Which of these strategies would eliminate a variable in the system of equations?

What is the equation of the midline for the function f (x)? f (t) = 3 cos (x) – 2.5

zaharov [31]

Answer:

y = -2.5

Step-by-step explanation:

For such a problem as this, you can replace all sine or cosine functions with their midline value of 0. Then you have ...

f(x) = 0 -2.5

which simplifies to ...

f(x) = -2.5

You can leave the equation like this, or write it as ...

y = -2.5

_____

Perhaps you can see that the midline is the value of any constant added to a sine or cosine function.

6 0

3 years ago

A tunnel is in the shape of a parabola. The maximum height is 31 m and it is 13 m wide at the base as shown below.

yan [13]

Using the given values from the problem and the illustration, three points are known which are (0,0), (6.5,-31), (-6.5,-31). The first step in solving this problem is to determine the equation of the parabola.
y = ax²
-31 = a(6.5)²
-31 = 42.25a
a = -31/42.25
a = -124/169

Therefore, the equation of the parabola is y = (-124/169)x². The value 4.5 is then substituted in the equation as x to get the answer which is 16.14 meters.

6 0

3 years ago

Will give brainliest :)

Whitepunk [10]

Answer:

90 degrees

Step-by-step explanation:

BCO = 66

The whole ABC is 180

So BCO and BDO = 90

Therefore BAO must = 90 degrees

5 0

3 years ago

Dave has 8000 to invest for 15 years. He finds a bank that offers an interest rate of 3.1% compounded monthly. How much money wi

Lynna [10]

Answer: he will have $12720 after 15 years

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1 + r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = $8000

r = 3.1% = 3.1/100 = 0.031

n = 12 because it was compounded 12 times in a year.

t = 15 years

Therefore,

A = 8000(1 + 0.031/12)^12 × 15

A = 8000(1 + 0.00258)^180

A = 8000(1.00258)^180

A = $12720

4 0

3 years ago

Multiple choice a. 12 pie cm b. 21 pie cm c. 35 pie cm

Karolina [17]

Answer:

The correct option is;

a. 12 pie cm

Step-by-step explanation:

Cavalieri's principle states that if the cross-sectional area of two or more figures of the same altitude are the same at each level of the figures, then the volumes of the figures are also the same;

Given that the base area of the square based prism and the cylinder are the same, and that the square based prism and the cylinder have equal height of 4 cm, then by Cavalieri's principle, their volumes are the same

The volume of the square based prism = 452 cm³

Therefore, the volume of the cylinder (of equal base area) = 452 cm³

The formula for the volume of square based prism = Area of base × Height

∴ The volume of square based prism, 452 cm³ = Area of base × 4 cm

Which gives;

Area of the base of the square based prism = 452/4 = 113 cm²

The area of the base of the cylinder $A_c$ = The area of the base of the square based prism = 113 cm²

The area of the base of the cylinder, $A_c$ is given by the following equation;

$A_c$ = π×r² = 113 cm²

r = √(113/π) = √35.97 ≈ √36 = 6 cm

The circumference of the base of the cylinder, $C_c$ is given by the following equation

$C_c$ = 2×π×r ≈ 2×π×6 = 12×π cm

The correct option is 12 pie cm.

7 0

3 years ago