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1 year ago

Answer this please !

Mathematics

2 answers:

zavuch27 [327]1 year ago

8 0

Answer:

slope = 6

Step-by-step explanation:

substitute the given points into the equation of the curve to find a and b

(2, a )

$\frac{a}{2}$ = 2² - 7 = 4 - 7 = - 3 ( multiply both sides by 2 to clear the fraction )

a = - 6

then point (2, a ) = (2, - 6 )

(1, b )

$\frac{b}{2}$ = 1² - 7 = 1 - 7 = - 6 ( multiply both sides by 2 )

b = - 12

then point (1, b ) = (1, - 12 )

calculate the slope m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (2, - 6 ) and (x₂, y₂ ) = (1, - 12 )

m = $\frac{-12-(-6)}{1-2}$ = $\frac{-12+6}{-1}$ = $\frac{-6}{-1}$ = 6

SpyIntel [72]1 year ago

3 0

Answer:

Step-by-step explanation:

$\frac{y}{2} =x^{2} -7$

$\frac{a}{2} =2^{2} -7$

$\frac{a}{2} =-3$

$a=-6$

$\frac{b}{2} =1^{2} -7$

$\frac{b}{2} =-6$

$b=-12$

From the calculations above, we learn that line l and the curve intersect at (2, -6) and (1, -12). Next, we will set up a system of linear equations to solve for the slope and the y-intercept of line l.

$-6=2m+b$

$-12=m+b$

$-24=2m+2b$

$18=-b$

$b=-18$

$-12=m-18$

$m=6$

Therefore, the slope of line l is 6.

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lapo4ka [179]

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Step-by-step explanation:

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2 years ago

PLEASE HELP!! URGENT!! WILL GIVE BRAINLIEST TO FASTEST ANSWER!! TAKING TEST ON EDGE 2020!!

Leto [7]

Answer:

expressions which represent exponential decay:

A. 900(0.05)^t

B. 700(0.9)^x

Step-by-step explanation:

Exponential decay functions has the next form:

y = ab^x

where b < 1

A. 900(0.05)^t , a = 900, b = 0.05, the variable is t instead of x. 0.05 < 1, then it represents exponential decay

B. 700(0.9)^x , a = 700, b = 0.9 < 1, then it represents exponential decay

C. 53(1.75)^(0.3x) = 53(1.75)^(0.3)(1.75)^x, a = 53(1.75)^(0.3), b = 1.75 > 1, then it doesn't represent exponential decay

D. 90(1.2)^t, a = 90, b = 1.2 > 1, then it doesn't represent exponential decay. (the variable is t instead of x)

E. .300(2.4)^(1.2y) = 300(2.4)^(1.2)(2.4)^y, a = 300(2.4)^(1.2), b = 2.4 > 1, then it doesn't represent exponential decay. (the variable is y instead of x)

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3 0

3 years ago

What is 2(9)+4(3)+2-3

Illusion [34]

Answer:29

Step-by-step explanation:

simplified: 18+12-1=29

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3 years ago

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Calculus 2 master needed; stuck on evaluating the integral please show steps <img src="https://tex.z-dn.net/?f=%5Cint%20%7Bsec%2

kakasveta [241]

Answer:

$\int \sec(\frac{x}{2})\tan^5({\frac{x}{2}})dx=\frac{2\sec^5(\frac{1}{2}x)}{5}-\frac{4\sec^3(\frac{1}{2}x)}{3}+2\sec(\frac{1}{2}x)+C$

Step-by-step explanation:

So we have the integral:

$\int \sec(\frac{x}{2})\tan^5({\frac{x}{2}})dx$

First, let's use substitution to get rid of the x/2. I'm going to use the variable y. So, let y be x/2. Thus:

$y=\frac{x}{2}\\dy=\frac{1}{2}dx\\2dy=dx$

Therefore, the integral is:

$=2\int \sec(y)\tan^5(y)dy$

Now, as you had done, let's expand the tangent term. However, let's do it to the fourth. Thus:

$=2\int \sec(y)\tan^4(y)\tan(y)dy$

Now, we can use a variation of the trigonometric identity:

$\tan^2(y)+1=\sec^2(y)$

So:

$\tan^2(y)=\sec^2(y)-1$

Substitute this into the integral. Note that tan^4(x) is the same as (tan^2(x))^2. Thus:

$=2\int \sec(y)(\tan^2(y))^2\tan(y)dy\\=2\int \sec(y)(\sec^2(y)-1)^2\tan(y)dy$

Now, we can use substitution. We will use it for sec(x). Recall what the derivative of secant is. Thus:

$u=\sec(y)\\du=\sec(y)\tan(y)dy$

Substitute:

$2\int (\sec^2(y)-1)^2(\sec(y)\tan(y))dy\\=2\int(u^2-1)^2 du$

Expand the binomial:

$=2\int u^4-2u^2+1du$

Spilt the integral:

$=2(\int u^4 du+\int-2u^2du+\int +1du)$

Factor out the constant multiple:

$=2(\int u^4du-2\int u^2du+\int(1)du)$

Reverse Power Rule:

$=2(\frac{u^{4+1}}{4+1}-2(\frac{u^{2+1}}{2+1})+(\frac{u^{0+1}}{0+1}}))$

Simplify:

$=2(\frac{u^5}{5}-\frac{2u^3}{3}+u)$

Distribute the 2:

$=\frac{2u^5}{5}-\frac{4u^3}{3}+2u$

Substitute back secant for u:

$=\frac{2\sec^5(y)}{5}-\frac{4\sec^3(y)}{3}+2\sec(y)$

And substitute back 1/2x for y. Therefore:

$=\frac{2\sec^5(\frac{1}{2}x)}{5}-\frac{4\sec^3(\frac{1}{2}x)}{3}+2\sec(\frac{1}{2}x)$

And, finally, C:

$=\frac{2\sec^5(\frac{1}{2}x)}{5}-\frac{4\sec^3(\frac{1}{2}x)}{3}+2\sec(\frac{1}{2}x)+C$

And we're done!

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2 years ago

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Vitek1552 [10]

Answer:

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swipe on solution for full explanation

3 0

2 years ago