Elena's bed measures 80 cm by 120 cm on the scale drawing. What are the actual measurements of her bed?

Mathematics

1 answer:

Semenov [28]3 years ago

3 0

Answer: 9600cm

Step-by-step explanation: 120

*80

9600

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Derivative of these questions

shtirl [24]

Answer: $\bold{y'=\dfrac{1}{2(a-b)^2}\bigg(\dfrac{1}{\sqrt{x+a}}+\dfrac{1}{\sqrt{x+b}}\bigg)}$

Step-by-step explanation:

$y=\dfrac{1}{\sqrt{x+a}-\sqrt{x+b}}\\\\\\\text{Rationalize the denominator:}\\y=\dfrac{1}{\sqrt{x+a}-\sqrt{x+b}}\bigg(\dfrac{\sqrt{x+a}+\sqrt{x+b}}{\sqrt{x+a}+\sqrt{x+b}}\bigg)\\\\\\y=\dfrac{\sqrt{x+a}+\sqrt{x+b}}{x+a-x-b}\\\\\\y=\dfrac{\sqrt{x+a}+\sqrt{x+b}}{a-b}\\\\\\\text{Apply the derivative (derivative of the numerator (top) divided by the}\\\text{denominator (bottom) squared).}$

$\text{Derivative of }\sqrt{x+a}\quad \rightarrow \quad (x+a)^{\frac{1}{2}}\quad = \quad \dfrac{1}{2}(x + a)^{-\frac{1}{2}}\\\\\text{Derivative of }\sqrt{x+b}\quad \rightarrow \quad (x+b)^{\frac{1}{2}}\quad = \quad \dfrac{1}{2}(x + b)^{-\frac{1}{2}}\\\\\\\text{Derivative of}\ \dfrac{\sqrt{x+a}+\sqrt{x+b}}{a-b}:\\\\= \dfrac{\dfrac{1}{2}(x + a)^{-\frac{1}{2}}+\dfrac{1}{2}(x + b)^{-\frac{1}{2}}}{(a-b)^2}$

$\text{Factor out }\dfrac{1}{2}\ \text{from the numerator:}\\\\\dfrac{(x+a)^{-\frac{1}{2}}+(x+b)^{-\frac{1}{2}}}{2(a-b)^2}\\\\\\\text{Move the terms with negative exponents to the denominator:}\\\\=\dfrac{1}{2(a-b)^2}\bigg(\dfrac{1}{\sqrt{x+a}}+\dfrac{1}{\sqrt{x+b}}\bigg)$

3 0

3 years ago

Which of the following relations is a function? A.{ (-2, 4), (-1, 3), (5, 2), (1, 4) } B.{ (1, 7), (1, 8), (2, 7), (3, 8) } C.{

siniylev [52]

From the pairs of x,y, if the set has two "x" of the same value, that is, "x" repeats, or an x-repeat, then is NOT a function

so, the group that doesn't have any x-repeats, is a function, now let's check

$\bf A.\{ (-2, 4), (-1, 3), (5, 2), (1, 4) \}\\\\
B.\{ (\boxed{1}, 7), (\boxed{1}, 8), (2, 7), (3, 8) \}\impliedby \textit{has one re}\textit{peat, no dice}\\\\
C.\{ (2, 4), (\boxed{4}, 6), (\boxed{4}, 8), (6, 4) \}\impliedby \textit{also has one re}\textit{peat, no dice}\\\\
D.\{ (\boxed{5}, 7), (6, 3), (8, 6), (\boxed{5}, 4) \}\impliedby \textit{same, has one re}\textit{peat, no dice}$

3 0

3 years ago

Mike drank 60% of his glass of milk. Afterwards, 80ml of milk remained in the glass. What volume of milk was initially in the gl

Alina [70]

Answer:

Step-by-step explanation:

$x$ is the total volume of milk.