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2 years ago

A tank is being filled with water at a rate of 5.5 gallons per

Mathematics

2 answers:

Sonja [21]2 years ago

6 0

Arithmetic sqaure: a + (n-1) * d

where "a" is the first term, "d" is the common difference

Here given:

a = 10 gallons

d = 5.5 gallons

nth term: 10 + (n-1) * 5.5

Solve for first 5 terms:

10 + (1-1) * 5.5 = 10

10 + (2-1) * 5.5 = 15.5

10 + (3-1) * 5.5 = 21

10 + (4-1) * 5.5 = 26.5

10 + (5-1) * 5.5 = 32

first five terms: 10, 15.5, 21, 26.5, 32

irinina [24]2 years ago

6 0

First term=a=10
common difference a=5.5

General formula

a_n=a+(n-1)d
a_n=10+(n-1)5.5

a_1=10
a_2=10+5.5=15.5
a_3=10+11=21
a_4=10+16.5=26.5
a_5=10+22=32
a_6=10+27.5=37.5

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Rick is 27 years old. Pretend D is David and R is Rick

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3 years ago

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Solve the system of linear equation 8X plus 5Y equals 18 and 6X plus Y equals -2 by using the linear Combination method Emmaus d

Hunter-Best [27]

$\text{The solution is } x = \frac{-14}{11} \text{ and } y = \frac{62}{11}$

Solution:

Given system of equations are:

8x + 5y = 18 ------- eqn 1

6x + y = -2 -------- eqn 2

Multiply eqn 2 by -5

-30x -5y = 10 ----- eqn 3

Add eqn 1 and eqn 3 so that y terms gets eliminated

8x + 5y = 18

-30x -5y = 10

( + ) --------------

-22x = 28

Divide both sides by -22

$x = \frac{28}{-22}\\\\x = \frac{-14}{11}$

Substitute the x value in eqn 1

$8(\frac{-14}{11}) + 5y = 18\\\\\frac{-112}{11} + 5y = 18\\\\5y = 18 + \frac{112}{11}\\\\5y = \frac{310}{11}\\\\y = \frac{62}{11}$

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Answer:

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3 years ago

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Answer:

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3 years ago

I need help with this problem

Arada [10]

Answer:

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Step-by-step explanation:

We know that if we take dot product of two vectors then it is equal to the product of magnitudes of the vectors and cosine of the angle between them

That is let p and q be any two vectors and A be the angle between them

So, p·q=|p|*|q|*cosA

⇒ $cosA=\frac{u.v}{|u||v|}$

Given u=-8i-3j and v=-8i+8j

$|u|=\sqrt{(-8)^{2}+ (-3)^{2}} =8.544$

$|v|=\sqrt{(-8)^{2}+ (8)^{2}} =11.3137$

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