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mafiozo [28]
3 years ago
12

What is the perimeter of the triangle? units

Mathematics
1 answer:
skelet666 [1.2K]3 years ago
8 0

Answer:

Perimeter = 30

Step-by-step explanation:

hypotenuse = \sqrt{5^2+12^2}

hypotenuse = \sqrt{25+144}

hypotenuse = \sqrt{169}

hypotenuse = 13

Perimeter = 5+12+13

Perimeter = 30

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A high rise building has a sink on the fourth floor located 2-feet above the floor. Each floor is 10-feet above the other. Calcu
kap26 [50]
The pressure at a certain height is the pressure at sea level plus the hydrostatic pressure.

P = 80 psi + ΔP
where
ΔP = ρgh
ρ is the density of water equal to 62.4 lbm/ft³
ΔP = (62.4 lbm/ft³)(1 lbf/lbm)(4*10 + 2 ft)(1 ft/12 in)² = 18.2 psi

Thus,
P = 80 + 18.2
<em>P = 98.2 psi</em>
8 0
4 years ago
Geometric Sequence S = 1.0011892 + ... + 1.0012 + 1.001 + 1
leva [86]

Answer:

<em />S_{1893} =5632.98<em />

<em />

Step-by-step explanation:

The correct form of the question is:

S = 1.001^{1892} + ... + 1.001^2 + 1.001 + 1

Required

Solve for Sum of the sequence

The above sequence represents sum of Geometric Sequence and will be solved using:

S_n = \frac{a(1 - r^n)}{1 - r}

But first, we need to get the number of terms in the sequence using:

T_n = ar^{n-1}

Where

a = First\ Term

a = 1.001^{1892}

r = common\ ratio

r = \frac{1}{1.001}

T_n = Last\ Term

T_n = 1

So, we have:

T_n = ar^{n-1}

1 = 1.001^{1892} * (\frac{1}{1.001})^{n-1}

Apply law of indices:

1 = 1.001^{1892} * (1.001^{-1})^{n-1}

1 = 1.001^{1892} * (1.001)^{-n+1}

Apply law of indices:

1 = 1.001^{1892-n+1}

1 = 1.001^{1892+1-n}

1 = 1.001^{1893-n}

Represent 1 as 1.001^0

1.001^0 = 1.001^{1893-n}

They have the same base:

So, we have

0 = 1893-n

Solve for n

n = 1893

So, there are 1893 terms in the sequence given.

Solving further:

S_n = \frac{a(1 - r^n)}{1 - r}

Where

a = 1.001^{1892}

r = \frac{1}{1.001}

n = 1893

So, we have:

S_{1893} =\frac{1.001^{1892} *(1 -\frac{1}{1.001}^{1893})}{1 -\frac{1}{1.001} }

S_{1893} =\frac{1.001^{1892} *(1 -\frac{1}{1.001}^{1893})}{\frac{1.001 -1}{1.001} }

S_{1893} =\frac{1.001^{1892} *(1 -\frac{1}{1.001}^{1893})}{\frac{0.001}{1.001} }

S_{1893} =\frac{1.001^{1892} *(1 -\frac{1}{1.001^{1893}})}{\frac{0.001}{1.001} }

Simplify the numerator

S_{1893} =\frac{1.001^{1892}  -\frac{1.001^{1892}}{1.001^{1893}}}{\frac{0.001}{1.001} }

S_{1893} =\frac{1.001^{1892}  -1.001^{1892-1893}}{\frac{0.001}{1.001} }

S_{1893} =\frac{1.001^{1892}  -1.001^{-1}}{\frac{0.001}{1.001} }

S_{1893} =(1.001^{1892}  -1.001^{-1})/({\frac{0.001}{1.001} })

S_{1893} =(1.001^{1892}  -1.001^{-1})*{\frac{1.001}{0.001}}

S_{1893} =\frac{(1.001^{1892}  -1.001^{-1}) * 1.001}{0.001}

Open Bracket

S_{1893} =\frac{1.001^{1892}* 1.001  -1.001^{-1}* 1.001 }{0.001}

S_{1893} =\frac{1.001^{1892+1}  -1.001^{-1+1}}{0.001}

S_{1893} =\frac{1.001^{1893}  -1.001^{0}}{0.001}

S_{1893} =\frac{1.001^{1893}  -1}{0.001}

S_{1893} =5632.97970294

Hence, the sum of the sequence is:

<em />S_{1893} =5632.98<em> ----- approximated</em>

4 0
3 years ago
I need to know the distance between the red river
zysi [14]

Answer:

B) 1.5

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
In 5 years, Dad will be three times as old as his daughter Jill will be then. If the sum of their present ages is 50, how old ar
Nataliya [291]
The answer is <span>b.3x + 15 = 55 - x
</span>
x - Jill's present age
y - dad's present age

<span>In 5 years, Dad will be three times as old as his daughter Jill will be then:
y + 5 = 3(x + 5)

</span><span>The sum of their present ages is 50:
x + y = 50

We have the system of two equations now:
</span>y + 5 = 3(x + 5)
x + y = 50

Let's rearrange the second equation:
If:         x + y = 50     
Then:  y = 50 - x

Now, substitute y from the second equation (y = 50 - x) into the first one:
y + 5 = 3(x + 5)
50 - x + 5 = 3(x + 5)
50 + 5 - x = 3*x + 3*5
55 - x = 3x + 15

Rearrange it a bit:
3x + 15 = 55 - x
Therefore, the correct choice is b.
5 0
3 years ago
Will the value of y ever equal 0 y=3^x
Evgesh-ka [11]
No x- intercept/ zero/ 0
6 0
3 years ago
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