Ask question

Ask question

All categories

3 years ago

12

A ball is launched from a sling shot. Its height, h(x), can be represented by a quadratic function in terms of time, x, in secon

ds.
After 1 second, the ball is 148 feet in the air; after 2 seconds, it is 272 feet in the air.

Find the height, in feet, of the ball after 6 seconds in the air.

I have no idea any help?

1 answer:

Vikki [24]3 years ago

5 0

From the data given, generate first the quadratic equation which best describe the height of the ball. The quadratic function has a general form of
f(x) = Ax^2 + Bx

Substituting the known data,

(1) 148 = A(1^2) + B(1)
(2) 272 = A (2^2) + B (2)
solving for A and B simultaneously,

A = -12
B = 160

To answer this problem, substitute 6 to x. Thus, after 6 seconds, the height is 528 feet.

You might be interested in

Somebody, please help! This is my exam.

Kazeer [188]

Answer is B if it isn’t I’m sorry

7 0

3 years ago

Read 2 more answers

Katen [24]

Answer:

Q2. (16,8)

Q3. $k=\frac{2}{3}$ , ratio=5:1

Q4. Ratio=2:1

Q5. Ratio=1:1

Step-by-step explanation:

Q2. Let (2a,a) be the coordinates of P.

Since P is equidistant from Q (2,-5) and R (-3, 6), we have

$|PQ|=|PR|$

This gives us:

$\sqrt{(2a-2)^2+(a+5)^2}=\sqrt{(2a+3)^2+(6-a)^2}$

$\implies (2a-2)^2+(a+5)^2=(2a+3)^2+(6-a)^2$

Expand:

$4a^2-8a+4+a^2+10a+25=4a^2+12a+9+a^2 -12a+36$

$2a=16$

$a=8$

The coordinates of P are $(16,8)$

Q.3 The equation of the line segment joining the points

A (5.-6) and B (-1,-4) is $x+3y=-13$ .

The x-coordinate of the point that divides AB in the ratio m:n is

$x=\frac{mx_2+nx_1}{m+n}$

The y-axis meets this line at $(0,-\frac{13}{3})$

We substitute $x_2=-1,x_1=5,x=0$ into this equation and solve for m and n.

$0=\frac{-m+5n}{m+n}$

$m=5n$

$\frac{m}{n}=\frac{5}{1}$

Therefore the ratio is m:n=5:1

Q.4 The equation of the line segment joining

the points (-5,-4) and (-2,3) is $-7x+3y=23$ .

The point (-3, k) must satisfy this line because it lies on it.

$-7(-3)+3k=23$ .

$\implies k=\frac{2}{3}$

We again use the equation $x=\frac{mx_2+nx_1}{m+n}$ to find the given ratio.

Substitute: $x_2=-2,x_1=-5$

$4=\frac{-2m+-5n}{m+n}$

$\implies m=2n$

$\frac{m}{n}= \frac{2}{1}$

The ratio is m:n=2:1

Q. 5 The equation of the line joining A (2,3) and B(6,-3) is $3x+2y=12$ .

We substitute (4,m) to get:

12+4m=12

4m=0

m=0

It is obvious that: (4,0) is the midpoint of A(2,3) and B(6,-3).

Hence the ratio is 1:1

5 0

3 years ago

Please anyone can help me to solve the questions please

Dafna11 [192]

Answer:

144 169 225

Step-by-step explanation:

12² = 144

13² = 169

15² = 225

5 0

3 years ago

Read 2 more answers

Will give brainliest if done properly

k0ka [10]

Answer:

$\sf \boxed{ \sf y - 3 = \dfrac{3}{2} (x - 6)}$

Explanation:

$\sf Given \ equation: y = \dfrac{3}{2} x - 5$

Comparing it with slope intercept form "y = mx + b" where 'm' is slope and 'b' is y-intercept.

Here slope: 3/2 and y-intercept: -5

Parallel slope has the same tangent slope.

Pass through point (x, y) = (6, 3)

Equation:

$\sf y - y_1 = m(x - x_1)$

$\rightarrow \sf y - 3 = \dfrac{3}{2} (x - 6)$

6 0

1 year ago

5) Two machines M1, M2 are used to manufacture resistors with a design

Basile [38]

Answer:

Since M1 has the higher probability of being in the desired range, we choose M1.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Two machines M1, M2 are used to manufacture resistors with a design specification of 1000 ohm with 10% tolerance.

So we need the machines to be within 1000 - 0.1*1000 = 900 ohms and 1000 + 0.1*1000 = 1100 ohms.

For each machine, we need to find the probabilty of the machine being in this range. We choose the one with the higher probability.

M1:

Resistors of M1 are found to follow normal distribution with mean 1050 ohm and standard deviation of 100 ohm. This means that $\mu = 1050, \sigma = 100$

The probability is the pvalue of Z when X = 1100 subtracted by the pvalue of Z when X = 900. So

X = 1100

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1100 - 1050}{100}$

$Z = 0.5$

$Z = 0.5$ has a pvalue of 0.6915.

X = 900

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{900 - 1050}{100}$

$Z = -1.5$

$Z = -1.5$ has a pvalue of 0.0668

0.6915 - 0.0668 = 0.6247.

M1 has a 62.47% probability of being in the desired range.

M2:

M2 are found to follow normal distribution with mean 1000 ohm and standard deviation of 120 ohm. This means that $\mu = 1000, \sigma = 120$

X = 1100

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1100 - 1000}{120}$

$Z = 0.83$

$Z = 0.83$ has a pvalue of 0.7967.

X = 900

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{900 - 1000}{120}$

$Z = -0.83$

$Z = -0.83$ has a pvalue of 0.2033

0.7967 - 0.2033 = 0.5934

M2 has a 59.34% probability of being in the desired range.

Since M1 has the higher probability of being in the desired range, we choose M1.

8 0

3 years ago