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2 years ago

Which equation can be used to solve for x in the following diagram?

Mathematics

2 answers:

lions [1.4K]2 years ago

6 0

Answer:

Step-by-step explanation:

NNADVOKAT [17]2 years ago

6 0

Answer:

Step-by-step explanation:

to find the answer you have to set everything equal to 180

then simplify

then you get x

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1. The equation c = 2.95g shows how much it costs to buy gas at a gas station on a

Karolina [17]

Answer:

see the procedure

Step-by-step explanation:

we have

$c=2.95g$

where

c -----> the cost in dollars

g ----> the number gallons of gas purchased

1) For g=1 gal

substitute the value of g in the equation and solve for c

$c=2.95(1)$

$c=\$2.95$

The pair (1,2.95) fit the relationship

2) For g=3 gal

substitute the value of g in the equation and solve for c

$c=2.95(3)$

$c=\$8.85$

The pair (3,8.85) fit the relationship

3) For g=5 gal

substitute the value of g in the equation and solve for c

$c=2.95(5)$

$c=\$14.75$

The pair (5,14.75) fit the relationship

4) For c=$20.65

substitute the value of c in the equation and solve for g

$20.65=2.95g$

$g=20.65/2.95$

$g=7\ gal$

The pair (7,20.65) fit the relationship

7 0

2 years ago

Find the center of mass of the wire that lies along the curve r and has density =4(1 sin4tcos4t)

dolphi86 [110]

The mass of the wire is found to be 40π√2 units.

To calculate the mass of the wire which runs along the curve r ( t ) with the density function δ=5.

The general formula is,

Mass = $\int_a^b \delta\left|r^{\prime}(t)\right| d t$

To find, we must differentiate this same given curve r ( t ) with respect to t to estimate |r'(t)|.

The given integration limits in this case are a = 0, b = 2π.

Now, as per the question;

The equation of the curve is given as;

r(t) = (4cost)i + (4sint)j + 4tk

Now, differentiate this same given curve r ( t ) with respect to t.

$\begin{aligned}\left|r^{\prime}(t)\right| &=\sqrt{(-4 \sin t)^2+(4 \cos t)^2+4^2} \\&=\sqrt{16 \sin ^2 t+16 \cos ^2 t+16} \\&=\sqrt{16\left(\sin t^2+\cos ^2 t\right)+16}\end{aligned}$

Further simplifying;

$\begin{aligned}&=\sqrt{16(1)+16} \\&=\sqrt{16+16} \\&=\sqrt{32} \\\left|r^{\prime}(t)\right| &=4 \sqrt{2}\end{aligned}$

Now, use integration to find the mass of the wire;

$\begin{aligned}&=\int_a^b \delta\left|r^{\prime}(t)\right| d t \\&=\int_0^{2 \pi} 54 \sqrt{2} d t \\&=20 \sqrt{2} \int_0^{2 \pi} d t \\&=20 \sqrt{2}[t]_0^{2 \pi} \\&=20 \sqrt{2}[2 \pi-0] \\&=40 \pi \sqrt{2}\end{aligned}$