I need to know how to solve this

Daniel dives into a swimming pool. The height of his head is represented by the function h(t) = -8t2 - 28t + 60, where t is the

8_murik_8 [283]

So, h(t) is how far is Daniel's head from the surface of the water, namely the surface itself is when the height is nill, so his head is at the surface and the height of it is just 0, thus h(t) = 0. Namely, what is "t" when h(t) is 0?

$\bf h(t)=-8t^2-28t+60\implies \stackrel{h(t)}{0}=-8t^2-28t+60
\\\\\\
0=-2t^2-7t+15\implies 2t^2+7t-15=0\implies (2t+3)(t-5)=0
\\\\\\
\begin{cases}
2t+3=0\implies 2t=-3\implies &t=-\frac{3}{2}\\\\
t-5=0\implies &\boxed{t=5}
\end{cases}$

clearly the seconds cannot be a negative unit, so is not -3/2.

6 0

2 years ago

Area of square floor is 100 square centimeters,and the scale of the drawing is 1 centimeter:2ft,what is the area of the actual f

Taya2010 [7]

100 square centimeters means the dimensions are 10x10
but the actual floor will be 1cm:2ft
so 10cm=20feet
making the dimensions 20feetx20feet
the area of the actual floor is 400 feet

4 0

3 years ago

If a recipe for 24 cookies needs 2 cups of flour, how many cups would we need to make 42 cookies?

TEA [102]

Answer:

3 1/2 cups

Step-by-step explanation:

24=2

42=x

24x=84

/24 /24

3.5

6 0

2 years ago

Write an equation of a parabola that passes through (3,-30) and has x-intercepts of -2 and 18. Then find the average rate of cha

Nookie1986 [14]

Answer:

The equation of the parabola is $y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}$ . The average rate of change of the parabola is -4.

Step-by-step explanation:

We must remember that a parabola is represented by a quadratic function, which can be formed by knowing three different points. A quadratic function is standard form is represented by:

$y = a\cdot x^{2}+b\cdot x + c$

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$a$ , $b$ , $c$ - Coefficients, dimensionless.

If we know that $(3, -30)$ , $(-2, 0)$ and $(18, 0)$ are part of the parabola, the following linear system of equations is formed:

$9\cdot a +3\cdot b + c = -30$

$4\cdot a -2\cdot b +c = 0$

$324\cdot a +18\cdot b + c = 0$

This system can be solved both by algebraic means (substitution, elimination, equalization, determinant) and by numerical methods. The solution of the linear system is:

$a = \frac{2}{5}$ , $b = -\frac{32}{5}$ , $c = -\frac{72}{5}$ .