Answer:
4/1
Step-by-step explanation:
Answer:
(x, y) ⇒ (2x, 2y)
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Dilation is the increase or decrease in size of a figure. If a figure with point A(x, y) is dilated by a scale factor of k, the new location is at A'(kx, ky). If k > 1, it is an enlargement and if k < 1, it is a reduction.
Given that the inner circle has a radius of 1 r and the outer one has a radius of 2 r. To map the inner circle onto the outer circle, the inner circle would need to be enlarged. The scale factor is:
k = outer circle radius / inner circle radius = 2r / 1r = 2
A dilation with a scale factor of 2 would be needed to map the inner circle onto the outer circle.
That is:
(x, y) ⇒ (kx, ky)
1)Rewrite the table:
70, 49, 34.3, 24.01, 11.807
2) write the quotient of each number by the number before & notice the value:
49/70= 0.7
34.3/49 = 0.7
24.01/34.3 =0.7
16.0807/24.01 = 0.67 ≈0.7
You notice this is a geometric progression with r 0.7
The last term in a GP =ar^(n-1)
a=70; r= 0.7 n-1= number of terms (days -1)
For last term = 1 ==> then 1=70(0.7)^(n-1)
1/70 = (0.7)^(n-1)
log(1/70) =log[(0.7)^(n-1) ==> log1 - log 70 = (n-1) log(0.7) & you will find that it need 11.92 days to equal on & to be less than it will necessitate 12 Days
3) Domain and Range of this function:
Last term = a₁.rⁿ⁻¹. let last term be y==> f(n) = y =70(0.7)ⁿ⁻¹
or f(n) = y = 70(0.7)ⁿ / 0.7==> f(n) = [(0.7)ⁿ ]/ 100.
This is a decreasing exponential function where the coefficient
raised to n is < 1.
The domain is for all n>= 0.
When n→∞, f(n)→0; For n=0==>f(n) =70. So the range of f(n) is:<=70
Answer:
the third table
Step-by-step explanation:
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1) The sculptor created a marble basin with an approximate volume of 94,509.6 cubic centimeters - Option D, 2) The approximate area of the heart-shaped cake is 283 square inches - Option B, 3) The length of the wooden frame around the window is 94.3 inches - Option B.
In this question we should make use of geometric formulas for volumes and areas and key information from statement in order to find the right choices.
1) In this case, the volume occupied by the marble water basin (), in cubic centimeters, by subtracting the volume of the hemisphere from the volume of the cylinder:
(1)
Where:
- - Radius of the cylinder, in centimeters.
- - Height of the cylinder, in centimeters.
- - Radius of the cylinder, in centimeters.
If we know that , and , then the volume of the marble is:
The right choice is D.
2) To determine the approximate surface area of the cake covered in red frosting (), in square inches, we need to find the sum of the surface area of the entire circle and the surface area of the square:
(2)
Where:
- - Side length of the square, in inches.
- - Height of the cakes, in inches.
- - Diameter of the cakes, in inches.
If we know that , and , then the <em>approximate</em> area covered in red frosting:
The right choice is B.
3) The frame around the window is found by means of the following perimeter formula (), in inches:
(3)
Where:
- - Radius, in inches.
- - Height of the rectangle, in inches.
If we know that and , then the length of the frame around the window is:
The right choice is B.
We kindly invite to see question on volumes: brainly.com/question/1578538