Answer:
A). Surface area = 222 cm²
Volume = 180 cm³
B). Surface area = 375 cm²
Volume = 360 cm³
C). % increase in surface area = 67.57%
% increase in volume = 100%
Step-by-step explanation:
In the figure attached base of a prism has been given.
A). Surface area of the prism = (Perimeter of the base of the prism) × height + 2(area of the base)
Perimeter of the base = 5 + 3 + 2 + 2 + 2 + 3 + 5 + 8
= 30
Area of the base = 8×5 - 2×2 = 36 cm²
Surface area of the prism = 30×5 + 2×(36)= 222 cm²
Volume of the prism = volume of the bigger prism - volume of the smaller prism cut off
= 8×5×5 - 2×2×5
= 200 - 20
= 180 cm³
B). Surface area of the prism if it's height is 10 cm,
Surface area = 30×10 + 2×(36) = 372 cm²
Volume of the prism = 8×5×10 - 2×2×10
= 400 - 40
= 360 cm³
C). Increase in surface area = 372 - 222 = 150 cm²
% increase in the surface area = 
= 67.57%
Increase in volume = 360 - 180 = 180 cm³
% increase in volume = 
= 100%
Answer:
2.34 grams
Step-by-step explanation:
In this problem, we need to find how many grams in 2.34mL. To solve the problem, we must know the relationship between grams and millilitre.
We know that,
1 milliitre = 1 gram
Hence,
2.34 mL = 2.34 grams.
Answer:
The correct option is D.
Step-by-step explanation:
The given graph is the graph of a cosine function, which shifts 1 unit left.
The cosine function is defined as
Where, a is amplitude, b is frequency, c is phase shift and d is vertical shift.
If c>0, then the graph shifts c units left and if c<0, then the graph shifts c units right.
Since the graph show only phase shift and the graph shifts only one unit left, therefore required function is
Option D is correct.
Answer:
Step-by-step explanation:
The easiest and most proper way to approach this task is to combine like terms inside parentheses: (24x + 7 – 12x) => (12x + 7).
Then (1/4)(24x + 7 – 12x) = (1/4)(12x + 7). This is an acceptable answer. There is the option of carrying out the multiplication, which results in
3x + 7/4, which is another acceptable answer.
Answer:
(1.2, –4.7)
Step-by-step explanation:
Since in the question it is mentioned that on the plane of coordinate, a line is made from point A (7,-2) to point B(-8,-9)
Also, the ratio of A to B is 5:8
Based on this, the x and y coordinates at point C is
![= [\frac{5\times (-8) + 8\times 7}{5 + 8} , \frac{5\times (-9) + 8\times -2}{5 + 8}]\\\\= [\frac{16}{3}, \frac{-61}{13}]](https://tex.z-dn.net/?f=%3D%20%5B%5Cfrac%7B5%5Ctimes%20%28-8%29%20%2B%208%5Ctimes%207%7D%7B5%20%2B%208%7D%20%2C%20%5Cfrac%7B5%5Ctimes%20%28-9%29%20%2B%208%5Ctimes%20-2%7D%7B5%20%2B%208%7D%5D%5C%5C%5C%5C%3D%20%5B%5Cfrac%7B16%7D%7B3%7D%2C%20%5Cfrac%7B-61%7D%7B13%7D%5D)
= (1.2, –4.7)
Hence, the x and y coordinates of point C is (1.2, –4.7)
Therefore the last option is correct
