Answer:
Step-by-step explanation:
The general equation is
y = 2.49x + 24.99
The number of cones bought is x
The cake cost is 24.99
The total cost is y
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So the meaning of (5,37.44) is that she bought 5 cones and 1 cake. Let's just check that out.
Check
y = 2.49*5 + 24.99
y = 12.45 + 24.99
y = 37.44
So the total cost (y) of 5 cones (2.49 each) and 1 cake ($24.99) is 37.44
Answer:
5.9125in^2
Step-by-step explanation:
Step one:
Given data
Dimension of square= 5.25 in
Area of sqaure= 5.25^2= 27.5625 in^2
We are told that the sides of the circle touch the sides of the square
hence the diameter of the circle is 5.25in
radius= 5.25/2= 2.625 in
Area of circle= πr^2
Area of circle = 3.142*2.625^2
Area of circle=3.142*6.890625
Area of circle= 21.65 in^2
Step two:
The area that is not inside the circle
=Area of square-Area of circle
=27.5625- 21.65
=5.9125in^2
Answer: To clear an equation of decimals, multiply each term on both sides by the power of ten that will make all the decimals whole numbers. In our example above, if we multiply .25 by 100, we will get 25, a whole number. Since each decimal only goes to the hundredths place, 100 will work for all three terms.
So let's multiply each term by 100 to clear the decimals:
(100)0.25x + (100)0.35 = (100)(-0.29)
25x + 35 = -29
Now we can solve the equation as normal:
25x + 35 - 35 = -29 - 35
25x = -64
x = -2.56 Since the original was in decimal form, the answer should most likely also be in decimal form.
Let's look at one more:
1.75x + 4 = 6.2
We have to think a little more carefully about what multiple of ten to use here. 6.2 only needs to be multiplied by 10, but 1.25 needs 100, so we will multiply every term by 100. Don't forget to multiply the 4 by 100 as well.
(100)(1.75x) + (100)(4) = (100)(6.2)
175x + 400 = 620
We had to be extra careful as we multiplied by 100. Now we can solve the equation as normal:
175x + 400 - 400 = 620 - 400
175x = 220
x = 1.26
Step-by-step explanation:
Answer:
The volume is:
Step-by-step explanation:
See the sketch of the region in the attached graph.
We set the integral using washer method:
Notice here the radius of the washer is the difference of the given curves:
So the integral becomes:
We solve it:
Factor 
out and distribute the exponent (you can use FOIL):
Notice: 
So the integral becomes:
Then using the basic rule to evaluate the integral:
Simplifying a bit:
Then plugging the limits of the integral:
![\displaystyle\pi\left[\frac{4^3}{3}-\frac{4(4)^{5/2}}{5}+\frac{4^2}{2}-\left(\frac{1}{3}-\frac{4}{5}+\frac{1}{2}\right)\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cpi%5Cleft%5B%5Cfrac%7B4%5E3%7D%7B3%7D-%5Cfrac%7B4%284%29%5E%7B5%2F2%7D%7D%7B5%7D%2B%5Cfrac%7B4%5E2%7D%7B2%7D-%5Cleft%28%5Cfrac%7B1%7D%7B3%7D-%5Cfrac%7B4%7D%7B5%7D%2B%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5Cright%5D)
Taking the root (rational exponents):
![\displaystyle\pi\left[\frac{4^3}{3}-\frac{4(2)^{5}}{5}+\frac{4^2}{2}-\left(\frac{1}{3}-\frac{4}{5}+\frac{1}{2}\right)\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cpi%5Cleft%5B%5Cfrac%7B4%5E3%7D%7B3%7D-%5Cfrac%7B4%282%29%5E%7B5%7D%7D%7B5%7D%2B%5Cfrac%7B4%5E2%7D%7B2%7D-%5Cleft%28%5Cfrac%7B1%7D%7B3%7D-%5Cfrac%7B4%7D%7B5%7D%2B%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5Cright%5D)
Then doing those arithmetic computations we get:
No solution means u can graph the two equations and it would form parallel lines and would never intersect while, no real solution when graph the two equations would form the same line. When dealing with absolute value equation an equation with a degree larger than one,theres a chance it can be multiple solutions
