3 years ago

A recipie for a tomato soup calls for 3.5 cups of crushed

Mathematics

1 answer:

-BARSIC- [3]3 years ago

7 0

Answer:

Step-by-step explanation:

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8. Suppose the curve y = x4 + ax3 + bx2 + cx + d has a tangent line when

erastova [34]

Answer:

a=1, b=-6, c=2, d=1

Step-by-step explanation:

You are given the function

$y=x^4+ax^3+bx^2+cx+d$

Find the derivative:

$y'=4x^3+3ax^2+2bx+c$

The curve has a tangent line when x = 0 with equation y = 2x + 1, so

$y'(0)=2\\ \\y(0)=1$

Hence,

$y'(0)=4\cdot 0^3+3a\cdot 0^2+2b\cdot 0+c=2\Rightarrow c=2\\ \\y(0)=0^4+a\cdot 0^3+b\cdot 0^2+2\cdot 0+d=1\Rightarrow d=1$

The curve has a tangent line when x = 1 with equation y = -3x + 2, so

$y'(1)=-3\\ \\y(1)=-3+2=-1$

So,

$y'(1)=4\cdot 1^3+3a\cdot 1^2+2b\cdot 1+c=4+3a+2b+2=-3\Rightarrow 3a+2b=-9\\ \\y(1)=1^4+a\cdot 1^3+b\cdot 1^2+2\cdot 1+d=1+a+b+2+1=-1\Rightarrow a+b=-5$

From the second equation, a=-5-b, substitute it into the first one:

$3(-5-b)+2b=-9\\ \\-15-3b+2b=-9\\ \\-b=-9+15\\ \\-b=6\\ \\b=-6\\ \\a=-5-b=-5-(-6)=-5+6=1$

7 0

4 years ago

Which point is on the circle described by (x - 2)2 + (y + 3)2 = 4?

hodyreva [135]

The first one (2,-5)

6 0

3 years ago

Find the mean -3, -8, 12, 9, -15

mihalych1998 [28]

Answer:

-1

Step-by-step explanation:

-3-8+12+9-15 divided by 5

gives -5/5=5

mean means average total number over frequency

5 0

3 years ago

Kam

inn [45]

Answer:

Step-by-step explanation:

im on plato just passed the test

7 0

3 years ago

0.3(8-2x) - 1.2(2-3x) < -21

Semmy [17]

Answer:

x=-7

Step-by-step explanation:

0.3(8-2x) - 1.2(2-3x) < -21

2.4 - 0.6x - 2.4 + 3.6x < -21

3x < -21

x < -7

8 0

2 years ago