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3 years ago

How to do this help please

Mathematics

1 answer:

andre [41]3 years ago

6 0

Answer:

y = - $\frac{8}{15}$ x + $\frac{289}{15}$

Step-by-step explanation:

The angle between the tangent and the radius at point P is 90°

Calculate the slope of the radius m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₂ - x₁ )

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (8, 15)

m = $\frac{15-0}{8-0}$ = $\frac{15}{8}$

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{\frac{15}{8} }$ = - $\frac{8}{15}$ , thus

y = - $\frac{8}{15}$ x + b ← is the partial equation

To find b substitute (8, 15) into the partial equation

15 = - $\frac{64}{15}$ + b ⇒ b = 15 + $\frac{64}{15}$ = $\frac{289}{15}$

y = - $\frac{8}{15}$ x + $\frac{289}{15}$ ← equation of tangent

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Out of 10 students, 1 student is wearing brown shoes, 7 students are wearing black shoes. What fraction of the students are not

iVinArrow [24]

Answer:

$Fraction=\frac{1}{5}$

Step-by-step explanation:

Total number of students $=10$

Students wearing brown shoes $=1$

Students wearing black shoes $=7$

Number of students wearing black or brown shoes $=1+7=8$

Number of students not wearing brown or black $=10-8=2$

Fraction of students not wearing brown or black $=\frac{2}{10}=\frac{1}{5}$

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3 years ago

The base and sides of a container is made of wood panels. The container does not have a lid. The base and sides are rectangular.

vfiekz [6]

Answer:

Minimum surface area = $70.77 cm^2$

Step-by-step explanation:

We are given that

Width of container=x cm

Length of container=2x cm

Volume of container= $54 cm^3$

We have to find the minimum surface areas that this container will have.

Volume of container= $l\times b\times h$

$x\times 2x\times h=54$

$2x^2h=54$

$h=\frac{54}{2x^2}=\frac{27}{x^2}$

Surface area of container= $2(b+l)h+lb$

Because the container does not have lid

Surface area of container= $S=2(2x+x)\times \frac{27}{x^2}+2x\times x$

$S=\frac{162}{x}+2x^2$

Differentiate w.r.t x

$\frac{dS}{dx}=-\frac{162}{x^2}+4x$

$\frac{dx^n}{dx}=nx^{n-1}$

Substitute $\frac{dS}{dx}=0$

$-\frac{162}{x^2}+4x=0$

$4x=\frac{162}{x^2}$

$x^3=\frac{162}{4}=40.5$

$x^3=40.5$

$x=(40.5)^{\frac{1}{3}}$

$x=3.4$

Again differentiate w.r.t x

$\frac{d^2S}{dx^2}=\frac{324}{x^3}+4$

Substitute x=3.4

$\frac{d^2S}{dx^2}=\frac{324}{(3.4)^3}+4=12.24>0$

Hence, function is minimum at x=3.4

Substitute x=3.4

Then, we get

Minimum surface area = $\frac{162}{(3.4)}+2(3.4)^2=70.77 cm^2$

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3 years ago

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So you would break 247 in to 200,40and 7
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4 years ago

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Answer:

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3 years ago

A random sample of 50 units is drawn from a production process every half hour. the true fraction of nonconforming products manu

Naya [18.7K]

solution:

The probability mass function for binomial distribution is,

Where,

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binomial (50,0.02)

Also, the estimate of the true probability is,

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The probability mass function for binomial distribution is,

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X=0,1,2,3,…..; q=1-p

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3 years ago