What is the length of the missing leg?

Mathematics

1 answer:

Dmitry [639]2 years ago

7 0

Answer: b = 8

Step-by-step explanation:

Use the Pythagorean theorem

A square + B square = C square

C square - A square = B square

C square - B square = A square

10 - 6 = b --Square it

100 - 36 = 64 (square root)

64 = 8

b = 8 miles

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Use CALCULUS to find coordinates of the turning point on C.

antiseptic1488 [7]

Oi

Just calculating the differential. Step by step:

$y=12 \sqrt{x} -x \frac{3}{2}-10 \\ \\ y=12x^{ \frac{1}{2} } -x \frac{3}{2}-10 \ \ \ \boxed{transform \ \sqrt{x} =x^{ \frac{1}{2} }} \\ \\ Differentiating \\ \\ y'=12. \frac{1}{2}.x^{ \frac{1}{2}-1 } -1.x^{1-1}. \frac{3}{2}-0 \\ \\ y'=6.x^{ -\frac{1}{2} } -x^{0}. \frac{3}{2} \\ \\ y'=6. \frac{1}{x^{ \frac{1}{2} }} -1. \frac{3}{2} \\ \\ \boxed{y'=\frac{6}{ \sqrt{x} } -\frac{3}{2}}$

If you want to know where the tangent has no slope:

$\frac{6}{ \sqrt{x} } - \frac{3}{2} =0 \\ \\ \frac{6}{ \sqrt{x} } = \frac{3}{2} \\ \\ 3 \sqrt{x} =12 \\ \\ \sqrt{x} = \frac{12}{3} \\ \\ \sqrt{x} =4 \\ \\ (\sqrt{x})^2 =4^2 \\ \\ x=16$

3 0

2 years ago

Help please Factorise x²-x-56 its due in 4 minutes

Iteru [2.4K]

Answer:

(x-8)(x+7)

Step-by-step explanation:

using quadratic formula we have

x= $\frac{-b+-\sqrt{b^{2}-4*a*c}}{2*a}$