(Y-3)^2 = 4y -12 <=> Y^2 - 6Y + 9 = 4y - 12 <=> 4y = Y^2 - 6Y + 21 <=> y = (Y^2 - 6Y + 21)/4. Solving the equation for y means that we have to express y relative to the other quantities in the equation.

8 0

3 years ago

Evaluate using Definite integrals

swat32

Since $[0,4]=[0,1]\cup(1,4]$ , we can rewrite the integral as

$\displaystyle \int_0^1f(t)\;dt + \int_1^4 f(t)\; dt$

Now there is no ambiguity about the definition of f(t), because in each integral we are integrating a single part of its piecewise definition:

$\displaystyle \int_0^1f(t)\;dt = \int_0^11-3t^2\;dt,\quad \int_1^4 f(t)\; dt = \int_1^4 2t\; dt$

Both integrals are quite immediate: you only need to use the power rule

$\displaystyle \int x^n\;dx=\dfrac{x^{n+1}}{n+1}$

to get

$\displaystyle \int_0^11-3t^2\;dt = \left[t-t^3\right]_0^1,\quad \int_1^4 2t\; dt = \left[t^2\right]_1^4$

Now we only need to evaluate the antiderivatives:

$\left[t-t^3\right]_0^1 = 1-1^3=0,\quad \left[t^2\right]_1^4 = 4^2-1^2=15$

So, the final answer is 15.

4 0

3 years ago

How do I subtract decimals from whole numbers?

Gekata [30.6K]

Answer:

Just use long subtraction by expanding the decimal places of the whole number. This is done by adding a point, and enough zeros to it to match the number of decimal digits in the other number (digits after the decimal point).

12345678

i.e: 5 - 2.48374827, 2.48374827 has 8 decimal digits, so add 8 zeros after the point.

1 1 1 1 1 1 1

5.00000000

2.48374827

_______________

2.51625173

7 + 3 = 10, 7 + 2 + 1 = 10, 8 + 1 + 1= 10, 5 + 4 + 1 = 10, 2 + 7 + 1 = 10, 3 + 6 + 1 = 10, 1 + 8 + 1 = 10, 5 + 4 + 1 = 10, 2 + 2 + 1 = 5 : 5.00000000

This is basically borrowing a group of 10s which are the same as 1s in the next decimal place up.

For each digit except the first to the right, let 10 subtract that number from it and minus 1 since the 1 is carried over.

7 0

3 years ago

What type of number is - 5.41

Romashka [77]

Answer:

irrational number i believe

Step-by-step explanation:

3 0

2 years ago