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3 years ago

If one leg of a right triangle is 6 units and the other leg is 8 units, what is the length of the hypotenuse?

Mathematics

2 answers:

natulia [17]3 years ago

6 0

The answer I believe is 10?

ArbitrLikvidat [17]3 years ago

5 0

Answer: The length of the hypotenuse is 10 units.

Step-by-step explanation: If we use the Pythagorean theorem, we can figure out that 6 squared plus 8 squared equals 100. The square root of 100 is 10, so that is the length of the hypotenuse.

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A customer left a 15% tip for a meal that cost $64. What was the total amount the customer paid for the meal and tip?

Inessa05 [86]

Answer:

73.6

Step-by-step explanation:

64x15%=9.6

9.6+64=73.6

4 0

2 years ago

If f (n)(0) = (n + 1)! for n = 0, 1, 2, , find the taylor series at a=0 for f.

Pie

Given that $f^{(n)}(0)=(n+1)!$ , we have for $f(x)$ the Taylor series expansion about 0 as

$f(x)=\displaystyle\sum_{n=0}^\infty\frac{(n+1)!}{n!}x^n=\sum_{n=0}^\infty(n+1)x^n$

Replace $n+1$ with $n$ , so that the series is equivalent to

$f(x)=\displaystyle\sum_{n=1}^\infty nx^{n-1}$

and notice that

$\displaystyle\frac{\mathrm d}{\mathrm dx}\sum_{n=0}^\infty x^n=\sum_{n=1}^\infty nx^{n-1}$

Recall that for $|x|$ , we have

$\displaystyle\sum_{n=0}^\infty x^n=\frac1{1-x}$

which means

$f(x)=\displaystyle\sum_{n=1}^\infty nx^{n-1}=\frac{\mathrm d}{\mathrm dx}\frac1{1-x}$
$\implies f(x)=\dfrac1{(1-x)^2}$

5 0

2 years ago

Explain why triangle abc is similar to triangle ade.

mihalych1998 [28]

Answer:

They are both right triangles

Step-by-step explanation:

The triangles are both the same shape but one is bigger than the other.

5 0

3 years ago

During his high school football career a running back averaged 81 yards/game with a standard

hodyreva [135]

The answer is ym=b your welcome

4 0

2 years ago

O, R and S are points in the same horizontal plane. /OR/ = 20m and /OS/= 32m.The bearing of R and S from O are 030° and 135° res

Viktor [21]

<h3>Answer: roughly 12.6274 meters</h3>

The more accurate value is 12.6274169979696, though it's not fully exact.

Round this however you need to.

The exact distance 32*sin(45) - 10 meters.

===========================================================

Explanation:

Refer to the diagram below.

I'll use point A in place of point O since the letter 'oh' is very similar looking to the number zero.

Plot point A at the origin (0,0). While at point A, look directly north. Then turn 30 degrees eastward to look at the bearing 030°. Next, move 20 meters along that bearing direction to arrive at point R. Segment AR is 20 meters long.

In the diagram, note how angle RAB is 30 degrees. The side opposite this is BR = m.

We can use the sine ratio to say that

sin(angle) = opposite/hypotenuse

sin(A) = BR/AR

sin(30) = m/20

m = 20*sin(30)

m = 10

-----------------------------------

While still at point A, look directly north and turn 135 degrees clockwise (ie toward the east) and move 32 meters along that bearing. You'll arrive at point S as the diagram shows.

Notice how

angle RAB + angle RAC + angle CAS = 30+60+45 = 135

The remaining angle DAS is 180-135 = 45 degrees.

When focusing on triangle DAS, we can say

sin(A) = DS/AS

sin(45) = n/32

n = 32*sin(45)

n = 22.6274169979696

This value is approximate.

----------------------------------

Subtract the values of m and n

n - m = 32*sin(45) - 10 = exact distance

n - m = 22.6274169979696 - 10

n - m = 12.6274169979696

n - m = 12.6274 = approximate distance

Round it however you need to. I'm choosing to round to four decimal places.

So we see that point S is roughly 12.6274 meters east of point R.

If your teacher wants the exact distance, then stick with 32*sin(45)-10.

8 0

2 years ago