Find the unit price rounded to the nearest cent: 5.8 lbs for $4.89.

An ice cream shop sells cones at the volume of 94.2 cubic meters they want to double the volume of the cones without changing th

marin [14]

The volume of a cone is $V=\pi r^2\frac{h}3$ where r = radius and h = height. If the cone has a volume of 94.2 cm³ (I assume you didn't mean m³ because that would be ridiculously huge) and a height of 10 cm, we can plug these values into the formula to find the radius. Don't do any rounding.

$94.2 = \pi r^2\frac{10}3 \\ 282.6 = \pi r^2 *10 \\ 28.26 = \pi r^2 \\ 8.99543738355 = r^2 \\ 2.99923946752=r$

Now we know that's going to be the radius of our <em>new </em>cone as well since we're keeping the diameter the same. The volume is going to be double 94.2 which is 188.4. Let's solve for the height.

$188.4 = \pi (2.99923946752)^2\frac{h}3 \\ 188.4 = \pi(8.99543738355)\frac{h}3 \\ 188.4 = 28.26\frac{h}3 \\ 565.2 = 28.26h \\\\ \boxed{h = 20, r\approx 3}$

5 0

3 years ago

Find the constant of variation k for the inverse variation. Then write an equation for the inverse variation. Y=4.5 when x = 3

Nookie1986 [14]

$\bf \qquad \qquad \textit{inverse proportional variation}\\\\
\textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------\\\\
\textit{we also know that }
\begin{cases}
y=4.5\\
x=3
\end{cases}\implies 4.5=\cfrac{k}{3}\implies 4.5(3)=k
\\\\\\
13.5=k\qquad therefore\qquad \boxed{y=\cfrac{13.5}{x}}$

8 0

2 years ago

What value of x satisfies the equation below?<br> 12 ( x - 2 ) + 3 x = 1 2 ( x + 6 ) + 2

Sergeu [11.5K]

Answer:

x = 32.6666667

Step-by-step explanation:

12(x - 2) + 3x = 12(x + 6) + 2

Distribute;

12x - 24 + 3x = 12x + 72 + 2

Collect like terms;

15x - 24 = 12x + 74

Subtract 12x from both sides;

3x - 24 = 74

Add 24 to both sides;

3x = 98

Divide both sides by 3;

x = 32.6666667

4 0

2 years ago

Consider the case of a triangle with sides 5, 12, and the angle between them 90°.

Daniel [21]

Answer:

a) Applying Pithagoras Theorem

b) Trigonometric relations

c) No we can not

d) No we can not

e) See step-by-step explanation

f) See step-by-step-explanation

Step-by-step explanation:

a) The easiest method for calculating the missing side is applying Pithagoras Theorem

c² = a² + b²

c² = (5)² + (12)² ⇒ c² = 25 + 144 ⇒ c² = 169 ⇒ c = 13

b) The easiest method to find the missing angles, is to calculate the sin∠ and then look for arcsin fuction in tables.

sin ∠α = 5/13 sin ∠α = 0.3846 ⇒ arcsin (0.3846 ) α = 23⁰

Now we can either get the other angle subtracting 180 - 90 - 23 = 67⁰

Or calculating sinβ = 12 /13 sinβ = 0.9230 arcsin(0.9230) β = 67⁰

c) The law of cosines should not be applied to right triangles, in fact for instance in our particular case we have:

Question a)

c² = a² + b² - 2*a*b*cos90⁰ (law of cosines ) but cos 90⁰ = 0

then c² = a² + b² which is the expression for theorem of Pithagoras

In case you look for calculating the missing angles

c² = a² + b² - 2*5*13*cos α

169 = 25 + 144 - 2*5*13* cos α

As you can see 169 - 25 - 144 = 0

Then we can not apply law of cosine in right triangles, we shoul apply trigonometric relations and Pithagoras theorem, and as we saw you can get the expression of Pithagoras theorem from cosine law

c² = a² + b² - 2*a*b*cos∠90° cos ∠ 90° = 0

Then c² = a² + b²

3 0

3 years ago

Can someone help me with this problem having trouble

lora16 [44]

So the bottom line is for vehicle weight so if you look at the bar at the top it says 25 so go to the graph and put a dot on 25 and then it says city mp is 27 so you put a dot between 25 and 30 and the connect it with a line

4 0

1 year ago