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3 years ago

At what point on the graph of y=2e^X -1 is the tangent line parallel to the line y= 5x -1

1 answer:

5 0

Paralell has same slope
y=mx+b
m=slope
y=5x-1
when is the slope 5?

take the derivitive of 2e^x
f'(2e^x)=2f'(e^x)=2e^x

that is the slope
5=2e^x
divide both sides by 2
2.5=e^x
take the ln of both sides
ln2.5=x

when x=ln2.5 they are paralell

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Write the limit as a definite integral on the interval [a, b], where ci is any point in the ith subinterval. Limit Interval lim

geniusboy [140]

Answer:

The corresponding definite integral may be written as

$\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x$

The answer of the above definite integral is

$\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x = 98$

Step-by-step explanation:

The given limit interval is

$\lim_{||\Delta|| \to 0} \sum\limits_{i=1}^n (4c_i + 11) \Delta x_i$

$[a, b] = [-8, 6]$

The corresponding definite integral may be written as

$\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x$

$\int_{-8}^6 \mathrm{(4x + 11)}\,\mathrm{d}x$

Bonus:

The definite integral may be solved as

$\int_{-8}^6 \mathrm{(4x + 11)}\,\mathrm{d}x \\\\\frac{4x^2}{2} + 11x \left \|{b=6} \atop {a=-8}} \right. \\\\2x^2 + 11x \left \|{b=6} \atop {a=-8}} \right. \\\\ 2(6^2 -(-8)^2 ) + 11(6 - (-8) \\\\2(36 - 64 ) + 11(6 + 8) \\\\2(-28 ) + 11(14) \\\\-56 +154 \\\\98$

Therefore, the answer to the integral is

$\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x = 98$

5 0

3 years ago

Vikki wants to determine whether students in her school would rather attend sporting event or a concert. Which would be the BEST

nevsk [136]

Most likely ill go with D.

7 0

3 years ago

Read 2 more answers

At Pizzazz Pizza, the total price for 5

ira [324]

Answer:

The answer to your question is $9.5

Step-by-step explanation:

Data

Large pizza = L

Medium pizza = m

Write equation for both situations

Situation 1 5L + 2m = 81.5

Situation 2 4L + 3m = 78.5

Solve the system of equation by elimination

Multiply situation 1 by -3 and situation 2 by 2

-15L - 6m = -244.5

8L + 6m = 157

-7L = -87.5

Solve for L L = -87.5/-7

L = $12.5

Substitute L in Situation 1 to find m

5(12.5) + 2m = 81.5

62.5 + 2m = 81.5

2m = 81.5 - 62.5

2m = 19

m = 19/2

m = $ 9.5

The prize of a medium pizza is $9.5

8 0

3 years ago

900 is what percent of 1200

xeze [42]

Answer:

75%

Step-by-step explanation:

900 /1200= .75=75%

8 0

3 years ago

Solve the inequality: (x+3)(x−4)<−12

melamori03 [73]

Answer:

0<x<1

Step-by-step explanation:

(x+3)(x−4)<−12

FOIL

x^2 -4x+3x -12 <-12

x^2 -x -12 <-12

Add 12 to each side

x^2 -x -12+12 <-12+12

x^2 -x <0

Factor out an x

x(x-1) <0

Using the zero product property

x(x-1) =0

x=0 x-1=0

x=0 x=1

Check the ranges

x<0

x(x-1) <0

- * - >0

False

0<x<1

x(x-1) <0

+ * - <0

True

x>1

x(x-1) <0

+ * + >0

False

3 0

3 years ago