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2 years ago

Question 7 of 10

Mathematics

1 answer:

xeze [42]2 years ago

5 0

Answer:40

Step-by-step explanation:

there are 6 triangles / 2= 3,add that tothe squares(37) = 40

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2 years ago

Does anyone know how he got from step 1 to step 2??????????

padilas [110]

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Explanation:

Both sides of the equation are squared.

$\dfrac{x-12}{4}=\sqrt{x} \qquad\text{given}\\\\ \left(\dfrac{x-12}{4}\right)^2=x \qquad\text{square both sides}\\\\ \left(\dfrac{x}{4}-3\right)^2=x \qquad\text{divide out the fraction}\\\\ \dfrac{x^2}{4^2}-\dfrac{6}{4}x+9=x \qquad\text{$(a-b)^2=a^2-2ab+b^2$}\\\\\dfrac{x^2}{16}-\dfrac{5x}{2}+9=0 \qquad\text{subtract $x$}$

I like this better without fractions, so would multiply by 16 at this point (or earlier).

x^2 -40x +144 = 0

(x -36)(x -4) = 0

x = 4 or 36 . . . . . . x = 4 is extraneous

The solution is x = 36.

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Read 2 more answers

A robotic machine fills containers with an acid solution at the rate of 50 + 5 t milliliters (mL) per second, where t is in seco

Alika [10]

Answer:

12,000

Step-by-step explanation:

The machine fills the containers at a rate of 50+5t milliliters (mL) per second.

Therefore, the rate of change of the number of containers, N is:

$\dfrac{dN}{dt}=50+5t, 0\leq t\leq 60$

$dN=(50+5t)dt\\$Taking integrals of both sides\\\int dN=\int (50+5t)dt\\N(t)=50t+\frac{5t^2}{2}+C $(C a constant of integration)\\\\When t=0, , No containers are filled, therefore:$ N(t)=0\\0=50(0)+\frac{5(0)^2}{2}+C\\C=0\\$Therefore, N(t)=50t+2.5t^2$

When t=60 seconds

$N(60)=50(60)+2.5(60)^2\\N(60)=12000$ mL$

Therefore, 12,000 milliliters of acid solution are put into a container in 60 seconds.

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2 years ago