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2 years ago

10

A prism is completely filled with 96 cubes that have edge length of 1 cm. What is the volume of the prism? Enter your answer in

the box. . 412 cm

1 answer:

Igoryamba2 years ago

7 0

Answer:

96

y-step explanation:

volume of 1cm cubes = 1 x 1 x 1 = 1 cm^3

so it will take 96 cubes to fill the prism

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A ladder is leaning against a vertical wall. The distance from the top of the ladder to the base of the wall is 17 feet. The dis

Gennadij [26K]

Answer:

18.4 feet

Step-by-step explanation:

-use the formula C^2 = A^2 + B^2 for a right triangle, which is made by the ladder and the wall.

-let the ladder be C, the wall be a, the base to the bottom be b.

-substitude into the equation, which will leave us with:

C^2 = 17^2 + 7^2

C^2 = 289 + 49

C^2 = 338

C = square root of 338, which is 18.4 feet!

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3 years ago

Choose the correct sum of the polynomials (4x3 − 2x − 9) + (2x3 + 5x + 3).

Harlamova29_29 [7]

The answer is 6x3+3x-6 because all you need to do is combine your like terms

4 0

3 years ago

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Find the general solution of the nonhomogeneous differential equation x^2y''-2y=3(x^2) -1, (x>0).

Ira Lisetskai [31]

Answer:

G.S= $C_1\frac{1}{x}+C_2x^2+x^2logx+\frac{1}{2}$

Step-by-step explanation:

We are given that non-homogeneous differential equation

$x^2y''-2y=3(x^2)-1$

It is Cauchy Euler equation

Substitute x=e^t x>0

Auxillary equation

$D'(D'-1)-2=0$

$D'^2-D'-2=0$

$(D'-2)(D'+1)=0$

$D'-2=0 \implies D'=2$

$D'+1=0\implies D'=-1$

Complementary solution

$y=C_1e^{-t}+C_2e^{2t}$

$y=C_1\frac{1}{x}+C_2x^2$

Particular solution

$y_p=\frac{3e^{2t}}{D'^2-D'-2}-\frac{e^{0t}}{D'^2-D'-2}$

$y_p=te^{2t}+\frac{1}{2}=x^2logx+\frac{1}{2}$

G.S= $C_1\frac{1}{x}+C_2x^2+x^2logx+\frac{1}{2}$

Hence, general solution G.S= $C_1\frac{1}{x}+C_2x^2+x^2logx+\frac{1}{2}$

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4 years ago

SHALL GIVE BRAINLIEST ANSWER!! A 40% solution of fertilizer is to be mixed with an 80% solution of fertilizer in order to get

sdas [7]

Answer:

20 gallons of the 40% solution, 60 gallons of the 80% solution

Step-by-step explanation:

Let x = the gallons of the 40% solution, and y = the gallons of a 80% solution. The first thing we want to do here is to convert each percentage into decimal form - including the 70% solution mixture.

40% = 0.40,

80% = 0.80, respectively 70% = 0.70

As you can tell, 0.40 is associated with x gallons, 0.80 is associated with y gallons, and the mixture contains 0.70 $*$ 80 solution, as 0.70 is associated with 80. Therefore we can formulate the following expression,

0.40x + 0.80y = 0.70 $*$ 80

At the same time x + y = 80, as the solution ( mixture ) is present with 80 gallons. Isolating x, x = 80 - y. Let us plug that into our expression, solving for y, following by x gallons.

$0.40\left(\:80\:-\:y\:\right)\:+\:0.80y\:=\:0.70\:\cdot \:80$

$0.4\left(80-y\right)+0.8y=56$ ( Multiply either side by 10 )

$4\left(80-y\right)+8y=560$ ( Expand )

$320-4y+8y=560$

$320+4y=560$

$4y=240$

$y = \frac{240}{4} = 60$ ( Substitute to solve for x )

$x = 80 - y = 80 - 60 = 20$

As you can see there are 20 gallons of the 40% solution, and 60 gallons of the 80% solution.

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4 years ago

Which pair of angles are alternate interior angles?

Paraphin [41]

we know that

<u>Alternate interior angles</u> are two interior angles which lie on different parallel lines and on opposite sides of a transversal. Alternate interior angles are congruent

see the attached figure with letters to better understand the problem

in this problem

the parallel lines are the lines a and b

the transversal line is the line c

so

the alternate interior angles are the Angle $3$ and Angle $6$

m∠3=m∠6

therefore

<u>the answer is the option</u>

Angle $3$ and Angle $6$

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3 years ago

Read 2 more answers