Solve for x: 7x = 63

Mathematics

2 answers:

elena55 [62]3 years ago

4 0

Answer:

x = 9

Step-by-step explanation:

7x = 63

Divide each side by 7 to isolate x

7x/7 = 63/7

x = 9

shutvik [7]3 years ago

4 0

Answer: x = 9

Step-by-step explanation: To solve for x in this equation, we want to get x by itself on the left side of the equation.

Since x is being multiplied by 7, to get x by itself, we need to divide by 7 on the left side of the equation. Since we divided by 7 on the left side, we must also divide by 7 on the right side. On the left side, notice that the 7's cancel out so we're simply left with x. On the right side we have 63 divided by 7 which is 9 so we have x = 9.

Finally, remember to check your answer by substituting a 9 back into the original equation. So we have 7(9) = 63 which is a true statement.

So our answer, x = 9, is correct.

I have attached my work in the image below.

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Use the mid-point rule with n = 4 to approximate the area of the region bounded by y = x3 and y = x. (10 points)

USPshnik [31]

See the graph attached.

The midpoint rule states that you can calculate the area under a curve by using the formula:
$M_{n} = \frac{b - a}{2} [ f(\frac{x_{0} + x_{1} }{2}) + f(\frac{x_{1} + x_{2} }{2}) + ... + f(\frac{x_{n-1} + x_{n} }{2})]$

In your case:
a = 0
b = 1
n = 4
x₀ = 0
x₁ = 1/4
x₂ = 1/2
x₃ = 3/4
x₄ = 1

Therefore, you'll have:
$M_{4} = \frac{1 - 0}{4} [ f(\frac{0 + \frac{1}{4} }{2}) + f(\frac{ \frac{1}{4} + \frac{1}{2} }{2}) + f(\frac{\frac{1}{2} + \frac{3}{4} }{2}) + f(\frac{\frac{3}{4} + 1} {2})]$
$M_{4} = \frac{1}{4} [ f(\frac{1}{8}) + f(\frac{3}{8}) + f(\frac{5}{8}) + f(\frac{7}{8})]$

Now, to evaluate your f(x), you need to look at the graph and notice that:
f(x) = x - x³

Therefore:
$M_{4} = \frac{1}{4} [(\frac{1}{8} - (\frac{1}{8})^{3}) + (\frac{3}{8} - (\frac{3}{8})^{3}) + (\frac{5}{8} - (\frac{5}{8})^{3}) + (\frac{7}{8} - (\frac{7}{8})^{3})]$

$M_{4} = \frac{1}{4} [(\frac{1}{8} - \frac{1}{512}) + (\frac{3}{8} - \frac{27}{512}) + (\frac{5}{8} - \frac{125}{512}) + (\frac{7}{8} - \frac{343}{512})]$

M₄ = 1/4 · (2 - 478/512)
= 0.2666

Hence, the area of the region bounded by y = x³ and y = x is approximately 0.267 square units.