All categories

3 years ago

Two similar solids have a scale factor of 6 : 7. What is the ratio of their volumes, expressed in lowest terms?

Mathematics

2 answers:

Anarel [89]3 years ago

7 0

The ratio of volumes is equal to the ratio of the cubes of the scale factor. Thus,
Volume ratio:
6³ : 7³
216 : 343

creativ13 [48]3 years ago

3 0

Answer:

The ratio of their volumes is equal to $\frac{216}{343}$

Step-by-step explanation:

we know that

If two solids are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z-----> the scale factor

x/y----> the ratio of its volumes

$z^{3}=\frac{x}{y}$

we have

$z=\frac{6}{7}$

substitute

$(\frac{6}{7})^{3}=\frac{x}{y}$

$(\frac{216}{343})=\frac{x}{y}$

rewrite

$\frac{x}{y}=(\frac{216}{343})$ -----> the fraction is irreducible

You might be interested in

If (9 to the 2nd power)p = 9 to the 8th power , what is the value of p?

Novay_Z [31]

$(9^2)^p=9^8\\\\9^{2p}=9^8\\\\2p=8\\\\p=4$

3 0

3 years ago

Read 2 more answers

A) 172 b) 192 C) 212 D) 232

tigry1 [53]

Answer:

212

Step-by-step explanation:

volume of new figure = sum of the two individual figures

volume of one cuboid=l*b*h

volume of first cuboid=92

volume of second cuboid=120

sum of two figures=212

hope this helps

plzz mark me brainliest

8 0

3 years ago

Read 2 more answers

A person standing at the edge of a cliff throws a rock upward from a height of 180ft above ground level with an initial velocity

taurus [48]

Answer: 8.73 ft/s

Step-by-step explanation:

We have the following equation that models the motion of the rock:

$h(t)=-16t^{2}+64t+180$

Where $h(t)$ is the height of the rock at a time $t$ .

Now, if $h(t)=48 ft$ we can find $t$ and then the velocity of the rock at that height:

$48=-16t^{2}+64t+180$

Rearranging the equation:

$-16t^{2}+64t+132=0$

Multiplying the equation by -1:

$16t^{2}-64t-132=0$

Solving with the quadratic formula $t=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ , where $a=16$ , $b=-64$ , $c=-132$ .

$t=\frac{-(-64)\pm\sqrt{(-64)^{2}-4(16)(-132)}}{2(16)}$

Choosing the positive result of the equation:

$t=5.5 s$

Since velocity $V$ is defined as the traveled distance $h(t)$ in a given time $t$ , we have:

$V=\frac{h(t)}{t}$

$V=\frac{48 ft}{5.5 s}$

$V=8.727 ft/s \approx 8.73 ft/s$ This is the velocity of the rock at the height of 48 feet

7 0

2 years ago

Let T:R²->R² be a linear transformation ,and assume that T (1,2)=(-1,1) and T(1,-1)=(2,3)

zavuch27 [327]

Answer:

(-4,-1)

Step-by-step explanation:

We are given T(1,2)=(-1,1) and T(1,-1)=(2,3) and T is a linear transformation.

This implies for scalars a and b that

T(a(1,2)+b(-1,1))=aT(1,2)+bT(-1,1)

T((a,2a)+(-b,b))=a(-1,1)+b(2,3)

T((a-b,2a+b))=(-a,a)+(2b,3b)

T((a-b,2a+b))=(-a+2b,a+3b)

This means we should be able to solve the system below to find a and b for T(3,3):

a-b=3 and 2a+b=3

Add equations to eliminate b and solve for a:

3a=6

Divide 3 on both sides:

a=2

If a-b=3 and a=2, then b=-1.

Plug in a=2, b=-1:

T((a-b,2a+b))=(-a+2b,a+3b)

T((2--1,2×2+-1)=(-2+2×-1,2+3×-1)

T(3,3)=(-4,-1).

4 0

2 years ago

The output is the cube of the input.

chubhunter [2.5K]

Yes it is right because you are measuring by either the base to height or length times width

4 0

3 years ago