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3 years ago

Simplify the expression -4x2(3x − 7)

Mathematics

2 answers:

Anna007 [38]3 years ago

5 0

-4x2(3x-7)
multiply -4 and 2
-8(3x-7)
distribute the -8
-24x+56

Paul [167]3 years ago

5 0

Its -12x^3+28x^2 hope it helps

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Solve the equation. -36=-6(2x-14)

Savatey [412]

Answer:

x= 10

Step-by-step explanation:

-36= -6(2x-14) distribute the 6

-36= -12x+84 subtract 84 from both sides

-120= -12x divide by -12

x= 10

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3 years ago

Find the average rate of change of the area of a circle with respect to its radius r as r changes from 3 to each

GarryVolchara [31]

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Find the average rate of change of the area of a circle with respect to its radius r as r changes from 3 to each of the following.

(i) 3 to 4

(ii) 3 to 3.5

(iii) 3 to 3.1

(b) Find the instantaneous rate of change when r = 3. A'(3)

Area of a circle A(r)= πr²

The average rate of change of the area of a circle with respect to its radius

ΔA(r)/Δr = πr₂²-πr₁²/r₂-r₁

ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁

i) If the radius changes from 3 to 4

ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁

ΔA(r)/Δr = π(4²-3²)/4-3

ΔA(r)/Δr = π(16-9)/1

ΔA(r)/Δr = 7π

Hence, average rate of the area of a circle when the radius changes from 3 to 4 is 7π

ii) If the radius changes from 3 to 3.1

ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁

ΔA(r)/Δr = π(3.5²-3²)/3.5-3

ΔA(r)/Δr = π(12.25-9)/0.5

ΔA(r)/Δr = 3.25π/0.5

ΔA(r)/Δr = 6.5π

Hence, average rate of the area of a circle when the radius changes from 3 to 3.5 is 6.5π

iii) If the radius changes from 3 to 3.1

ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁

ΔA(r)/Δr = π(3.1²-3²)/3.1-3

ΔA(r)/Δr = π(9.61-9)/0.1

ΔA(r)/Δr = 0.61π/0.1

ΔA(r)/Δr = 6.1π

Hence, average rate of the area of a circle when the radius changes from 3 to 3.1 is 6.1π

iv) Instantaneous rate of change A'(r) = 2πr

When r = 3;

A'(3) = 2π(3)

A'(3) = 6π

Hence, the instantaneous rate of change when r = 3 is 6π

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3 years ago

Circle A has an area of 500 in? The diameter of circle B is three times the diameter of circle A. Estimate the area of circle B.

Monica [59]

Step-by-step explanation:

circle has an area of 500 inches if we multiply it by 3 we get 1500 inches

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2 years ago

Calculate and express your answer in Decimal from 1/2×17

prohojiy [21]

Answer:

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Step-by-step explanation:

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2 years ago

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A dairy scientist is testing a new feed additive. She chooses 13 cows at random from a large population of cows. She randomly as

mina [271]

Answer:

Step-by-step explanation:

Given that a dairy scientist is testing a new feed additive. She chooses 13 cows at random from a large population of cows. She randomly assigns nold = 8 to get the old diet, and nnew = 5 to get the new diet including the additive.

From the data given we get the following

N Mean StDev SE Mean

Sample 1 8 43 5.1824 1.832

Sample 2 5 73 21.0832 9.429

df = 11

Std dev for difference = 13.3689

a) Yes the two are independent. The two sets of cows randomly chosen are definitely independent. Paired means equal number should be there and homogeneous conditions should be maintained.

b) Enclosed

c) Comparison of two means is the test recommended here. Because independent samples are used.\

d) Test statistic= -3.1233

(because of unequal variances we use that method)

95% confidence interval = ( -56.6676 , -3.3324 )

p value <0.05 our alpha

So reject null hypothesis.

The two means are statistically significantly different.

3 0

3 years ago