Answer:
1. D.
.
2. D.
.
Step-by-step explanation:
1.
, where,
r = Radius of the cone,
h = Height of the cone.
Upon substituting our given values we will get,
![\text{Volume of an oblique cone}=\frac{1}{3}\pi r^2h](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20an%20oblique%20cone%7D%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2h)
![\text{Volume of an oblique cone}=\frac{1}{3}\pi(8\text{ cm})^2\times 15\text{ cm}](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20an%20oblique%20cone%7D%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%288%5Ctext%7B%20cm%7D%29%5E2%5Ctimes%2015%5Ctext%7B%20cm%7D)
![\text{Volume of an oblique cone}=\frac{1}{3}\pi(64\text{ cm}^2)\times 15\text{ cm}](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20an%20oblique%20cone%7D%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%2864%5Ctext%7B%20cm%7D%5E2%29%5Ctimes%2015%5Ctext%7B%20cm%7D)
![\text{Volume of an oblique cone}=\pi(64\text{ cm}^2)\times 5\text{ cm}](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20an%20oblique%20cone%7D%3D%5Cpi%2864%5Ctext%7B%20cm%7D%5E2%29%5Ctimes%205%5Ctext%7B%20cm%7D)
![\text{Volume of an oblique cone}=320\pi\text{ cm}^3](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20an%20oblique%20cone%7D%3D320%5Cpi%5Ctext%7B%20cm%7D%5E3)
Therefore, the volume of our given oblique cone is
and option D is the correct choice.
2.
, where,
r = Radius of the cone,
h = Height of the cone.
Upon substituting our given values we will get,
![\text{Volume of right cone}=300\pi \text{ cm}^3](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20right%20cone%7D%3D300%5Cpi%20%5Ctext%7B%20cm%7D%5E3)
Therefore, the volume of our given right cone is
and option D is the correct choice.
Answer:
![\displaystyle x_1=\frac{5+\sqrt{13}}{2}\approx4.3\text{ and } x_2=\frac{5+\sqrt{13}}{2}\approx0.7](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x_1%3D%5Cfrac%7B5%2B%5Csqrt%7B13%7D%7D%7B2%7D%5Capprox4.3%5Ctext%7B%20and%20%7D%20x_2%3D%5Cfrac%7B5%2B%5Csqrt%7B13%7D%7D%7B2%7D%5Capprox0.7)
Step-by-step explanation:
We are given:
![x^2-5x+3=0](https://tex.z-dn.net/?f=x%5E2-5x%2B3%3D0)
And we want to solve this via completing the square.
First, we will subtract 3 from both sides. This yields:
![x^2-5x=-3](https://tex.z-dn.net/?f=x%5E2-5x%3D-3)
Next, we will factor out the leading coefficient from the left.
In this case, the leading coefficient is simply 1 so we can leave it as is.
Next, we want to add a constant that is half of the b coefficient squared.
In this case, b = -5.
Half of that is -5/2.
Squaring yields 25/4.
So, we will add 25/4 to both sides. Since our leading coefficient is 1, we don't need to multiply by anything when we add it on the right. Hence:
![\displaystyle x^2-5x+\frac{25}{4}=-3+\frac{25}{4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%5E2-5x%2B%5Cfrac%7B25%7D%7B4%7D%3D-3%2B%5Cfrac%7B25%7D%7B4%7D)
The left side constitutes a perfect square trinomial as shown:
![\displaystyle (x)^2-2\Big(\frac{5}{2} \Big)(x)+\Big(\frac{5}{2}\Big)^2=-\frac{12}{4}+\frac{25}{4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%28x%29%5E2-2%5CBig%28%5Cfrac%7B5%7D%7B2%7D%20%5CBig%29%28x%29%2B%5CBig%28%5Cfrac%7B5%7D%7B2%7D%5CBig%29%5E2%3D-%5Cfrac%7B12%7D%7B4%7D%2B%5Cfrac%7B25%7D%7B4%7D)
Factor and subtract:
![\displaystyle \Big(x-\frac{5}{2}\Big)^2=\frac{13}{4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5CBig%28x-%5Cfrac%7B5%7D%7B2%7D%5CBig%29%5E2%3D%5Cfrac%7B13%7D%7B4%7D)
Taking the square root of both sides gives:
![\displaystyle x-\frac{5}{2}=\pm\frac{\sqrt{13}}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x-%5Cfrac%7B5%7D%7B2%7D%3D%5Cpm%5Cfrac%7B%5Csqrt%7B13%7D%7D%7B2%7D)
Hence:
![\displaystyle x=\frac{5}{2}\pm\frac{\sqrt{13}}{2}}=\frac{5\pm\sqrt{13}}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B5%7D%7B2%7D%5Cpm%5Cfrac%7B%5Csqrt%7B13%7D%7D%7B2%7D%7D%3D%5Cfrac%7B5%5Cpm%5Csqrt%7B13%7D%7D%7B2%7D)
Approximate:
![\displaystyle x_1=\frac{5+\sqrt{13}}{2}\approx4.3\text{ and } x_2=\frac{5-\sqrt{13}}{2}\approx0.7](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x_1%3D%5Cfrac%7B5%2B%5Csqrt%7B13%7D%7D%7B2%7D%5Capprox4.3%5Ctext%7B%20and%20%7D%20x_2%3D%5Cfrac%7B5-%5Csqrt%7B13%7D%7D%7B2%7D%5Capprox0.7)
11/12 is the answer, I did this math problem before
9 5/6 - 2 1/3 is 7 1/2.
You could get this answer by finding the same denominator of the fractions. The LCM of both is 6. Multiply the 1 of the second fraction 2 times because you had to multiply the denominator 2 times to get to 6.
You should have 2 2/6.
Now get 9 5/6 - 2 2/6.
The answer is 7 3/6, simplifies into 7 1/2.
9 5/6 - 2 1/3 is 7 1/2.
Answer: 49.45
Step-by-step explanation:
From the information, we are informed that June was thinking of a number and then doubles it and gets and gets an answer of 98.9.
Let the number be represented by x.
Since she doubles it, thus implies that:
2x = 98.9
x = 98.9 / 2
x = 49.45
The number is 49.45