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3 years ago

How do you divide numbers

Mathematics

1 answer:

densk [106]3 years ago

7 0

That is a example of division problem if u have any other questions about division just ask I will help u the best I can

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The base of a solid is the region enclosed by the graphs of y=e^x, y=0, x=0, and x = 1. If each cross-section perpendicular to t

yanalaym [24]

Answer:

Step-by-step explanation:

The base of a solid in the region enclosed by the graphs of y = eˣ, y = 0, x = 0, and x = 1. Each cross-section perpendicular to the x-axis is an equilateral triangle. We want to find the volume of the solid.

Please refer to the graph below. We are concerned with the red region.

In order to find the volume, we essentially sum up the area of the figure at each x value. So, we integrate from x = 0 to x = 1.

The area for an equilateral triangle is given by:

$\displaystyle A=\frac{\sqrt{3}}{4}s^2$

Where s is the side length of the triangle.

Since the triangle lies perpendicular on the region, the side length of the triangle at x is simply y, which is eˣ.

Therefore, our volume is:

$\displaystyle V=\int_0^1\frac{\sqrt3}{4}(y)^2\, dx$

Substitute:

$\displaystyle V=\int_0^1\frac{\sqrt3}{4}(e^x)^2\, dx$

Evaluate the integral. Simplify:

$\displaystyle V=\frac{\sqrt3}{4}\int_0^1e^{2x}\, dx$

Integrate using u-substitution:

$\displaystyle V=\frac{\sqrt3}{8}\left(e^{2x}\Big|_0^1\right)$

Evaluate:

$\displaystyle V=\frac{\sqrt3}{8}\left(e^{2(1)}-e^{2(0)} \right)$

Therefore, the volume of the solid is:

$\displaystyle V=\frac{\sqrt3}{8}\left(e^2-1\right)$

Our answer is A.

3 0

3 years ago

Read 2 more answers

Please Please Please help me with this answer

nignag [31]

Alright, lets gets tarted.

Suppose there are x rows of tomato plants Krystyn make.

Again suppose there are n plants in each row.

We could find total plants by multiplying number of plants in each row with number of rows.

Hence total number of plants will be = $x * n$

But as per question, total number of plants are 54. It means

$x * n = 54$

Now, the number of plants in each row was 3 more than the number of rows means

$n = x + 3$

Putting this value of n in first equation we made

$x * (x+3) = 54$

$x^{2} + 3x = 54$

Subtracting 54 in both sides

$x^{2} + 3x - 54 = 54 - 54$

$x^{2} + 3 x - 54 = 0$

Factoring

$(x-6)(x+9) = 0$

Means x = 6 or x = -9

The number of rows can not be negaive.

Hence x = 6

It means number of rows of tomato plants will be 6. : Answer

Hope it will help :).

4 0

4 years ago

Read 2 more answers

Write an explicit rule for the nth term of the sequence 64,48,36,27

melisa1 [442]

Answer:

aₙ = 64(3/4)ⁿ⁻¹

Step-by-step explanation:

Given sequence:

64, 48, 36, 27

We can observe that:

27/36 = 3/4
36/48 = 3/4
48/64 = 3/4

This is a GP with the first term of 64 and common ratio of 3/4.

The equation for the nth term is:

aₙ = 64(3/4)ⁿ⁻¹

6 0

3 years ago

How do I go about solving this?

Stels [109]

Hello,

Here i am using vectors

$\vec{AB}=\vec{DC}=3\vec{i}+3\vec{j}$
==> AB//DC and AD//BC (definition of a translation)

The quadrilater ABCD is a parallelogram:
so
1) his diagonals have the same length;

2) his diagonals are cutting in the middle.

(these are proprieties of a parallelogram)

4 0

3 years ago

For what value of k is the expression x^4 + kx^2 + 49 a perfect square?

mote1985 [20]

Answer:

$k=14$

Step-by-step explanation:

Completing the square gives

$x^4 + kx^2 + 49\\= (x^2+7)^2 - 14x^2 + kx^2$

So we have to cancel the latter two terms out for the expression to always become a square (otherwise we are dealing with a square plus something else, which doesn't always result in a square), giving us our answer directly.

7 0

3 years ago

Read 2 more answers