All categories

3 years ago

the 41st term of the arithmetic sequence is -539 and the 54th term is -708. Find the value of the 80th term

Mathematics

1 answer:

yulyashka [42]3 years ago

7 0

Answer:

$a _{n} = a _{1} + (n - 1)d \\ a _{41} = - 534 \\ a _{54} = - 708 \\ a _{41} = a _{1} + (41 - 1)d = - 534 \\ a _{1} + 40d = - 534 \: \: ...(1)\\ a _{54} = a _{1} + (54 - 1)d =- 708 \\ a _{1} + 53d = - 708 \: \: ...(2)$

Try to solve the similtanious equation to find the first term and the common difference, then use that information to figure out the 80th term... Update me if you need further help ...

You might be interested in

Which expression is equivalent to ^5√32x^5y^10z^15

sattari [20]

$\sqrt[5]{32x^5y^{10}z^{15}}=\sqrt[5]{32}\cdot\sqrt[5]{x^5}\cdot\sqrt[5]{(y^2)^5}\cdot\sqrt[5]{(z^3)^5}=2xy^2z^3$

Used:

$(a^n)^m=a^{n\cdot m}\\\\\sqrt[n]{a^n}=a$

Answer: b- 2xy^2z^3

6 0

3 years ago

Read 2 more answers

The function y=-16x^2+16x+32 represents the height in feet of a firework x seconds after it is launched

Nadya [2.5K]

Answer:

36feet

Step-by-step explanation:

Since we are not asked what to find, we can as well find the maximum height reached by the rocket

At max height, velocity is zero

V = dy/dx = 0

dy/dx = -32x + 16

0 = -32x+16

32x = 16

x = 16/32

x = 0.5s

Get the maximum height

y = -16(0.5)^2+16(0.5) + 32

y = -4+8+32

y = 36feet

Hence the max height reached by the rocket is 36feet

8 0

3 years ago

What's bigger 0.60 or 0.600

mihalych1998 [28]

Answer is 0.600
Welcomeee

4 0

2 years ago

Read 2 more answers

A photographer is 6 feet tall and cast a shadow that is 2 feet long. He is photographing a palm tree with a shadow that is 7 fee

Novay_Z [31]

Answer: The height of the tree is 21 feet.

Step-by-step explanation:

Here we can assume that the angle at which the sun impacts the photographer and the tree to be the same angle.

Then we can think in both cases as triangles rectangles, where the height is a cathetus, and the shadow is the other cathetus.

Then we will have a relationship like:

Tg(angle) = shadow/height

height = shadow/Tg(angle)

Now, because for both triangles we have the same angle, then Tg(angle) will be the same number for both cases, and we can just think of it as constant K

Tg(angle) = K

Then we have the equation:

Height = Shadow/K

We know that the photographer is 6ft tall, and his shadow is 2 ft long, we can replace those two things in the above equation and find the value of k:

6ft = 2ft/K

K = 2ft/6ft = (1/3)

Now we know that the shadow of the tree is 7ft long, then the height will be:

height = 7ft/(1/3) = 7ft*3 = 21ft

The tree is 21 ft tall.

6 0

3 years ago

Henrietta has a sample of a pure substance in a beaker. She heats the substance to a temperature of 100°C. What will determine i

erica [24]

The answer is c
have a good day

3 0

2 years ago

Read 2 more answers