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Answer:
a) k = 5; (-10, -35)
Step-by-step explanation:
Given:
Co-ordinates:
Pre-Image = (-12,3)
After dilation
Image = (-60,15)
The dilation about the origin can be given as :
Pre-Image
where represents the scalar factor.
We can find value of for the given co-ordinates by finding the ratio of
or
co-ordinates of the image and pre-image.
For the given co-ordinates.
Pre-Image = (-12,3)
Image = (-60,15)
The value of
or
As we get for both ratios i.e of
and
co-ordinates, so we can say the image has been dilated by a factor of 5 about the origin.
To find the image of (-2,-7), after same dilation, we will multiply the co-ordinates with the scalar factor.
Pre-Image Image
Pre-Image Image
(Answer)
Answer:
The volume required to fill the punch bowl till 1 inch from the top is 1385.44 inches³
Step-by-step explanation:
Total Height of the punch bowl = 10 inches
Diameter of the bowl = d = 14 inches
Since, radius is half of the diameter, the radius of the bowl would be = r = 7 inches.
The shape of punch bowl is given to be cylindrical and we have to find the volume of the bowl. The formula to calculate the volume of a cylinder is:
Here, h represents the height.
We have to find the volume to fill the bowl till 1 inch from the top. Since, the height of bowl is 10 inches, we have to fill it to 9 inches. Therefore, the value of height(h) which we will substitute in the formula will be 9. Using the values in the formula gives us:
This means, the volume required to fill the punch bowl till 1 inch from the top is 1385.44 inches³