2 years ago

What is the gradient of the graph shown?

Mathematics

1 answer:

JulijaS [17]2 years ago

5 0

Answer:

Step-by-step explanation:

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Michelle wants to save $150 for a trip to Six Flags. If she saves $12 each week, how many weeks will it take her to save enough

valentina_108 [34]

12.5 weeks. You take the do 150 divided by 12 to get 12 in a half

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3 years ago

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Malcolm has $638.54 in his checking account. He must maintain a $500 balance to avoid a fee. He wrote a check for $159.50 today.

lubasha [3.4K]

Let any variable such as x represent the least amount of money that Malcolm needs to deposit. His balance from his checking account is $638.54. Subtract $159.50 from this amount.

With the condition that he must maintain $500, the inequality becomes,

(638.54 - 159.50) + x ≥ 500

479.04 + x ≥ 500

x ≥ 20.96

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3 years ago

Calculate the integral of f(x,y)=8x over the region  bounded above by y=x(2−x) and below by x=y(2−y).

Elden [556K]

Answer:

$\frac{1}{3}$

Step-by-step explanation:

Let's first find the intersection points.

$y = x(2-x)\\x = y(2-y)\\y = y(2-y)(2-y(2-y))\\x = x(2-x)(2-x(2-x))$

So intersection points for x = 0, 1 and for y = 0, 1.

Now, let's write x = y(2-y) instead of y.

$x - 1 = 2y - y^2 - 1\\x - 1 = -(y-1)^2\\1-x = (y-1)^2\\y = 1 - \sqrt{1-x}$

$\int_D f(x,y)dA=\int\limits^1_0[x(2-x)-(1-\sqrt{1-x})]dx=\\\\= (x^2-\frac{x^3}{3} -x-\frac{2}{3}(1-x)^{\frac{3}{2} } )|^1_0=-\frac{1}{3} +\frac{2}{3}= \frac{1}{3}$