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3 years ago

Estimate the measurement of the angle formed by the clock. Assume that the hands are pointing directly at the numbers.

Mathematics

2 answers:

Deffense [45]3 years ago

5 0

I think the Answer is the third option 120

Romashka-Z-Leto [24]3 years ago

3 0

I hope this helps you

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Find the area that the curve encloses and then sketch it.<br> r = 3 + 8 sin(6)

Rudiy27

Answer:

$A=41\pi\: \text{units}^2\approxA\approx128.8053\:\text{units}^2$

Step-by-step explanation:

I assume you mean $r=3+8\sin\theta$ :

Use the formula $\displaystyle A=\int\limits^a_b \frac{1}{2} {r(\theta)^2} \, d\theta$ where $a$ and $b$ are the lower and upper bounds and $r(\theta)$ is the equation of the polar curve.

Since the graph is symmetrical about the line $\displaystyle \theta=\frac{\pi}{2}$ , let the bounds of integration be $\displaystyle \biggr(-\frac{\pi}{2},\frac{\pi}{2}\biggr)$ to find half the area of the curve, and then find twice of that area:

$\displaystyle A=\int\limits^a_b \frac{1}{2} {r(\theta)^2} \, d\theta\\\\A=2\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \frac{1}{2} {(3+8\sin\theta)^2} \, d\theta\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} 9+48\sin\theta+64\sin^2\theta \, d\theta\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} 9+48\sin\theta+64\biggr(\frac{1-\cos2\theta}{2} \biggr) \, d\theta\\\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} (9+48\sin\theta+32-32\cos2\theta) \, d\theta$

$\displaystyle A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} (41+48\sin\theta-32\cos2\theta) \, d\theta\\\\A=41\theta-48\cos\theta-16\sin2\theta\biggr|^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\$

$A=\biggr[41\biggr(\frac{\pi}{2}\biggr)-48\cos\biggr(\frac{\pi}{2}\biggr)-16\sin2\biggr(\frac{\pi}{2}\biggr)\biggr]-\biggr[41\biggr(-\frac{\pi}{2}\biggr)-48\cos\biggr(-\frac{\pi}{2}\biggr)-16\sin2\biggr(-\frac{\pi}{2}\biggr)\biggr]\\\\A=\biggr[\frac{41\pi}{2}-24\sqrt{2}\biggr]-\biggr[-\frac{41\pi}{2}+24\sqrt{2}\biggr]\\ \\A=41\pi\\\\A\approx128.8053$

Thus, the area of the curve is 41π square units. See below for a graph of the curve and its shaded area.

7 0

3 years ago

A submarine sandwich shop makes sandwiches with one kind of bread, one protein, one choice of cheese, and two vegetables. How ma

brilliants [131]

Answer:

480 different sandwiches

Step-by-step explanation:

To find how many sandwiches can be made, we need to find the number of possibilities for each choice: bread, protein, cheese, vegetables.

Bread: 3 types -> combination of 3 choose 1 -> 3

Protein: 4 types -> combination of 4 choose 1 -> 4

Cheese: 4 types -> combination of 4 choose 1 -> 4

Vegetables: 5 types -> combination of 5 choose 2 -> 5!/(3!*2!) = 5*4/2 = 10

So the number of different sandwiches is:

3 * 4 * 4 * 10 = 480

5 0

3 years ago

Show how you can use repeated subtraction to find 84 divided by 6

Lunna [17]

84-6-6-6-6-6-6-6-6-6-6-6-6-6-6=0 So 84÷6= 14

6 0

3 years ago

A man has 32 coins in his pocket, all of which are dimes and quarters. If the total value of his change is 545 cents, how many d

inn [45]

A dime is worth 10 cents and a quarter is worth 25 cents.

Let D be the number of dimes and Q be the number of quarters.

Since the total amount of coins in the pocket is 32, then:

$D+Q=32$

On the other hand, the total value of D dimes is 10D, while the total value of Q dimes is 25Q. Then, the total value of D dimes and Q cuarters is 10D+25Q, which must be equal to 545. Then:

$10D+25Q=545$

Notice that we have found a 2x2 system of equations:

$\begin{gathered} D+Q=32 \\ 10D+25Q=545 \end{gathered}$

Solve the system using the substitution method. To do so, isolate D from the first equation and replace the expression for D into the second equation to obtain a single equation in terms of Q:

$\begin{gathered} D+Q=32 \\ \Rightarrow D=32-Q \\ \\ 10D+25Q=545 \\ \Rightarrow10(32-Q)+25Q=545 \\ \Rightarrow320-10Q+25Q=545 \\ \Rightarrow25Q-10Q=545-320 \\ \Rightarrow15Q=225 \\ \Rightarrow Q=\frac{225}{15} \\ \\ \therefore Q=15 \end{gathered}$

Replace back Q=15 into the expression for D to find the amount of dimes:

$\begin{gathered} D=32-Q \\ =32-15 \\ =17 \end{gathered}$

Therefore, the amount of dimes that the man has is 17.

7 0

1 year ago

Solve this equation -3x - 8 = 18

Molodets [167]

8.67 (rounded to the nearest tenth)

6 0

3 years ago