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Sav [38]
2 years ago
7

Consider the arithmetic sequence where the 15th term is 0 and the 40th term is -50.

Mathematics
1 answer:
ira [324]2 years ago
3 0

Answer:

a_n=28-2(n-1)

Step-by-step explanation:

We want to find the formula for this problem in the explicit form of:

a_n=a_1+d(n-1), where a_n is the nth term, a_1 is the first term, and d is the common difference

Here, we can say that the "first term" is the 15th term, which is 0, so instead of a_1, we have a_15. The nth term is the 40th term, which is -50, so instead of a_n, we have a_40:

a_n=a_1+d(n-1)

a_{40}=a_{15}+d(40-15)

-50=0+d(25)

d = -2

Now, we need to find the first term:

a_{15}=a_1+d(15-1)

0=a_1+(-2)(14)

a_1 = 28

Finally, our equation is: a_n=28-2(n-1)

Hope this helps!

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Pls help due today plsss
svetoff [14.1K]

Answer: the 2 graph it’s gonna be the answer

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8 0
3 years ago
How do you add vectors? Add the vector <3,4> to the vector that goes 7 units at an angle of 2π/3.
lawyer [7]

Answer:

The sum of the two vectors is the vector <-0.5 , 4+3.5\sqrt{3} >

Step-by-step explanation:

The horizontal component (x) of a vector whose magnitude is b units and its direction is Ф° is b cos Ф

The vertical component (y) of a vector whose magnitude is b and its direction is Ф is b sin Ф

The vector is <b cos Ф , b sin Ф>

∵ The vector goes 7 units at an angle \frac{2\pi }{3}

- That means its magnitude is 7 and its direction is  \frac{2\pi }{3}

∴ x = 7 cos(  \frac{2\pi }{3} )

∴ y = 7 sin(  \frac{2\pi }{3} )

∵ cos(  \frac{2\pi }{3} ) =  -\frac{1}{2}

∵ sin(  \frac{2\pi }{3} ) =  \frac{\sqrt{3}}{2}

- Substitute them in x and y

∴ x = (7)( -\frac{1}{2} )

∴ x = -3.5

∴ y = (7)( \frac{\sqrt{3}}{2} )

∴ y = 3.5\sqrt{3}

∴ The vector is <-3.5 , 3.5\sqrt{3}>

Now lets add the vectors by adding xs and ys components

∵ <3 , 4> + <-3.5 , 3.5\sqrt{3} > = <3 + -3.5 , 4 + 3.5\sqrt{3} >

∴  <3 , 4> + <-3.5 , 3.5\sqrt{3}> = <-0.5 , 4+3.5\sqrt{3} >

∴ The sum of the two vectors is the vector <-0.5 , 4+3.5\sqrt{3} >

5 0
3 years ago
A shop keeper has 8 gallons, 3 quarts,
ioda

Answer:

I believe it would be 86 cups left of milk.

Step-by-step explanation:

8 gallons= 128 cups of milk

3 quarts= 12 cups

Plus the 1 cup of milk he had equals 141 of milk in total

Now the customer wants 2 gallons (32 cups of milk), 5 quarts ( 20 cups), and 3 cups which is 55 cups of milk.

Now we minus what the customer bought from what the shop keeper had so:

55-141=86

6 0
3 years ago
30 is 120% of what number? show ur work
Yanka [14]

Answer:

30 is 120% of 25

Step-by-step explanation:

30 = 120% of y

\frac{120}{100} × y = 30

After multiplying both sides by 100 and dividing both sides by 120, we have

y = 30 × \frac{100}{120}

y = 25

3 0
3 years ago
Find an equation for the nth term of the arithmetic sequence. a19 = -58, a21 = -164
Elodia [21]
So the formula would be -1856 +98[n-1]
8 0
3 years ago
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