Rewrite the expression 27x3y3 with only one exponent

lubasha [3.4K]

31-27+12-23-(-25)+(-6)= 12

4 0

3 years ago

Jeremy is buying a new bicycle. For the style he likes best, the bicycle shop sells 26-inch and 29-inch frames in blue, red, and

Leno4ka [110]

Answer:

1 out of 6

Step-by-step explanation:

there are 6 different combinations

26in - blue

26in- red

26in- black

29in - blue

29in - red

29in - black

The probability then come out to 1 out of 6

8 0

3 years ago

Deva bought 9 1/2 m of cloth for rupees 28 1/2.Samruth buys 26 1/3 m of same cloth. how much should samruth pay the shopkeeper?

likoan [24]

For this case we can make the following rule of three:

9 1/2 m --------------> 28 1/2 rupees

26 1/3 m -------------> x

From here, we clear the value of x.

We have then:

$x = (\frac{26+\frac{1}{3}}{9+\frac{1}{2}}) (28+\frac{1}{2})$

Rewriting we have:

$x = (\frac{\frac{79}{3}}{\frac{19}{2}}) (\frac{57}{2})$

$x = (\frac{158}{57}) (\frac{57}{2})$

$x = \frac{158}{2}$

$x = 79$

Answer:

samruth should pay 79 rupees to the shopkeeper

5 0

3 years ago

What is the slope of a line perpendicular to the line with a slope of 1/2

frosja888 [35]

Answer:

-2

Step-by-step explanation:

To answer this, just take the negative reciprocal of 1/2. We obtain -2.

7 0

4 years ago

Approximate area under the curve f(x) =-x^2+2x+4 from x=0 to x=3 by using summation notation with six rectangles and use the the

bekas [8.4K]

Answer:

Summation notation:

$\frac{1}{2}\sum_{k=1}^6f((.5k))$

or after using your function part:

$\frac{1}{2}\sum_{k=1}^6(-(.5k)^2+2(.5k)+4)$

After evaluating you get 11.125 square units.

Step-by-step explanation:

The width of each rectangle is the same so we want to take the distance from x=0 to x=3 and divide by 6 since we want 6 equal base lengths for our rectangles.

The distance between x=0 and x=3 is (3-0)=3.

We want to divide that length of 3 units by 6 which gives a length of a half per each base length.

We are doing right endpoint value so I'm going to stat at x=3. The first rectangle will be drawn to the height of f(3).

The next right endpoint is x=3-1/2=5/2=2.5, and the second rectangle will have a height of f(2.5).

The next will be at x=2.5-.5=2, and the third rectangle will have a height of f(2).

The fourth rectangle will have a height of f(2-.5)=f(1.5).

The fifth one will have a height of f(1.5-.5)=f(1).

The last one because it is the sixth one will have a height of f(1-.5)=f(.5).

So to find the area of a rectangle you do base*time.

So we just need to evaluate:

$\frac{1}{2}f(3)+\frac{1}{2}f(2.5)+\frac{1}{2}f(2)+\frac{1}{2}f(1.5)+\frac{1}{2}f(1)+\frac{1}{2}f(.5)$

or by factoring out the 1/2 part:

$\frac{1}{2}(f(3)+f(2.5)+f(2)+f(1.5)+f(1)+f(.5))$

To find f(3) replace x in -x^2+2x+4 with 3:

-3^2+2(3)+4

-9+6+4

1

To find f(2.5) replace x in -x^2+2x+4 with 2.5:

-2.5^2+2(2.5)+4

-6.25+5+4

2.75

To find f(2) replace x in -x^2+2x+4 with 2:

-2^2+2(2)+4

-4+4+4

4

To find (1.5) replace x in -x^2+2x+4 with 1.5:

-1.5^2+2(1.5)+4

-2.25+3+4

4.75

To find f(1) replace x in -x^2+2x+4 with 1:

-1^2+2(1)+4

-1+2+4

5

To find f(.5) replace x in -x^2+2x+4 with .5:

-.5^2+2(.5)+4

-.25+1+4

4.75

Now let's add those heights. After we obtain this sum we multiply by 1/2 and we have our approximate area:

$\frac{1}{2}(f(3)+f(2.5)+f(2)+f(1.5)+f(1)+f(.5))$

$\frac{1}{2}(1+2.75+4+4.75+5+4.75)$

$\frac{1}{2}(22.25)$

$11.125$

Okay now if you wanted the summation notation for:

$\frac{1}{2}(f(3)+f(2.5)+f(2)+f(1.5)+f(1)+f(.5))$

is it

$\frac{1}{2}\sum_{k=1}^{6}(f(.5+.5(k-1)))$

or after simplifying a bit:

$\frac{1}{2}\sum_{k=1}^6 f((.5+.5k-.5))$

$\frac{1}{2}\sum_{k=1}^6f((.5k))$

If you are wondering how I obtain the .5+.5(k-1):

I realize that 3,2.5,2,1.5,1,.5 is an arithmetic sequence with first term .5 if you the sequence from right to left (instead of left to right) and it is going up by .5 (reading from right to left.)

6 0

3 years ago