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Mademuasel [1]
2 years ago
15

A small cube with side length 6y is placed inside a larger cube with side length 4x^2. What is the difference in the volume of t

he cubes?
Mathematics
2 answers:
sleet_krkn [62]2 years ago
6 0

Answer:

(64x^{6}-216y^{3})\ units^{3}

Step-by-step explanation:

we know that

The volume of a cube is equal to

V=s^{3}

where

s is the length side of a cube

Step 1

Find the volume of the smaller cube

we have

s=6y\ units

substitute the value in the formula

V1=(6y)^{3}=216y^{3}\ units^{3}

Step 2

Find the volume of the larger cube

we have

s=4x^{2}\ units

substitute the value in the formula

V2=(4x^{2})^{3}=64x^{6}\ units^{3}

Step 3

Find the difference in the volume of the cubes

V2-V1=(64x^{6}-216y^{3})\ units^{3}


fomenos2 years ago
3 0

the different volume is the numbers. 4*2*6=?


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A million years ago, an alien species built a vertical tower on a horizontal plane. When they returned they discovered that the
velikii [3]

Answer:

\theta=cos^{-1}(\frac{2}{3})

Step-by-step explanation:

We are given that measurements of three points on the ground gave coordinates of (0,0,0),(1,2,0) and (0,2,1)

We have to find the angle by which the tower now deviate from the vertical

We find cross product of <1,2,0> and <0,2,1>

\times =\begin{vmatrix}i&j&k\\1&2&0\\0&2&1\end{vmatrix}

\times =2\hat{i}-\hat{j}+2\hat{k}

Now, we are finding the angle between  \timesand vertical vector <0,0,1>

Angle between two vectors formula

cos\theta=\frac{a.b}{\mid a\mid\cdot\mid b\mid }

Now, using this formula

cos\theta=\frac{2}{1\cdot 3}=\frac{2}{3}

\theta=cos^{-1}(\frac{2}{3})

Hence, the tower deviate from the vertical by the angle \theta=cos^{-1}(\frac{2}{3})

6 0
2 years ago
Identify the segment bisector of JK
nordsb [41]

Answer:

A segment whose length is 9 units.

Step-by-step explanation:

A segment whose length is 9 units.

All we have is a bisection that divides equally segment JK in two parts. And M is the Midpoint what reassures us that JM=MK, so plugging in:

3x+15=8x+25

3x-8x=25-15

-5x=10

5x=-10

x=-2

JM=3(-2)+15 =9

MK=8(-2)+25=9

4 0
2 years ago
After dinner 3/4 of a pie remains. if tasha eats 1/6 of the remaining pie
astraxan [27]

Answer: 1/8

Step-by-step explanation: 3/4 x 1/6 = 24/3 (simplify to 1/8)

4 0
2 years ago
In the Fall STA 2023 Beginning of the Semester Survey, students were asked how many parties they attended every week and how man
Shtirlitz [24]

Answer:

-95.78

Step-by-step explanation:

As the researcher decided to make the number of parties attended per week the explanatory variable, this would be variable x in the regression line, and of course, the variable y would be the number of text messages sent per day.

After constructing the linear regression equation, the researcher found that an approximate value \hat y for the actual value of y could be represented by the line

\hat y=64.96+25.41x

Since this is an approximate value, it is not expected that it coincides with the actual value of y. We define then the residual for each value of x as the difference between the actual value of y and the approximation for the given x.

For the value x = 2 (the student attended 2 parties that week) the actual value of y is 20 (the student sent 20 text messages per day that week).

The approximate value of y would be according to the regression line

\hat y(2)=64.96+25.41(2)=64.96+50.82=115.78

Hence, the residual value for x=2 would be

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5 0
2 years ago
Dante's Mom wants to build a fence around their yard. Here are the measurements of the yard. What are the measurements of the mi
timama [110]

Answer:

(a)The missing measurements are 9 feet and 16\frac{1}{4}$ feet.

(b)Therefore, the length of the fence is  97\frac{1}{2}$ feet

Step-by-step explanation:

The diagram of the yard is attached below.

(a)I have labeled the missing dimensions of the yard as x and y.

Therefore:

y+8\frac{1}{4}=17 \frac{1}{4}\\y=17 \frac{1}{4}-8\frac{1}{4}\\y=9$ feet

Similarly:

x+15\frac{1}{4}=31\frac{1}{2}\\x=31\frac{1}{2}-15\frac{1}{4}\\x=31-15+\frac{1}{2}-\frac{1}{4}\\x=16+\frac{1}{4}\\x=16\frac{1}{4}$ feet

The missing measurements are 9 feet and 16\frac{1}{4}$ feet.

(b)Length of the Fence

The fence is rectangular shaped with:

Length = 31\frac{1}{2}$ feet

Width = 17 \frac{1}{4}$ feet

Perimeter of a Rectangle = 2(L+W)

Therefore, the length of the fence

=2(31\frac{1}{2}+17 \frac{1}{4})\\=2(31+17+\frac{1}{2}+ \frac{1}{4})\\=2(48+ \frac{3}{4})\\=96+\frac{3}{2}\\=97\frac{1}{2}$ feet

8 0
2 years ago
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