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IceJOKER [234]
3 years ago
14

Consider the function f(x) = x² – 3x – 4 and complete parts (a) through (C). (a) Find f(a+h); f(a+h)-f(a) (b) Find (c) Find the

instantaneous rate of change of f when a = 7. (a) f(a+h) = (Simplify your answer. Do not factor.)
Mathematics
1 answer:
Artist 52 [7]3 years ago
7 0

Answer:

(a)

f(a+h)=a^{2} +2ah+h^{2} -3a-3h-4

(b)

f(a+h)-f(a)=2ah+h^{2} -3h

(c)

\frac{df(a+h)}{dx} \left \{ { \atop {a=7}} \right. =2h+11

Step-by-step explanation:

(a)

Simply evaluate (a+h) in the function:

f(a+h)=(a+h)^{2} -3(a+h)-4=a^{2} +2ah+h^{2} -3a-3h-4

(b)

Evaluate (a) in the function:

f(a)=a^{2} -3a-4

Using the previous answers lets calculate f(a+h)-f(a)

f(a+h)-f(a)=a^{2} +2ah+h^{2} -3a-3h-4-(a^{2} -3a-4)=2ah+h^{2} -3h

(c) To find the rate of change of f(a+1) when a=7 we need to calculate its derivate at that point:

\frac{df(a+h)}{dx} \left \{ { \atop {a=7}} \right. =2a+2h-3=2(7)+2h-3=2h+14-3=2h+11

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Review the expression below -2(a+b-5)+3(-5a+2b)+b(6a+b-8)
Oduvanchick [21]

Answer:

6ab + b^2 - 17a - 4b + 10

Step-by-step explanation:

-2(a+b-5)+3(-5a+2b)+b(6a+b-8)

Now we break the parenthesis. To break that, we multiply each of the value inside the parenthesis by the adjacent number. That is, for the first part of the expression, we multiply by -2, then by 3, and then by b.

Algebraic Operations need to be considered:

[ (-) x (-) = (+); (-) x (+) = (-)]

= [-(2*a) + (-2*b) - (-2*5)] + [3*(-5a) + (3*2b)] + [(b*6a) + (b*b) - (b*8)]

= -2a - 2b +10 -15a + 6b + 6ab + b^2 - 8b

Now, we will make the adjustment by the similarity value.

= - 2a - 15a - 2b + 6b - 8b + 6ab + b^2 + 10

= - 17a - 4b + 6ab + b^2 + 10

= 6ab + b^2 - 17a - 4b + 10

Therefore, the answer of the expression is = 6ab + b^2 - 17a - 4b + 10

6 0
3 years ago
A students home is 3.25 miles from school. A soda shop is located 900 feet farther down the road from school. What is the total
notka56 [123]

1 mile = 5,280 feet.

Convert the 0.25 mile to feet:

0.25 miles = 0.25 x 5,280 = 1,320 feet.

Add the soda shop distance to this:

1,320 + 900 = 2,220 feet.


Total distance is 3 miles and 2,220 feet


5 0
3 years ago
Type the correct answer in the box. express your answer to two significant figures. a reaction between 1.7 moles of zinc iodide
irga5000 [103]

The percent yield of zinc carbonate is 5.91%.

<h3>What is chemical reaction?</h3>

The chemical reaction is the reaction between two reactants which led to the formation of products.

The products are substances which forms after reaction. The reactants are the substances which are original materials.

Given is a reaction between 1.7 moles of zinc iodide and excess sodium carbonate yields 12.6 grams of zinc carbonate.

The given balanced equation is:  Na₂CO₃ + ZnI₂ → 2NaI + ZnCO₃

From given moles of zinc iodide, the moles of zinc carbonate

1.7 moles of ZnI₂ = 1.7 moles of ZnCO₃

Molar mass of zinc carbonate is 125.38 g/mol

Theoretical yield =  1.7 moles of ZnCO₃ x  125.38 g/mol = 213.15 g  ZnCO₃

Theoretical yield is 213.15 g and the actual yield is given as 12.6 g.

percent yield = [ 12.6 g / 213.15 g  ZnCO₃ ] x 100

percent yield = 5.91%

The percent yield of zinc carbonate is 5.91%.

Learn more about chemical reaction.

brainly.com/question/22817140

#SPJ1

7 0
2 years ago
A ball is thrown vertically upward from the ground with an initial velocity of 111 ft/sec. Use the quadratic function h(t) = −16
ddd [48]

Answer:

t=3.5 seconds

Step-by-step explanation:

Given

h(t) = −16t^2 + 111t + 0

h'(t)= -32t + 111

Maximum height occurs when h(t) = 0 and the ball begins to fall

h(t)= -32t + 111=0

-32t + 111=0

-32t=-111

Divide both sides by -32

t=3.46872

Approximately, t=3.5 seconds

Recall,

Maximum height occurs when h(t) = 0

h(t)= -32t + 111=0

= -32(3.46872)+111

= -110.99904+111

= 0.00096 ft

4 0
3 years ago
Which statement is true about a section of the graph?
daser333 [38]

Answer: i put B an got it correct

Step-by-step explanation:

8 0
2 years ago
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