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3 years ago

I'LL GIVE BRAINLIEST HELP

Mathematics

1 answer:

sesenic [268]3 years ago

8 0

Answer:

a. O = h - 40

b. 0, 4, 8, 12

Step-by-step explanation:

Let numver of overtime hours Jim workes for defined by O.

Standard working hours in a week for Jim = 40 Hours

If Jim is working for h hours then number of overtime hours will be given as difference between total hours he worked and standard working hours in a week.

⇒ O = h - 40

now, if jim has worked for 40, 44, 48 and 52 hours then his over time for all these cases will be

O = 40 - 40 = 0 Hours

O = 44 - 40 = 4 Hours

O = 48 - 40 = 8 Hours

O = 52 - 40 = 12 Hours respectively.

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If an orange seller bought 5 dozen oranges at the rate of tk.60 per four and sold them at the rate of tk50 per four,how much did

hodyreva [135]

Answer:

tk 30

Step-by-step explanation:

5 dozen = 5 * 12 = 60 oranges

12/4 = 3

total cost = 60 * 3 = tk.180

total sell = 50 * 3 = tk 150

total lose = 180 - 150 = tk 30

7 0

3 years ago

Find the area that the curve encloses and then sketch it. 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

0.04 with 4 repeating as a fraction. Not the 04 repeating just the 4 is repeating. What is the answer???

Dmitriy789 [7]

Answer:

2/45

Step-by-step explanation:

0.04... is the same as 0.1 * 0.4... because we are moving it up a decimal place, it's the same as multiplying by ten: we needed to multiply by a tenth to cancel that out. 0.4... is the same as 4/9 and 0.1 is the same as 1/10. We can rewrite the expression above as: $(\frac{1}{10} )(\frac{4}{9} )$ . Multiplying the two fractions results in 4/90 which can be simplified to 2/45.