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3 years ago

Dean needs 6060 inches of wood to build a rectangular picture frame.

1 answer:

5 0

What we know:
Perimeter=60
Perimeter formula=2l+2w
l=2w

This perimeter has the following set up using p=60 and l=2w:
perimeter =2(l)+2w
60=2(2w)+2w
60=4w+2w
60=6w

Now that we know how many w's we need to have we can use this information to find which equations have 6 w's and which one does not.
Look at the first equation:
2(2w+w)=60 distributive power
4w+2w=60 like terms
6w=60 correct

second equation:
w+2w+w+2w=60
6w=60 like terms, correct

third equation:
2w+2x2w=60 multiplication property
2w+4w=60 like terms
6w=60 correct

fourth equation:
w+2w=60 like terms
3w=60 not correct

Fourth equation is not correct.

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Evaluate the integral using the indicated trigonometric substitution. (use c for the constant of integration.) x^3 / sqrt x^2 +

slava [35]

$\displaystyle\int\frac{x^3}{\sqrt{x^2+49}}\,\mathrm dx$

Taking $x=7\tan\theta$ gives $\mathrm dx=7\sec^2\theta\,\mathrm d\theta$ , so that the integral becomes

$\displaystyle\int\frac{(7\tan\theta)^3}{\sqrt{(7\tan\theta)^2+49}}(7\sec^2\theta)\,\mathrm d\theta$
$=\displaystyle7^4\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{49\tan^2\theta+49}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{\tan^2\theta+1}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{\sec^2\theta}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{|\sec\theta|}\,\mathrm d\theta$

When $\sec\theta>0$ , we have

$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sec\theta}\,\mathrm d\theta$
$=\displaystyle7^3\int\tan^3\theta\sec^2\theta\,\mathrm d\theta$

and from here we can substitute $u=\tan\theta$ to proceed from here.

Quick note: When we set $x=7\tan\theta$ , we are implicitly enforcing $-\dfrac\pi2$ just so that the substitution can be undone later via $\theta=\tan^{-1}\dfrac x7$ . But note that over this domain, we automatically guarantee that $\sec\theta>0$ , so the absolute value bars can be dropped immediately.

6 0

3 years ago

A straight line has equation 3y-3x=4. Write down the equation of another straight line parallel to it

Sophie [7]

Y = 3x + 4/3
............

8 0

4 years ago

To determine whether the inverse of a function is a function you can perform the horizontal line test.

iris [78.8K]

Answer:

$\boxed{\text{TRUE}}$

Step-by-step explanation:

If a horizontal line intersects the graph of a function in all places at exactly one point (the horizontal line test), the inverse of the function is also a function.

For example, the inverse of a hyperbola (like ƒ(x) =1/x) is a function, because every horizontal line intersects with the graph at exactly one point.

However, the inverse of a parabola (like ƒ(x) = x²) is not a function, because a horizontal line intersects with the graph at two points.

7 0

3 years ago

Help ASAP PLZZZZZZ I really need the answer

Kitty [74]

The last one because a perpendicular triangle would be drawn from the vertice to the bottom.

3 0

3 years ago

What are the slope and Y intercept of the linear function graft to the left?

Anna35 [415]

Answer:

Slope - $\\\frac{1}{2}$

Y intercept 1

so option 2 or B

Step-by-step explanation:

Slope is rise over run so 1 over -2

so -1/2

and y intercept is where the line crosses the y axis and it crosses on this graph at positive 1.

6 0

3 years ago