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3 years ago

State the domain and range.

Mathematics

1 answer:

AleksandrR [38]3 years ago

6 0

Answer:

domain is {-infinity, +infinity}

Step-by-step explanation:

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Use implicit differentiation to find an equation of the tangent line to the curve at the given point. 7x2 + xy + 7y2 = 15, (1, 1

riadik2000 [5.3K]

Assume $y=y(x)$ .

$7x^2+xy+7y^2=15$
$\dfrac{\mathrm d}{\mathrm dx}[7x^2+xy+7y^2]=\dfrac{\mathrm d}{\mathrm dx}[15]$
$14x+y+x\dfrac{\mathrm dy}{\mathrm dx}+14y\dfrac{\mathrm dy}{\mathrm dx}=0$
$\dfrac{\mathrm dy}{\mathrm dx}(x+14y)=-(14x+y)$
$\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{14x+y}{x+14y}$

The slope of the tangent line to the curve at $(a,b)$ is then $-\dfrac{14a+b}{a+14b}$ , so the tangent to $(1,1)$ has slope

$\dfrac{\mathrm dy}{\mathrm dx}\bigg|_{x=1,y=1}=-\dfrac{15}{15}=-1$

The point-slope form of the tangent line is then

$y-1=-(x-1)\iff y=-x+2$

7 0

3 years ago

A farmer uses a lot of fertilizer to grow his crops. The farmer's manager thinks fertilizer products from distributor A contain

noname [10]

Answer:

$Z_{H0}$ = 1.56

Step-by-step explanation:

Hello!

You have two independent samples of fertilizers from distributor A and B, and need to test if the average content of nitrogen from fertilizer distributed by A is greater than the average content of nitrogen from fertilizer distributed by B.

Sample 1

X₁: Content of nitrogen of a fertilizer batch distributed by A

n₁= 4 batches

Sample mean X₁[bar]= 23pound/batch

σ₁= 4 poundes/batch

Sample 2

X₂: Content of nitrogen of a fertilizer batch distributed by B

n₂= 4 batches

Sample mean X₂[bar]= 18pound/batch

σ₂= 5 pounds/batch

Both variables have a normal distribution. Now since you have the information on the variables distribution and the values of the population standard deviations, you could use a pooled Z-test.

Your hypothesis are:

H₀: μ₁ ≤ μ₂

H₁: μ₁ > μ₂

The statistic to use is:

Z= X₁[bar] - X₂[bar] - (μ₁ - μ₂) ~N(0;1)

√(δ²₁/n₁ + δ²₂/n₂)

$Z_{H0}$ = (23 - 18) - 0 = 1.56

√(16/4 + 25/4)

I hope this helps!

8 0

3 years ago

What is an equation of the line that passes through the points (6,1) and (7, 2)?

deff fn [24]

It’s a line UWU becuase of teh timeline and the universe glimpse

5 0

2 years ago

Read 2 more answers

What is the measurement of the indicated angle?

White raven [17]

A triangle angles all add up to 180 degrees and you have a 90 and 40 degree angle so you are at 130 degrees so the answer is B) x=50 degrees

3 0

2 years ago

2 (y+6) + 6 (y+6) Expand and simplify

san4es73 [151]

Hi there! The answer is 8y + 48.

$2(y + 6) + 6(y + 6)$
First work out the parenthesis.

$2y + 12 + 6y + 36$
Rewrite the expression in order to collect the terms.

$2y + 6y + 12 + 36$
Next up, collect the terms.

$8y + 48$
Now we've found our answer.

5 0

3 years ago