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Rom4ik [11]
2 years ago
10

A square pyramid has a base edge of 15 inches. The volume of the pyramid is 960 cubic inches. What is the height of the pyramid,

in inches?​
Mathematics
1 answer:
gizmo_the_mogwai [7]2 years ago
8 0

Answer:   h=12.8in

a Base edge 15   in

V Volume 960  in³

Using the formula

V=a2h

3

Solving for h

h=3V

a2=3·960

152=12.8in

Step-by-step explanation:

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Which of the values shown are potential roots of f(x) = 3x3 – 13x2 – 3x + 45? Select all that apply.
galina1969 [7]

Answer:

All potential roots are 3,3 and -\frac{5}{3}.

Step-by-step explanation:

Potential roots of the polynomial is all possible roots of f(x).

f(x)=3x^3-13x^2-3x+45

Using rational root theorem test. We will find all the possible or potential roots of the polynomial.

p=All the positive/negative factors of 45

q=All the positive/negative factors of 3

p=\pm 1,\pm 3,\pm 5\pm \pm 9,\pm 15\pm 45

q=\pm 1,\pm 3

All possible roots

\frac{p}{q}=\pm 1,\pm 3,\pm 5\pm \pm 9,\pm 15\pm 45,\pm \frac{1}{3},\pm \frac{5}{3}

Now we check each rational root and see which are possible roots for given function.

f(1)= 3\times 1^3-13\times 1^2-3\times 1+45\Rightarrow 32\neq 0

f(-1)= 3\times (-1)^3-13\times (-1)^2-3\times (-1)+45\Rightarrow \neq 32

f(-3)= 3\times (-3)^3-13\times (-3)^2-3\times (-3)+45\Rightarrow \neq -144

f(3)= 3\times (3)^3-13\times (3)^2-3\times (3)+45\Rightarrow =0\\\\ \therefore x=3\text{ Potential roots of function}

Similarly, we will check for all value of p/q and we get

f(-5/3)=0

Thus, All potential roots are 3,3 and -\frac{5}{3}.


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