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3 years ago

Which represents the solution(s) of the equation x2 = 49?

Mathematics

2 answers:

Lady_Fox [76]3 years ago

8 0

Answer: 7,-7

Step-by-step explanation: 7 squared is 7 times 7 which equals 49

-7 times -7 is also 49 bc the negatives cancel each other out

Dmitriy789 [7]3 years ago

7 0

Answer:

If it's x², the possible answers are 7 and -7.

Step-by-step explanation:

7²=49, (-7)²=49

Those two numbers are the only numbers that fit the equation x²=49.

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A block of wood measures 9.5 inches by 1.5 inches by 8 inches. What is the volume of the block of wood?

MatroZZZ [7]

114 is the answer hope this helps good luck and god bless!

6 0

3 years ago

37. Verify Green's theorem in the plane for f (3x2- 8y2) dx + (4y - 6xy) dy, where C is the boundary of the

Nastasia [14]

I'll only look at (37) here, since

• (38) was addressed in 24438105

• (39) was addressed in 24434477

• (40) and (41) were both addressed in 24434541

In both parts, we're considering the line integral

$\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dy$

and I assume C has a positive orientation in both cases

(a) It looks like the region has the curves y = x and y = x ² as its boundary***, so that the interior of C is the set D given by

$D = \left\{(x,y) \mid 0\le x\le1 \text{ and }x^2\le y\le x\right\}$

• Compute the line integral directly by splitting up C into two component curves,

C₁ : x = t and y = t ² with 0 ≤ t ≤ 1

C₂ : x = 1 - t and y = 1 - t with 0 ≤ t ≤ 1

Then

$\displaystyle \int_C = \int_{C_1} + \int_{C_2} \\\\ = \int_0^1 \left((3t^2-8t^4)+(4t^2-6t^3)(2t))\right)\,\mathrm dt \\+ \int_0^1 \left((-5(1-t)^2)(-1)+(4(1-t)-6(1-t)^2)(-1)\right)\,\mathrm dt \\\\ = \int_0^1 (7-18t+14t^2+8t^3-20t^4)\,\mathrm dt = \boxed{\frac23}$

*** Obviously this interpretation is incorrect if the solution is supposed to be 3/2, so make the appropriate adjustment when you work this out for yourself.

• Compute the same integral using Green's theorem:

$\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dy = \iint_D \frac{\partial(4y-6xy)}{\partial x} - \frac{\partial(3x^2-8y^2)}{\partial y}\,\mathrm dx\,\mathrm dy \\\\ = \int_0^1\int_{x^2}^x 10y\,\mathrm dy\,\mathrm dx = \boxed{\frac23}$

(b) C is the boundary of the region

$D = \left\{(x,y) \mid 0\le x\le 1\text{ and }0\le y\le1-x\right\}$

• Compute the line integral directly, splitting up C into 3 components,

C₁ : x = t and y = 0 with 0 ≤ t ≤ 1

C₂ : x = 1 - t and y = t with 0 ≤ t ≤ 1

C₃ : x = 0 and y = 1 - t with 0 ≤ t ≤ 1

Then

$\displaystyle \int_C = \int_{C_1} + \int_{C_2} + \int_{C_3} \\\\ = \int_0^1 3t^2\,\mathrm dt + \int_0^1 (11t^2+4t-3)\,\mathrm dt + \int_0^1(4t-4)\,\mathrm dt \\\\ = \int_0^1 (14t^2+8t-7)\,\mathrm dt = \boxed{\frac53}$

• Using Green's theorem:

$\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dx = \int_0^1\int_0^{1-x}10y\,\mathrm dy\,\mathrm dx = \boxed{\frac53}$

4 0

3 years ago

Pls help a girl out ;-;

Sveta_85 [38]

The order of locations from highest to lowest is Caspian sea, lammefjord, Trins Alexanderpolder, Fenland, Raczki

Explanation:

The order of the locations from highest to lowest can be determined using the values of meters below sea level.

From the data, the highest to lowest value can be written as

28 meters

8 meters

7 meters

4 meters

2 meters

Thus, from the data, the locations from highest to lowest can be written as

Caspian sea

Lammefjord

Trins Alexanderpolder

Fenland

Raczki

8 0

3 years ago

Please help ASAP I’ll mark you as brainlister

zavuch27 [327]

Answer:

So Sorry Omg Wait I'll will come back

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3 years ago

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A stain glass window is shaped like a semicircle. The bottom edge of the window is 36 inches long. What is the area of the stain

Lubov Fominskaja [6]

I don't really have a calculator on me. But I'll tell you how to go through it.
So the formula for the area of a circle is Pi x radius^2.
So since the diameter is 36, divide that by 2 to get the radius, and you're left with 18. Now do 18 squared and then times that by Pi. Now you've got the area of the whole circle, but since we only have a semicircle, you need to divide your answer by two to get the area of the semi circle

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3 years ago