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-1/4x + 2 < 8 solve and graph for x
1 answer:
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Answer:
360 cm²
Step-by-step explanation:
For the smaller rectangle, we know its height and we not the area. Let's first find out the length of the base. Since we know the area is the product of both sides:
A = b * h
We can deduce that b = A/h = 160 / 10 = 16 cm
Now, let's find the base of the larger rectangle.
We know the rectangle are similar... so their sides must be relative, so we can get:
if we isolate x, we get
x = (15 * 16) / 10 = 240 / 10 = 24
Now that we have the base of the second rectangle (24), we can calculate its area:
A = b * h = 24 * 15 = 360 cm²
*The complete question is in the picture attached below.
Answer:
756πcm³
Step-by-step Explanation:
The volume of the solid shape = volume of cone + volume of the hemisphere.
==> 270πcm³ + ½(4/3*π*r³)
To calculate the volume of the hemisphere, we need to get the radius of the hemisphere = the radius of the cone.
Since volume of cone = 270πcm³, we can find r using the formula for the volume of cone.
==> Volume of cone = ⅓πr²h
⅓*π*r²*10 = 270π
⅓*10*r²(π) = 270 (π)
10/3 * r² = 270
r² = 270 * ³/10
r² = 81
r = √81
r = 9 cm
Thus, volume of hemisphere = ½(4/3*π*r³)
==> Volume of hemisphere = ½(⁴/3 * π * 9³)
= ½(972π)
Volume of hemisphere = 486πcm³
Volume of the solid shape
= volume of cone + volume of the hemisphere.
==> 270πcm³ + 486πcm³
= 756πcm³
Answer:
(See the graph)
Step-by-step explanation:
Red:
(-2, 10)
Left two, up ten
Blue:
(-1, 6)
Left one, up six
Green:
(0, 2)
Up two
Purple:
(1, -2)
Right one, down two
Using the continuity concept, it is found that the function is continuous for all real values.
<h3>What is the continuity concept?</h3>A function f(x) is continuous at x = a if it is defined at x = a, and:
In this problem, we are given a piece-wise function, hence we have to look at the points where the definition of the function changes. In this problem, it can only be discontinuous at x = 0, which we have to verify.
Then:
.
.
.
The 3 values are equal, hence the function is continuous at x = 0 and for all real values.
More can be learned about the continuity of a function at brainly.com/question/24637240
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