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4 years ago

5

A box was measured with a degree of accuracy to the nearest 2cm; 24cm × 24cm × 20cm. What is the smallest possible volume of the

box to the nearest cm3?

2 answers:

Strike441 [17]4 years ago

4 0

Each measurement is accurate to 2cm so they can each be “off” by 2. Since we want the smallest possible volume let’s assume each is actually 2 less than what is given.

The sides would then measure: 22, 22 and 18cm respectively. We obtain the volume by multiplying length, width and height...the three values given.

Thus the smallest volume is 22x22x18=8,712 cm^3

densk [106]4 years ago

3 0

Answer:

8712 $cm^{3}$

Step-by-step explanation:

since the box was measured to the nearest 2 cm

we will assume its dimensions would be ( + or - ) 2cm each

hence for the smallest possible volume of the box the dimensions would be

= (24 - 2 ) cm * ( 24 - 2 ) cm * ( 20 - 2 ) cm

= 22 * 22 * 18 = 8712 $cm^{3}$

this would be the smallest possible volume of the box to the nearest cm3

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Find an m > 0 such that the the equation x^4−(3m+2)x^2+m^2=0 has four real solutions that form an arithmetic sequence.

Aleonysh [2.5K]

Answer:

The value of m is 6.

Step-by-step explanation:

Here, the given equation,

$x^4-(3m+2)x^2+m^2=0$

$x^4+0x^3-(3m+2)x^2+0x+m^2=0$

Let the roots of the equation are a-3b, a-b, a+b and a + 3b, ( they must be form an AP )

Thus, we can write,

$a-3b+a-b+a+b+a+3b=\frac{\text{coefficient of }x^3}{\text{coefficient of }x^4}$

$=\frac{0}{1}=0$

$\implies a=0----(1)$

$(-3b)(-b)+(-b)(b)+(b)(3b)+(3b)(-3b)+(-b)(3b)+(-3b)(b)=\frac{\text{coefficient of }x^2}{\text{coefficient of }x^4}}$

$=\frac{-3m-2}{1}$

$3b^2-b^2+3b^2-9b^2-3b^2-3b^2=-3m-2$

$-10b^2=-3m-2$

$\implies b^2=\frac{3m+2}{10}-----(2)$

$(-3b)(-b)(b)(3b)=\frac{\text{Constant term}}{\text{coefficient of}x^4}= m^2$

$9b^4=m^2$

$9(\frac{3m+2}{10})^2=m^2$

$9(\frac{9m^2+4+12m}{100})=m^2$

$81m^2+36+108m=100m^2$

$-19m^2+108m+36=0$

$19m^2-108m-36=0$

$19m^2-114m+6m-36=0$

$19m(m-6)+6(m-6)=0$

$(19m+6)(m-6)=0$

$\implies m=-\frac{6}{19}\text{ or }m=6$

But m > 0,

Hence, the value of m is 6.

4 0

3 years ago

Hi , step by step please

Zigmanuir [339]

Answer:

Eldest: $335,500 Middle: $182,750 Youngest: $167,750

Step-by-step explanation:

Let's represent the amount of money the youngest sibling received as x.

The amount the eldest received can be represented as: 2x

The amount the middle sibling received can be represented as: x + 15,000

If we combined the amount of money that all of the siblings received, it would be $686,000. We can write this as an equation:

686,000 = 2x + (x + 15,000) + x

Now let's solve for x. First, combine like terms

686,000 = 4x + 15,000

Subtract 15000 from both sides to isolate the 4x

671,000 = 4x

Divide both sides by 4 to isolate the x

167,750 = x

Now we know that the amount of money the youngest received is $167,750. We can use this amount to figure out how much the other two siblings received.

Eldest: 2 * 167,750 = $335,500

Middle: 167,750 + 15,000 = $182,750

We can check to make sure these answers are correct by adding them all together to make sure that they equal 686,000

167,750 + 335,500 + 182,750 = 686,000

7 0

3 years ago

Plz help by the way I have iPhone 11

Anon25 [30]

Answer:

3 times 4

Step-by-step explanation:

3 groups of 4...............

4 0

3 years ago

Read 2 more answers

The cosine of 23° is equivalent to the sine of what angle

Archy [21]

Answer:

So 67 degrees is one value that we can take the sine of such that is equal to cos(23 degrees).

(There are more values since we can go around the circle from 67 degrees numerous times.)

Step-by-step explanation:

You can use a co-function identity.

The co-function of sine is cosine just like the co-function of cosine is sine.

Notice that cosine is co-(sine).

Anyways co-functions have this identity:

$\cos(90^\circ-x)=\sin(x)$

or

$\sin(90^\circ-x)=\cos(x)$

You can prove those drawing a right triangle.

I drew a triangle in my picture just so I can have something to reference proving both of the identities I just wrote:

The sum of the angles is 180.

So 90+x+(missing angle)=180.

Let's solve for the missing angle.

Subtract 90 on both sides:

x+(missing angle)=90

Subtract x on both sides:

(missing angle)=90-x.

So the missing angle has measurement (90-x).

So cos(90-x)=a/c

and sin(x)=a/c.

Since cos(90-x) and sin(x) have the same value of a/c, then one can conclude that cos(90-x)=sin(x).

We can do this also for cos(x) and sin(90-x).

cos(x)=b/c

sin(90-x)=b/c

This means sin(90-x)=cos(x).

So back to the problem:

cos(23)=sin(90-23)

cos(23)=sin(67)

So 67 degrees is one value that we can take the sine of such that is equal to cos(23 degrees).

6 0

3 years ago

Find the area of the parallelogram shown below.<br> 6<br> 5

rjkz [21]

Area of parallelogram = base x height

Area = 6 x 5
= 30 unit ^2

8 0

3 years ago