A woman walks 100 yards east along a straight shoreline and then swims 30 yards south into the ocean on a line that is perpendicular to the shoreline. Using her starting point as the pole and the east direction as the polar axis, give her current position polar coordinates. Round the coordinates to the nearest hundredth. Express θ in degrees. (11.40, –88.28°) (104.40, –88.28°) (11.40, –16.70°) (104.40, –16.70°)

She invests some amount in a saving account of fixed interest compounded half-yearly. It says to find its Future Value after six years.

The principal amount is P = $4,848.

Annual interest rate is 5% i.e. r = 0.05

Compounding period is two times per year i.e. n = 2.

Time of investment is t = 6 years.

We know the formula of Future Value is given by :-

[tex] FV=P*(1+\frac{r}{n})^{nt} [/tex]

We can plug the given values in the formula to calculate the answer.

[tex] FV = 4848*(1+\frac{0.05}{2})^{(2*6)} \\\\
FV = 4848*(1+0.025)^{(12)} \\\\
FV = 4848*(1.025)^{(12)} \\\\
FV = 4848*(1.344888) \\\\
FV = 6520.02102 [/tex]

Hence, future value of investment after six years is 6,520.02 dollars.

The question involves calculation of compound interest. The formula to use is A = P (1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, t is the time in years, n is the number of times interest is compounded per year and A is the amount of money accumulated after n years.

This question involves the concept of compound interest. Compound interest is calculated each period on the original deposit, or principal, along with any interest previously earned. Unlike simple interest which only takes into account the principal amount, compound interest accounts for the interest that accumulates on the initial amount as well as the interest that has previously been added.

In Brenda's case, as she's benefiting from compounded interest, the formula to use here is A = P (1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, t is the time in years, n is the number of times interest is compounded per year and A is the amount of money accumulated after n years.

So, plug in the given values: P=$4848, r=0.05 (as 5% = 5/100), t=6, and n=2 (since it's compounded semi-annually). This will allow us to find the final account balance after 6 years.

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Answer: The answer is actually 6.

Step-by-step explanation:

The value of x is 6, rounded to the nearest whole number.

To solve for x given the conditions:

1. Define the variables based on the problem:

  - Length of the rectangle [tex](\( L \)) = \( x + 2 \)[/tex]

  - Width of the rectangle [tex](\( W \)) = \( 2x - 5 \)[/tex]

2. Write the equation for the area of the rectangle:

  - Area [tex](\( A \)) = \( L \times W \)[/tex]

  - Given that the area is 56 cm², we have:

[tex]\[ (x + 2)(2x - 5) = 56 \][/tex]

3. Expand the equation:

[tex]\[ (x + 2)(2x - 5) = 2x^2 - 5x + 4x - 10 = 2x^2 - x - 10 \][/tex]

4. Set up the equation:

[tex]\[ 2x^2 - x - 10 = 56 \][/tex]

5. Move all terms to one side of the equation to set it to zero:

[tex]\[ 2x^2 - x - 10 - 56 = 0 \] \[ 2x^2 - x - 66 = 0 \][/tex]

6. Solve the quadratic equation using the quadratic formula:

[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]\\ where \( a = 2 \), \( b = -1 \), and \( c = -66 \).[/tex]

7. Calculate the discriminant:

[tex]\[ \Delta = b^2 - 4ac = (-1)^2 - 4(2)(-66) = 1 + 528 = 529 \][/tex]

8. Calculate the roots:

[tex]\[ x = \frac{-(-1) \pm \sqrt{529}}{2(2)} = \frac{1 \pm 23}{4} \][/tex]

So, the solutions are:

[tex]\[ x = \frac{1 + 23}{4} = \frac{24}{4} = 6 \][/tex]

and

[tex]\[ x = \frac{1 - 23}{4} = \frac{-22}{4} = -5.5 \][/tex]

Since x must be a positive value in the context of this problem, we have: x = 6

9. Verify the solution:

Length L = x + 2 = 6 + 2 = 8 cm

Width W = 2x - 5 = 2(6) - 5 = 12 - 5 = 7  cm

Area = [tex]\( 8 \times 7 = 56 \)[/tex] cm², which matches the given area.

Therefore, ( x = 6).

Answer:

Step-by-step explanation:

11.4

Answer: First option is correct.

Step-by-step explanation:

Since we have given that

There is a geometric sequence:

where a₁ = 2

r = √2

We need to find a₉:

As we know the formula for "nth term ":

[tex]a_n=ar^{n-1}\\\\a_9=ar^{9-1}\\\\a_9=ar^8\\\\a_9=2\times (\sqrt{2})^8\\\\a_9=32[/tex]

Hence, First option is correct.

central angle theta (in radians) = arc length / radius

So theta = 5.6/8 = 0.7 radians

The central angle measure for a circle with an 8 cm radius and a 5.6 cm intercepted arc length is 0.7 radians.

The question asks to find the measure in radians for the central angle of a circle with a radius of 8 cm and an intercepted arc length of 5.6 cm. To calculate the central angle in radians, we use the formula θ = [tex]\frac{l}{r}[/tex], where θ is the central angle in radians, l is the arc length, and r is the radius of the circle. Substituting the given values, we get θ =  [tex]\frac{5.6}{8}[/tex]

Through calculation, θ = 0.7 radians. So, the measure of the central angle that intercepts an arc length of 5.6 cm in a circle with a radius of 8 cm is 0.7 radians.

Answer:

[tex]1\frac{2}{5}[/tex] gallon of milk is needed to make one gallon of ice cream

Step-by-step explanation:

Using unitary method,  

Unitary method is a method use to find the value of a unit quantity.

[tex]6\frac{3} {10}[/tex] gallon of milk needed to make [tex]4\frac{1}{2}[/tex] gallon of milk

[tex]\frac{63}{10}[/tex] gallon of milk needed to make [tex]\frac{9}{2}[/tex] gallon of ice cream

One gallon of ice cream needed = [tex]\frac{63}{10} \times \frac{2}{9}[/tex] gallon of milk

                                                        = [tex]\frac{7}{5}[/tex] gallon of milk

                                                         = [tex]1\frac{2}{5}[/tex] gallon of milk

Thus, [tex]1\frac{2}{5}[/tex] gallon of milk is needed to make one gallon of ice cream.

The value of x in the equation Sin(x+22 degrees) = Cos(2x-7 degrees) can be found by using the identity sin(90° - x) = cos(x), leading to x = 22.67° (or in radians by converting degrees to radians).

To find the value of x in the equation Sin(x+22 degrees) = Cos(2x-7 degrees), we can utilize the trigonometric identity sin(90° - x) = cos(x). By setting the angle inside the cosine to equal 90° - (x + 22°), we can equate this to (2x - 7°) as both represent the same cosine value.

So we have the equation 90° - (x + 22°) = 2x - 7°. Solving for x, we combine like terms: 68° = 3x, which then gives us x = 68°/3. Therefore, x = 22.67°, which is the angle in degrees.

If we needed to find x in radians, we would have to convert degrees to radians by using the conversion factor: π radians = 180°. This would yield x as x = (22.67°/180°) * π.

Solution:

Let volume of cylinder be K times more than volume of Cone.

⇒K × Volume of Cone = Volume of Cylinder

[tex]K \times \frac{\pi\times r^2 \times h }{3}=\pi \times R^2 \times H\\\\K \times 5^2 \times 10= 3 \times 10^2 \times 20\\\\250 K=3 \times 100 \times 20\\\\K=\frac{6000}{250}\\\\K=24[/tex]

⇒Number of times one needs to use the completely fill cone to completely fill the cylinder with water is=24

To simplify expressions, one needs to apply rules correctly, such as combining like terms and using exponentiation rules. The process includes correctly applying the rule that simplifies multiplications of the same base by adding their exponents. Cubing exponentials involves multiplying the original exponent by 3.

To simplify mathematical expressions, it's crucial to follow the correct rules and operations. In this case, the example provided shows the exponentiation and multiplication rules. Specifically, when dealing with expressions like 3².3⁵, this is equivalent to multiplying 3 x 3 and then taking that result and multiplying it by 3 five more times. According to the rule xPx9 = x(p+q), where x is the base and p and q are the exponents, it simplifies to adding the exponents when the base number is the same and multiplied together.

The process of simplifying expressions involves several steps:

Additionally, when cubing exponentials, one should cube the digit normally and multiply the existing exponent by 3, a rule demonstrated in squaring operations as well.

Answer:

The answer is 72 degrees

Step-by-step explanation:

The picture that Helpmetnx showed does work. But they made a mistake and assumed that the diagonal is a angle bisector, and it's not.

1. rectangle ABCD, BD & AC are the diagonals. ∠ABD =36 degrees

2. ∠ABD= ∠BDC = 36 - alternate interior angles

3. ∠DBC = 90 - 36 = 54. ∠DBC =∠ADB = ∠BCA = 54

4. Now we know that the triangle formed between the two diagonals is a isosceles triangle because of base angle theorem.

5. 180 - 54*2 = 72 degrees

I hope this helps!

factor X + 1 is the answer