During a pumpkin launching contest, two pumpkins are launched at the same time. The path of pumpkin A is modeled by the equation h(x) = –0.01x2 + 0.32x + 4. The path of pumpkin B is modeled by the equation h(x) = –0.01x2 + 0.18x + 5. If x represents the distance the pumpkin traveled and h(x) represents height, what does the intersection point of the equations represent?

Answers

Answer 1

Answer: You just need to solve for x in the equation:
–0.01x^2 + 0.32x + 4 = –0.01x^2 + 0.18x + 5
0.18x=1
x= 5.55
h(5.55) = -0.01*30.86+0.18*5.55+5 = -0.3086+1+5=5.6914

The intersection point is (5.55, 5.69).
I hope that this is the answer that you were looking for and it has helped you.

Answer 2

Answer:

D.) The distance at which the height of the pumpkins are the same.

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A vehicle travels a distance of 5t4 − 10t2 + 6 miles in t + 2 minutes. What is the vehicle's speed?

Answers

Let distance be s and velocity be v
s = 5t⁴ - 10t² + 6
We know velocity is the change in distance per unit time, so
v = ds/dt
v = 20t³ - 20t

Answer:

The speed is 5t^3 - 10t^2 + 10t - 20 + 46/(t+2) miles per minute

Step-by-step explanation:

How are fractions and ratios the same? How are they different?

Answers

Answer:

Step-by-step explanation:

Ratios depend on the numbers that are being compared. When you are describing a part of a whole, a fraction is appropriate. When you are comparing two numbers, a ratio is appropriate.

Basically you can write ratio as fraction

Ex-4:2, 4/2

See what I mean?

Question 1 Which expression is the simplified form of the square root 150 times b cubed?

6 times b times the square root of 5 times b

5 times b times the square root of 6

6 times b times the square root of 5

5 times b times the square root of 6 times b

Answers

5 times b times the square root of 6 times b;
$\sqrt{150* b^(3) }$
$\sqrt{25*6* b^(3) }$
=5b $√(6b)$

Answer:

The simplified form of the given expression is:

5 times b times the square root of 6 times b .

Step-by-step explanation:

We are given a expression in words as:

square root 150 times b cubed.

Now mathematically it is expressed as:

$√(150b^3)$

Now on simplifying as follows:

$√(150b^3)=√(5^2* 3* 2* b^2* b)\n\n√(150b^3)=√((5b)^2* 6b)\n\n√(150b^3)=√((5b)^2)* √(6b)\n\n√(150b^3)=5b√(6b)$

Hence, we obtain the expression:

5 times b times the square root of 6 times b .

(i.e. $5b√(6b)$ )

How do you solve ∣∣x∣∣-8 < -4

Answers

$||x||-8 < -4\n|x|< 4\nx<4 \wedge x>-4\nx\in(-4,4)$

Trig-Please help ASAP! Use either the law of cosines or the law of sines to find the measure of angle C

Answers

Answer:

C = 81.6 degrees

Step-by-step explanation:

The formula for law of sines

sin A sin B sin C

-------- = ----------- = -------------

a b c

Looking at the diagram, we know A = 54, b = 7.4 and c = 15.8

not enough to use the law of sines

We will need to use the law of cosines

a^2 = b^2 + c^2 - 2ac cos A

Using the law of cosines, we can calculate the length of a

a^2 = 7.4^2 + 15.8^ -2*7.4*15.8 cos 54

a^2 = 54.6+249.64-233.84cos54

a^2 =166.7922966

a = 12.921

Now we can use the law of sines to find C

sin 54 sin C

-------- = -------------

12.921 15.8

Using cross products

15.8 * sin 54 = 12.921 * sin C

Divide each side by 12.921

15.8 /12.921 * sin 54 = sin C

Take the arcsin of each side

arcsin (15.8 /12.921 * sin 54) = arcsin (sin C)

arcsin (15.8 /12.921 * sin 54) = C

C = 81.6 degrees

Use the following number line to determine if the expressions are true or false.

Answers

Answer:

${ \tt{a < b→true}} \n { \bf{reason :because \: - 1 \: is \: less \: than \: 4.5 }}\n \n { \tt{ |a| > b →false}} \n { \bf{reason :1 \: is \: not \: greater \: than \: 4.5 }}\n \n { \tt{a < |b| →true}}$

Answer:

true

false

true

Step-by-step explanation:

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