Answer:
Look at the picture
Step-by-step explanation:
y = x^2 + 4 replace x and y
x = y^2 + 4 subtract 4 from both sides
x - 4 = y^2 sqaure root both sides
Total amount = 1 x 10 + 3 x 5 = $25
Amount spent = $9.30 + $4.20 = $13.50
Amount left = $25 - $13.50 = $11.50
Answer: $11.50
Without loss of generality, we can assume the semicircle has a radius of 1 and is described by
y = √(1 - x²)
Then the shorter base has length 2x and the longer base has length 2. The area of the trapezoid is
A = (1/2)(2x+2)√(1-x²) = (1+x)√(1-x²)
Differentiating with respect to x, we have
A' = √(1-x²) + (1+x)(-2x)/(2√(1-x²)
Setting this to zero, we get
0 = (1-x²) +(1+x)(-x)
0 = 2x² +x -1
(2x-1)(x+1) = 0
x = {-1, 1/2} . . . . . -1 is an extraneous solution that gives minimum area
So, for x = 1/2, the area is
A = (1 + 1/2)√(1 - (1/2)² = (3/2)√(3/4)
A = (3/4)√3
Of course, if the radius of the semicircle is "r", the maximum area is
A = (r²·3·√3)/4
Step-by-step explanation:
rim
job
blow
job
69
Step-by-step explanation:
The American Civil War (also known by other names) was a civil war in the United States from 1861 to 1865, fought between northern states loyal to the Union and southern states that had seceded to form the Confederate States of America. The principal cause of the war was the status of slavery in the United States, especially in the territories. After Abraham Lincoln won the November 1860 presidential election on an anti-slavery platform, an initial seven slave states declared their secession from the country to form the Confederacy. War broke out in April 1861 when secessionist forces attacked Fort Sumter in South Carolina, just over a month after Lincoln's inauguration. An additional four slave states joined the Confederacy in the following two months. The Confederacy grew to control at least a majority of territory in those eleven states (out of the 34 U.S. states in February 1861), and it claimed the additional states of Kentucky and Missouri by assertions from native secessionists fleeing Union authority. These states were given full representation in the Confederate Congress throughout the Civil War. The two remaining slave states, Delaware and Maryland, were invited to join the Confederacy, but Delaware declined and nothing substantial developed in Maryland due to intervention by federal troops. The Confederate states were never diplomatically recognized as a joint entity by the government of the United States, nor by that of any foreign country. The states that remained loyal to the U.S. were known as the Union. The Union and the Confederacy quickly raised volunteer and conscription armies that fought mostly in the South for four years. Intense combat left between 620,000 and 750,000 soldiers dead, along with an undetermined number of civilians. The Civil War remains the deadliest military conflict in American history, and accounted for more American military deaths than all other wars combined until the Vietnam War. The war effectively ended on April 9, 1865, when Confederate General Robert E. Lee surrendered to Union Ge…
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