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3 years ago

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Eleanor and Max used two rectangular pieces of plywood, placed end-to-end, to make a long rectangular stage for the school play.

One board was 7 feet long, and the other was 6 1/2 feet long. The two pieces of plywood had equal widths. The total area of the stage was 84 3/8 square feet. What was the width of the plywood?

1 answer:

Flauer [41]3 years ago

3 0

Answer:the width of plywood = 6.25 feet wide or 6 1/4 feet wide

Step-by-step explanation:

Step 1

Area of a rectangular plywood = length x width

Area of Ist Plywood= 7 x w

Area of 2nd Plywood= 61/2 x w=6.5 xw

But Total Arae of trhe two Plywoods are = 84 3/8 square feet.

Therefore Our equation to solve the problem becomes

Area of Ist Plywood + Area of 2nd Plywood =84 3/8 square feet.

7w + 6.5w = 84 3/8

13.5w= 84 3/8

w = 84 3/8/13.5

675/8 / 13.5

w=6.25

Therefore the width of plywood = 6.25 feet wide or 6 1/4 feet.

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Calculate the limit values:

Nataliya [291]

A) This particular limit is of the indeterminate form,
$\frac{ \infty }{ \infty }$
if we plug in infinity directly, though it is not a number just to check.

If a limit is in this form, we apply L'Hopital's Rule.

's
$Lim_{x \rightarrow \infty } \frac{ ln(x ^{2} + 1 ) }{x} = Lim_ {x \rightarrow \infty } \frac{( ln(x ^{2} + 1 ) ) '}{x ' }$
So we take the derivatives and obtain,

$Lim_ {x \rightarrow \infty } \frac{ ln(x ^{2} + 1 ) }{x} = Lim_{x \rightarrow \infty } \frac{ \frac{2x}{x^{2} + 1} }{1}$

Still it is of the same indeterminate form, so we apply the rule again,

$Lim_{x \rightarrow \infty } \frac{ ln(x ^{2} + 1 ) }{x} = Lim_{x \rightarrow \infty } \frac{ 2 }{2x}$

This simplifies to,

$Lim_{x \rightarrow \infty } \frac{ ln(x ^{2} + 1 ) }{x} = Lim_{x \rightarrow \infty } \frac{ 1 }{x} = 0$

b) This limit is also of the indeterminate form,

$\frac{0}{0}$
we still apply the L'Hopital's Rule,

$Lim_ {x \rightarrow0 }\frac{ tanx}{x} = Lim_ {x \rightarrow0 } \frac{ (tanx)'}{x ' }$

$Lim_ {x \rightarrow0 }\frac{ tanx}{x} = Lim_ {x \rightarrow0 } \frac{ \sec ^{2} (x) }{1 }$

When we plug in zero now we obtain,

$Lim_ {x \rightarrow0 }\frac{ tanx}{x} = Lim_ {x \rightarrow0 } \frac{ \sec ^{2} (0) }{1 } = \frac{1}{1} = 1$
c) This also in the same indeterminate form

$Lim_ {x \rightarrow0 }\frac{ {e}^{2x} - 1 - 2x}{ {x}^{2} } = Lim_ {x \rightarrow0 } \frac{ ({e}^{2x} - 1 - 2x)'}{( {x}^{2} ) ' }$

$Lim_ {x \rightarrow0 }\frac{ {e}^{2x} - 1 - 2x}{ {x}^{2} } = Lim_ {x \rightarrow0 } \frac{ (2{e}^{2x} - 2)}{ 2x }$

It is still of that indeterminate form so we apply the rule again, to obtain;

$Lim_ {x \rightarrow0 }\frac{ {e}^{2x} - 1 - 2x}{ {x}^{2} } = Lim_ {x \rightarrow0 } \frac{ (4{e}^{2x} )}{ 2 }$

Now we have remove the discontinuity, we can evaluate the limit now, plugging in zero to obtain;

$Lim_ {x \rightarrow0 }\frac{ {e}^{2x} - 1 - 2x}{ {x}^{2} } = \frac{ (4{e}^{2(0)} )}{ 2 }$

This gives us;

$Lim_ {x \rightarrow0 }\frac{ {e}^{2x} - 1 - 2x}{ {x}^{2} } =\frac{ (4(1) )}{ 2 }=2$

d) $Lim_ {x \rightarrow +\infty }\sqrt{x^2+2x}-x$

For this kind of question we need to rationalize the radical function, to obtain;

$Lim_ {x \rightarrow +\infty }\frac{2x}{\sqrt{x^2+2x}+x}$

We now divide both the numerator and denominator by x, to obtain,

$Lim_ {x \rightarrow +\infty }\frac{2}{\sqrt{1+\frac{2}{x}}+1}$

This simplifies to,

$=\frac{2}{\sqrt{1+0}+1}=1$

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3 years ago

HELP PLEASE!!!!! PLEASE EXPLAIN WHEN GIVING THE ANSWER!!!! GIVING BRAINLIEST TO THE BEST EXPLANATION!!!!

atroni [7]

Answer:Simplificando

5 (2j + 3 + j) = 0

Reordene os termos:

5 (3 + 2j + j) = 0

Combine termos semelhantes: 2j + j = 3j

5 (3 + 3j) = 0

(3 * 5 + 3j * 5) = 0

(15 + 15j) = 0

Resolvendo

15 + 15j = 0

a verdadeira questão é por que o vizinho de Sarah quer dentes de tubarão

Step-by-step explanation:

Mova todos os termos contendo j para a esquerda, todos os outros termos para a direita.

Adicione '-15' a cada lado da equação.

15 + -15 + 15j = 0 + -15

Combine termos semelhantes: 15 + -15 = 0

0 + 15j = 0 + -15

15j = 0 + -15

Combine termos semelhantes: 0 + -15 = -15

15j = -15

Divida cada lado por '15'.

j = -1

Simplificando

j = -1

Tubarão ou cação é um tipo de peixe de esqueleto cartilaginoso e um corpo hidrodinâmico (com exceção dos Squatiniformes, Hexanchiformes e Orectolobiformes)

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3 years ago

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What is the reason for Statement 3 of the two-column proof?

Ivenika [448]

Refer to the attached image.

Given:

The measure of $\angle JMK= 52^\circ$ and $\angle KML= 38^\circ$ .

Also, Three rays ML, MK, and MJ share an endpoint M. Ray MK forms a bisector as shown in the attached image and the bisector divides angle JML into two parts.

To Prove: $\angle JML$ is a right angle.

Proof:

Statements Reasons

1. $m \angle JMK=52^\circ$ Given

2. $m \angle KML=38^\circ$ Given

3. $m \angle JMK+m \angle KML=m \angle JML$

The reason for statement 3 is Angle addition postulate. As angle JML is composed of 2 angles that is angle JMK and angle KML. So by adding the measures of angles JMK and KML, we will get the measure of angle JML which is referred as Angle addition postulate.

4. $52^\circ+38^\circ = m \angle JML$ Substitution property of equality

5. $90^\circ = m \angle JML$ Simplification

6. $\angle$ JML is a right angle. Definition of right angle

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