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Step-by-step explanation:
the mean value is the sum of all data points divided by the number of data points.
first we have 7 tests and their mean value :
(t1 + t2 + t3 + t4 + t5 + t6 + t7) / 7 = 54
that means
(t1 + t2 + t3 + t4 + t5 + t6 + t7) = 54 × 7 = 378
in order for the mean value to be at least 60% after 8 tests, we need to add a t8, so that
(t1 + t2 + t3 + t4 + t5 + t6 + t7 + t8) = 60 × 8 = 480
because only then we have
(t1 + t2 + t3 + t4 + t5 + t6 + t7 + t8) / 8 = 60
and the student passes.
so,
(t1 + t2 + t3 + t4 + t5 + t6 + t7) + t8 = 480
378 + t8 = 480
t8 = 480 - 378 = 102%
the student would have to achieve 102% on the 8th test.
which would be normally impossible, but maybe the tests involve some bonus points.
Answer:
521,400 meters squared
Step-by-step explanation:
With the 1cm = 100m scale
6.6 cm = 660m
7.9 cm = 790m
Area = 660 x 790 = 521,400 meters squared
Let the curve C be the intersection of the cylinder
and the plane
The projection of C on to the x-y plane is the ellipse
To see clearly that this is an ellipse, le us divide through by 16, to get
or
,
We can write the following parametric equations,
for
Since C lies on the plane,
it must satisfy its equation.
Let us make z the subject first,
This implies that,
We can now write the vector equation of C, to obtain,
The length of the curve of the intersection of the cylinder and the plane is now given by,
But
Therefore the length of the curve of the intersection intersection of the cylinder and the plane is 24.0878 units correct to four decimal places.
Answer:
a) 58.24 square centimeters
b) 5cm
Step-by-step explanation:
a) Area of a parallelogram
The formula for the Area of a parallelogram = Base × Height
Height : 5.2cm
Base : 11.2cm
Area = 5.2 cm × 11.2cm
= 58.24 square centimeters
b) Volume of a cuboid
The formula for the Volume of a cuboid = Length × Width × Height
7cm = Width
3cm = Length
y = Height
Volume = 105cm³
We are to find y
Hence,
105cm³ = 7cm × 3cm × y
y = 105cm³/7cm × 3cm
y = 5cm