Another way to think about this is... The total cost was $52. Subtracting out the cost of the layer cake ($16) leaves us with $36 to pay for the 24 cupcakes. <span>This means that each cupcake must have cost $1.50 ( = $36 / 24 cupcakes ).</span>

7 0

4 years ago

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Suppose r(t) = (et cos t)i + (et sin t)j. Show that the angle between r and a never changes. What is the angle?

tatyana61 [14]

Answer:

Angle = Ф = $cos^{-1}$ (0) = 0

Hence, it is proved that angle between position vector r and acceleration vector a = 0 and is it never changes.

Step-by-step explanation:

Given vector r(t) = $e^{t}cost i + e^{t}sint j$

As we know that,

velocity vector = v = $\frac{dr}{dt}$

Implies that

velocity vector = $(e^{t} cost - e^{t} sint)i + (e^{t} sint - e^{t}cost )j$

As acceleration is velocity over time so:

acceleration vector = a = $\frac{dv}{dt}$

Implies that

vector a =

$(e^{t}cost - e^{t}sint - e^{t}sint - e^{t}cost )i + ( e^{t}sint + e^{t}cost + e^{t}cost - e^{t}sint )j$

vector a = $(-2e^{t}sint) i + ( 2e^{t}cost)j$

Now scalar product of position vector r and acceleration vector a:

r. a = $. \\$

r.a = $-2e^{2t}sintcost + 2e^{2t}sintcost$

r.a = 0

Now, for angle between position vector r and acceleration vector a is given by:

cosФ = $\frac{r.a}{|r|.|a|}$ = $\frac{0}{|r|.|a|} = 0$

Ф = $cos^{-1}$ (0) = 0

Hence, it is proved that angle between position vector r and acceleration vector a = 0 and is it never changes.

4 0

3 years ago

Ada needs to make 140 egg tarts for the wedding. How many eggs should she buy from the store? Remember, her recipe makes 40 egg

just olya [345]

Answer:

Ada should buy 385 eggs from the store.

Step-by-step explanation:

Given that you know that Ada can make 40 egg tarts using 110 eggs, you can use a rule of three to find the amount eggs to make 140 egg tarts:

40 egg tarts → 110 eggs

140 egg tarts → x

x=(140*110)/40=385 eggs

According to this, the answer is that Ada should buy 385 eggs from the store.

7 0

3 years ago

different animals have different fields of view. humans can generally see a 180° arc in front of them. horses can see 215° arc.

IgorLugansk [536]

Answer:

The area of the riders field of view is 987.5 square yards.

Step-by-step explanation:

The human has a 180° arc view. If the rider can see only 25 yards, the area of the riders field of view is a semi-circle (180° arc) of 25 yards of radius.

The semi-circle of 25 yards of radius has an area of:

$S=\dfrac{1}{2}\pi r^2=\dfrac{1}{2}\cdot3.16\cdot (25)^2=\dfrac{1}{2}\cdot3.16\cdot625=987.5$

The area of the riders field of view is 987.5 square yards.

4 0

3 years ago