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chubhunter [2.5K]

3 years ago

11

a cone has a radius of 1.2 inches and a height of 2.9 inches. What is the volume, rounded to the nearest tenth of a cubic inch,

of the cone? possible answers are A.)3.6 B.) 4.4 C.) 10.6 D.) 13.1

1 answer:

n200080 [17]3 years ago

3 0

The volume of the cone is defined as
Volume = pi * r^2 * (h/3)
Volume = pi * 1.2^2 * (2.9/3)
Volume = 4.37310 in^3

If the answer is <span>rounded to the nearest tenth of a cubic inch,
then the final answer is letter (B) 4.4 in^3</span>

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What is the length of the hypotenuse? Answer : 17

leonid [27]

Answer:

Below.

Step-by-step explanation:

Finding the hypotenuse:

Recall the formula of Pythagoras'theorem,

(Hypotenuse)² = (Base)² + (Perpendicular)²

Given that base = 8 and perpendicular = 15

Plugging the values,we obtain

H² = 8² + (15)²
H² = 64 + 225
H² = 289
H = √(17*17)
H = 17

Now applying trigonometric functions:

Recall SOHCAHTOA , it's very helpful.

Sin θ = Sin A = Opposite/Hypotenuse

Sin A = 15/17 ≈ 0.88

cos θ = cos A = Adjacent/Hypotenuse

cos A = 8/17 ≈ 0.47

Tan θ = tan A = Opposite/Adjacent

tan A = 15/8 ≈ 1.88

Note: The values in decimal are rounded to nearest hundredth.

3 0

2 years ago

Which is the graph of the linear inequality y < 3x + 1?

mestny [16]

Start at +1 on the x axis and then use 3/1 for rise over run. So you will start at +1 and then from that point rise 3 run 1

5 0

3 years ago

Factor by grouping <br> 6x^2-12x+x-2<br> factor completely

Marianna [84]

Uh ye here you go stranger hoped this help

5 0

3 years ago

Match the parabolas represented by the equations with their foci.

Elenna [48]

Function 1 $f(x)=- x^{2} +4x+8$

First step: Finding when $f(x)$ is minimum/maximum
The function has a negative value $x^{2}$ hence the $f(x)$ has a maximum value which happens when $x=- \frac{b}{2a}=- \frac{4}{(2)(1)}=2$ . The foci of this parabola lies on $x=2$ .

Second step: Find the value of y-coordinate by substituting $x=2$ into $f(x)$ which give $y=- (2)^{2} +4(2)+8=12$

Third step: Find the distance of the foci from the y-coordinate
$y=- x^{2} +4x+8$ - Multiply all term by -1 to get a positive $x^{2}$
$-y= x^{2} -4x-8$ - then manipulate the constant of y to get a multiply of 4
$4(- \frac{1}{4})y= x^{2} -4x-8$
So the distance of focus is 0.25 to the south of y-coordinates of the maximum, which is $12- \frac{1}{4}=11.75$

Hence the coordinate of the foci is (2, 11.75)

Function 2: $f(x)= 2x^{2}+16x+18$

The function has a positive $x^{2}$ so it has a minimum

First step - $x=- \frac{b}{2a}=- \frac{16}{(2)(2)}=-4$
Second step - $y=2(-4)^{2}+16(-4)+18=-14$
Third step - Manipulating $f(x)$ to leave $x^{2}$ with constant of 1
$y=2 x^{2} +16x+18$ - Divide all terms by 2
$\frac{1}{2}y= x^{2} +8x+9$ - Manipulate the constant of y to get a multiply of 4
$4( \frac{1}{8}y= x^{2} +8x+9$

So the distance of focus from y-coordinate is $\frac{1}{8}$ to the north of $y=-14$
Hence the coordinate of foci is (-4, -14+0.125) = (-4, -13.875)

Function 3: $f(x)=-2 x^{2} +5x+14$

First step: the function's maximum value happens when $x=- \frac{b}{2a}=- \frac{5}{(-2)(2)}= \frac{5}{4}=1.25$
Second step: $y=-2(1.25)^{2}+5(1.25)+14=17.125$
Third step: Manipulating $f(x)$
$y=-2 x^{2} +5x+14$ - Divide all terms by -2
$-2y= x^{2} -2.5x-7$ - Manipulate coefficient of y to get a multiply of 4
$4(- \frac{1}{8})y= x^{2} -2.5x-7$
So the distance of the foci from the y-coordinate is - $\frac{1}{8}$ south to y-coordinate

Hence the coordinate of foci is (1.25, 17)

Function 4: following the steps above, the maximum value is when $x=8.5$ and $y=79.25$ . The distance from y-coordinate is 0.25 to the south of y-coordinate, hence the coordinate of foci is (8.5, 79.25-0.25)=(8.5,79)

Function 5: the minimum value of the function is when $x=-2.75$ and $y=-10.125$ . Manipulating coefficient of y, the distance of foci from y-coordinate is $\frac{1}{8}$ to the north. Hence the coordinate of the foci is (-2.75, -10.125+0.125)=(-2.75, -10)

Function 6: The maximum value happens when $x=1.5$ and $y=9.5$ . The distance of the foci from the y-coordinate is $\frac{1}{8}$ to the south. Hence the coordinate of foci is (1.5, 9.5-0.125)=(1.5, 9.375)

8 0

3 years ago

Express 20 gallons in liters

lys-0071 [83]

Answer: 75.7082

Step-by-step explanation:

7 0

2 years ago