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ipn [44]
3 years ago
7

Use synthetic division to determine f(-2) for the function f(x)=9x^3-18x^2-16x+32

Mathematics
1 answer:
Verizon [17]3 years ago
7 0

Answer: -80

Step-by-step explanation:

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The profile of the cables on a suspension bridge may be modeled by a parabola. The central span of the bridge is 1210 m long and
brilliants [131]

Answer:

The approximated length of the cables that stretch between the tops of the two towers is 1245.25 meters.

Step-by-step explanation:

The equation of the parabola is:

y=0.00035x^{2}

Compute the first order derivative of <em>y</em> as follows:

 y=0.00035x^{2}

\frac{\text{d}y}{\text{dx}}=\frac{\text{d}}{\text{dx}}[0.00035x^{2}]

    =2\cdot 0.00035x\\\\=0.0007x

Now, it is provided that |<em>x </em>| ≤ 605.

⇒ -605 ≤ <em>x</em> ≤ 605

Compute the arc length as follows:

\text{Arc Length}=\int\limits^{x}_{-x} {1+(\frac{\text{dy}}{\text{dx}})^{2}} \, dx

                  =\int\limits^{605}_{-605} {\sqrt{1+(0.0007x)^{2}}} \, dx \\\\={\displaystyle\int\limits^{605}_{-605}}\sqrt{\dfrac{49x^2}{100000000}+1}\,\mathrm{d}x\\\\={\dfrac{1}{10000}}}{\displaystyle\int\limits^{605}_{-605}}\sqrt{49x^2+100000000}\,\mathrm{d}x\\\\

Now, let

x=\dfrac{10000\tan\left(u\right)}{7}\\\\\Rightarrow u=\arctan\left(\dfrac{7x}{10000}\right)\\\\\Rightarrow \mathrm{d}x=\dfrac{10000\sec^2\left(u\right)}{7}\,\mathrm{d}u

\int dx={\displaystyle\int\limits}\dfrac{10000\sec^2\left(u\right)\sqrt{100000000\tan^2\left(u\right)+100000000}}{7}\,\mathrm{d}u

                  ={\dfrac{100000000}{7}}}{\displaystyle\int}\sec^3\left(u\right)\,\mathrm{d}u\\\\=\dfrac{50000000\ln\left(\tan\left(u\right)+\sec\left(u\right)\right)}{7}+\dfrac{50000000\sec\left(u\right)\tan\left(u\right)}{7}\\\\=\dfrac{50000000\ln\left(\sqrt{\frac{49x^2}{100000000}+1}+\frac{7x}{10000}\right)}{7}+5000x\sqrt{\dfrac{49x^2}{100000000}+1}

Plug in the solved integrals in Arc Length and solve as follows:

\text{Arc Length}=\dfrac{5000\ln\left(\sqrt{\frac{49x^2}{100000000}+1}+\frac{7x}{10000}\right)}{7}+\dfrac{x\sqrt{\frac{49x^2}{100000000}+1}}{2}|_{limits^{605}_{-605}}\\\\

                  =1245.253707795227\\\\\approx 1245.25

Thus, the approximated length of the cables that stretch between the tops of the two towers is 1245.25 meters.

7 0
3 years ago
Write the first five terms of the geometric sequence in which a1=64 and the common ratio is 5/4
natita [175]

Remember that finding terms in a geometric sequence is done by multiplying the previous term by a common ratio r. For example, we can say:

a_2 = a_1 r

a_3 = a_2 r = (a_1 r)r = a_1 r^2


We have a_1 = 64. To find a_2, let's multiply this term by \frac{5}{4}:

a_2 = 64 \cdot \frac{5}{4} = 80


Now, let's use this to find all of our other terms:

a_3 = 80 \cdot \frac{5}{4} = 100

a_4 = 100 \cdot \frac{5}{4} = 125

a_5 = 125 \cdot \frac{5}{4} = \frac{625}{4}


Thus, our terms are 64, 80, 100, 125, and (625/4).

8 0
3 years ago
When the turnpike littered the toll, traffic increased from 1,500 cars per day to 2,700
umka21 [38]

Answer:

  80%

Step-by-step explanation:

The percentage change between two numbers can be calculated as ...

  percentage change = ((new value)/(old value) -1) × 100%

  = (2700/1500 -1) × 100% = (1.80 -1) × 100% = 80%

Traffic volume increased 80%.

6 0
4 years ago
Help please!<br> please make the answers original.
baherus [9]

Answer:

I will do it but what is the GCF of part B

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
I need help plz find m M
Firlakuza [10]

Answer:

60°

I think that answer

8 0
3 years ago
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