The ratio of boys to girls in a summer camp is 2 to 3. how many boys and girls are there if the camp has 350 students?

The height h of a projectile is a function of the time t it is in the air. the height in feet for t seconds is given by the func

alexgriva [62]

Domain means the values of independent variable(input) which will give defined output to the function.

Given:

The height h of a projectile is a function of the time t it is in the air. The height in feet for t seconds is given by the function

$h(t)=-16t^2 + 96t$

Solution:

To get defined output, the height h(t) need to be greater than or equal to zero. We need to set up an inequality and solve it to find the domain values.

$To \; find \; domain:\\\\h(t) \geq0\\\\-16t^2+96t \geq 0\\Factoring \; -16t \; in \; the \; left \; side \; of \; the \; inequality\\\\-16t(t-6) \geq 0\\Step \; 1: Find \; Boundary \; Points \; by \; setting \; up \; above \; inequality \; to \; zero.\\\\t(t-6)=0\\Use \; zero \; factor \; property \; to \; solve\\\\t=0 \; (or) \; t = 6\\\\Step \; 2: \; List \; the \; possible \; solution \; interval \; using \; boundary \; points\\(- \infty,0], \; [0, 6], \& [6, \infty)$

$Step \; 3:Pick \; test \; point \; from \; each \; interval \; to \; check \; whether \\\; makes \; the \; inequality \; TRUE \; or \; FALSE\\\\When \; t = -1\\-16(-1)(-1-6) \geq 0\\-112 \geq 0 \; FALSE\\(-\infty, 0] \; is \; not \; solution\\Also \; Logically \; time \; t \; cannot \; be \; negative\\\\When \; t = 1\\-16(1)(1-6) \geq 0\\80 \geq 0 \; TRUE\\ \; [0, 6] \; is \; a \; solution\\\\When \; t = 7\\-16(7)(7-6) \geq 0\\-112 \geq 0 \; FALSE\\ \; [6, -\infty) \; is \; not \; solution$

Conclusion:

The domain of the function is the time in between 0 to 6 seconds

$0 \leq t \leq 6$

The height will be positive in the above interval.

7 0

3 years ago

Read 2 more answers

Sara wants to keep her phone bill under $40 each month. There is a flat fee of $34 and she is charged $0.05 per text message, t.

alukav5142 [94]

Answer:

320 messages

Step-by-step explanation:

20 messages per dollar,

20 x 16 equals 320

8 0

2 years ago

Which of the following is equal to the fraction below?

Vesna [10]

In mathematics there is a rule of exponents where we can "distribute" the powers/exponents in the numerator and denominator of any expression. Therefore, given an expression as $(\frac{a}{b})^n$ , the exponent n can be "distributed" as: $(\frac{a}{b})^n= \frac{a^n}{b^n}$ .

In our case, the power, n=11; a=7 and b=4. Thus, the expression $(\frac{7}{4})^{11}$ , can be written as $\frac{7^{11}}{4^{11}}$ .

Thus, out of the given options, option A is the correct option.

6 0

3 years ago

Read 2 more answers

Multiply and simplify: (2b2+2b)2

sveta [45]

Answer:

4b^2+2b (b^2 means b squared)

Step-by-step explanation:

4 0

2 years ago

Drag numbers to the table so it shows a proportional relationship between x and y.

Marat540 [252]

Using the proportional relationship equation, the missing values are:

Third row: x = 6 and y = 9

Fourth row: x = 15

<h3>What is a Proportional Relationship?</h3>

A proportional relationship can be described as a relationship between two variables, x and y, that have equivalent ratios. In order words, one variable always equals a constant when multiplied by the other variable.

The constant is called the constant of proportionality which can be represented as k.

Thus, k = y/x.

A proportional relationship between x and y can be represented with the equation, y = kx, where k is the constant of proportionality.

Using the pairs given in the table, (3, 4.5), find the constant of proportionality, k:

k = y/x = 4.5/3

k = 1.5

The equation that models the proportional relationship of the values in the table would be: y = 1.5x.

Use the equation to find the rest of the missing values.

Third row:

If x = 6 and y = 9, then,

k = y/x = 9/6 = 1.5

The missing values for the third row would be: x = 6 and y = 9

Fourth row: Substitute y = 2.5 into y = 1.5x to find x

22.5 = 1.5x

22.5/1.5 = x

15 = x

x = 15

Missing value in the fourth row will be: x = 15.

Learn more about proportional relationship on:

brainly.com/question/15618632

#SPJ1

4 0

2 years ago