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3 years ago

A play tent is shown.how much fabric was used to make the front(Base 1=36.5) (Base 2=23). And the height =32

Mathematics

2 answers:

Ira Lisetskai [31]3 years ago

8 0

Answer:

In order to make the front it is needed 952 squared units.

Step-by-step explanation:

The front of the tent has the shape of a trapezoid, thus in order to find out how much material is needed we can find the area of the trapezoid using the following formula

$A = \cfrac{b_1+b_2}{2}h$

Finding the front area of the tent.

We can identify the given information for the front area, we have:

$b_1=36.5\\b_2=23\\h=32\\$

Replacing on the trapezoid formula we get

$A =\cfrac{36.5 + 23}2\times 32$

Evaluating will give us

$A = 952 units^2$

Since the area is 952 squared units , then 952 squared units of fabric was used to make the front.

xxMikexx [17]3 years ago

4 0

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alukav5142 [94]

Answer:

a) y = |x/2 -2| +4

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d) y = |(x-1)/2 -2| +3

Step-by-step explanation:

To translate the function f(x) by (h, k) in the (right, up) direction, you transform it to ...

g(x) = f(x -h) +k

a) one unit up

Add 1 to the function value.

$y=\left|\dfrac{x}{2}-2\right|+3+1\\\\\boxed{y=\left|\dfrac{x}{2}-2\right|+4}$

b) one unit down

Subtract 1 from the function value.

$y=\left|\dfrac{x}{2}-2\right|+3-1\\\\\boxed{y=\left|\dfrac{x}{2}-2\right|+2}$

c) one unit left

Replace x with x-(-1).

$y=\left|\dfrac{x-(-1)}{2}-2\right|+3\\\\\boxed{y=\left|\dfrac{x+1}{2}-2\right|+3}$

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3 years ago

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Answer:

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Step-by-step explanation:

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Mnenie [13.5K]

Answer:

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Step-by-step explanation:

For this case we have the following differential equationÑ

$\frac{du}{dt}= -k (u-T)$

We can reorder the expression like this:

$\frac{du}{u-T} = -k dt$

We can use the substitution $w = u-T$ and $dw =du$ so then we have:

$\frac{dw}{w} =-k dt$

IF we integrate both sides we got:

$ln |w| = -kt +C$

If we apply exponential in both sides we got:

$w = e^{-kt} *e^c$

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We can also express the solution in the following terms:

$u(t) = (T_i -T_{amb}) e^{kt} +T_{amb}$

For this case we know that $k =-0.15 hr$ since w ehave a cooloing, $T_{i}= 70 F, T_{amb}=11F$ , we have this model:

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If we apply natural logs on both sides we got:

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So it would takes approximately 6.9 hours to reach 32 F.

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