I NEED HELP ASAP PLEASE!!! THIS IS EXTREMELY URGENT! I WILL MARK BRAINLIEST!

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

PLS HELP CAN’T FIGURE OUT HOW TO FIND b OR c ASAPPPPPPPPP

natita [175]

Answer:

b = 0.35 ; c = 2.03

Step-by-step explanation:

tan = opposite/hypotenuse

Therefore, tan (10) = b/2

b = 2 tan (10) = about 0.35

Use the Pythagorean theorem to find that c = 2.03

5 0

2 years ago

Find x such that 3^x = 27 mod 32 (b)

gregori [183]

Answer:

The value of x is 11.

Step-by-step explanation:

Consider the provided information.

It is given that $3^x = 27 mod\ 32$

We know that:

$3^4=81$

Now if we divide the number 81 with 32 it will gives us remainder 17.

This can be written as:

$3^4\equiv 17(mod\ 32)$

Now use the property: $a^n\equiv b^n(mod\ m)$

$(3^4)^2\equiv 17^2(mod\ 32)$

17²=289, if we divide 289 with 32 it will gives us remainder 1, thus.

$3^8\equiv 1(mod\ 32)$

Multiply both the sides by 3³.

$3^8\times 3^3\equiv 3^3(mod\ 32)$

$3^{11}\equiv 27(mod\ 32)$

Hence, the value of x is 11.

7 0

4 years ago

Will give brainly

notsponge [240]

1000 times becuaee there are 1000 meters in a kilometer

3 0

4 years ago

Melissa and Tomas are playing a game with complex numbers. If Melissa has a score of 5-4i and Tomas has a score of 3+2i, what is

Gemiola [76]

8-2i is their total score. You can't combine the imaginary numbers and real numbers.

3 0

3 years ago

Read 2 more answers