Step-by-step explanation:
Mathematicians seek and use patterns[8][9] to formulate new conjectures; they resolve the truth or falsity of such by mathematical proof. When mathematical structures are good models of real phenomena, mathematical reasoning can be used to provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.
Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements.[10] Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.[11]
Mathematics is essential in many fields, including natural science, engineering, medicine, finance, and the social sciences.
The volume of the composite figure is 3532.5 cubic inches
<h3>How to determine the volume of the composite figure?</h3>
From the given figure, we have the following dimensions:
- Height, h = 15 inches
- Radius of small cylinder, r = 5 inches
- Radius of large cylinder, R = 10 inches
The volume of a cylinder is
V = πr^2h
So, the volume of the composite figure is
V = πR^2h - πr^2h
Substitute the known values in the above equation
V = 3.14 * 10^2 * 15 - 3.14 * 5^2 * 15
Evaluate the product
V = 3532.5
Hence, the volume of the composite figure is 3532.5 cubic inches
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Answer:
<h2>x = -2, y = 1</h2>
Step-by-step explanation:
given the system of equations y=1/2x+2 and y=-2x+-3, since the 2 equations are functions of y, we will equate both equations together and calculate the value of x as shown
1/2x+2 = -2x-3
x/2+2x = -3-2
5x/2 = -5
5x = -10
x = -10/5
x = -2
Substituting x = -2 into any of the equation to get the value of y we have;
y = -2(-2)-3
y = 4-3
y = 1
The solution to the system of equation (x, y) = (-2, 1)
False:))))))))))))))
-2x3x3=-18
Answer:
the measure of AB equals the measure of BC
2x+1=3x-4
4+1=3x-2x
5=x
BC=3x-4=3*5-4=15-4=11
AB=2x+1=2*5+1=10+1=11
AC=AB+BC=11+11=22
Step-by-step explanation:
