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3 years ago

Solve for x. Round your answer to the nearest tenth if necessary.

Mathematics

1 answer:

Kay [80]3 years ago

8 0

Answer: 8.8

Step-by-step explanation:

Because $\angle S \cong \angle S$ by the reflexive property, we know that $\triangle STU \sim \triangle SQR$ by AA.

So, by the triangle proportionality theorem,

$\frac{x}{5.3}=\frac{11.1}{6.7}\\x=(11.1/6.7)(5.3) \approx \boxed{8.8}$

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Evaluate expression 3(7+x2);x=2

satela [25.4K]

So assuming that x2=x^2 and not 2x
3(7+2^2)
3(7+4)
3(11)
33

4 0

3 years ago

Use the Divergence Theorem to evaluate the following integral S F · N dS and find the outward flux of F through the surface of t

Xelga [282]

Answer:

Result;

$\int\limits\int\limits_S { \textbf{F}} \, \cdot \textbf{N} d {S} = 32\pi$

Step-by-step explanation:

Where:

F(x, y, z) = 2(x·i +y·j +z·k) and

S: z = 0, z = 4 -x² - y²

For the solid region between the paraboloid

z = 4 - x² - y²

div F

For S: z = 0, z = 4 -x² - y²

We have the equation of a parabola

To verify the result for F(x, y, z) = 2(x·i +y·j +z·k)

We have for the surface S₁ the outward normal is N₁ = -k and the outward normal for surface S₂ is N₂ given by

$N_2 = \frac{2x \textbf{i} +2y \textbf{j} + \textbf{k}}{\sqrt{4x^2+4y^2+1} }$

Solving we have;

$\int\limits\int\limits_S { \textbf{F}} \, \cdot \textbf{N} d {S} = \int\limits\int\limits_{S1} { \textbf{F}} \, \cdot \textbf{N}_1 d {S} + \int\limits\int\limits_{S2} { \textbf{F}} \, \cdot \textbf{N}_2 d {S}$

Plugging the values for N₁ and N₂, we have

$= \int\limits\int\limits_{S1} { \textbf{F}} \, \cdot \textbf{(-k)}d {S} + \int\limits\int\limits_{S2} { \textbf{F}} \, \cdot \frac{2x \textbf{i} +2y \textbf{j} + \textbf{k}}{\sqrt{4x^2+4y^2+1} } d {S}$

Where:

F(x, y, z) = 2(xi +yj +zk) we have

$= -\int\limits\int\limits_{S1} 2z \ dA + \int\limits\int\limits_{S2} 4x^2+4y^2+2z \ dA$

$= -\int\limits^2_{-2} \int\limits^{\sqrt{4-y^2}} _{-\sqrt{4-y^2}} 2z \ dA + \int\limits^2_{-2} \int\limits^{\sqrt{4-y^2}} _{-\sqrt{4-y^2}} 4x^2+4y^2+2z \ dA$

$= \int\limits^2_{-2} \int\limits^{\sqrt{4-y^2}} _{-\sqrt{4-y^2}} 4x^2+4y^2 \ dxdy$

$= \int\limits^2_{-2} \frac{(16y^2 +32)\sqrt{-(y^2-4)} }{3} dy$

= 32π.

6 0

4 years ago

What does X equal?<br><br> 2x + 2 = 4x + 4

Inessa [10]

Answer:

x = -1

Step-by-step explanation:

Given

2x + 2 = 4x + 4 ( subtract 4x from both sides )

- 2x + 2 = 4 ( subtract 2 from both sides )

- 2x = 2 ( divide both sides by - 2 )

x = - 1

8 0

3 years ago

The length of one leg of a right triangle is 24 feet and the length of the hypotenuse is 40 ft what is the length of the other l

Rama09 [41]

To solve for the other leg, you need to use Pythagorean theory.

The theory states that C^2 = A^2 + B^2

In your case, you have to solve for B.
C = 40 (hypotenuse) A = 24 (leg 1)

The formula rewritten for B is $b= \sqrt{c^{2}-a^{2} }$

Now, you can solve.

$b= \sqrt{c^{2}-a^{2} }

b= \sqrt{40^{2}-24^2 }

b = \sqrt{1600 - 576}

b = \sqrt{1024}

b = 32$

Therefore, B = 32.

So the second leg is 32 feet.

7 0

4 years ago

A giant circular fair ride has a radius of 60m, with 12passenger pods spaced around the circumference at equal distances. How fa

nekit [7.7K]

Answer:

The distance between the 6th and 10th seat is approximately 126m

Step-by-step explanation:

First of all, we will need to calculate the circumference of the circular fair ride.

This is $2\pi r= 2 \times \pi \times 60=377m$

hence the circumference of the circle is 377m

At this point, we will have to take note that the pods are equally spaced.

To get the distance between the sixth pod and the tenth pod, we will have to use the principle of fractions of a whole.

There are 12 seats in total, the distance between the 6th and tenth seat is 4 seats. Expressing this distance in terms of seats, as a fraction is 4/12 equally spaced seats.

This ratio can be related to the circumference of the circle as

$\frac{4}{12} \times377=125.66m \approx 126m$

Therefore, the distance between the 6th and 10th seat is approximately 126m

8 0

3 years ago