Answer:
yeah
Step-by-step explanation:
Answer:
Do C and D (Option 3 + 4)
Answer:
6. C. 16.64 km
7. B. P 216.00
8. B. P 565 425
9. C. 0.27
10. D. 24.6875
11. B. 3 kg
12. B. ratio
13. A. Proportion
14. D. 6:10
15. B. 2:3
Step-by-step explanation:
6. Mr. Bernard travels 5.12 km per hour on his bike. How far can he travel in 3.25 hours?
Speed = 5.12km/hr
Time = 3.25 hr
To find the distance;
Distance = speed * time
Distance = 5.12 * 3.25
Distance = 16.64 km
7. Mrs. Allysa purchased 48 pencils at P 4.50 each. How much did she pay for all the pencils?
Quantity = 48 pencils
Cost price = P 4.50
To find the total selling price;
Total = quantity * cost price
Total = 48 * 4.50
Total = P 216
8. The Villaroel family bought a 125.65 square meter lot at P 4500.00 per square meter. How much did they
pay?
Quantity = 125.65 m²
Cost price = P 4500
Total price = 125.65 * 4500
Total price = P 565425
9. What is 2.7/10 = 0.27
10. What is 98.75/4 = 24.6875
11. A store owner has 63 kilograms of candy. If she puts the candy into 21 jars, how much candy will each jar
contain?
Mass = 63 kg
Amount = 21 jars
Each jar = 63/21 = 3 kg
12. Ratio: It is the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.
13. Proportion: It is a statement that two ratios are equal.
14. What ratio is equal to 3:5?
We would multiply both ratio by 2
3:5 * 2 = 6:10
15. What ratio is proportional to 4:6?
We would divide both ratio by 2
4:6 / 2 = 2:3
Ugh, these questions.
21x^3y^4 + 15x^2y^2 - 12xy^3
3xy^2 (7x^2y^2 + 5x - 4y)
Clearing up clutter...
3xy² (7x²y² + 5x - 4y)
That's your answer. Thanks for working my brain. ;)
Answer:
V = (About) 22.2, Graph = First graph/Graph in the attachment
Step-by-step explanation:
Remember that in all these cases, we have a specified method to use, the washer method, disk method, and the cylindrical shell method. Keep in mind that the washer and disk method are one in the same, but I feel that the disk method is better as it avoids splitting the integral into two, and rewriting the curves. Here we will go with the disk method.
![\mathrm{V\:=\:\pi \int _a^b\left(r\right)^2dy\:},\\\mathrm{V\:=\:\int _1^3\:\pi \left[\left(1+\frac{2}{y}\right)^2-1\right]dy}](https://tex.z-dn.net/?f=%5Cmathrm%7BV%5C%3A%3D%5C%3A%5Cpi%20%5Cint%20_a%5Eb%5Cleft%28r%5Cright%29%5E2dy%5C%3A%7D%2C%5C%5C%5Cmathrm%7BV%5C%3A%3D%5C%3A%5Cint%20_1%5E3%5C%3A%5Cpi%20%5Cleft%5B%5Cleft%281%2B%5Cfrac%7B2%7D%7By%7D%5Cright%29%5E2-1%5Cright%5Ddy%7D)
The plus 1 in '1 + 2/x' is shifting this graph up from where it is rotating, but the negative 1 is subtracting the area between the y-axis and the shaded region, so that when it's flipped around, it becomes a washer.
![V\:=\:\int _1^3\:\pi \left[\left(1+\frac{2}{y}\right)^2-1\right]dy,\\\\\mathrm{Take\:the\:constant\:out}:\quad \int a\cdot f\left(x\right)dx=a\cdot \int f\left(x\right)dx\\=\pi \cdot \int _1^3\left(1+\frac{2}{y}\right)^2-1dy\\\\\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx\\= \pi \left(\int _1^3\left(1+\frac{2}{y}\right)^2dy-\int _1^31dy\right)\\\\](https://tex.z-dn.net/?f=V%5C%3A%3D%5C%3A%5Cint%20_1%5E3%5C%3A%5Cpi%20%5Cleft%5B%5Cleft%281%2B%5Cfrac%7B2%7D%7By%7D%5Cright%29%5E2-1%5Cright%5Ddy%2C%5C%5C%5C%5C%5Cmathrm%7BTake%5C%3Athe%5C%3Aconstant%5C%3Aout%7D%3A%5Cquad%20%5Cint%20a%5Ccdot%20f%5Cleft%28x%5Cright%29dx%3Da%5Ccdot%20%5Cint%20f%5Cleft%28x%5Cright%29dx%5C%5C%3D%5Cpi%20%5Ccdot%20%5Cint%20_1%5E3%5Cleft%281%2B%5Cfrac%7B2%7D%7By%7D%5Cright%29%5E2-1dy%5C%5C%5C%5C%5Cmathrm%7BApply%5C%3Athe%5C%3ASum%5C%3ARule%7D%3A%5Cquad%20%5Cint%20f%5Cleft%28x%5Cright%29%5Cpm%20g%5Cleft%28x%5Cright%29dx%3D%5Cint%20f%5Cleft%28x%5Cright%29dx%5Cpm%20%5Cint%20g%5Cleft%28x%5Cright%29dx%5C%5C%3D%20%5Cpi%20%5Cleft%28%5Cint%20_1%5E3%5Cleft%281%2B%5Cfrac%7B2%7D%7By%7D%5Cright%29%5E2dy-%5Cint%20_1%5E31dy%5Cright%29%5C%5C%5C%5C)
Our exact solution will be V = π(4In(3) + 8/3). In decimal form it will be about 22.2 however. Try both solution if you like, but it would be better to use 22.2. Your graph will just be a plot under the curve y = 2/x, the first graph.
