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2 years ago

7

Which expression is equal to 6(−3m)4?

1 answer:

Anarel [89]2 years ago

7 0

Answer:

-72m

Step-by-step explanation:

6(-3m)4

-18m(4)

-72m

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A pebble is tossed into the air from the top of a cliff. The height, in feet, of the pebble over time is modeled by the equation

Charra [1.4K]

Answer:

96

Step-by-step explanation:

The maximum height reached by the pebble modeled by the quadratic function,

$h(t)=-16t^2+32t+80$ , can be found by finding the vertex.

Let's first find the t-coordinate of the vertex . The max height will correspond to this value of t which means we have to find the h(t)-coordinate.

When comparing $h$ to $at^2+bt+c$ , we see that:

$a=-16$

$b=32$

$c=80$

We need to evaluate the following to find the t-coordinate of the vertex:

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

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

$t=\frac{-32}{-32}$

$t=1$

So now to find the correspond h(t)-coordinate, we will need to replace t in $-16t^2+32t+80$ with 1:

$-16(1)^2+32(1)+80$

$-16(1)+32+80$

$-16+32+80$

$16+80$

$96$

5 0

2 years ago

. A 25-ft ladder is leaning against a wall. If we push the ladder toward the wall at a rate of 1 ft/sec, and the bottom of the l

Vlada [557]

Answer:

0.75 feet per second.

Step-by-step explanation:

Please find the attachment.

We have been given that a 25-ft ladder is leaning against a wall. We can see from the attachment that ladder forms a right triangle with respect to wall and ground.

So we can set a Pythagoras theorem as:

$x^2+y^2=25^2$

$x^2+y^2=625$

Now, we need to find the derivative of above equation with respect to time.

$2x\cdot \frac{dx}{dt}+2y\cdot \frac{dy}{dt}=0$

Since the adder is moving toward the wall at a rate of 1 ft/sec for 5 sec, so x after 5 seconds would be: $20-1(5)=20-5=15$

Let us solve for y using Pythagoras theorem.

$y^2+15^2=25^2$

$y^2+225=625$

$y^2=625-225$

$y^2=400$

Take positive square root:

$\sqrt{y^2}=\sqrt{400}$

$y=20$

Upon substituting our given values in derivative equation, we will get:

$2x\cdot \frac{dx}{dt}+2y\cdot \frac{dy}{dt}=0$

$2(15)\cdot(-1)+2(20)\cdot \frac{dy}{dt}=0$

$-30+40\cdot \frac{dy}{dt}=0$

$40\cdot \frac{dy}{dt}=30$

$\frac{dy}{dt}=\frac{30}{40}$

$\frac{dy}{dt}=0.75$

Therefore, the ladder is moving up at a rate of 0.75 feet per second.

3 0

2 years ago

Raj drove his car 5 times farther than Gary drives his car. Together they drive 624 miles. How many miles does Raj drive?

12345 [234]

Raj drove 124.8 miles

5 0

2 years ago

Read 2 more answers

Based on the graph shown to the right, whose phones cost varies directly with the amount of time spent talking?

Lena [83]

Answer:

B

Step-by-step explanation:

Given 2 quantities that vary directly, then the graph must pass through the origin.

Nikiya's graph is the only one to do this ⇒ B

8 0

2 years ago

Read 2 more answers

The quotient of 9 3/4 and 5/8

suter [353]

Answer:

15.6

Step-by-step explanation:

$9\frac{3}{4} = \frac{39}{4}$
Plug 39/4 in: 39/4 ÷ 5/8
39/4 ÷ 5/8 = 39/4 × 8/5
39/4 × 8/5 = 312/20
$\frac{312}{20} = 15.6$

I hope this helps!

4 0

2 years ago

Read 2 more answers