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3 years ago

7

Devon made a paper cone to hold a gift for a friend. The paper cone was 15 inches high and had a radius of 3 inches. Find the vo

lume of the paper cone. Use 3.14 as pi

1 answer:

yawa3891 [41]3 years ago

6 0

141.3 is the right answer
You use pemdas so radius squared equals 9, 9 times 3.14 equals 28.26, 15/3 = 5 so 5 times 28.26

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The difference between two numbers is 2 and their product is 224. What are the numbers?

Sati [7]

Let $x,y$ be the two numbers. We have two pieces of information:

$x-y=2$ (the difference between the two numbers is 2)

$xy=224$ (their product is 224)

From the first equation, we can deduce $x=y+2$

If we plug this expression in the second equation, we have

$xy = (y+2)y = 224 \iff y^2+2y-224 =0$

If you solve this equation with the usual quadratic formula you get the solutions

$y=-16,\quad y=14$

So, you have the following couple of solutions, recalling that x is 2 more than y:

$\begin{cases} x = -14\\y=-16\end{cases},\quad\begin{cases} x = 16\\y=14\end{cases}$

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3 years ago

What is the distance between -60 and -10 0n a number line?

JulsSmile [24]

Answer: 70

Step-by-step explanation: The absolute value of a number is its distance from zero on the number line. Since absolute value is a distance, it is always greater than or equal to zero.

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2 years ago

The point P(1,1/2) lies on the curve y=x/(1+x). (a) If Q is the point (x,x/(1+x)), find the slope of the secant line PQ correct

lukranit [14]

Answer:

See explanation

Step-by-step explanation:

You are given the equation of the curve

$y=\dfrac{x}{1+x}$

Point $P\left(1,\dfrac{1}{2}\right)$ lies on the curve.

Point $Q\left(x,\dfrac{x}{1+x}\right)$ is an arbitrary point on the curve.

The slope of the secant line PQ is

$\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{\frac{x}{1+x}-\frac{1}{2}}{x-1}=\dfrac{\frac{2x-(1+x)}{2(x+1)}}{x-1}=\dfrac{\frac{2x-1-x}{2(x+1)}}{x-1}=\\ \\=\dfrac{\frac{x-1}{2(x+1)}}{x-1}=\dfrac{x-1}{2(x+1)}\cdot \dfrac{1}{x-1}=\dfrac{1}{2(x+1)}\ [\text{When}\ x\neq 1]$

1. If x=0.5, then the slope is

$\dfrac{1}{2(0.5+1)}=\dfrac{1}{3}\approx 0.3333$

2. If x=0.9, then the slope is

$\dfrac{1}{2(0.9+1)}=\dfrac{1}{3.8}\approx 0.2632$

3. If x=0.99, then the slope is

$\dfrac{1}{2(0.99+1)}=\dfrac{1}{3.98}\approx 0.2513$

4. If x=0.999, then the slope is

$\dfrac{1}{2(0.999+1)}=\dfrac{1}{3.998}\approx 0.2501$

5. If x=1.5, then the slope is

$\dfrac{1}{2(1.5+1)}=\dfrac{1}{5}\approx 0.2$

6. If x=1.1, then the slope is

$\dfrac{1}{2(1.1+1)}=\dfrac{1}{4.2}\approx 0.2381$

7. If x=1.01, then the slope is

$\dfrac{1}{2(1.01+1)}=\dfrac{1}{4.02}\approx 0.2488$

8. If x=1.001, then the slope is

$\dfrac{1}{2(1.001+1)}=\dfrac{1}{4.002}\approx 0.2499$

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3 years ago

Harvey rides his bike at an average speed of 12 miles per hour. In other words, he rides 12 miles in 1 hour, 24 miles in 2 hours

timama [110]

Answer:

Step-by-step explanation:

Harvey rides his bike at an average speed of 12 miles in 1 hour, 24 miles in 2 hours, and so on. Let h be the number of hours he rides and d be distance traveled. Write the equation for the relationship between distance and time in point-slope form.

----

You have three points relating time and distance:

(1,12),(2,24),(3,36)

-----

The slope for your equation would be (24-12)/(2-1) = 12/1 = 12

-------------------------------

The intercept is the distance you would travel in no time; that would be zero.

---------------------------------

The equation is: distance = 12(time)

d = 12t

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3 years ago

What expression is equivalent to -2x + 7

NARA [144]

I think that’s the answer

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2 years ago