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3 years ago

Given the two sets: A = {1, 2, 3} B = {3, 2, 1}

Mathematics

1 answer:

Aloiza [94]3 years ago

7 0

Answer:

Step-by-step explanation:

Given : A = { 1,2,3} B = { a,b,c} The Cartesian product of sets A and B is the set of all possible. hope that helps.

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Loren drove 200 miles at a certain rate, and his wife, Lois, drove 100 miles at a rate 10 mph slower. If Loren had driven for th

NeX [460]

As long as Loren drove, the law of motion was

$200 = st_1 \implies t_1 = \dfrac{200}{s}$

As long as Loid drove, the law of motion was

$100 = (s-10)t_2 \implies t_2 = \dfrac{100}{s-10}$

So, the total time they took is

$t_1+t_2=\dfrac{200}{s}+\dfrac{100}{s-10}$

Had Loren driven the whole time, the law of motion would have been

$300=st_3 \implies t_3 = \dfrac{300}{s}$

And we know that this time would have been 30 minutes (i.e. 0.5 hours) faster. So, we have

$t_3 = t_1+t_2-0.5$

This translates into

$\dfrac{300}{s}=\dfrac{200}{s}+\dfrac{100}{s-10}-\dfrac{1}{2}$

If we subtract 200/s from both sides, we have

$\dfrac{100}{s}=\dfrac{100}{s-10}-\dfrac{1}{2}$

We can simplify the right hand side by summing the two fractions:

$\dfrac{100}{s-10}-\dfrac{1}{2} = \dfrac{200-(s-10)}{2(s-10)}=\dfrac{210-s}{2(s-10)}$

So, we have to solve

$\dfrac{100}{s}=\dfrac{210-s}{2(s-10)}$

If we cross multiply the denominators, we have

$200(s-10)=s(210-s) \iff 200s-2000=210s-s^2 \iff s^2-10s-2000=0$

Which yields the solutions

$s=-40,\quad s=50$

We accept the positive solution, because the negative would mean to travel backwards, so Loren's rate was 50mph

5 0

3 years ago

Read 2 more answers

Find the perimeter of the figure

nalin [4]

Answer:

The perimeter is 66.9 units

Step-by-step explanation:

See the attached figure with letters to better understand the problem

step 1

In the right triangle ABD

<em>Find the length side AD</em>

$tan(33^o)=\frac{8}{AD}$ ----> by TOA (opposite side divided by the adjacent side)

$AD=\frac{8}{tan(33^o)}=12.3\ units$

Find the length side BD

$sin(33^o)=\frac{8}{BD}$ ---> by SOH (opposite side divided by the hypotenuse)

$BD=\frac{8}{sin(33^o)}=14.7\ units$

step 2

In the right triangle CDE

Find the length side CE

$cos(64^o)=\frac{CD}{CE}$ --> by CAH (adjacent side divided by the hypotenuse)

we have

$CD=BD/2=14.7/2=7.35\ units$

substitute

$CE=\frac{7.35}{cos(64^o)}=16.8\ units$

Find the length side DE

$tan(64^o)=\frac{DE}{CD}$ --> by TOA (opposite side divided by the adjacent side)

$DE=tan(64^o){7.35}=15.1\ units$

step 3

Find the perimeter of the figure

The perimeter is equal to

$P=AB+AD+BD+CE+DE$

substitute the values

$P=8+12.3+14.7+16.8+15.1=66.9\ units$

5 0

3 years ago

A telescope is regularly priced at $180, but is on sale for 25% off. What is the price after the discount and 5% sales tax??????

sashaice [31]

100-25=75
100+5=105

180*0.75*1.05=141.75

final price is $141.75

4 0

3 years ago

PLSSS HELPPP!!!<br> i don’t know

Alexxx [7]

Answer:

Volume of a sphere is 4/3(pi r ^3)

You were given d = 10 so r = 5

4 0

3 years ago

The area, a, of an ellipse can be determined using the formula a = πxy, where x and y are half the lengths of the largest and sm

Lisa [10]

The formula can also be proved using a trigonometric substitution . Each of above proofs will generalize to show that the volume of an ellipsoid with semi-axes A, B and C is just

(4/3)*Pi*A*B*C

6 0

3 years ago

Read 2 more answers