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padilas [110]
2 years ago
13

Write the binomial expansion of (t-3)^5

Mathematics
1 answer:
postnew [5]2 years ago
5 0

Answer:

Step-by-step explanation:

(t-3)^5 is the same as (t + (-3))^5

First:  t starts at the highest power and goes down and (-3) starts at the lowest power and goes up

Second: from the Pascal triangles take the coefficients  1  5  10  10  5  1

1*t^{5} (-3)^{0} + 5*t^{4} (-3)^{1} +10*t^{3} (-3)^{2} +10*t^{2} (-3)^{3} +5*t^{1} (-3)^{4} +1*t^{0} (-3)^{5}

Anything to power 0 is equal to 1

Negative number to an odd power is negative, to a even power is positive

t^{5}  -15t^{4}  +90t^{3}  -270t^{2}  +405t  -243

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Answer:

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Step-by-step explanation:

7 0
2 years ago
Find all the antiderivatives of the following function. Check your work by taking the derivative.
Rom4ik [11]

\int 10e^x dx = 10 \int e^x dx = 10 e^x + C

The first step, factoring out the constant 10, is due to the Constant Multiple Rule:

\int k \cdot f(x) dx = k \cdot \int f(x) dx

The derivative of the natural exponential function is itself! \frac{d}{dx} \left( e^x \right) = e^x. Reversing this,

\int e^x dx = e^x + C

3 0
3 years ago
How do I translate the product of h and 4 is subtracted from one-fifth of x is 35 to an equation?
kolezko [41]

So we know that the word 'product' means multiplication, and that means that h and 4 are being multiplied. Also, one-fifth of x is another way of saying that one-fifth is being multiplied with x. So then we can construct the equation:

\frac{1}{5} x-(4*h)=35

And we can then simplify this by taking out the multiplication sign:

\frac{1}{5}x-4h=35

And so since we do not know what x or h is equal to, this is as far as we can go.

8 0
3 years ago
If 12a - 5 = 4a + 11 ,then a= what?
FinnZ [79.3K]

Answer:

a=2

Step-by-step explanation:

12a - 5 = 4a + 11

Subtract 4a from each side

12a-4a - 5 = 4a-4a + 11

8a -5 = 11

Add 5 to each side

8a -5+5 = 11+5

8a = 16

8a/8 = 16/8

a =2

7 0
3 years ago
Read 2 more answers
The area A (in square feet) of the rectangular shed is given by
a_sh-v [17]

This question is incomplete.

Complete Question

The area A (in square feet) of the rectangular shed is given by 6x³+7x²+11x+21.And one side of the rectangular is 2x+3. Use polynomial long division to find an expression for the length (in feet) of the shed.

Answer:

3x² - x +7

Step-by-step explanation:

Using the long division method:

We have :

Divisor : 6x³+7x²+11x+21

Dividend : 2x+3

Quotient : the length (in feet) of the shed = ???

Hence, we solve below

6x³+7x²+11x+21 ÷ 2x + 3

3x² -x + 7

______________________

2x+3 l 6x³+7x²+11x+21

6x³+9x²

__________

-2x²+11x

-2x²-3x

__________

14x+21

14x+21

_______

0

Therefore, an expression for the length (in feet) of the shed is 3x² - x +7

8 0
2 years ago
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