Some paint is made by mixing 2 cans of white paint for every 5 cans of red

Mixed nuts sell for $7.89 a pound. Leticia fills a bag and weighs it. The bag weighs 2.3 pounds.

Maurinko [17]

Answer:

i think the answer is 18.15

Step-by-step explanation:

8 0

3 years ago

Find the function r that satisfies the given condition. r'(t) = (e^t, sin t, sec^2 t): r(0) = (2, 2, 2) r(t) = ()

lesantik [10]

Answer:

r(t) = (e^t +1, -cos(t) + 3, tan(t) + 2)

Step-by-step explanation:

A primitive of e^t is e^t+c, since r(0) has 2 in its first cooridnate, then

e^0+c = 2

1+c = 2

c = 1

Thus, the first coordinate of r(t) is e^t + 1.

A primitive of sin(t) is -cos(t) + c (remember that the derivate of cos(t) is -sin(t)). SInce r(0) in its second coordinate is 2, then

-cos(0)+c = 2

-1+c = 2

c = 3

Therefore, in the second coordinate r(t) is equal to -cos(t)+3.

Now, lets see the last coordinate.

A primitive of sec²(t) is tan(t)+c (you can check this by derivating tan(t) = sin(t)/cos(t) using the divition rule and the property that cos²(t)+sin²(t) = 1 for all t). Since in its third coordinate r(0) is also 2, then we have that

2 = tan(0)+c = sin(0)/cos(0) + c = 0/1 + c = 0

Thus, c = 2

As a consecuence, the third coordinate of r(t) is tan(t) + 2.

As a result, r(t) = (e^t +1, -cos(t) + 3, tan(t) + 2).

6 0

3 years ago

Suppose the population of a town is 98,000 in 2014. The population increases at a rate of 3.7 percent every year. What will the

Setler [38]

Answer: 121871

Step-by-step explanation:

Current population = 98000

Rate of increase = 3.7% / year

Total time = 2020 - 2014 = 6 years

Population in 2020 = 98000 * (1+ (3.7/100))^6

= 98000 * (1.037)^6 = 98000 * 1.243576 = 121870.505

Rounding off to nearest whole number we get the population = 121871

3 0

3 years ago

Question 12 Multiple Choice Worth 1 points)(07.05 MC)1086Which of the following functions best represents the graph?fix)=(x-2)(x

vlada-n [284]

The graph of a function is given. It is required to find the function that represents the graph.

Notice from the graph that the function has roots or zeros at -3,-2, and 2.

Hence, the function takes the form:

$\begin{gathered} f(x)=a(x-(-3))(x-(-2))(x-2) \\ \Rightarrow f(x)=a(x+3)(x+2)(x-2) \end{gathered}$

Where a is a constant to be determined.

Notice that the given graph passes through the point (0,-12).

Substitute x=0 and f(x)=-12 into the equation of the function to find a:

$\begin{gathered} -12=a(0+3)(0+2)(0-2) \\ \Rightarrow-12=a(3)(2)(-2) \\ \Rightarrow-12=-12a \\ \text{ Swap the sides of the equation:} \\ \Rightarrow-12a=-12 \\ \text{ Divide both sides by }-12: \\ \Rightarrow\frac{-12a}{-12}=\frac{-12}{-12} \\ \Rightarrow a=1 \end{gathered}$

Hence, the function is:

$\begin{gathered} f(x)=1(x+3)(x+2)(x-2) \\ \Rightarrow f(x)=(x+2)(x+3)(x-2) \end{gathered}$ <h2>The third option is the answer: f(x)=(x+2)(x+3)(x-2).</h2>

5 0

1 year ago

Write an equation of a quadratic function that has x-intercepts -1 and 4 and a y-intercept of 3.

igomit [66]

Y=(x+1)(x-4)

this should be correct.

5 0

3 years ago