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2 years ago

MARK AS BRAINLIEST

Mathematics

1 answer:

labwork [276]2 years ago

6 0

Answer:

C [-2 < x]

Step-by-step explanation:

-6(x - 2) < 24

________ ___

-6 -6

x - 2 > -4

+ 2 + 2

_________

x > -2

** Whenever you divide\multiply by a negative, you reverse the inequality symbol.

I am joyous to assist you anytime.

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Find the Area of a circle with a diameter of 10 inches

LekaFEV [45]

Answer:

78.5 inch²

Step-by-step explanation:

Given

diameter (d) = 10 inches

radius (r) = 10 / 2 = 5 inches

Area of circle

= πr²

= 3.14 * ( 5)²

= 3.14 * 25

= 78.5 inch²

6 0

2 years ago

Find an equation of the tangent to the curve x =5+lnt, y=t2+5 at the point (5,6) by both eliminating the parameter and without e

svet-max [94.6K]

ANSWER

$y = 2x -4$

EXPLANATION

Part a)

Eliminating the parameter:

The parametric equation is

$x = 5 + ln(t)$

$y = {t}^{2} + 5$

From the first equation we make t the subject to get;

$x - 5 = ln(t)$

$t = {e}^{x - 5}$

We put it into the second equation.

$y = { ({e}^{x - 5}) }^{2} + 5$

$y = { ({e}^{2(x - 5)}) } + 5$

We differentiate to get;

$\frac{dy}{dx} = 2 {e}^{2(x - 5)}$

At x=5,

$\frac{dy}{dx} = 2 {e}^{2(5 - 5)}$

$\frac{dy}{dx} = 2 {e}^{0} = 2$

The slope of the tangent is 2.

The equation of the tangent through

(5,6) is given by

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

$y - 6 = 2(x - 5)$

$y = 2x - 10 + 6$

$y = 2x -4$

Without eliminating the parameter,

$\frac{dy}{dx} = \frac{ \frac{dy}{dt} }{ \frac{dx}{dt} }$

$\frac{dy}{dx} = \frac{ 2t}{ \frac{1}{t} }$

$\frac{dy}{dx} = 2 {t}^{2}$

At x=5,

$5 = 5 + ln(t)$

$ln(t) = 0$

$t = {e}^{0} = 1$

This implies that,

$\frac{dy}{dx} = 2 {(1)}^{2} = 2$

The slope of the tangent is 2.

The equation of the tangent through

(5,6) is given by

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

$y - 6 = 2(x - 5) =$

$y = 2x -4$

5 0

3 years ago

N a region, there is a 0.70.7 probability chance that a randomly selected person of the population has brown eyes. assume 1414

taurus [48]

'll use the binomial approach. We need to calculate the probabilities that 9, 10 or 11
people have brown eyes. The probability that any one person has brown eyes is 0.8, 
so the probability that they don't is 1 - 0.8 = 0.2. So the appropriate binomial terms are 

(11 C 9)(0.8)^9*(0.2)^2 + (11 C 10)(0.8)^10*(0.2)^1 + (11 C 11)(0.8)^11*(0.2)^0 = 

0.2953 + 0.2362 + 0.0859 = 0.6174, or about 61.7 %. Since this is over 50%, it 

is more likely than not that 9 of 11 randomly chosen people have brown eyes, at 
least in this region. 

Note that (n C r) = n!/((n-r)!*r!). So (11 C 9) = 55, (11 C 10) = 11 and (11 C 0) = 1.

8 0

2 years ago

What are the slope and the y-intercept of the graph of the linear function shown on the grid?

poizon [28]

Y-intercept looks like -1.5 and slope is -1/4

8 0

2 years ago

Help! I’ll give extra points:)

Fofino [41]

Answer:

if I'm not wrong I think it's B

3 0

2 years ago