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Aleksandr-060686 [28]

3 years ago

13

Anita bought 3.74 ounces of chocolate. 0.81 ounces of it was milk chocolate and the rest was dark chocolate. How much dark choco

late did Anita buy? Add, subtract, multiply, and divide decimals: word problems

1 answer:

soldi70 [24.7K]3 years ago

7 0

Anita bought 2.93 ounces of dark chocolate. You’d get 2.93 by subtracting 0.81 from 3.74.

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Solve the equation. 3x + 5 = x - 3

Luden [163]

Answer:

x=-4

Step-by-step explanation:

Subtract x from 3x ( 2x )

2x+5=-3

Subtract 5 from -3 ( -8 )

2x=-8

Divide ( -4 )

x=-4

3 0

3 years ago

Distance between two ships At noon, ship A was 12 nautical miles due north of ship B. Ship A was sailing south at 12 knots (naut

frozen [14]

Answer:

a) $\sqrt{144-288t+208t^2}$ b.) -12knots, 8 knots c) No e) $4\sqrt{13}$

Step-by-step explanation:

We know that the initial distance between ships A and B was 12 nautical miles. Ship A moves at 12 knots(nautical miles per hour) south. Ship B moves at 8 knots east.

a)

We know that at time t , the ship A has moved $12\dot t (n.m)$ and ship B has moved $8\dot t (n.m)$ . We also know that the ship A moves closer to the line of the movement of B and that ship B moves further on its line.

Using Pythagorean theorem, we can write the distance s as:

$\sqrt{(12-12\dot t)^2 + (8\dot t)^2}\\s=\sqrt{144-288t+144t^2+64t^2}\\s=\sqrt{144-288t+208t^2}$

b)

We want to find $\frac{ds}{dt}$ for t=0 and t=1

$\sqrt{144-288t+208t^2}|\frac{d}{dt}\\\\\frac{ds}{dt}=\frac{1}{2\sqrt{144-288t+208t^2}}\dot (-288+416t)\\\\\frac{ds}{dt}=\frac{208t-144}{\sqrt{144-288t+208t^2}}\\\\\frac{ds}{dt}(0)=\frac{208\dot 0-144}{\sqrt{144-288\dot 0 + 209\dot 0^2}}=-12knots\\\\\frac{ds}{dt}(1)=\frac{208\dot 1-144}{\sqrt{144-288\dot 1 + 209\dot 1^2}}=8knots$

c)

We know that the visibility was 5n.m. We want to see whether the distance s was under 5 miles at any point.

Ships have seen each other = $s\leq 5\\\\\sqrt{144-288t+208t^2}\leq 5\\\\144-288t+208t^2\leq 25\\\\199-288t+208t^2\leq 0$

Since function $f(x)=199-288x+208x^2$ is quadratic, concave up and has no real roots, we know that $199-288x+208x^2>0$ for every t. So, the ships haven't seen each other.

d)

Attachedis the graph of s(red) and ds/dt(blue). We can see that our results from parts b and c were correct.

e)

Function ds/dt has a horizontal asympote in the first quadrant if

$\lim_{t \to \infty} \frac{ds}{dt}$

So, lets check this limit:

$\lim_{t \to \infty} \frac{ds}{dt}=\lim_{t \to \infty} \frac{208t-144}{\sqrt{144-288t+208t^2}}\\\\=\lim_{t \to \infty} \frac{208-\frac{144}{t}}{\sqrt{\frac{144}{t^2}-\frac{288}{t}+208}}\\\\=\frac{208-0}{\sqrt{0-0+208}}\\\\=\frac{208}{\sqrt{208}}\\\\=4\sqrt{13}$

Notice that:

$4\sqrt{13}=\sqrt{12^2+5^2}$ =√(speed of ship A² + speed of ship B²)

5 0

3 years ago

Please Help me!

hoa [83]

Answer:

domain (-4,infinity) range (negative infinity, infinity)

Step-by-step explanation:

The domain is the x axis. the x axis starts at -4 and keeps going meaning it goes to infinity. the range is the y axis. the range has no determined starting point or end point meaning it goes to negative infinity and positive infinity

8 0

3 years ago

What two numbers have a sum of -7 and a difference of 14?

Ksivusya [100]

Answer:

The sum of two numbers is 14 and their difference is 10

Step-by-step explanation:

"2 numbers (x and y)

x+y = 14

and x-y + 10

If you each equation by positive 2, one gets 2x+2y = 28 and 2x-2y = 20

The 'y-terms' cancel out or equal zero when adding, so 4x = 48, divide by 4 on each side and x or the first number equals 12.

Plug 12 back into the equation for 'x' and subtract 12 on both sides so that y=2

The difference of 12-2=10 and the addition of 12 and 2 equals 14"

hopes this helps

7 0

3 years ago

Read 2 more answers

Samuel has 52 marbles in a bag. Fourteen are red, 13 are green and 25 are blue. If a marble is chosen at random, what is the pro

lorasvet [3.4K]

.25
you can come to this conclusion by calculating 13/52

7 0

3 years ago