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3 years ago

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Carl is using a pine board to make a frame for a picture. He wants the dimensions of the frame to be 2 feet by 18 inches. How lo

ng of a pine board will Carl need for his frame?

1 answer:

jeka57 [31]3 years ago

7 0

The answer is 36....hope this helped

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Estimate the integral ∫6,0 x^2dx by the midpoint estimate, n = 6

Anettt [7]

Splitting up the interval [0, 6] into 6 subintervals means we have

$[0,1]\cup[1,2]\cup[2,3]\cup\cdots\cup[5,6]$

and the respective midpoints are $\dfrac12,\dfrac32,\dfrac52,\ldots,\dfrac{11}2$ . We can write these sequentially as ${x_i}^*=\dfrac{2i+1}2$ where $0\le i\le5$ .

So the integral is approximately

$\displaystyle\int_0^6x^2\,\mathrm dx\approx\sum_{i=0}^5({x_i}^*)^2\Delta x_i=\frac{6-0}6\sum_{i=0}^5({x_i}^*)^2=\sum_{i=0}^5\left(\frac{2i+1}2\right)^2$

Recall that

$\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6$
$\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2$
$\displaystyle\sum_{i=1}^n1=n$

so our sum becomes

$\displaystyle\sum_{i=0}^5\left(\frac{2i+1}2\right)^2=\sum_{i=0}^5\left(i^2+i+\frac14\right)$
$=\displaystyle\frac{5(6)(11)}6+\frac{5(6)}2+\frac54=\frac{143}2$

8 0

3 years ago

What is the surface area of this prism?<br> 5 yd<br> 5 yd<br> 11 yd<br> 6 yd

vovikov84 [41]

Is (A) because of u multiple all the triangle sides u will get 5 yd so (a) the answer

5 0

3 years ago

What number is equivalent to 2.34 x 1.08 x 5.6?

tangare [24]

The answer is 14.15232

8 0

2 years ago

Read 2 more answers

AAA Packages Plus sends packages overnight for $5 plus $0.25 per ounce. United Packages charges $2 plus $0.35 per ounce.

Nata [24]

A.)
The equation for AAA packages plus would be .25x+5
The equation for United packages would be
.35x+2

B.) his package would need to be 30 ounces for them to be the same price

7 0

3 years ago

Use foil (a + 3)(a - 2)

blsea [12.9K]

Answer:

$\left(a+3\right)\left(a-2\right)=a^2+a-6=$

Step-by-step explanation:

Given expression is $\left(a+3\right)\left(a-2\right)$ .

Now we need to multiply this using FOIL.

F = First $=\left(a\right)\left(a\right)= a^2$

O = Outside $=\left(a\right)\left(-2\right)= -2a$

I = Inside $=\left(3\right)\left(a\right)= 3a$

L = Last $=\left(3\right)\left(-2\right)= -6$

Hence we get :

$\left(a+3\right)\left(a-2\right)=a^2-2a+3a-6=a^2+a-6=$

7 0

3 years ago

Read 2 more answers