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3 years ago

Solve for x in the diagram below. 110° (8x +30°

Mathematics

1 answer:

Ulleksa [173]3 years ago

6 0

Answer:

880x+30

880 880

x=29.3 repeating

Step-by-step explanation: Hope this helps

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Function p(x), shown below, is translated 10 units up to create function q(x).

natulia [17]

Answer: q(x) = 0.005(x - 40)² + 70

Step-by-step explanation:

f(x) = a(x - h)² + k where a is the vertical stretch and (h, k) is the vertex.

Which coordinate shifts the graph up? The y-coordinate for the vertex is k.

p(x) = 0.005(x - 40)² + 60

q(x) = 0.005(x - 40)² + 60 + 10

= 0.005(x - 40)² + 70

3 0

3 years ago

A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 30 ft/s. Its height

Crank

Answer:

a) h = 0.1: $\bar v = -11\,\frac{ft}{s}$ , h = 0.01: $\bar v = -10.1\,\frac{ft}{s}$ , h = 0.001: $\bar v = -10\,\frac{ft}{s}$ , b) The instantaneous velocity of the ball when $t = 2\,s$ is $-10$ feet per second.

Step-by-step explanation:

a) We know that $y = 30\cdot t -10\cdot t^{2}$ describes the position of the ball, measured in feet, in time, measured in seconds, and the average velocity ( $\bar v$ ), measured in feet per second, can be done by means of the following definition:

$\bar v = \frac{y(2+h)-y(2)}{h}$

Where:

$y(2)$ - Position of the ball evaluated at $t = 2\,s$ , measured in feet.

$y(2+h)$ - Position of the ball evaluated at $t =(2+h)\,s$ , measured in feet.

$h$ - Change interval, measured in seconds.

Now, we obtained different average velocities by means of different change intervals:

$h = 0.1\,s$

$y(2) = 30\cdot (2) - 10\cdot (2)^{2}$

$y (2) = 20\,ft$

$y(2.1) = 30\cdot (2.1)-10\cdot (2.1)^{2}$

$y(2.1) = 18.9\,ft$

$\bar v = \frac{18.9\,ft-20\,ft}{0.1\,s}$

$\bar v = -11\,\frac{ft}{s}$

$h = 0.01\,s$

$y(2) = 30\cdot (2) - 10\cdot (2)^{2}$

$y (2) = 20\,ft$

$y(2.01) = 30\cdot (2.01)-10\cdot (2.01)^{2}$

$y(2.01) = 19.899\,ft$

$\bar v = \frac{19.899\,ft-20\,ft}{0.01\,s}$

$\bar v = -10.1\,\frac{ft}{s}$

$h = 0.001\,s$

$y(2) = 30\cdot (2) - 10\cdot (2)^{2}$

$y (2) = 20\,ft$

$y(2.001) = 30\cdot (2.001)-10\cdot (2.001)^{2}$

$y(2.001) = 19.99\,ft$

$\bar v = \frac{19.99\,ft-20\,ft}{0.001\,s}$

$\bar v = -10\,\frac{ft}{s}$

b) The instantaneous velocity when $t = 2\,s$ can be obtained by using the following limit:

$v(t) = \lim_{h \to 0} \frac{x(t+h)-x(t)}{h}$

$v(t) = \lim_{h \to 0} \frac{30\cdot (t+h)-10\cdot (t+h)^{2}-30\cdot t +10\cdot t^{2}}{h}$

$v(t) = \lim_{h \to 0} \frac{30\cdot t +30\cdot h -10\cdot (t^{2}+2\cdot t\cdot h +h^{2})-30\cdot t +10\cdot t^{2}}{h}$

$v(t) = \lim_{h \to 0} \frac{30\cdot t +30\cdot h-10\cdot t^{2}-20\cdot t \cdot h-10\cdot h^{2}-30\cdot t +10\cdot t^{2}}{h}$

$v(t) = \lim_{h \to 0} \frac{30\cdot h-20\cdot t\cdot h-10\cdot h^{2}}{h}$

$v(t) = \lim_{h \to 0} 30-20\cdot t-10\cdot h$

$v(t) = 30\cdot \lim_{h \to 0} 1 - 20\cdot t \cdot \lim_{h \to 0} 1 - 10\cdot \lim_{h \to 0} h$

$v(t) = 30-20\cdot t$

And we finally evaluate the instantaneous velocity at $t = 2\,s$ :

$v(2) = 30-20\cdot (2)$

$v(2) = -10\,\frac{ft}{s}$

The instantaneous velocity of the ball when $t = 2\,s$ is $-10$ feet per second.

8 0

3 years ago

at the Fall Fest Parade members of the cat lovers club and the dog lovers Club will March in equal rows. there will be six membe

Triss [41]

The fall is waiting on 67-66

7 0

2 years ago

One long-distance company offers a plan such that each minute costs $0.10 and each call has a $0.25 service

gladu [14]

Answer:

y=0.10(t)+0.25

27 minutes and 30 seconds

Step-by-step explanation:

We know that you start with 25 cents as a service fee, this is for making the call. For each minute you talk, 10 cents are added. Multiply the number of minutes spent by 10 cents a minute for the cost based on the call. Then add the 25 cents service fee.

If you talked for 5 minutes:

y=0.10(5)+0.25

y=0.50+0.25

y=0.75

75 Cents

For three dollars, you would plug in 3 for y

3.00=0.10(t)+0.25

-0.25 -0.25

2.75=0.10(t)

divide both sides by 0.10 to get

27.5=t

You can talk for 27 minutes and 30 seconds

27 minutes

Hope this helps :-)

3 0

3 years ago

Please explain so I can understand

Tju [1.3M]

Answer:

well im pretty sure its ( 1,1,3)

Step-by-step explanation:

21-1-2

4 0

2 years ago