How do you Evaluate 3f(2)

Diagonal cross-section of a sphere produces which two dimensional shape

Leni [432]

Every cross-section of a sphere will be a circle.

Answer: circle

Any further questions about this? Or how I got my answer?

7 0

2 years ago

Erik's disabled sailboat is floating stationary 3 miles east and 2 miles north of Kingston. A ferry leaves Kingston heading towa

sergij07 [2.7K]

Answer:

Step-by-step explanation:

Let's suppose that Ballard is an origin with coordinates (0;0)

Ballard is 8 miles south and 1 mile west of Edmonds ⇒ Edmonds is 1 mile east and 8 miles north of Ballard.

Thus, coordinates of Edmonds (0+1; 0+8) (1;8)

Edmonds is 6 miles due east of Kingston. So, is 6 miles due of Edmonds

Thus, Kingston coordinates (1-6;8) (-5:8)

Sailboat is 3 miles east and 2 miles north of kingston

So, coordinates of sailboat are (-5+3; 8+2) (-2;10)

a)

Ferry leaves Kingston towards Edmonds at mph and Edmonds is 6 miles due east of Kingston.

Initial ferry coordinates as calculated above are equal to Kingston coordinates (-5;8)

After 20 minutes the ferry turns to south.

This distance travelled (20min) is d=9mph*20/60h=3 miles

So, ferry travelled 3 miles toward east in 20 min

Then, coordinates became (-5+3;8+0) (-2;8)

Thus, we have a line connecting two points (-5;8) and (-2;8)

Line connecting them has an equation:

y-8 = (8-8)/(-2+5) * (x+5)

y-8=0

y=8 - This is the equation for the first 20 minutes of travel

Then, ferry turns due south (-2;8) and has a vertiacl line

The equation of verical line is x=a, so the equation will be x=2

b) The sailboat has a radar scope that will detect any object within 3 miles of the sailboat.

region looks like a circular disc with a center (-2;10)

(x+2)^2+(y-10)^2=3^2

(x+2)^2+(y-10)^2 <9 (interior of the circular disc)

(x+2)^2+(y-10)^2 >9 (exterior)

The equation of the line joining the Kingston and Edmonds is y=8

the point of intersection:

(x+2)^2+(8-10)^2=9

(x+2)^2=5

x is approximately 0.24; -4.24

(0.24;8) (-4.24;8) - intersection points

c) The ferry exits the radar during the trid due south long x=-2

The points of intersection of the circle and the line x=-2:

(-2+2)^2+(y-10)^2=9

0+(y-10)^2=0

y is 7.13

(-2;7)

d) Takes south turn at (-2;8), then ferry travels 0.8 miles up to point (-2;7) where it exists the radar zone

Speed is 9mph

The time taken to cover 1 mile = t=1/9hr=1/9 *60=6.667min

So, it exists after 6.67 minutes

e) Ferry enters at (-4.24;8) and takes turn due to south at (-2;8)

The distance travelled is = [-4.24+2]=2.24 miles

The time taken to cover these miles is = t=2.24/9 *60=14.93 min

After turning to south ferry remains in radar for 6.7 min

So, it remains in radar zone for 14.93+6.7=21.63min

8 0

2 years ago

A parabolic satellite dish reflects signals to the dish’s focal point. An antenna designer analyzed signals transmitted to a sat

ivolga24 [154]

Answer:

$c=\frac{16}{39}$

Step-by-step explanation:

The probability density function is :

$f(x)=c(1-\frac{1}{16}x^{2})$

With 0 < x < 3

To be a valid probability density function :

$\int\limits^b_a {f(x)} \,dx=1$

Where a < x < b

And also

f(x) ≥ 0 for a < x < b

Applying this to the probability density function of the exercise :

$\int\limits^3_0 {c(1-\frac{1}{16}x^{2})} \, dx=1$

$c\int\limits^3_0 {(1-\frac{1}{16}x^{2})} \, dx=1$

$c(3-\frac{1}{16}\frac{3^{3}}{3})=1$

$c(\frac{39}{16})=1$

$c=\frac{16}{39}$

We can verify by replacing ''c'' in the original probability density function and integrating :

$\int\limits^3_0 {\frac{16}{39}(1-\frac{1}{16}x^{2})} \, dx=$

$=\frac{16}{39}.(3)-\frac{1}{39}.(\frac{3^{3}}{3})=\frac{16}{13}-\frac{3}{13}=\frac{13}{13}=1$

Also, f(x) ≥ 0 for 0 < x < 3

4 0

2 years ago

Looking into the sky one night, Tori wondered how far into outer space she would get if she drove a car for 3.21 × 103 hours at

Westkost [7]

Answer:

$\large\boxed{\large\boxed{3\times 10^8meters}}$

Explanation:

One of the applications of scientific notation is to make estimations rounding the whole part of the numbers, i.e. the digits before the decimal point, to the nearest integer, and adding the exponents of the powers of base 10.

Here, you must estimate this product of two numbers written is scientific notation:

$(3.21\times 10^3)(1.13\times 10^5)$

Then, for an estimation you round 3.21 to 3 and 1.13 to 1, then multiply 3 × 1 = 3. That will be the coefficient of your new power of 10.

The power or exponent will be the sum of the powers of the numbers that are being multiplied, i.e. 3 + 5 = 8.

And the result is $3\times 10^8$

The unit is meters, so you write your answer as: $3\times 10^8meters$

5 0

2 years ago

Read 2 more answers

A 12 oz bottle of clean green dish soap is $1.09 while a 20 oz bottle cost 1.99 which is the better to buy

Jlenok [28]

The 12 oz

Step-by-step explanation:

The twelve ounce because if you buys two of them its 2.18 and youll have four more ounces for only 19 more cents than the 20oz

4 0

2 years ago

Read 2 more answers