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3 years ago

QUICK QUICK I NEED YOUR ANSWER FAST! 2 MINUTES ONLY! WITH AN EXPLANATION PLEASE! THEN YOU WILL BE THE BRAINLIEST!

Mathematics

1 answer:

8090 [49]3 years ago

5 0

Answer:

4 sections with a small left over

Step-by-step explanation:

theres 36ft of wire so you cut it into 8.5 sections so devide them by eachother and you with get 4.2

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Find the equation of the tangent line to the curve (a lemniscate)

olya-2409 [2.1K]

Answer:

$m=\frac{9}{13}$ and $b=\frac{40}{13}$

Step-by-step explanation:

The equation of curve is

$2(x^2+y^2)^2=25(x^2-y^2)$

We need to find the equation of the tangent line to the curve at the point (-3, 1).

Differentiate with respect to x.

$2[2(x^2+y^2)\frac{d}{dx}(x^2+y^2)]=25(2x-2y\frac{dy}{dx})$

$4(x^2+y^2)(2x+2y\frac{dy}{dx})=25(2x-2y\frac{dy}{dx})$

The point of tangency is (-3,1). It means the slope of tangent is $\frac{dy}{dx}_{(-3,1)}$ .

Substitute x=-3 and y=1 in the above equation.

$4((-3)^2+(1)^2)(2(-3)+2(1)\frac{dy}{dx})=25(2(-3)-2(1)\frac{dy}{dx})$

$40(-6+2\frac{dy}{dx})=25(-6-2\frac{dy}{dx})$

$-240+80\frac{dy}{dx})=-150-50\frac{dy}{dx}$

$80\frac{dy}{dx}+50\frac{dy}{dx}=-150+240$

$130\frac{dy}{dx}=90$

Divide both sides by 130.

$\frac{dy}{dx}=\frac{9}{13}$

If a line passes through a points $(x_1,y_1)$ with slope m, then the point slope form of the line is

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

The slope of tangent line is $\frac{9}{13}$ and it passes through the point (-3,1). So, the equation of tangent is

$y-1=\frac{9}{13}(x-(-3))$

$y-1=\frac{9}{13}(x)+\frac{27}{13}$

Add 1 on both sides.

$y=\frac{9}{13}(x)+\frac{27}{13}+1$

$y=\frac{9}{13}(x)+\frac{40}{13}$

Therefore, $m=\frac{9}{13}$ and $b=\frac{40}{13}$ .

5 0

3 years ago

Can you help me on question 17?!

fomenos

Answer:

x³+57

step by step explanation

8 0

3 years ago

Solve the following pairs of simultaneous equations.

Sergeeva-Olga [200]

Answer and step-by-step explanation:

a) -4x + 5y = -9 (2)

2x + 3y = 21

Multiply the second equation by 2, you will get:

4x + 6y = 42 (1)

Use (1) plus with (2), you will get:

4x + (-4x) + 6y + 5y = -9 + 42

11y = 33

y = 33/11

y = 3

4x + 18 = 42

4x = 24

x = 6

b) 2x + 5y = -6

3x + 2y = 2

Multiply first equation by 3, you will get:

6x + 15y = -18 (1)

Multiply the second equation by 2 and you will get:

6x + 4y = 4 (2)

Subtract (1) by (2), we got:

6x -6x + 15y - 4y = -18 - 4

11y = -22

y = -22/11

y = -2

6x + 4y = 4

6x -8 = 4

6x = 12

x = 2

c) 2x - 2y = -4

5x + 4y = 17 (2)

Multiply the first euation by 2, we got:

4x - 4y = -4 (3)

Use (3) minus for (2), we get:

4x - 5x -4y + 4y = -4 - 17

-x = -21

x = 21

4x - 4y = -4

84 - 4y = -4

-4y = -4 + 84

-4y = 80

y = 80 / -4

y = -20

d) 2x - 3y = 6

4x - 5y = 9 (1)

Multiply the first equation by 2, we got:

4x - 6y = 12 (2)

Use (1) minus for (2), we got:

4x -4x - 5y - 6y = 9 -12

-11y = -3

y = -3/-11

y = 3/11

2x - 3y = 6

2x - 9/11 = 6

2x = 66/11 + 9/ 11

2x = 75/11

x = 75/11 * 1/2

x = 75 / 22

e) x/2 + y/3 = 2

x/4 + y/3 = 4

Use the first equation subtract the second equation, we got:

x/2 - x/4 + y/3 - y/3 = 2 - 4

2x/4 -x/4 = -2

x/ 4 = -2

x = -2 * 4

x = -8

x/2 + y/3 = 2

-8 / 2 + y/3 = 2

y / 3 = 2 + 4

y/3 = 6

y = 6*3

y = 18

f) x/3 + y/2 = 3/2 (1)

x/2 + y/5 = -1/2 (2)

I don't know how to solve this, sr

Hope this helped :3

3 0

3 years ago

Proving a Quadrilateral Is a Parallelogram

Schach [20]

Answer: a. yes, one pair of opposite sides could measure 10in., and the other pair could measure 13 in.

Step-by-step explanation: i just took it

8 0

3 years ago

Suppose a consumer group suspects that the proportion of households that have three cell phones NOT known to be 30%. A cell phon

leva [86]

Answer:

We conclude that the actual percentage of households is equal to 30%.

Step-by-step explanation:

We are given that a consumer group suspects that the proportion of households that have three cell phones NOT known to be 30%.

Their marketing people survey 150 households with the result that 43 of the households have three cell phones.

Let p = proportion of households that have three cell phones NOT known.

So, Null Hypothesis, $H_0$ : p = 30% {means that the actual percentage of households is equal to 30%}

Alternate Hypothesis, $H_A$ : p $\neq$ 30% {means that the actual percentage of households different from 30%}

The test statistics that would be used here One-sample z-test for proportions;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of households having three cell phones = $\frac{43}{150}$ = 0.29

n = sample of households = 150

So, the test statistics = $\frac{0.29-0.30}{\sqrt{\frac{0.30(1-0.30)}{150} } }$

= -0.27

The value of z test statistic is -0.27.

Also, P-value of the test statistics is given by;

P-value = P(Z < -0.27) = 1 - P(Z $\leq$ 0.27)

= 1 - 0.6064 = 0.3936

Now, at 1% significance level the z table gives critical value of -2.58 and 2.58 for two-tailed test.

Since our test statistic lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the actual percentage of households is equal to 30%.

4 0

3 years ago