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4 years ago

Tom had 7/12 of a pizza. His little sister came along and took 2/5 of his pizza away. How much pizza does Tom have left?

1 answer:

3 0

To find the answer,we can first calculate how much her sister took away by multiplying the original amount he has to the amount her sister took.

Her sister has:
7/12×2/5
=7/30

We can then find the amount of pizza left by deducting the pizza he has to the answer we found above:

7/12-7/30
=35/60- 14/60
=21/60
=7/20

Therefore he has 7/20 of a pizza left.

An alternative way to find the answer:
7/12×(1-2/5)
=7/12×3/5
=7/20

Hope it helps!

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How do I find the perimeter of this?

guajiro [1.7K]

41.2 cm

Step-by-step explanation:

subtract the y's and x's to get the distances

left & right sides are hypotenuses

top :

10 - (-2) = 12

bottom :

5 - (-7) = 12

left :

3 - (-4) = 7 = height

-7 -(-2) = -5 = 5 = base

pythagorean theorem

49 + 25 = 74

square root of 74 = 8.6

right :

same

perimeter :

12 + 12 + 8.6 + 8.6 = 41.2

7 0

2 years ago

A cylinder has a volume of 432 cubic meters. What is the volume of a cylinder with dimensions one-third of the original?

alexandr1967 [171]

Cylindervolume=hpir^2

V=432
432=hpir^2=original

if each is divided by 3 then
h turns to (1/3)h
r turns to (1/3)r
input and find the effect

(1/3)hpi[(1/3)r]^2
(1/3)hpi(1/9)r^2
move 1/9 to front
(1/27)hpir^2
compared to original volume (which was hpir^2)

so therefor we multiply the original volume by 1/27

432*1/27=16

the new volume is 16 cubic meters

5 0

3 years ago

Read 2 more answers

AP CALC 98 POINTS!!!!!!

bekas [8.4K]

Looking at this question again, I don't understand why you're told "for y=11". That doesn't seem relevant at all... So you can disregard the answer I posted a few minutes ago on your other question.

a) With $x^2=-2+y+5\cos y$ , differentiate both sides with respect to $x$ to get

$2x=\dfrac{\mathrm dy}{\mathrm dx}-5\sin y\dfrac{\mathrm dy}{\mathrm dx}$

$\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2x}{1-5\sin y}$

b) The point P occurs at $x=2$ , which corresponds to a $y$ -coordinate of

$4=-2+y+5\cos y\implies y\approx4.928$

The slope of the line tangent to this point is approximately

$\dfrac{\mathrm dy}{\mathrm dx}\approx\dfrac{2(2)}{1-5\sin(4.928)}\approx0.68$

so the equation of the tangent line is approximately

$y-4.928=0.68(x-2)\implies y=0.68x+3.57$

c) The tangent line to the graphed curve is vertical when $\dfrac{\mathrm dy}{\mathrm dx}$ is undefined. This happens when $1-5\sin y=0$ , or $y=\pi-\sin^{-1}\dfrac15+2n\pi$ and $y=\sin^{-1}\dfrac15+2n\pi$ where $n$ is any integer.

In case you're not sure where the general solution came from: We have

$\sin y=\dfrac15$

which has an infinite number of solutions. $\sin^{-1}\dfrac15$ is one of them, which we obtain by taking the inverse sine of both sides of this equation. Since $\sin(\pi-x)=\sin x$ , we also know that $\pi-\sin^{-1}\dfrac15$ is a solution. And since $\sin(x+2n\pi)=\sin x$ for integers $n$ , we also know that we can add any multiple of $2\pi$ to these two solutions to get infinitely more solutions.