2/3 times 1/8. Simplified answer.

Answer:

the first one

Step-by-step explanation:

The area of the polygon is solved to be  1044 squared cm

The area of the composite polygon is solved by dividing the object into two sections. Then adding up the areas

Section 1 has dimensions:

length * width = 46 * 14 = 644

section 2 has dimensions:

length = 46 - 21 = 25

width = 30 - 14 = 16

Area = 25 * 16 = 400

Area of the composite figure

section 1  + section 2

= 644 + 400

= 1044 squared cm

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The value of the triple integral ∭E​2xdV over the region E is π.

We have,

To evaluate the triple integral ∭E​2xdV, where E is bounded by the paraboloid x = y² + z² and the plane x = 1, we need to determine the limits of integration.

The plane x = 1 intersects the paraboloid x = y² + z² when x = 1.

Substituting x = 1 into the paraboloid equation gives:

1 = y² + z²

This equation represents a circle in the yz-plane with a radius of 1.

So, we can express the bounds for y and z as follows:

-1 ≤ y ≤ 1

-√(1 - y²) ≤ z ≤ √(1 - y²)

For the x-coordinate, since we are integrating over the entire region between the paraboloid and the plane, the limits are 0 ≤ x ≤ 1.

Now, we can set up the triple integral:

∭E​2xdV = ∫[0,1]∫[-1,1]∫[-√(1 - y²), √(1 - y²)] 2x dz dy dx

Integrating with respect to z first:

∭E​2xdV = ∫[0,1]∫[-1,1] [2xz] evaluated from -√(1 - y²) to √(1 - y²) dy dx

Simplifying:

∭E​2xdV = ∫[0,1]∫[-1,1] 2x(√(1 - y²) - (-√(1 - y²))) dy dx

∭E​2xdV = ∫[0,1]∫[-1,1] 4x√(1 - y²) dy dx

Now, integrating with respect to y:

∭E​2xdV = ∫[0,1] [4x(π/2)] dx

∭E​2xdV = 2π∫[0,1] x dx

∭E​2xdV = 2π[x²/2] evaluated from 0 to 1

∭E​2xdV = 2π(1/2 - 0) = π

Therefore,

The value of the triple integral ∭E​2xdV over the region E is π.

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Answer:

x = 8/3

y = 10/3

Step-by-step explanation:

We add (1) and (2) to get 3x = 8. This means that x = 8/3. We substitute it back into (1) to get 8/3 + y = 6 which shows that y = 10/3

Approximate percent increase in how much the student pays with Optin 2 versus Option is 20%

$540 plus 15% sales tax now.=$515

Pay exactly $120 now and then $58 each month for 9 months=$642

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Given,The slope is inclined at 30° below the horizontal velocity of the agent is 50 km/h. The agent has to clear a gorge 60 m wide to survive and land on the snow 100 m below.

The following are the units required to solve the problem;

(a) seconds(s)(b) meters(m)(c) Yes or No (True or False)The solution to the problem is given below;The agent has to cover a horizontal distance of 60 m and a vertical distance of 100 m.We can use the equations of motion to solve this problem.Here, the acceleration is a = g

9.8 m/s².

(a) Time taken to drop 100 m can be found using the following equation, {tex}s=ut+\frac{1}{2}at^2 {/tex}.

Here, u = 0,

s = -100 m (negative since the displacement is in the downward direction), and

a = g

= 9.8 m/s².∴ -100

= 0 + 1/2 × 9.8 × t²

⇒ t = √20 s ≈ 4.5 s

∴ The time taken to drop 100 m is approximately 4.5 s.

(b) The horizontal distance covered by the agent can be found using the formula, {tex}s=vt {/tex}. Here, v is the horizontal velocity of the agent. The horizontal component of the velocity can be calculated as, v = u cos θ

where u = 50 km/h and

θ = 30°

∴ v = 50 × cos 30° km/h

= 50 × √3 / 2

= 25√3 km/h

We can convert km/h to m/s as follows;1 km/h = 1000 / 3600 m/s

= 5/18 m/s

∴ v = 25√3 × 5/18 m/s

= 125/18√3 m/s

∴ The horizontal distance covered by the agent in 4.5 s is given by,

s = vt

= (125/18√3) × 4.5

≈ 38.7 m.

∴ The agent has traveled 38.7 m horizontally in 4.5 seconds.(c) The agent has to cover a horizontal distance of 60 m to land on the snow 100 m below.

As per our calculation, the horizontal distance covered by the agent in 4.5 seconds is 38.7 m. Since 38.7 m < 60 m, the agent cannot make it to the snow and will fall in the gorge.

Therefore, the answer is No (False).

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Answer:

A radioactive substance decays to 10g in 40 days

Step-by-step explanation:

the mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of 7% per day

The exact value is sin(θ + φ) = 3/125.

We have,

Let θ = sin^{-1} (7/25) and φ = cos^{-1} (-3/5).

Then,

sin(θ) = 7/25 and cos(φ) = -3/5.

We know that sin(π/2 - θ) = cos(θ) and cos(π/2 - φ) = sin(φ).

So,

sin(θ + φ) = sin(θ)cos(φ) + cos(θ)sin(φ)

= (7/25) (-3/5) + √(1 - (7/25)²) (√(1 - (3/5)^2))

= -21/125 + 24/125

= 3/125

Therefore,

The exact value is sin(θ + φ) = 3/125.

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Answer:3.40909

Step-by-step explanation:300ft dived the speed value by 88

Answer:

cos A = 24/51

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

Cos theta = adj side/ hypotenuse

cos A = 24/51

Step-by-step explanation:

We know that cosA=Base/hypontenuse

➡CosA=24/51

This is a right angle triangle

Cos theta=Base/hypontenuse

To find the value of x, we need to follow these steps:

1. Calculate the total sum of the ages of the 6 cars.
2. Subtract the sum of the known ages from the total sum.
3. The result will be the value of x.

Step 1: Since the average age of the 6 cars is 7 years, we multiply the average (7) by the number of cars (6) to find the total sum of ages.
Total sum of ages = 7 * 6 = 42 years

Step 2: Subtract the sum of the known ages (6, 14, 5, 1, and 8) from the total sum.
Sum of known ages = 6 + 14 + 5 + 1 + 8 = 34 years
42 (total sum of ages) - 34 (sum of known ages) = 8

Step 3: The result is the value of x.
x = 8

So the value of x is 8.

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Answer:

A, B and D

Step-by-step explanation:

492.350 rounds to 500,000 because the ten thousand place = 9, so the 4 rounds up to 5 and the rest of the digits change to zeroes.

Others which round to 500,000 also are A and B,

Answer:

\(x = 4 \frac{1}{2} \)

Step-by-step explanation:

5x = 35 divide both sides of the equation by 5

5x / 5 = 35 / 5

x=7

The equilibrium forward rate can be calculated based on the interest rate differentials between the two countries. In this case, with a spot rate of $1.91/Pound, a US interest rate of 3.19%, and a UK interest rate of 10.68%, the equilibrium forward rate can be determined.

The equilibrium forward rate can be calculated using the interest rate parity principle, which states that the difference in interest rates between two countries should equal the expected change in the exchange rate. In this case, the interest rate differential between the US and the UK is 7.49% (10.68% - 3.19%). According to interest rate parity, the equilibrium forward rate should reflect this interest rate differential.

To calculate the equilibrium forward rate, we can use the formula:

Forward Rate = Spot Rate x (1 + Domestic Interest Rate) / (1 + Foreign Interest Rate)

Plugging in the values, we get:

Forward Rate = $1.91 x (1 + 0.0319) / (1 + 0.1068)

Calculating the equation yields the equilibrium forward rate.

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Answer:

Average rate of change

=

26.5

Explanation:

Use the slope formula to find average rate of change:

m

=

y

2

−

y

1

x

2

−

x

1

To use the slope formula, you need 2 points on the curve - we only have to x values, so we need to find f(8) and f(10).

f

(

8

)

=

92

f

(

10

)

=

145

These means are points are

(

x

1

,

y

1

)

=

(

8

,

92

)

and

(

x

2

,

y

2

)

=

(

10

,

145

)

.

m

=

145

−

92

10

−

8

m

=

53

2

m

=

26.5

Step-by-step explanation:

The average rate of change on the interval from 0 to 10 is 30

The function is given as:

f(x)=3x^2-8

The interval is given as:

0 to 10

Calculate f(0) and f(10)

f(0)=3 *(0)^2 -8

f(0) = -8

f(10)=3 *(10)^2 -8

f(10) = 292

The average rate of change is then calculated as:

Rate = (f(10) - f(0))/(10 - 0)

This gives

Rate = (292 +8 )/(10 - 0)

Evaluate

Rate = 30

Hence, the average rate of change on the interval from 0 to 10 is 30

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Answer:

Step-by-step explanation:

Directed line segment from (−8,5) to (4,−3).

Ratio is 5/3.

The required coordinates are:

The solutions are given below.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

Part A

the dotted line formes the thrid side of the triangle.

part B

The length is the unknon side increases while kepping the known side lenths fixed, measuremnt of anggle Z will increas. So, the tringle will not fir the given conditions anymore.

part c

If the length of he unknown side decrases while keeping h known side lengths fixed,the measure of angle will decrease so he tringle will not fit the given conditions anymore.

part D

You know the given conditions for the triangle are fixed you also know the unknown side length is fixed. What dose the this tell you angles adjacent to the unknown side.

part e

The given condiction are fixed and the unknown side lenghtis fixed, the angles adjacent to the unknown side must much also be fixed.

part f

Given two side lengths and the measurement of the angle between them, only one triangle can be constructed. Part G The length of the unknown side (c) is 9.76 centimeters

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Answer:

length= 9

width= 3

Step-by-step explanation:

x= width

length = x+6

x+6+x+6+x+x=24

4x+12=24

take 12 from both sides

4x= 12

x=3

Answer:

The solution of a system of linear equations is:

D. The values of the variables that satisfy both equations.

Answer:

See below.

Step-by-step explanation:

The answer is D. The solution is when the two lines intersect, or are satisfied.

-hope it helps

Answer:

(Choice B) B 10 ( h + 3 + 5 j ) 10(h+3+5j)10, left parenthesis, h, plus, 3, plus, 5, j, right parenthesis

(Choice C) C 2 ( 5 h + 15 + 25 j ) 2(5h+15+25j)2, left parenthesis, 5, h, plus, 15, plus, 25, j, right parenthesis

Step-by-step explanation:

10h+30+50j

There are two answers

First answer

Factorise using 10 as common factor

10h+30+50j

=10(h+3+5j)

(Choice B) B 10 ( h + 3 + 5 j ) 10(h+3+5j)10, left parenthesis, h, plus, 3, plus, 5, j, right parenthesis

Second answer

Factorise using 2 as the common factor

10h+30+50j

=2(5h+15+25j)

(Choice C) C 2 ( 5 h + 15 + 25 j ) 2(5h+15+25j)2, left parenthesis, 5, h, plus, 15, plus, 25, j, right parenthesis

Answer: Choice B and C

Step-by-step explanation:

Answer:

y=21.14

Step-by-step explanation:

x=6 because after 6 weeks

y= 3.27(6)+ 1.52

y=19.62 + 1.52

y=21.14

when x = 0.5, the value of 4x - 5 is -3. Let's go through the steps to work out the value of 4x - 5 when x = 0.5.

Step 1: Substitute the value of x into the expression.

We are given that x = 0.5, so we replace "x" in the expression 4x - 5 with the value 0.5:

4 * 0.5 - 5

Step 2: Perform the multiplication.

Multiply 4 by 0.5:

4 * 0.5 = 2

Step 3: Perform the subtraction.

Now, subtract 5 from the result obtained in Step 2:

2 - 5 = -3

Step 4: Final result.

The final result is -3.

So, when x = 0.5, the value of 4x - 5 is -3.

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Answer:

circumference 69.08 area 379.94

Step-by-step explanation:

Answer:

4z

Step-by-step explanation:

Answer:

x = 4.5

Step-by-step explanation

When z is 6 that means x is 1.5 which means that when z is 18 then x is 4.5 because we add 3+1.5 which is 4.5

Answer:

C)

\(area = height \times base \\ area = (5 \times 9) \: {cm}^{2} \\ area = 45 \: {cm}^{2} \)

Answer:

slope is 2

Step-by-step explanation:

Answer:

31

Step-by-step explanation:

a + (n-1)d  where a = first term;  n = which number we want;  d = common difference.

=> 4 + (10 - 1)3

=> 4 + (9)*3

=> 4 + 27

=> 31