All categories

3 years ago

Write the decimal -1.2--- as a mixed number

Mathematics

1 answer:

Anastaziya [24]3 years ago

6 0

Answer:

-1 $\frac{11}{50}$

Step-by-step explanation:

Have a good day :)

You might be interested in

Kryptonite is a material found on the planet Krypton and has various effects, most importantly on Superman. The most common type

Rashid [163]

Answer:

The maximum amount of red kryptonite present is 33.27 g after 4.93 hours.

Step-by-step explanation:

dy/dt = y(1/t - k)

separating the variables, we have

dy/y = (1/t - k)dt

dy/y = dt/t - kdt

integrating both sides, we have

∫dy/y = ∫dt/t - ∫kdt

㏑y = ㏑t - kt + C

㏑y - ㏑t = -kt + C

㏑(y/t) = -kt + C

taking exponents of both sides, we have

$\frac{y}{t} = e^{-kt + C} \\\frac{y}{t} = e^{-kt}e^{C} \\\frac{y}{t} = Ae^{-kt} (A = e^{C})\\y = Ate^{-kt}$

when t = 1 hour, y = 15 grams. So,

$y = Ate^{-kt}\\15 = A(1)e^{-kX1}\\15 = Ae^{-k}$ (1)

when t = 3 hours, y = 30 grams. So,

$y = Ate^{-kt}\\30 = A(3)e^{-kX3}\\30 = 3Ae^{-3k}$ (2)

dividing (2) by (1), we have

$\frac{30}{15} = \frac{3Ae^{-3k}}{Ae^{-k}} \\2 = 3e^{-2k}\\\frac{2}{3} = e^{-2k}$

taking natural logarithm of both sides, we have

-2k = ㏑(2/3)

-2k = -0.4055

k = -0.4055/-2

k = 0.203

From (1)

$A = 15e^{k} \\A = 15e^{0.203} \\A = 15 X 1.225\\A = 18.36$

Substituting A and k into y, we have

$y = 18.36te^{-0.203t}$

The maximum value of y is obtained when dy/dt = 0

dy/dt = y(1/t - k) = 0

y(1/t - k) = 0

Since y ≠ 0, (1/t - k) = 0.

So, 1/t = k

t = 1/k

So, the maximum value of y is obtained when t = 1/k = 1/0.203 = 4.93 hours

$y = 18.36(1/0.203)e^{-0.203t}\\y = \frac{18.36}{0.203}e^{-0.203X1/0.203}\\y = 90.44e^{-1}\\y = 90.44 X 0.3679\\y = 33.27 g$

<u>So the maximum amount of red kryptonite present is 33.27 g after 4.93 hours.</u>

3 0

3 years ago

To save money, you put $200 in your bank account each week. After saving for 4 weeks, you have $1,700 dollars in your account. W

kati45 [8]

it is c y−1,700=200(x−4)

8 0

3 years ago

Solve for x. 2 1/2x−3/4(2x+5)=3/8<br><br> Please hurry

Fofino [41]

Answer:

x= - 1.48 or 0.48

Step-by-step explanation:

I used general formula. Hope I'm on a right path.

8 0

3 years ago

Which of the following expressions is equivalent to 3(4h+2k)?

Wewaii [24]

Answer:

12h + 6k

Step-by-step explanation:

3 times 4h = 12h

3 times 2k = 6k

7 0

3 years ago

Read 2 more answers

Given the expression: 3x^10 − 48x^2

photoshop1234 [79]

Answer:

Part A: 3x²(x⁸ - 16)

Part B: 3x²(x² - 2)(x² + 2) (x² - 2x + 2)(x² + 2x + 2)

Step-by-step explanation:

Part A. Factor out the greatest common factor

3x¹⁰ - 48 x²

= 3x²(x⁸ - 16)

Part B. Factor the expression completely

(i) Factor the difference of squares

x⁸ - 16

= (x⁴ - 4)(x⁴ + 4)

= (x² - 2)(x² + 2)(x⁴ + 4)

3x¹⁰ - 48 x² = 3x²(x² - 2)(x² + 2)(x⁴ + 4)

(ii) Factor the sum of squares

Use the Sophie Germain Identity to factor x⁴ + 4.

x⁴ + 4

= (x²)² + 2² (Still a sum of squares)

= (x² + 2)² - 4x² (Factor this as a difference of squares)

= (x² + 2 - 2x)(x² + 2 + 2x)

3x¹⁰ - 48 x² = 3x² (x² - 2)(x² + 2) (x² - 2x + 2)(x² + 2x + 2)

8 0

3 years ago

Write the decimal -1.2--- as a mixed number​

Write the decimal -1.2--- as a mixed number