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3 years ago

Solve the absolute value equation |13x-1|=0

Mathematics

1 answer:

olasank [31]3 years ago

3 0

Since $|x|=0$ whenever $x=0$ , you have

$|13x-1|=0\implies 13x-1=0\implies 13x=1\implies x=\dfrac1{13}$

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A toy rocket is launched from a platform that is 48 ft high. The rocket height above the ground is modeled by h=-16t^2+32t+48. a

Komok [63]

Answer:

a) 64 feet

b) 3 seconds

Step-by-step explanation:

The maximum height of $h=h(t)$ can be bound by finding the y-coordinate of the vertex of $y=-16x^2+32x+48$ .

Compare this equation to $y=ax^2+bx+c$ to find the values of $a,b,\text{ and } c$ .

$a=-16$

$b=32$

$c=48$ .

The x-coordinate of the vertex can be found by evaluating:

$\frac{-b}{2a}=\frac{-32}{2(-16)$

$\frac{-b}{2a}=\frac{-32}{-32}$

$\frac{-b}{2a}=1$

So the x-coordinate of the vertex is 1.

The y-coordinate can be found be evaluating $y=-16x^2+32x+48$ at $x=1$ :

$y=-16(1)^2+32(1)+48$

$y=-16+32+48$

$y=16+48$

$y=64$

So the maximum height of the rocket is 64 ft high.

When the rocket hit's the ground the height that the rocket will be from the ground is 0 ft.

So we are trying to find the second t such that:

$0=-16t^2+32t+48$

I'm going to divide both sides by -16:

$0=t^2-2t-3$

Now we need to find two numbers that multiply to be -3 and add to be -2.

Those numbers are -3 and 1 since (-3)(1)=-3 and (-3)+(1)=-2.

$0=(t-3)(t+1)$

This implies we have either $t-3=0$ or $t+1=0$

The first equation can be solved by adding 3 on both sides: $t=3$ .

The second equation can be solved by subtracting 1 on both sides: $t=-1$ .

So when $t=3$ seconds, is when the rocket has hit the ground.

5 0

3 years ago

I need help please and thank you

AnnyKZ [126]

The answer is s = 2t - 1/2r

5 0

3 years ago

In act 2 scene 1 who is the first person mama tells she bought a house

ioda

Her Grandson Travis. Walter asks what she has done. Ruth is in the kitchen, Travis runs in and Mama tells Travis she went out and bought a house

4 0

3 years ago

Read 2 more answers

State the additive property of zero using the variable b.

Juli2301 [7.4K]

Answer with Step-by-step explanation:

We are given a variable b

We have to state the additive property of zero using the variable b.

Additive property of zero: It states that when any number b is added to zero then we get sum is equal to number itself.

Mathematical representation:

$b+0=0+b=b$

Suppose, a number b=9

Then, 9+0=9

0+9=9

This property is called additive property of zero because when 9 is added to 0 then we get sum equals to 9.

7 0

3 years ago

How do I find a2 and a3 for the following geometric sequence? 54, a2, a3, 128

vlada-n [284]

The formula for the nth term of a geometric sequence:
$a_n=a_1 \times r^{n-1}$
a₁ - the first term, r - the common ratio

$54, a_2, a_3, 128 \\ \\
a_1=54 \\
a_4=128 \\ \\
a_n=a_1 \times r^{n-1} \\
a_4=a_1 \times r^3 \\
128=54 \times r^3 \\
\frac{128}{54}=r^3 \\ \frac{128 \div 2}{54 \div 2}=r^3 \\
\frac{64}{27}=r^3 \\
\sqrt[3]{\frac{64}{27}}=\sqrt[3]{r^3} \\
\frac{\sqrt[3]{64}}{\sqrt[3]{27}}=r \\
r=\frac{4}{3}$

$a_2=a_1 \times r= 54 \times \frac{4}{3}=18 \times 4=72 \\
a_3=a_2 \times r=72 \times \frac{4}{3}=24 \times 4=96 \\ \\
\boxed{a_2=72, a_3=96}$

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3 years ago

Read 2 more answers