equations:

x: Represents the amount of small popcorn tubs

y: Represents the amount of large popcorn tubs

According to the data we have to:

$3x + 4y = 24$ (Spending all the money in your wallet)

$x + y = 7$ (Buying 7 popcorn tubs)

From the second equation we have:

$x = 7-y$

Substituting in the first equation:

$3 (7-y) + 4y = 24\\21-3y + 4y = 24\\21 + y = 24\\y = 24-21\\y = 3$

Thus, Katie can buy 3 large tubs of popcorn.

So:

$x = 7-3\\x = 4$

In addition, you can buy 4 small tubs of popcorn.

Answer:

3 large popcorn tubs.

4 small popcorn tubs.

8 0

2 years ago

Select the curve generated by the parametric equations. Indicate with an arrow the direction in which the curve is traced as t i

bixtya [17]

Answer:

length of the curve = 8

Step-by-step explanation:

Given parametric equations are x = t + sin(t) and y = cos(t) and given interval is

−π ≤ t ≤ π

Given data the arrow the direction in which the curve is traces means

the length of the curve of the given parametric equations.

The formula of length of the curve is

$\int\limits^a_b {\sqrt{\frac{(dx}{dt}) ^{2}+(\frac{dy}{dt}) ^2 } } \, dx$

Given limits values are −π ≤ t ≤ π

x = t + sin(t) ...….. (1)

y = cos(t).......(2)

differentiating equation (1) with respective to 'x'

$\frac{dx}{dt} = 1+cost$

differentiating equation (2) with respective to 'y'

$\frac{dy}{dt} = -sint$

The length of curve is

$\int\limits^\pi_\pi {\sqrt{(1+cost)^{2}+(-sint)^2 } } \, dt$

$\int\limits^\pi_\pi \, {\sqrt{(1+cost)^{2}+2cost+(sint)^2 } } \, dt$

on simplification , we get

here using sin^2(t) +cos^2(t) =1 and after simplification , we get

$\int\limits^\pi_\pi \, {\sqrt{(2+2cost } } \, dt$

$\sqrt{2} \int\limits^\pi_\pi \, {\sqrt{(1+1cost } } \, dt$

again using formula, 1+cost = 2cos^2(t/2)

$\sqrt{2} \int\limits^\pi _\pi {\sqrt{2cos^2\frac{t}{2} } } \, dt$

Taking common $\sqrt{2}$ we get ,

$\sqrt{2}\sqrt{2} \int\limits^\pi _\pi ( {\sqrt{cos^2\frac{t}{2} } } \, dt$

$2(\int\limits^\pi _\pi {cos\frac{t}{2} } \, dt$

$2(\frac{sin(\frac{t}{2} }{\frac{t}{2} } )^{\pi } _{-\pi }$

length of curve = $4(sin(\frac{\pi }{2} )- sin(\frac{-\pi }{2} ))$

length of the curve is = 4(1+1) = 8

<u>conclusion</u>:-

The arrow of the direction or the length of curve = 8

7 0

3 years ago

An arithmetic sequence has a common difference of 5 and the 3rd term is 15. What is the 5th term?

trapecia [35]

Answer:

an=8n−14

Step-by-step explanation:

for an AP

where

a

1

=

the first term

d

=

the common difference

then we have

a

1

,

(

a

1

+

d

)

,

(

a

1

+

2

d

)

,

...

,

a

1

+

(

n

−

1

)

d

)

,

.

we are given the third term

10

=

a

1

+

2

d

−

(

1

)

and the fifth term

26

=

a

1

+

4

d

−

(

2

)

subtract

(

2

)

−

(

1

)

16

=

2

d

⇒

d

=

8

sub into

(

1

)

10

=

a

1

+

2

×

8

⇒

a

1

=

−

6

so the nth term

a

n

=

a

+

(

n

−

1

)

will be

a

n

=

−

6

+

8

(

n

−

1

)

a

n

=

8

n

−

14

3 0

2 years ago

On the first day of the year you have $700 in your bank account you spend $35 per week your friend starts the year with 450 in h

Zielflug [23.3K]

700 - 35W = 450 + 15W
+35W +35W
700 = 450 + 50W
-450 -450
350 = 50W

7 = W

It will take 7 weeks for their bank accounts to be the same.

6 0

2 years ago

Read 2 more answers