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3 years ago

Pls help i will give you 30 points asap

Mathematics

1 answer:

Olegator [25]3 years ago

3 0

In y = mx + b form, the slope can be found in the m position and the y intercept can be found in the b position.

y = mx + b

y = 2x + 15

slope(m) = 2 and y int (b) = 15

The initial amount is the y intercept, which is 15. The rate of change (the slope) is 2

example :

baskets picked in 1 hr :

y = 2(1) + 15

y = 2 + 15

y = 17

baskets picked in 2 hrs :

y = 2(2) + 15

y = 4 + 15

y = 19

so the slope ( rate of change) is basically saying for every hr of picking, you pick 2 baskets...so your picking 2 baskets per hr.

The y intercept (15) is telling us that they already had 15 baskets to start with.

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UNO [17]

Answer:

B is P(x)=(x-3)^2 +2

C is P(x)=(x-1)^2 -5

Step-by-step explanation:

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2 years ago

If a cyclist increases his speed by 3 miles per hour, he can reduce the time required for a 6 mile trip by 10 minutes. What is t

raketka [301]

Answer:

Slower speed = 9 mph

Step-by-step explanation:

Let the initial speed (slower speed) = s mph

Speed 's' = $\frac{\text{Distance}}{\text{Time}}$

s = $\frac{6}{t}$ -------(1)

If the cyclist increases the speed by 3 mph then the final speed = (s + 3) mph

He can reduce the time 't' by 10 minutes ( $\frac{1}{6}$ hours)

Now, (s + 3) = $\frac{6}{t-\frac{1}{6}}$

s + 3 = $\frac{36}{6t-1}$ --------(2)

Substitute the value of 's' from equation (1) to the equation (2).

$\frac{6}{t}+3=\frac{36}{6t-1}$

$\frac{2}{t}+1=\frac{12}{6t-1}$

$\frac{2}{t}-\frac{12}{6t-1}=-1$

$\frac{2(6t-1)-12t}{t(6t-1)}=-1$

$\frac{12t-2-12t}{t(6t-1)}=-1$

$-\frac{2}{t(6t-1)}=-1$

6t² - t = 2

6t² - t - 2 = 0

6t² - 4t + 3t - 2 = 0

2t(3t - 2) + 1(3t - 2) = 0

(2t + 1)(3t - 2) = 0

t = $-\frac{1}{2},\frac{2}{3}$ hours

But the time can't be negative.

Therefore, t = $\frac{2}{3}$ hours is the answer.

From equation (1),

s = $\frac{6}{\frac{2}{3}}$

s = 9 miles per hour.

Slower speed = 9 mph is the answer.

6 0

2 years ago

A small rocket is fired from a launch pad 10 m above the ground with an initial velocity left angle 250 comma 450 comma 500 righ

jonny [76]

Let $\vec r(t),\vec v(t),\vec a(t)$ denote the rocket's position, velocity, and acceleration vectors at time $t$ .

We're given its initial position

$\vec r(0)=\langle0,0,10\rangle\,\mathrm m$

and velocity

$\vec v(0)=\langle250,450,500\rangle\dfrac{\rm m}{\rm s}$

Immediately after launch, the rocket is subject to gravity, so its acceleration is

$\vec a(t)=\langle0,2.5,-g\rangle\dfrac{\rm m}{\mathrm s^2}$

where $g=9.8\frac{\rm m}{\mathrm s^2}$ .

a. We can obtain the velocity and position vectors by respectively integrating the acceleration and velocity functions. By the fundamental theorem of calculus,

$\vec v(t)=\left(\vec v(0)+\displaystyle\int_0^t\vec a(u)\,\mathrm du\right)\dfrac{\rm m}{\rm s}$

$\vec v(t)=\left(\langle250,450,500\rangle+\langle0,2.5u,-gu\rangle\bigg|_0^t\right)\dfrac{\rm m}{\rm s}$

(the integral of 0 is a constant, but it ultimately doesn't matter in this case)

$\boxed{\vec v(t)=\langle250,450+2.5t,500-gt\rangle\dfrac{\rm m}{\rm s}}$

and

$\vec r(t)=\left(\vec r(0)+\displaystyle\int_0^t\vec v(u)\,\mathrm du\right)\,\rm m$

$\vec r(t)=\left(\langle0,0,10\rangle+\left\langle250u,450u+1.25u^2,500u-\dfrac g2u^2\right\rangle\bigg|_0^t\right)\,\rm m$

$\boxed{\vec r(t)=\left\langle250t,450t+1.25t^2,10+500t-\dfrac g2t^2\right\rangle\,\rm m}$

b. The rocket stays in the air for as long as it takes until $z=0$ , where $z$ is the $z$ -component of the position vector.

$10+500t-\dfrac g2t^2=0\implies t\approx102\,\rm s$

The range of the rocket is the distance between the rocket's final position and the origin (0, 0, 0):

$\boxed{\|\vec r(102\,\mathrm s)\|\approx64,233\,\rm m}$

c. The rocket reaches its maximum height when its vertical velocity (the $z$ -component) is 0, at which point we have

$-\left(500\dfrac{\rm m}{\rm s}\right)^2=-2g(z_{\rm max}-10\,\mathrm m)$

$\implies\boxed{z_{\rm max}=125,010\,\rm m}$

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3 years ago

8. Solve for the given variable in the following equations. (4 marks total)

____ [38]

Step-by-step explanation:

V= π*r²*h

V/π = r²*h

v/(π*r²) = h

$\frac{x+y}{3}$ = 5

x+y = 15

x = 15-y

6 0

3 years ago

For what value is a is (a,9) a solution of the equation y=2x+1

yanalaym [24]

Answer:

a = 4

Step-by-step explanation:

y = 2x + 1 ......(1)

Going through y - y1 = m(x - x1)

m is slope and it is 2

y1 = 9 and x1 = a

y - 9 = 2(x - a)

y - 9 = 2x - 2a

y = 2x - 2a + 9 ........(2)

Equating (1) and (2)

2x + 1 = 2x - 2a + 9

Collecting like terms

2x - 2x + 2a = 9 - 1

2a = 8

a = 8/2

a = 4

7 0

3 years ago