All categories

3 years ago

Daniel kicks a soccer ball and the trajectory is modeled by f(t) =− 16t^2+ 32t .

Mathematics

1 answer:

vagabundo [1.1K]3 years ago

3 0

Answer:

f(1) = 16

Domain: 0 ≤ t ≤ 2

Step-by-step explanation:

Given

f(t) = -16t²+ 32t

Solving (a): f(1)

Substitute 1 for t in f(t)

f(t) =− 16t²+ 32t .

f(1) =− 16 * (1)²+ 32 * 1

f(1) = -16 * 1 + 32

f(1) = -16 + 32

f(1) = 16

Solving (b): The domain

The implication of the given parameter in (b) is that t ≤ 2.

Since t represents time, t can't be negative.

Hence, a reasonable domain is

0 ≤ t ≤ 2

You might be interested in

A recipe calls for 2 1/2 cups of flour. The recipe makes 5 servings.How many cups of flour are needed to make 7 servings.

iVinArrow [24]

Answer:

3 1/2 cups of flour

Step-by-step explanation:

I used this equation:

2.5/5 = x/7

Then I cross multiplied:

2.5 * 7 = 5x

After I found out that x = 3 1/2

3 0

3 years ago

For the cost function c equals 0.1 q squared plus 2.1 q plus 8, how fast does c change with respect to q when q equals 11? Det

Soloha48 [4]

Answer:

Rate of change of c with respect to q is 4.3

Percentage rate of change c with respect to q is 9.95%

Step-by-step explanation:

Cost function is given as, $c=0.1\:q^{2}+2.1\:q+8$

Given that c changes with respect to q that is, $\dfrac{dc}{dq}$ . So differentiating given function,

$\dfrac{dc}{dq}=\dfrac{d}{dq}\left (0.1\:q^{2}+2.1\:q+8 \right)$

Applying sum rule of derivative,

$\dfrac{dc}{dq}=\dfrac{d}{dq}\left(0.1\:q^{2}\right)+\dfrac{d}{dq}\left(2.1\:q\right)+\dfrac{d}{dq}\left(8\right)$

Applying power rule and constant rule of derivative,

$\dfrac{dc}{dt}=0.1\left(2\:q^{2-1}\right)+2.1\left(1\right)+0$

$\dfrac{dc}{dt}=0.1\left(2\:q\right)+2.1$

$\dfrac{dc}{dt}=0.2\left(q\right)+2.1$

Substituting the value of $q=11$ ,

$\dfrac{dc}{dt}=0.2\left(11\right)+21.$

$\dfrac{dc}{dt}=2.2+2.1$

$\dfrac{dc}{dt}=4.3$

Rate of change of c with respect to q is 4.3

Formula for percentage rate of change is given as,

$Percentage\:rate\:of\:change=\dfrac{Q'\left(x\right)}{Q\left(x\right)}\times 100$

Rewriting in terms of cost C,

$Percentage\:rate\:of\:change=\dfrac{C'\left(q\right)}{C\left(q\right)}\times 100$

Calculating value of $C\left(q \right)$

$C\left(q\right)=0.1\:q^{2}+2.1\:q+8$

Substituting the value of $q=11$ ,

$C\left(q\right)=0.1\left(11\right)^{2}+2.1\left(11\right)+8$

$C\left(q\right)=0.1\left(121\right)+23.1+8$

$C\left(q\right)=12.1+23.1+8$

$C\left(q\right)=43.2$

Now using the formula for percentage,

$Percentage\:rate\:of\:change=\dfrac{4.3}{43.2}\times 100$

$Percentage\:rate\:of\:change=0.0995\times 100$

$Percentage\:rate\:of\:change=9.95%$

Percentage rate of change of c with respect to q is 9.95%

7 0

3 years ago

Lakshmi has 11 more20-rupee notes than 10-rupee notes. If she has Rs 550 in total, how many notes of each kind does she have?

olganol [36]

Answer:

10rupee notes are 11

20rupee notes are 22

Step-by-step explanation:

Let 10-rupee note be x

20-rupee note will be x + 11

The equation will be

10x + 20(x + 11) = 550

10x + 20x + 220 = 550

30x = 330

x = 330/30 = 11 = 10rupee notes

y = 11+11 = 22 = 20rupee notes

6 0

3 years ago

Linear equations. Solve the equation: 10 = 7x - 4

lutik1710 [3]

Answer: $x = 2$

Step-by-step explanation:

$10 = 7x - 4$

Add 4 to both sides

$10 + 4 = 7x - 4 + 4$

$14 = 7x$

Divide through by 7

$\frac{14}{7}=\frac{7x}{7}$

$2 = x$

Therefore :

$x = 2$

5 0

3 years ago

Read 2 more answers

the ratio of red marbles to yellow marbles placed in a bag is 2:7. More marbles are added to the bag: 3 red and 3 yellow marbles

Anvisha [2.4K]

Answer: False.

Step-by-step explanation:

Initially, the ratio is 2:7

This means that if we have 2 red marbles, we must have 7 yellow ones.

The quotient here is 7/2 = 3.5

Now, if you add 3 marbles of each colour, then we have:

2 + 3 = 5 red marbles

7 + 3 = 10 yellow marbles.

Now the ratio is 5:10

This means that for every 5 red marbles, we have 10 yellow ones.

But now we can divide both numbers by the same positive integer, because they have a common factor equal to 5.

5/5 = 1

10/5 = 2

Then we have:

5:10 = 1:2

So the new ratio is 1:2

Then the ratio changed when we added the new marbles, which means that Maria was wrong.

8 0

3 years ago