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Delicious77 [7]
4 years ago
12

The area of the rectangle is 66m^2, and the length of the rectangle is 7m less than three times the width. Find the dimensions o

f the rectangle.
Length:
Width:
Mathematics
1 answer:
xxMikexx [17]4 years ago
3 0
Let width=x m
so length=3x-7
Since area =66m^2
L×B=66
(3x-7)×x=66
3x^2-7x=66
3x^2-7x-66=0
3x^2-(18-11)x-66=0
3x^2-18x+11x-66=0
3x(x-6)+11(x-6)=0
So (x-6)(3x-6)=0
So x=2 and x=6
If x=2
Width=2
Length=2×3-7=-1
So this value of x does not exist because length cannot be negative

So x=6m
Width=6m
length=3×6-7=11m

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Please help me solve this​
Viktor [21]

You can factor the 32 out of the sum:

\displaystyle \sum_{m=1}^\infty 32 \cdot \left(\dfrac{1}{2}\right)^{m-1} = 32\sum_{m=1}^\infty \left(\dfrac{1}{2}\right)^{m-1}

We can also change the index as follows

\displaystyle 32\sum_{m=1}^\infty \left(\dfrac{1}{2}\right)^{m-1} = 32\sum_{m=0}^\infty \left(\dfrac{1}{2}\right)^{m}

Now, we have a theorem that states that the series

\displaystyle \sum_{m=1}^\infty a^m

converges if and only if |a|, and in this case we have

\displaystyle \sum_{m=1}^\infty a^m = \dfrac{1}{1-a}

This is your case, because you have

|a|=\dfrac{1}{2}

which implies that your series converges, and the value is

\displaystyle 32\sum_{m=0}^\infty \left(\dfrac{1}{2}\right)^{m} = 32 \cdot \dfrac{1}{1-\frac{1}{2}} = 32\cdot 2 = 64

3 0
3 years ago
Simplify the expression below.<br> x4 • x4 • x4
beks73 [17]

Answer:

x^12.

Step-by-step explanation:

x^4 times x^4 times x^4.

Since we don't know x and the 4's are exponents we just add them together.

5 0
3 years ago
What is the solution to the linear equation?
gizmo_the_mogwai [7]

Answer:

p = 30/1/3 or 91/3 or 30.33

Step-by-step explanation:

2 + p = 7/3 + 30

p = 32/1/3 - 2

p = 30/1/3

3 0
3 years ago
3/4 times 2 1/2 times 4/5
amm1812
The answer to your problem is 6
5 0
3 years ago
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G(n)=-4n+2; find g(8)<br>​
yarga [219]

Answer:

-30

Step-by-step explanation:

In g(8) the 8 = n.  So, substitute 8 in for n in the expression -4n + 2

g(8)  =  -4(8) + 2 = -32 + 2 = -30

4 0
3 years ago
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