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3 years ago

Use elimination to solve the system of equations. 2X - 3Y = 9 -5X - 3Y = 30

Mathematics

1 answer:

shtirl [24]3 years ago

6 0

Answer:

X = -3

Y = -5

Step-by-step explanation:

2X - 3Y = 9

7X + 0Y = -21

X = -3

2(-3) - 3Y = 9

- 3Y = 15

Y = -5

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Find the radian measure of the central angle of a circle of radius r = 60 inches that intercepts an arc of length s = 70 inche

Finger [1]

Step-by-step explanation:

s = rθ

70 in = (60 in) θ

θ = 7/6 radians

θ ≈ 1.167 radians

7 0

3 years ago

Write the number 10 as a fraction

liq [111]

Answer:10/1

Step-by-step explanation:

Any number can become a fraction by adding a number underneath

6 0

3 years ago

If the local linear approximation of f(x) = 2cos x + e^2x at x = 2 is used to find the approximation for f(2.1), then the % erro

yKpoI14uk [10]

<u>Answer-</u>

The % error of this approximation is 1.64%

<u>Solution-</u>

Here,

$\Rightarrow f(x) = 2\cos x + e^{2x}$

$\Rightarrow f'(x) = -2\sin x + 2e^{2x}$

And,

$\Rightarrow f(2) = 2\cos 2 + e^{4}$

$\Rightarrow f'(2) = -2\sin 2 + 2e^{4}$

Taking (2, f(2)) as a point and slope as, f'(2), the function would be,

$\Rightarrow y-y_1=m(x-x_1)$

$\Rightarrow y-(2\cos 2 + e^{4})=(-2\sin 2 + 2e^{4})(x-2)$

$\Rightarrow y=(-2\sin 2 + 2e^{4})(x-2)+(2\cos 2 + e^{4})$

The value of f(2.1) will be

$\Rightarrow y=(-2\sin 2 + 2e^{4})(2.1-2)+(2\cos 2 + e^{4})$

$\Rightarrow y=(-2\sin 2 + 2e^{4})(0.1)+(2\cos 2 + e^{4})$

$\Rightarrow y=64.5946$

According to given function, f(2.1) will be,

$\Rightarrow f(2.1) = 2\cos 2.1 + e^{2(2.1)}$

$\Rightarrow f(2.1) = 65.6766$

$\therefore \%\ error=\dfrac{65.6766-64.5946}{65.6766}=0.0164=1.64\%$

5 0

3 years ago

Element X is a radioactive isotope such that every 51 years, its mass decreases by half. Given that the initial mass of a sample

pychu [463]

Answer: It will take 6 years for 7500 grams of X to reach 6900 grams.

Step-by-step explanation:

Expression for rate law for first order kinetics is given by:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant

t = age of sample

a = let initial amount of the reactant

a - x = amount left after decay process

a) for completion of half life:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

$51=\frac{0.69}{k}$

$k=\frac{0.69}{51}=0.0135years^{-1}$

b) for 7500 g to reach to 6900 g

$t=\frac{2.303}{0.0135}\log\frac{7500}{6900}$

$t=6years$

It will take 6 years for 7500 grams of X to reach 6900 grams.

5 0

2 years ago

Please help! im doing a test right now

GaryK [48]

Answer:

a.) Time = 6 hours

b.) Average Speed = 410 miles per hours

c.) Distance = 196 miles

Step-by-step explanation:

A coach drives 360 miles at a speed of 60 mph.

So,

Time = Distance ÷ Speed

Time = 360 ÷ 60

Time = 6 hours

A plan flies 1640 miles in 4 hours.

So,

Average Speed = Distance ÷ Time

Average Speed = 1640 ÷ 4

Average Speed = 410 miles per hours

A bus drives 3½ hour at an average Speed of 56 mph.

So,

3½ hour = 3.5 hour

Distance = Average Speed × Time

Distance = 56 × 3.5

Distance = 196 miles

<u>-TheUnknownScientist 72</u>

4 0

2 years ago