All categories

3 years ago

14. The two triangles below are similar. What is the length, in inches, of DE?

Mathematics

1 answer:

Ierofanga [76]3 years ago

4 0

18 2/3

Explanation:
The proportion is 3/4 just divide 14 by 0.75 (3/4) or whatever the proportion is in any problem like this to get the answer

You might be interested in

Use a half-angle identity to find the exact value of sinPi/8

stellarik [79]

Answer:

sin(π/8) = (1/2)√(2-√2)

Step-by-step explanation:

Using the half-angle formula ...

$\sin{\dfrac{\theta}{2}}=\sqrt{\dfrac{1-\cos{\theta}}{2}}$

We can let θ = π/4 and simplify the result as follows:

$\sin{\dfrac{\pi}{8}}=\sqrt{\dfrac{1-\cos{(\pi/4)}}{2}}=\sqrt{\dfrac{1-\dfrac{\sqrt{2}}{2}}{2}}=\sqrt{\dfrac{2-\sqrt{2}}{4}}\\\\=\boxed{\dfrac{1}{2}\sqrt{2-\sqrt{2}}}}$

5 0

3 years ago

Read 2 more answers

What is f(x) + f(x) + f(x)?

siniylev [52]

its 3f(x) i just answered it

5 0

4 years ago

Find the length of the curve given by ~r(t) = 1 2 cos(t 2 )~i + 1 2 sin(t 2 ) ~j + 2 5 t 5/2 ~k between t = 0 and t = 1. Simplif

xxMikexx [17]

Answer:

The length of the curve is

L ≈ 0.59501

Step-by-step explanation:

The length of a curve on an interval a ≤ t ≤ b is given as

L = Integral from a to b of √[(x')² + (y' )² + (z')²]

Where x' = dx/dt

y' = dy/dt

z' = dz/dt

Given the function r(t) = (1/2)cos(t²)i + (1/2)sin(t²)j + (2/5)t^(5/2)

We can write

x = (1/2)cos(t²)

y = (1/2)sin(t²)

z = (2/5)t^(5/2)

x' = -tsin(t²)

y' = tcos(t²)

z' = t^(3/2)

(x')² + (y')² + (z')² = [-tsin(t²)]² + [tcos(t²)]² + [t^(3/2)]²

= t²(-sin²(t²) + cos²(t²) + 1 )

................................................

But cos²(t²) + sin²(t²) = 1

=> cos²(t²) = 1 - sin²(t²)

................................................

So, we have

(x')² + (y')² + (z')² = t²[2cos²(t²)]

√[(x')² + (y')² + (z')²] = √[2t²cos²(t²)]

= (√2)tcos(t²)

Now,

L = integral of (√2)tcos(t²) from 0 to 1

= (1/√2)sin(t²) from 0 to 1

= (1/√2)[sin(1) - sin(0)]

= (1/√2)sin(1)

≈ 0.59501

8 0

3 years ago

What number is 15% of 43

Annette [7]

Step-by-step explanation:

So when a question asks what is x% of the y number. It's asking you to convert the x into decimal form by dividing by 100 and then multiply it by y. This gives you the equation: $y * \frac{x}{100}$ which gives you x% of y. so 15% of 43 is $43 * \frac{15}{100} = 6.45$ . 43% of 300 is $300 * \frac{43}{100} = 129$ .

the 12% of what number is 43 is a bit more tricky. It's asking you to instead find a number in which 12% of it is equal to 43. So instead of plugging solving for the percentage (which is already given) you solve for y. This gives you the following equation: $y * \frac{12}{100} = 43$ . Now all you do is calculate 12/100 which gives you $y * 0.12 = 43$ . now divide both sides by 0.12 to solve for y. This gives you $y = 358.\overline{33}$

43 is what percent of 106? This question is also a bit tricky, but instead of solving for y, you're solving for x. So plug in the known values, which gives you the equation: $106 * \frac{x}{100} = 43$ . Divide both sides by 106 to get $\frac{x}{100} \approx 0.406$ and now multiply both sides by 100. this gives you $x \approx 40.57$ which is the answer 40.57%

What percent of 43 is 6. This is asking the same thing just in a different way. So percentage = unknown, entire number = 43, entire number * percentage = 6. With these values we get the equation: $43 * \frac{x}{100} = 6$ . Divide both sides by 43 to get $\frac{x}{100} \approx 0.140$ now multiply by 100 to get $x \approx 13.95$ which is the answer 13.95%

7 0

2 years ago

8 – 5x = -4............

weeeeeb [17]

Answer:

8 - 5x = -4

x = 12/5 (Decimal: x = 2.4)

7 0

3 years ago